349. A Necessary Trade-off for Semiclassical Electrodynamics: Accurate Short-Range Coulomb Interactions versus the Enforcement of Causality?
T. E. Li, H.-Ta Chen, A. Nitzan, M. Sukharev and J. E. Subotnik                                  PDF
J. Phys. Chem. Lett., 9, 5955−5961 (2018)
We investigate two key representative semiclassical approaches for propagating resonant energy transfer (RET) between a pair of electronic two-level systems (donor and acceptor) with coupled Maxwell. Liouville equations. On the one hand, when the electromagnetic (EM) field is treated classically and Coulomb interactions are treated quantum-mechanically, we find that a quantum. classical mismatch leads to a violation of causality, i. e., the acceptor can be excited before the retarded EM field arrives. On the other hand, if we invoke a classical intermolecular Coulomb operator, we find that the energy transfer in the near field loses quantitative accuracy compared with Fo. rster theory, even though causality is strictly obeyed. Thus, our work raises a fundamental paradox when choosing a semiclassical electrodynamics algorithm. Namely, which is more important: Accurate short-range interactions or long-range causality? Apparently, one cannot have one_fs cake and eat it too.

348. Universal approach to quantum thermodynamics in the strong coupling regime
W. Dou, M. A. Ochoa, A. Nitzan and J. E. Subotnik                                                      PDF
Phys. Rev. B 98, 134306 (2018)
We present a protocol for the study of the dynamics and thermodynamics of quantum systems strongly coupled to a bath and subject to an external modulation. Our protocol quantifies the evolution of the system-bath composite by expanding the full density matrix as a series in the powers of the modulation rate, from which the functional form of work, heat, and entropy rates can be obtained. Under slow driving, thermodynamic laws are established. The entropy production rate is positive and is found to be related to the excess work dissipated by friction, at least up to second order in the driving speed. As an example of the present methodology, we reproduce the results for the quantum thermodynamics of the driven resonance level model. We also emphasize that our formalism is quite general and allows for electron-electron interactions, which can give rise to exotic Kondo resonances appearing in thermodynamic quantities.

347. Simultaneous weak measurement of non-commuting observables: a generalized Arthurs-Kelly protocol
M. A. Ochoa1, W. Belzig and A. Nitzan                                                                        PDF                                                                 
Scientific Reports, 8, 15781 (2018)
In contrast to a projective quantum measurement, in a weak measurement the system is only weakly perturbed while only partial information on the measured observable is obtained. A simultaneous measurement of non-commuting observables cannot be projective, however the strongest possible such measurement can be defined as providing their values at the smallest uncertainty limit. Starting with the Arthurs and Kelly (AK) protocol for such measurement of position and momentum, we derive a systematic extension to a corresponding weak measurement along three steps: First, a plausible form of the weak measurement operator analogous to the Gaussian Kraus operator, often used to model a weak measurement of a single observable, is obtained by projecting a naive extension (valid for commuting observable) onto the corresponding Gabor space. Second, we show that the so obtained set of measurement operators satisfies the normalization condition for the probability to obtain given values of the position and momentum in the weak measurement operation, namely that this set constitutes a positive operator valued measure (POVM) in the position-momentum space. Finally, we show that the so-obtained measurement operator corresponds to a generalization of the AK measurement protocol in which the initial detector wavefunctions is suitable broadened.

346. Electronic noise due to temperature differences in atomic-scale junctions
O. Shein Lumbroso, L. Simine, A. Nitzan, D. Segal and O. Tal                                  PDF
Nature, 562, 242 (2018)
Here we report measurements of a fundamental electronic noise that is generated by temperature differences across nanoscale conductors, which we term ‘delta-T noise’. We experimentally demonstrate this noise in atomic and molecular junctions, and analyse it theoretically using the Landauer formalism.

345. Upside/Downside statistical mechanics of nonequilibrium Brownian motion. II. Heat transfer and energy partitioning of a free particle
G. T. Craven, R. Chen and A. Nitzan                                                                          PDF
J. Chem. Phys. 149, 104103 (2018)
The energy partitioning during activation and relaxation events under steady-state conditions for a Brownian particle driven by multiple thermal reservoirs of different local temperatures is investigated. Specifically, we apply the formalism derived in Paper I [G. T. Craven and A. Nitzan, J. Chem. Phys. 148, 044101 (2018)] to examine the thermal transport properties of two sub-ensembles of Brownian processes, distinguished at any given time by the specification that all the trajectories in each group have, at that time, energy either above (upside) or below (downside) a preselected energy threshold. Dynamical properties describing energy accumulation and release during activation/relaxation events and relations for upside/downside energy partitioning between thermal reservoirs are derived. The implications for heat transport induced by upside and downside events are discussed.

344. Kinetic Schemes in Open Interacting Systems
A. Nitzan and M. Galperin                                                                                               PDF
J. Phys. Chem. Lett.  9, 4886−4892 (2018)
We discuss utilization of kinetic schemes for description of open interacting systems, focusing on vibrational energy relaxation for an oscillator coupled to a nonequilibirum electronic bath. Standard kinetic equations with constant rate coefficients are obtained under the assumption of time scale separation between the system and bath, with the bath dynamics much faster than that of the system of interest. This assumption may break down in certain limits, and we show that ignoring this may lead to qualitatively wrong predictions. Connection with more general, nonequilibrium Green's function (NEGF) analysis is demonstrated. Our considerations are illustrated within generic molecular junction models with electron-vibration coupling.

343. Mixed quantum-classical electrodynamics: Understanding spontaneous decay and zero-point energy
T. E. Li, A. Nitzan, M. Sukharev, T. Martinez, H.-Ta Chen and J. E. Subotnik              PDF
Phys. Rev. A 97, 032105 (2018)
The dynamics of an electronic two-level system coupled to an electromagnetic field are simulated explicitly for one- and three-dimensional systems through semiclassical propagation of the Maxwell-Liouville equations. We consider three flavors of mixed quantum-classical dynamics: (i) the classical path approximation (CPA), (ii) Ehrenfest dynamics, and (iii) symmetrical quasiclassical (SQC) dynamics. Our findings are as follows: (i) The CPA fails to recover a consistent description of spontaneous emission, (ii) a consistent "spontaneous" emission can be obtained from Ehrenfest dynamics, provided that one starts in an electronic superposition state, and (iii) spontaneous emission is always obtained using SQC dynamics. Using the SQC and Ehrenfest frameworks, we further calculate the dynamics following an incoming pulse, but here we find very different responses: SQC and Ehrenfest dynamics deviate sometimes strongly in the calculated rate of decay of the transient excited state. Nevertheless, our work confirms the earlier observations by Miller [J. Chem. Phys. 69, 2188 (1978)] that Ehrenfest dynamics can effectively describe some aspects of spontaneous emission and highlights interesting possibilities for studying light-matter interactions with semiclassical mechanics.

342. Upside/Downside statistical mechanics of nonequilibrium Brownian motion. I. Distributions, moments, and correlation functions of a free particle
G. T. Craven and A. Nitzan                                                                                   PDF
J. Chem. Phys 148, 044101 (2018)
Statistical properties of Brownian motion that arise by analyzing, separately, trajectories over which the system energy increases (upside) or decreases (downside) with respect to a threshold energy level are derived. This selective analysis is applied to examine transport properties of a nonequilibrium Brownian process that is coupled to multiple thermal sources characterized by different temperatures. Distributions, moments, and correlation functions of a free particle that occur during upside and downside events are investigated for energy activation and energy relaxation processes and also for positive and negative energy fluctuations from the average energy. The presented results are sufficiently general and can be applied without modification to the standard Brownian motion. This article focuses on the mathematical basis of this selective analysis. In subsequent articles in this series, we apply this general formalism to processes in which heat transfer between thermal reservoirs is mediated by activated rate processes that take place in a system bridging them.

341. Maicol A. Ochoa, N Zimbovskaya and A. Nitzan
Quantum thermodynamics for driven dissipative bosonic systems         PDF
Physical Review B 97, 085434 (2018)   (14 pages)
We investigate two prototypical dissipative bosonic systems under slow driving and arbitrary system-bath coupling strength, recovering their dynamic evolution as well as the heat and work rates, and we verify that thermodynamic laws are respected. Specifically, we look at the damped harmonic oscillator and the damped two-level system. For the former, we study independently the slow time-dependent perturbation in the oscillator frequency and in the coupling strength. For the latter, we concentrate on the slow modulation of the energy gap between the two levels. Importantly, we are able to find the entropy production rates for each case without explicitly defining nonequilibrium extensions for the entropy functional. This analysis also permits the definition of phenomenological friction coefficients in terms of structural properties of the system-bath composite.

340. N. A. Zimbovskaya and A. Nitzan
Thermally induced charge current through long molecules                  PDF
J. Chem. Phys 148, 024303 (2018)
In this work, we theoretically study steady state thermoelectric transport through a single-molecule junction with a long chain-like bridge. Electron transmission through the system is computed using a tight-binding model for the bridge. We analyze dependences of thermocurrent on the bridge length in unbiased and biased systems operating within and beyond the linear response regime. It is shown that the length-dependent thermocurrent is controlled by the lineshape of electron transmission in the interval corresponding to the HOMO/LUMO transport channel. Also, it is demonstrated that electron interactions with molecular vibrations may significantly affect the length-dependent thermocurrent.

339. M. Sukharev and A. Nitzan
Optics of exciton-plasmon nanomaterials                                            PDF
J. Phys.: Cond. Matt. 29, 443003 (2017)
This review provides a brief introduction to the physics of coupled exciton-plasmon systems, the theoretical description and experimental manifestation of such phenomena, followed by an account of the state-of-the-art methodology for the numerical simulations of such phenomena and supplemented by a number of FORTRAN codes, by which the interested reader can introduce himself/herself to the practice of such simulations. Applications to CW light scattering as well as transient response and relaxation are described. Particular attention is given to so-called strong coupling limit, where the hybrid exciton-plasmon nature of the system response is strongly expressed. While traditional descriptions of such phenomena usually rely on analysis of the electromagnetic response of inhomogeneous dielectric environments that individually support plasmon and exciton excitations, here we explore also the consequences of a more detailed description of the molecular environment in terms of its quantum density matrix (applied in a mean field approximation level). Such a description makes it possible to account for characteristics that cannot be described by the dielectric response model: the effects of dephasing on the molecular response on one hand, and nonlinear response on the other. It also highlights the still missing important ingredients in the numerical approach, in particular its limitation to a classical description of the radiation field and its reliance on a mean field description of the many-body molecular system. We end our review with an outlook to the near future, where these limitations will be addressed and new novel applications of the numerical approach will be pursued.

338. R. Chen, G. Craven and A. Nitzan    
Electron-transfer-induced and phononic heat transport in molecular environments
J. Chem. Phys. 147, 124101 (2017)                                                           PDF
A unified theory of heat transport in environments that sustain intersite phononic coupling and electron hopping is developed. The heat currents generated by both phononic transport and electron transfer between sites characterized by different local temperatures are calculated and compared. Using typical molecular parameters we find that the electron-transfer-induced heat current can be comparable to that of the standard phononic transport for donor-acceptor pairs with efficient bidirectional electron transfer rates (relatively small intersite distance and favorable free-energy difference). In most other situations, phononic transport is the dominant heat transfer mechanism.

337. G. T. Craven and A. Nitzan  
Electrothermal transistor effect and cyclic electronic currents in multithermal charge transfer networks
Phys. Rev. Lett. 118, 207201(2017)                                                                  PDF
The rate of electron transfer between a molecular species and a metal, each at a different local temperature, is examined theoretically through the implementation of a bithermal (characterized by two temperatures) Marcus formalism. Expressions for the rate constant and the electronic contribution to a heat transfer mechanism which is induced by the temperature gradient between a molecule and metal are constructed. The system of coupled dynamical equations describing the electronic and thermal currents are derived and examined over diverse ranges of reaction geometries and temperature gradients. It is shown that electron transfer across the molecule-metal interface is associated with heat transfer and that the electron exchange between metal and molecule makes a distinct contribution to the interfacial heat conduction even when the net electronic current vanishes.

336. G. Craven and A. Nitzan
Electron transfer at thermally heterogeneous molecule-metal interfaces            PDF
J. Chem. Phys. 146, 092305 (2017)   (10 pages)
The rate of electron transfer between a molecular species and a metal, each at a different local temperature, is examined theoretically through the implementation of a bithermal (characterized by two temperatures) Marcus formalism. Expressions for the rate constant and the electronic contribution to a heat transfer mechanism which is induced by the temperature gradient between a molecule and metal are constructed. The system of coupled dynamical equations describing the electronic and thermal currents are derived and examined over diverse ranges of reaction geometries and temperature gradients. It is shown that electron transfer across the molecule-metal interface is associated with heat transfer and that the electron exchange between metal and molecule makes a distinct contribution to the interfacial heat conduction even when the net electronic current vanishes.

335. M A. Ochoa, Anton Bruch and Abraham Nitzan
Energy distribution and local fluctuations in strongly coupled open quantum systems: The extended resonant level model
Phys. Rev. B 94, 035420 (2016)   (7 pages)                                                  PDF
We study the energy distribution in the extended resonant level model at equilibrium. Previous investigations [Phys. Rev. B 89, 161306 (2014); 93, 115318 (2016)] have found, for a resonant electronic level interacting with a thermal free-electron wide-band bath, that the expectation value for the energy of the interacting subsystem can be correctly calculated by considering a symmetric splitting of the interaction Hamiltonian between the subsystem and the bath. However, the general implications of this approach were questioned [Phys. Rev. B 92, 235440 (2015)]. Here, we show that, already at equilibrium, such splitting fails to describe the energy fluctuations, as measured here by the second and third central moments (namely, width and skewness) of the energy distribution. Furthermore, we find that when the wide-band approximation does not hold, no splitting of the system-bath interaction can describe the system thermodynamics. We conclude that in general no proper division subsystem of the Hamiltonian of the composite system can account for the energy distribution of the subsystem. This also implies that the thermodynamic effects due to local changes in the subsystem cannot in general be described by such splitting.

334. G. T. Craven and A. Nitzan                                                          
Electron transfer across a thermal gradient                                                        PDF
PNAS, 113, 9421–9429 (2016)
PNAS Commentary by D. V. Matyushov  www.pnas.org/cgi/doi/10.1073/pnas.1610542113
Charge transfer is a fundamental process that underlies a multitude of phenomena in chemistry and biology. Recent advances in observing and manipulating charge and heat transport at the nanoscale, and recently developed techniques for monitoring temperature at high temporal and spatial resolution, imply the need for considering electron transfer across thermal gradients. Here, a theory is developed for the rate of electron transfer and the associated heat transport between donor-acceptor pairs located at sites of different temperatures. To this end, through application of a generalized multidimensional transition state theory, the traditional Arrhenius picture of activation energy as a single point on a free energy surface is replaced with a bithermal property that is derived from statistical weighting over all configurations where the reactant and product states are equienergetic. The flow of energy associated with the electron transfer process is also examined, leading to relations between the rate of heat exchange among the donor and acceptor sites as functions of the temperature difference and the electronic driving bias. In particular, we find that an open electron transfer channel contributes to enhanced heat transport between sites even when they are in electronic equilibrium. The presented results provide a unified theory for charge transport and the associated heat conduction between sites at different temperatures.

333.  Y. Gao, M. Galperin, and A. Nitzan
On the widths of Stokes lines in Raman scattering                                            PDF
J. Chem. Phys. 144, 244114 (2016)      (8 pages)
Within a generic model we analyze the Stokes linewidth in surface enhanced Raman scattering (SERS) from molecules embedded as bridges in molecular junctions. We identify four main contributions to the off-resonant Stokes signal and show that under zero voltage bias (a situation pertaining also to standard SERS experiments) and at low bias junctions only one of these contributions is pronounced. The linewidth of this component is determined by the molecular vibrational relaxation rate, which is dominated by interactions with the essentially bosonic thermal environment when the relevant molecular electronic energy is far from the metal(s) Fermi energy(ies). It increases when the molecular electronic level is close to the metal Fermi level so that an additional vibrational relaxation channel due to electron-hole (eh) exciton in the molecule opens. Other contributions to the Raman signal, of considerably broader linewidths, can become important at larger junction bias.

332. C. Jia, A. Migliore, N. Xin, S. Huang, J. Wang, Q. Yang, S. Wang, H. Chen, D. Wang, B. Feng, Z. Liu, G. Zhang, D. Qu, Z. Liu, H. Tian, M. A. Ratner, H. Xu, A. Nitzan*, and X Guo* (*Corresponding Authors)
Covalently bonded single-molecule junctions with stable and reversible photoswitched conductivity
Science, 352, 1443-45 (2016)                                                                           PDF
Science perspective by C. D. Frisbie VOL 352 ISSUE 6292, page 1394
Through molecular engineering, single diarylethenes were covalently sandwiched between graphene electrodes to form stable molecular conduction junctions. Our experimental and theoretical studies of these junctions consistently show and interpret reversible conductance photoswitching at room temperature and stochastic switching between different conductive states at low temperature at a single-molecule level. We demonstrate a fully reversible, two-mode, single- molecule electrical switch with unprecedented levels of accuracy (on/off ratio of ~100), stability (over a year), and reproducibility (46 devices with more than 100 cycles for photoswitching and ~105 to 106 cycles for stochastic switching).

331. M. Einax and A. Nitzan
Maximum efficiency of state-space models of molecular scale engines                 PDF
J. Chem. Phys. 145, 014108 (2016)
The performance of nano-scale energy conversion devices is studied in the framework of state-space models where a device is described by a graph comprising states and transitions between them represented by nodes and links, respectively. Particular segments of this network represent input (driving) and output processes whose properly chosen flux ratio provides the energy conversion efficiency. Simple cyclical graphs yield Carnot efficiency for the maximum conversion yield. We give general proof that opening a link that separate between the two driving segments always leads to reduced efficiency. We illustrate these general result with simple models of a thermoelectric nanodevice and an organic photovoltaic cell. In the latter an intersecting link of the above type corresponds to non-radiative carriers recombination and the reduced maximum efficiency is manifested as a smaller open-circuit voltage.

330. A. Bruch, M. Thomas, S. V. Kusminsky, F. von Oppen and A. Nitzan
Quantum thermodynamics of the driven resonant level model                             PDF
Phys. Rev. B, 93, 115318 (2016)        (14 pages)
We present a consistent thermodynamic theory for the resonant level model in the wide-band limit, whose level energy is driven slowly by an external force. The problem of defining "system" and "bath" in the strong-coupling regime is circumvented by considering as the system everything that is influenced by the externally driven level. The thermodynamic functions that are obtained to first order beyond the quasistatic limit fulfill the first and second law with a positive entropy production, successfully connect to the forces experienced by the external driving, and reproduce the correct weak-coupling limit of stochastic thermodynamics.

329. M. Sukharev and A. Nitzan
Plasmon transmission through excitonic subwavelength gaps                                PDF
J. Chem. Phys. 144, 144703 (2016)   (8 pages)
We study the transfer of electromagnetic energy across a subwavelength gap separating two co-axial metal nanorods. In the absence of spacer in the gap separating the rods, the system exhibits strong coupling behavior between longitudinal plasmons in the two rods. The nature and magnitude of this coupling are studied by varying various geometrical parameters. As a function of frequency, the transmission is dominated by a split longitudinal plasmon peak. The two hybrid modes are the dipole-like "bonding" mode characterized by a peak intensity in the gap and a quadrupole-like "antibonding" mode whose amplitude vanishes at the gap center. When the length of one rod is varied, this mode spectrum exhibits the familiar anti-crossing behavior that depends on the coupling strength determined by the gap width. When off-resonant 2-level emitters are placed in the gap, almost no effect on the frequency dependent transmission is observed. In contrast, when the molecular system is resonant with the plasmonic line shape, the transmission is strongly modified, showing characteristics of strong exciton-plasmon coupling. Most strongly modified is the transmission near the lower frequency "bonding" plasmon mode. The presence of resonant molecules in the gap affects not only the molecule-field interaction but also the spatial distribution of the field intensity and the electromagnetic energy flux across the junction.

328. W. Dou, A. Nitzan J. Subotnik
Molecular Electronic States Near Metal Surfaces at Equilibrium Using Potential of Mean Force and Numerical Renormalization Group Methods: Hysteresis Revisited.
J. Chem. Phys., 144, 074109 (2016)    (12 pages)                                               PDF
We investigate equilibrium observables for molecules near metals by employing a potential of mean force (PMF) that takes level broadening into account. Through comparison with exact data, we demonstrate that this PMF approach performs quite well, even for cases where molecule-electrode couplings depend on nuclear position. As an application, we reexamine the possibility of hysteresis effects within the Anderson-Holstein model (i. e., an impurity coupled both to a metal surface and a nuclear oscillator). As compared against the standard mean field approach by Galperin et al. [Nano Lett. 5, 125 (2005)], our PMF approach agrees much better with exact results for average electronic populations both at zero and finite temperature; we find, however, that mean field theory can be very useful for predicting the onset of dynamical instabilities, metastable states, and hysteresis.

327. S. Dey, M. Banik, E. Hulkko, K. Rodriguez, V. A. Apkarian, M. Galperin and A. Nitzan
Observation and analysis of Fano-like lineshapes in the Raman spectra of molecules adsorbed at metal interfaces
Phys. Rev. B 93, 035411 (2016)    (6 pages)                                                       PDF
Surface-enhanced Raman scattering (SERS) from bipyridyl ethylene adsorbed on gold dumbbells shows Fano-like spectra at high incident light intensity. This is accompanied by an increased electronic temperature, while no vibrational anti-Stokes scattering is observed. Theory indicates that interference between vibrational and electronic Raman scattering can yield such asymmetric scattering lineshapes. The best fit to observations is however obtained by disregarding this coupling and accounting for the detailed lineshape of the continuous electronic component of the SERS.

326. M. Galperin and A. Nitzan
Nuclear Dynamics at Molecule-Metal Interfaces: A pseudoparticle perspective       PDF
J. Phys. Chem. Lett. 6, 4896-4903 (2015)
We discuss nuclear dynamics at molecule-metal interfaces including nonequilibrium molecular junctions. Starting from the many-body states (pseudoparticle) formulation of the molecule-metal system in the molecular vibronic basis, we introduce gradient expansion to reduce the adiabatic nuclear dynamics (that is, nuclear dynamics on a single molecular potential surface) into its semiclassical form while maintaining the effect of the nonadiabatic electronic transitions between different molecular charge states. This yields a set of equations for the nuclear dynamics in the presence of these nonadiabatic transitions, which reproduce the surface-hopping formulation in the limit of small metal-molecule coupling (where broadening of the molecular energy levels can be disregarded) and Ehrenfest dynamics (motion on the potential of mean force) when information on the different charging states is traced out.

325. W. Dou, A. Nitzan and J. E. Subotnik
Frictional effects near a metal surface                                        PDF
J. Chem. Phys. 143, 054103 (2015)   (9 pages)
When a classical master equation (CME) is used to describe the nonadiabatic dynamics of a molecule at metal surfaces, we show that in the regime of reasonably strong molecule-metal couplings, the CME can be reduced to a Fokker-Planck equation with an explicit form of electronic friction. For a single metal substrate at thermal equilibrium, the electronic friction and random force satisfy the fluctuation-dissipation theorem. When we investigate the time scale for an electron transfer (ET) event between the molecule and metal surface, we find that the ET rates show a turnover effect (just as in Kramer's theory) as a function of frictional damping.

324. W. Dou, A. Nitzan and J. E. Subotnik
Surface hopping with a manifold of electronic states, III: transients, broadening and the Marcus picture       PDF
J. Chem. Phys. 142, 234106 (2015)  (8 pages)
In a previous paper [Dou et al., J. Chem. Phys. 142, 084110 (2015)], we have introduced a surface hopping (SH) approach to deal with the Anderson-Holstein model. Here, we address some interesting aspects that have not been discussed previously, including transient phenomena and extensions to arbitrary impurity-bath couplings. In particular, in this paper we show that the SH approach captures phonon coherence beyond the secular approximation, and that SH rates agree with Marcus theory at steady state. Finally, we show that, in cases where the electronic tunneling rate depends on nuclear position, a straightforward use of Marcus theory rates yields a useful starting point for capturing level broadening. For a simple such model, we find I-V curves that exhibit negative differential resistance.

323. K. Kaasbjerg and A. Nitzan
Theory of light emission from quantum noise in plasmonic contacts: above-threshold emission from higher-order electron-plasmon scattering        PDF
We develop a theoretical framework for the description of light emission from plasmonic contacts based on the nonequilibrium Green function formalism. Our theory establishes a fundamental link between the nite-frequency quantum noise and AC conductance of the contact and the light emission. Calculating the quantum noise to higher orders in the electron-plasmon interaction, we identify a plasmon-induced electron-electron interaction as the source of experimentally observed above-threshold light emission from biased STM contacts. Our ndings provide important insight into the e ect of interactions on the light emission from atomic-scale contacts.

322. W. Dou, A. Nitzan and J. E. Subotnik
A Surface Hopping Approach For the Anderson-Holstein Model          PDF
We investigate a simple surface hopping (SH) approach for modeling a single impurity level coupled to a single phonon and an electronic (metal) bath (i. e., the Anderson-Holstein model). The phonon degree of freedom is treated classically with motion along-and hops between-diabatic potential energy surfaces. The hopping rate is determined by the dynamics of the electronic bath (which are treated implicitly). For the case of one electronic bath, in the limit of small coupling to the bath, SH recovers phonon relaxation to thermal equilibrium and yields the correct impurity electron population (as compared with numerical renormalization group). For the case of out of equilibrium dynamics, SH current-voltage (I-V) curve is compared with the quantum master equation (QME) over a range of parameters, spanning the quantum region to the classical region. In the limit of large temperature, SH and QME agree. Furthermore, we can show that, in the limit of low temperature, the QME agrees with real-time path integral calculations. As such, the simple procedure described here should be useful in many other contexts.

321. A. Migliore and A. Nitzan
Irreversibility in redox molecular conduction: single versus double metal-molecule interfaces
Electrochimica Acta 160, 363–375 (2015)                                                           PDF
In this work we analyze the onset and manifestation of irreversibility phenomena in the charge transport at single and double metal-redox molecule interfaces, with special emphasis on the role of the nuclear system reorganization energy in causing the distortion of cyclic voltammograms in the first case and the occurrence of hysteresis phenomena in the second case. Under physical conditions for which two states of the molecular system come into play, effects of irreversibility increase with the reorganization energy at a single interface, while an opposite trend is seen in the conduction through a molecular junction. The apparent contradiction between these two behaviors, which was raised in a previous work (Migliore, A.; Nitzan, A., J. Am. Chem. Soc. 2013, 135, 9420-32) is here resolved through detailed investigation of the connections between molecule reorganization energy, bias-dependent population of the molecular redox site(s), and threshold voltage scan rate for the onset of irreversible behavior. Moreover, our investigation of the effects of the reorganization energy on the voltammogram peaks proposes a strategy for extracting the value of the reorganization energy of the molecular system from the experimental behavior.


320. A. Novelli, W. Belzig and A. Nitzan
Landau-Zener evolution under weak measurement: Manifestation of the Zeno effect under diabatic and adiabatic measurement protocols
New J. Phys., 17, 01300 (2015)                                                                           PDF
The time evolution and the asymptotic outcome of a Landau-Zener-Stueckelberg-Majorana (LZ) process under continuousweak non-selectivemeasurement is analyzed. Wecompare twomeasurement protocols in which the populations of either the adiabatic or the non-adiabatic levels are (continuously and weakly)monitored. The weak measurement formalism, described using a Gaussian Kraus operator, leads to a time evolution characterized by a Markovian dephasing process, which, in the non-adiabaticmeasurement protocol is similar to earlier studies of LZ dynamics in a dephasing environment. Casting the problem in the language ofmeasurement theorymakes it possible for us to compare diabatic and adiabatic measurement scenarios, to consider engineered dephasing as a control device and to examine the manifestation of the Zeno effect under the differentmeasurement protocols. In particular, undermeasurement of the non-adiabatic populations, the Zeno effect is manifested not as a freezing of themeasured system in its initial state, but rather as an approach to equal asymptotic populations of the twodiabatic states. This behavior can be traced to theway by which the weak measurement formalism behaves in the strong measurement limit, with a built-in relationship between measurement time and strength.

319. M. Einax and A. Nitzan
Network analysis of photovoltaic energy conversion
J. Phys. Chem. C, 118, 27226-27234 (2014)                                      PDF
Photovoltaic energy conversion in photovoltaic cells has been analyzed by the detailed balance approach or by thermodynamic arguments. Here we introduce a network representation to analyze the performance of such systems once a suitable kinetic model (represented by a master equation in the space of the different system states) has been constructed.  Such network representation allows one to decompose the steady state dynamics into cycles, characterized by their cycle affinities. Both the maximum achievable efficiency and the open circuit voltage of the device are obtained in the zero affinity limit. This method is applied to analyze a microscopic model for a bulk heterojunction organic solar cell that includes the essential optical and interfacial electronic processes that characterize this system, leading to an explicit expression for the theoretical efficiency limit in such system. In particular, the deviation from Carnot’s efficiency associated with the exciton binding energy is quantified.


318. K. B. Whaley, A. A. Kocherzhenko and A. Nitzan
Coherent and Diffusive Timescales for Exciton Dissociation in Bulk Heterojuncion Photovoltaic Cells
J. Phys. Chem. C, 118, 27235−27244 (2014)                                     PDF
We study the dynamics of charge separation in bulk heterojunction organic photovoltaic systems in light of recent experimental observations that this process is characterized by multiple time scales in the range of 10 fs to 100 ps. Coherent evolution of the excitonic state has been suggested to dominate the early stages of the charge separation process and diffusion of localized excitons to be dominant at longer times. Both of these processes obviously depend on the system morphology, in particular on the grain sizes of the donor and acceptor phases. Here we analyze these mechanisms and their characteristic time scales, aiming to verify the consistency of the proposed mechanisms with the experimentally observed time scales of charge separation. We suggest that the coherent mechanism that dominates the early stage of charge separation involves delocalized excitons. These excitons are formed by optical excitation of clusters of strongly interacting donor sites, and the charge separation rate is determined by the probability that such sites lie at the donor-acceptor interface. The (relatively) slow diffusive rate is estimated from the mean first passage time for a diffusing exciton to reach the donor grain surface. Our estimates, based on available exciton diffusion rates and morphology data, are consistent with experimental observations.

CB30. A. Nitzan
Beyond molecular conduction: Optical and thermal effects in molecular junctions
Adv. Chem. Phys. 157, 135-158 (2014)                                                                                                                  PDF
This paper focuses on two subjects whose study pertains to, but go beyond, standard considerations of electronic transport in molecular conduction junctions. Thermal effects - heat generation in, and heat conduction through, such junctions have direct implications to junction stability. Optical interactions are obvious potential tools for junction characterization and control. An overview of recent experimental and theoretical studies of these subjects is provided.

CB29. M. S. Shishodia, B. D. Fainberg, and A. Nitzan
Theory of energy transfer interactions near sphere and nanoshell based plasmonic nanostructurein Plasmonics: Metallic Nanostructures and Their Optical Properties IX. Proc. of SPIE, M. I. Stockman, Ed. Bellingham, WA: SPIE, 2011, vol. 8096, p. 80961G                                         PDF
Theory of energy transfer interactions between a pair of two level molecules in the molecular nanojunction including surface plasmon (SP) dressed interaction of plasmonic nanostructure, replicating metallic leads is presented. Results on the modification of bare dipolar interaction, known to be responsible for molecular energy transfer processes, in the proximity of metallic nanosystem are presented. Specifically, the manuscript includes theoretical investigation of nanosphere (NSP) monomer, nanoshell (NSH) monomer, and coupled nanosphere pair (dimer) based nanosystems. Closed form analytical expressions for NSP and NSH structures tailored for molecular nanojunction geometry are derived in the theoretical framework of multipole spectral expansion (MSE) method, which is straightforwardly extendible to dimers and multimers. The role of size and dielectric environment on energy transfer is investigated and interpreted. Theory predicts that the monomer and dimer both enhance the dipolar interaction, yet, dimer geometry is favorable due to its spectral tuning potential originated from plasmon hybridization and true resemblance with typical molecular nanojunctions.

317. M. Einax, M. Dierl, Philip R. Schiff and A. Nitzan
Multiple state representation scheme for organic bulk heterojunction solar cells: A novel analysis perspective
European Phys. Let., 104, 40002 (2013) (6 pages)                                                                 PDF
The physics of organic bulk heterojunction solar cells is studied within a six state model, which is used to analyze the factors that affect current-voltage characteristics, powervoltage properties and efficiency, and their dependence on nonradiative losses, reorganization of the nuclear environment, and environmental polarization. Both environmental reorganization and polarity are explicitly taken into account by incorporating Marcus heterogeneous and homogeneous electron transfer rates. The environmental polarity is found to have a non-negligible influence both on the stationary current and on the overall solar cell performance. For our organic bulk heterojunction solar cell operating under steady-state open circuit condition, we also find that the open circuit voltage logarithmically decreases with increasing nonradiative electron-hole recombination processes.

316. M. Sukharev, N. Freifeld and A. Nitzan
Numerical calculations of radiative and non-radiative relaxation of molecules near metal particles
J. Phys. Chem. C, 118, 1054 (2014)
The dependence of the radiative emission and the non-radiative (energy transfer to the metal) relaxation rates of a molecule near a small metal particle on the molecule-to-particle distance and on the molecular orientation is calculated using a numerical solution of the Maxwell equations for a model that described the metal as a dispersive dielectric particle and the molecule as an oscillating point dipole. The emission rate is obtained by evaluating the total oscillating dipole in the system, while the non-radiative rate is inferred from the rate of heat production on the particle. For the distance dependence of the non-radiative rate we find, in agreement with experimental observations, marked deviation from the prediction of the standard theory of fluorescence resonance energy transfer (FRET). In departure from previous interpretations, we find that electromagnetic retardation is the main source of this deviation at large molecule-particle separations. The radiative emission rate reflects the total dipole induced in the molecule-particle system, and its behavior as function of distance and orientation stems mostly from the magnitude of the oscillating polarization on the metal particle (which, at resonance, is strongly affected by plasmon excitation), and from the way this polarization combines with the molecular dipole to form the total system dipole.

315. J. Gersten, K. Kaasbjerg and A. Nitzan
Induced spin filtering in electron transmission through chiral molecular layers adsorbed on metals with strong spin-orbit coupling
J. Chem. Phys. 139, 114111 (2013) (20 pages)                                                                PDF
Recent observations of considerable spin polarization in photoemission from metal surfaces through monolayers of chiral molecules were followed by several efforts to rationalize the results as the effect of spin-orbit interaction that accompanies electronic motion on helical, or more generally strongly curved, potential surfaces. In this paper we (a) argue, using simple models, that motion in curved force-fields with the typical energies used and the characteristic geometry of DNA cannot account for such observations; (b) introduce the concept of induced spin filtering, whereupon selectivity in the transmission of the electron orbital angular momentum can induce spin selectivity in the transmission process provided there is strong spin-orbit coupling in the substrate; and (c) show that the spin polarization in the tunneling current as well as the photoemission current from gold covered by helical adsorbates can be of the observed order of magnitude. Our results can account for most of the published observations that involved gold and silver substrates; however, recent results obtained with an aluminum substrate can be rationalized within the present model only if strong spin-orbit coupling is caused by the built-in electric field at the molecule-metal interface.

314. K. Kaasbjerg, T. Novotny and A. Nitzan
Carrier-induced renormalization of vibrational frequencies in nanoscale junctions: Signatures of vibrational damping and heating
Phys. Rev. B (Rapid Communication), 88, 201405(R) (2013)                                          PDF
In nanoscale junctions the interaction between charge carriers and the local vibrations results in renormalization, damping, and heating of the vibrational modes. Herewe formulate a nonequilibrium Green's function based theory to describe such effects. Studying a generic junction model with an off-resonant electronic level, we find a strong bias dependence of the frequency renormalization and vibrational damping accompanied by pronounced nonlinear vibrational heating in junctions with intermediate values of the coupling to the leads. Combining our theory with ab initio calculations, we furthermore show that the bias dependence of the Raman shifts and linewidths observed experimentally in an oligo(3)-phenylenevinylene (OPV3) junction [Ward et al., Nat. Nanotechnol. 6, 33 (2011)] may be explained by a combination of dynamic carrier screening and molecular charging.

313. A. Migliore and A. Nitzan
Irreversibility and hysteresis in redox molecular conduction junctions
J.Am.Chem.Soc, 135, 9420-32 (2013)                                                                          PDF
In this work we present and discuss theoretical models of redox molecular junctions that account for recent observations of nonlinear charge transport phenomena, such as hysteresis and hysteretic negative differential resistance (NDR). A defining feature in such models is the involvement of at least two conduction channelsñYa slow channel that determines transitions between charge states of the bridge and a fast channel that dominates its conduction. Using Marcus_f theory of heterogeneous electron transfer (ET) at metal. molecule interfaces we identify and describe different regimes of nonlinear conduction through redox molecular bridges, where the transferring charge can be highly localized around the redox moiety. This localization and its stabilization by polarization of the surrounding medium and/or conformational changes can lead to decoupling of the current response dynamics from the time scale of the voltage sweep (that is, the current does not adiabatically follow the voltage), hence to the appearance of memory (thermodynamic irreversibility) in this response that is manifested by hysteresis in current. voltage cycles. In standard voltammetry such irreversibility leads to a relative shift of the current peaks along the forward and backward voltage sweeps. The common origin of these behaviors is pointed out, and expressions of the threshold voltage sweep rates are provided. In addition, the theory is extended (a) to analyze the different ways by which such phenomena are manifested in single sweep cycles and in ensemble averages of such cycles and (b) to examine quantum effects in the fast transport channel.

312. A. White, A. Migliore, M. Galperin and A. Nitzan

Quantum Transport With Two Interacting Conduction Channels

J. Chem. Phys. 138, 174111 (2013) (6 pages)                                                                 PDF
The transport properties of a conduction junction model characterized by two mutually coupled channels that strongly differ in their couplings to the leads are investigated. Models of this type describe molecular redox junctions (where a level that is weakly coupled to the leads controls the molecular charge, while a strongly coupled one dominates the molecular conduction), and electron counting devices in which the current in a point contact is sensitive to the charging state of a nearby quantum dot. Here we consider the case where transport in the strongly coupled channel has to be described quantum mechanically (covering the full range between sequential tunneling and co-tunneling), while conduction through the weakly coupled channel is a sequential process that could by itself be described by a simple master equation. We compare the result of a full quantum calculation based on the pseudoparticle non-equilibrium Green function method to that obtained from an approximate mixed quantum-classical calculation, where correlations between the channels are taken into account through either the averaged rates or the averaged energy. We find, for the steady state current, that the approximation based on the averaged rates works well in most of the voltage regime, with marked deviations from the full quantum results only at the threshold for charging the weekly coupled level. These deviations are important for accurate description of the negative differential conduction behavior that often characterizes redox molecular junctions in the neighborhood of this threshold.

311. M. Kornbluth, T. Seideman and A. Nitzan
Light-induced electronic non-equilibrium in plasmonic particles
J. Chem. Phys. 138, 174707 (2013) (9 pages)                                                               PDF
We consider the transient non-equilibrium electronic distribution that is created in a metal nanoparticle upon plasmon excitation. Following light absorption, the created plasmons decohere within a few femtoseconds, producing uncorrelated electron-hole pairs. The corresponding non-thermal electronic distribution evolves in response to the photo-exciting pulse and to subsequent relaxation processes. First, on the femtosecond timescale, the electronic subsystem relaxes to a Fermi-Dirac distribution characterized by an electronic temperature. Next, within picoseconds, thermalization with the underlying lattice phonons leads to a hot particle in internal equilibrium that subsequently equilibrates with the environment. Here we focus on the early stage of this multistep relaxation process, and on the properties of the ensuing non-equilibrium electronic distribution. We consider the form of this distribution as derived from the balance between the optical absorption and the subsequent relaxation processes, and discuss its implication for (a) heating of illuminated plasmonic particles, (b) the possibility to optically induce current in junctions, and (c) the prospect for experimental observation of such light-driven transport phenomena.

310. S. K. Maiti and A. Nitzan
Mobility edge phenomenon in a Hubbard chain: A mean field study
Physics Letters A, 377, 1205-1209 (2013)                                                                    PDF
We show that a tight-binding one-dimensional chain composed of interacting and non-interacting atomic sites can exhibit multiple mobility edges at different values of carrier energy in presence of external electric field. Within a mean field Hartree-Fock approximation we numerically calculate two-terminal transport by using Green's function formalism. Several cases are analyzed depending on the arrangements of interacting and non-interacting atoms in the chain. The analysis may be helpful in designing mesoscale switching devices.

309. M. Galperin† and Abraham Nitzan
Cooperative effects in inelastic tunneling
J. Phys.Chem. B,  317, 4449-4453 (2013)                                                                    PDF
Several aspects of intermolecular effects in molecular conduction have been studied in recent years. These experimental and theoretical studies, made on several setups of molecular conduction junctions, have focused on the current-voltage characteristic that is usually dominated by the elastic transmission properties of such junctions. In this paper, we address cooperative intermolecular effects in the inelastic tunneling signal calculated for simple generic models of such systems. We find that peak heights in the inelastic (d2I/dE2 vs E) spectrum may be affected by such cooperative effects even when direct intermolecular interactions can be disregarded. This finding suggests that comparing experimental results to calculations made on single-molecule junctions should be done with care.

308. G. Li, B. Movaghar, A. Nitzan and M. A. Ratner
Polaron formation: Ehrenfest dynamics vs. exact results
J. Chem. Phys. 138, 044112 (2013)                                                                               PDF
We use a one-dimensional tight binding model with an impurity site characterized by electronvibration coupling, to describe electron transfer and localization at zero temperature, aiming to examine the process of polaron formation in this system. In particular we focus on comparing a semiclassical approach that describes nuclear motion in this many vibronic-states system on the Ehrenfest dynamics level to a numerically exact fully quantum calculation based on the Bonca-Trugman method [J. Bon¡ca and S. A. Trugman, Phys. Rev. Lett. 75, 2566 (1995)]. In both approaches, thermal relaxation in the nuclear subspace is implemented in equivalent approximate ways: In the Ehrenfest calculation the uncoupled (to the electronic subsystem) motion of the classical (harmonic) oscillator is simply damped as would be implied by coupling to a Markovian zero temperature bath. In the quantum calculation, thermal relaxation is implemented by augmenting the Liouville equation for the oscillator density matrix with kinetic terms that account for the same relaxation. In both cases we calculate the probability to trap the electron by forming a polaron and the probability that it escapes to infinity. Comparing these calculations, we find that while both result in similar long time yields for these processes, the Ehrenfest-dynamics based calculation fails to account for the correct time scale for the polaron formation. This failure results, as usual, from the fact that at the early stage of polaron formation the classical nuclear dynamics takes place on an unphysical average potential surface that reflects the distributed electronic population in the system, while the quantum calculation accounts fully for correlations between the electronic and vibrational subsystems.

307. G. Li, A. Nitzan and M. A. Ratner
Yield of exciton dissociation in a donor–acceptor photovoltaic junction
Phys. Chem. Chem. Phys. 14, 14270 (2012)                                                                PDF
A simple model is constructed to describe dissociation of charge transfer excitons in bulk heterojunction solar cells, and its dependence on the physical parameters of the system. In bulk heterojunction organic photovoltaics (OPVs), exciton dissociation occurs almost exclusively at the interface between the donor and acceptor, following one-electron initial excitation from the HOMO to the LUMO levels of the donor, and charge transfer to the acceptor to make a charge-transfer exciton. After exciton breakup, and neglecting the trapping of individual carriers, the electron may undergo two processes for decay: one process involves the electron and/or hole leaving the interface, and migrating to the electrode. This is treated here as the electron moving on a set of acceptor sites. The second loss process is radiationless decay following recombination of the acceptor electron with the donor cation; this is treated by adding a relaxation term. These two processes compete with one another. We model both the exciton breakup and the subsequent electron motion. Results depend on tunneling amplitude, energetics, disorder, Coulomb barriers, and energy level matchups, particularly the so-called LUMO-LUMO offset.

306. A. Migliore, P. Schiff and A. Nitzan
On the relationship between molecular state and single electron pictures in simple electrochemical junctions
Phys. Chem. Chem. Phys., 14, 13746 - 13753 (2012)                                                    PDF
We consider a molecular conduction junction that comprises a redox molecule bridging between metal electrodes, in the limit of weak coupling and high temperature where electron transport is dominated by Marcus electron transfer kinetics. We address the correspondence between the Marcus description in terms of nuclear potential energy surfaces associated with different charging states of the molecular bridge, and the single electron description commonly used in theories of molecular conduction. The relationship between the energy gap, reorganization energy and activation energy parameters of the Marcus theory and the corresponding energy parameters in the single electron description is elucidated. We point out that while transport in the normal Marcus regime involves activated (therefore relatively slow) transitions between at least two charging states of the molecular bridge, deep in the inverted regime only one of these states is locally stable and transitions into this state are activationless. The relatively slow rates that characterize the normal Marcus transport regime manifest themselves in the appearance of hysteresis in the system transport behavior as a function of gate or bias potentials for relatively slow scan rates of these potentials, but not bistability in the junction conduction behavior. We also consider the limit of fast solvent reorganization that may reflect the response of the electronic environment (electronic polarization of a solvent and of the metal electrodes) to the changing charging state of the bridge. In this limit, environmental reorganization appears as renormalization of the bridge electronic energy levels. We show that the effect of this reorganization on the junction conduction properties is not universal and depends on the particular bridge charging states that are involved in the conduction process.

305. M. Galperin and A. Nitzan
Molecular optoelectronics: The interaction of molecular conduction junctions with light
Phys. Chem. Chem. Phys., 14, 9421 - 9438 (2012)                                                        PDF
The interaction of light with molecular conduction junctions is attracting growing interest as a challenging experimental and theoretical problem on one hand, and because of its potential application as a characterization and control tool on the other. It stands at the interface between two important fields, molecular electronics and molecular plasmonics and has attracted attention as a challenging scientific problem with potentially important technological consequences. Here we review the present state of the art of this field, focusing on several key phenomena and applications: using light as a switching device, using light to control junction transport in the adiabatic and non-adiabatic regimes, light generation in biased junctions and Raman scattering from such systems. This field has seen remarkable progress in the past decade, and the growing availability of scanning tip configurations that can combine optical and electrical probes suggests that further progress towards the goal of realizing molecular optoelectronics on the nanoscale is imminent.

304. A. Migliore and A. Nitzan
On the evaluation of the Marcus-Hush-Chidsey integral
J. Electroanal. Chem. 671, 99-101 (2012)                                                                        PDF
The electrochemical rate constant obtained from the Marcus-Hush theory of heterogeneous electron transfer is given as a relatively complex integral. Recently, two apparently different expressions of this rate constant in the form of a series of analytical functions appeared in the literature. We demonstrate here the equivalence of these expressions and discuss their different approximations, resulting from the two distinct analytical derivations, which have implications in the practical calculation of electron transfer rate constants at electrode surfaces.

 303. M. Oren, M. Galperin and A. Nitzan
Raman scattering from molecular conduction junctions: the charge transfer mechanism
Phys. Rev. B, 85, 115435 (2012)  (12 pages)                                                                  PDF
We present a model for the charge transfer contribution to surface-enhanced Raman spectroscopy (SERS) in a molecular junction. The model is a generalization of the equilibrium scheme for SERS of a molecule adsorbed on a metal surface [B. N. J. Persson. Chem. Phys. Lett. 82, 561 (1981)].We extend the same physical consideration to a nonequilibrium situation in a biased molecular junction and to nonzero temperatures. Two approaches are considered and compared: a semiclassical approach appropriate for nonresonance Raman scattering, and a quantum approach based on the nonequilibrium Green's function method. Nonequilibrium effects on this contribution to SERS are demonstrated with numerical examples. It is shown that the semiclassical approach provides an excellent approximation to the full quantum calculation as long as the molecular electronic state is outside the Fermi window, that is, as long as the field-induced charge transfer is small.

302. G. Li, M. S. Shishodia, B. D. Fainberg, B. Apter,  M. Oren, A. Nitzan, M. A. Ratner
Compensation of Coulomb blocking and energy transfer in the current voltage characteristic of molecular conduction junctions
Nano Lettters, 12, 2228-32 (2012)                                                                                PDF
We have studied the influence of both exciton effects and Coulomb repulsion on current in molecular nanojunctions. We show that dipolar energy-transfer interactions between the sites in the wire can at high voltage compensate Coulomb blocking for particular relationships between their values. Tuning this relationship may be achieved by using the effect of plasmonic nanostructure on dipolar energy-transfer interactions.

301. D. Rai, O. Hod and A. Nitzan
Magnetic Fields Effects on the Electronic Conduction Properties of Molecular Ring Structures
Phys. Rev. B, 85, 155440 (2012) (21 pages)                                                                PDF
While mesoscopic conducting loops are sensitive to external magnetic fields, as is pronouncedly exemplified by observations of the Aharonov-Bohm (AB) effect in such structures, the small radius of molecular rings implies that the field needed to observe the AB periodicity is unrealistically large. In this paper, we study the effect of magnetic field on electronic transport in molecular conduction junctions involving ring molecules, aiming to identify conditions where magnetic field dependence can be realistically observed. We consider electronic conduction of molecular ring structures modeled both within the tight-binding (H"uckel) model and as continuous rings. We also show that much of the qualitative behavior of conduction in these models can be rationalized in terms of a much simpler junction model based on a two-state molecular bridge. Dephasing in these models is affected by two common tools: the B"uttiker probe method and coherence damping within a density matrix formulation. We show that current through a benzene ring can be controlled by moderate fields provided that several conditions are satisfied: (a) conduction must be dominated by degenerate (in the free molecule) molecular electronic resonances, associated with multiple pathways as is often the case with ring molecules, (b) molecular-leads electronic coupling must be weak so as to affect relatively distinct conduction resonances, (c) molecular binding to the leads must be asymmetric (e. g., for benzene, connection in the meta or ortho, but not para, configurations), and (d) dephasing has to be small. When these conditions are satisfied, considerable sensitivity to an imposed magnetic field normal to the molecular ring plane is found in benzene and other aromatic molecules. Interestingly, in symmetric junctions (e. g., para-connected benzene), the transmission coefficient can show sensitivity to magnetic field that is not reflected in the current-voltage characteristic. The analog of this behavior is also found in the continuous ring and the two-level models. Although sensitivity to magnetic field is suppressed by dephasing, quantitative estimates indicate that magnetic field control can be observed in suitable molecular conduction junctions.

300. M. Galperin and A. Nitzan                                                                                PDF
Raman scattering from biased molecular conduction junctions: The electronic background and its temperature
Phys. Rev. B 84, 195325 (2011) (10 pages)
The existence of background in the surface-enhanced Raman scattering from molecules adsorbed on metal surfaces has been known since the early studies about this phenomenon and is usually attributed to transitions between electronic states of the metal substrate. This paper reformulates the theory of this phenomenon in the framework of the nonequilibrium Green function formalism, which makes it possible to extend it to the case of Raman scattering from nonequilibrium (biased and current-carrying) molecular junctions. Following recent experiments, we address, in particular, the Raman-scattering measurement of current-induced electronic heating. The Raman temperature, defined by fitting the ratio between the Stokes and the anti-Stokes Raman signals to a Boltzmann factor is compared to another measure of electronic heating obtained by assuming that, close to the molecule-metal contact, the electronic distribution is dominated by the transmission process. We find that the Raman temperatures considerably exceed this upper bound to the metal-electron heating. In agreement with this observation, we show that the Raman temperature reflects the electronic nonequilibrium in the molecular bridge itself. We also show that the Raman-temperature concept breaks down at large biases.

299. M. Sukharev and A. Nitzan                                                                               PDF
Optics of atomic clusters in two dimensions: rigorous numerical studies
Phys. Rev. A 84, 043802 (2011)   (10 pages)
We consider the interaction of electromagnetic radiation of arbitrary polarization with multilevel atoms in a self-consistent manner, taking into account both spatial and temporal dependencies of local fields. This is done by numerically solving the corresponding system of coupled Maxwell-Liouville equations for various geometries. In particular, we scrutinize linear optical properties of nanoscale atomic clusters, demonstrating the significant role played by collective effects and dephasing. It is shown that subwavelength atomic clusters exhibit two resonant modes, one of which is localized slightly below the atomic transition frequency of an individual atom, while the other is positioned considerably above it. As an initial exploration of future applications of this approach, the optical response of core-shell nanostructures, with a core consisting of silver and a shell composed of resonant atoms, is examined.

298. M. Einax, M. Dierl and A. Nitzan                                                                    PDF
Heterojunction organic photovoltaic cells as molecular heat engines: A simple model for the performance analysis
J. Phys. Chem. C, 115, 21396–21401 (2011)
Organic heterojunction solar cells are analyzed within a minimal model that includes the essential physical features of such systems. The dynamical properties of this model, calculated using a master equation approach, account for the qualitative behavior of such systems. The model yields explicit results for currentvoltage behavior as well as performance characteristics expressed in terms of the thermodynamic efficiency as well as the power conversion efficiency at maximum power, making it possible to evaluate the optimal setup for this device model.

297. D. Rai, O. Hod and A. Nitzan                                                                           PDF
Magnetic Field Control of the Current through Molecular Ring Junctions
J. Phys. Chem. Lett. 2, 2118–2124 (2011)
Whereas conducting loops are, in principle, sensitive to external magnetic field, as is pronouncedly exemplified by the Aharonov-Bohm (AB) effect, the small radius of molecular rings makes the observation of such effects challenging. Indeed, the unrealistically large magnetic field needed to realize the AB effect in molecular rings has led to a widespread belief that molecular conduction is insensitive to laboratory realizable fields. Here we revisit this issue, presenting conditions under which magnetic field control of molecular ring conduction is realizable with pronounced effects on the IV characteristics. We find these conditions to be (a) weakmolecule-lead coupling, implying relatively distinct conduction resonances, (b) asymmetric junction structure (e. g., meta- or ortho-connected benzene rather than a para structure), and (c) minimal dephasing (implying low temperature) so as to maintain coherence between multiple pathways of conduction.

296. A. Migliore and A. Nitzan                                                                                PDF
Nonlinear charge transport in redox molecular junctions: a Marcus perspective
ACS Nano, 5, 6669-6685 (2011)
Redox molecular junctions are molecular conduction junctions that involve more than one oxidation state of the molecular bridge. This property is derived from the ability of the molecule to transiently localize transmitting electrons, implying relatively weak molecule-leads coupling and, in many cases, the validity of the Marcus theory of electron transfer. Here we study the implications of this property on the nonlinear transport properties of such junctions. We obtain an analytical solution of the integral equations that describe molecular conduction in the Marcus kinetic regime and use it in different physical limits to predict some important features of nonlinear transport in metalmoleculemetal junctions. In particular, conduction, rectification, and negative differential resistance can be obtained in different regimes of interplay between two different conduction channels associated with different localization properties of the excess molecular charge, without specific assumptions about the electronic structure of the molecular bridge. The predicted behaviors show temperature dependences typically observed in the experiment. The validity of the proposed model and ways to test its predictions and implement the implied control strategies are discussed.

295. A. Bednorz W. Belzig and A. Nitzan                                                                PDF
Time correlation functions in quantum continuous measurement
New J. Phys., 14, 013009(2012) [20 pages]
A continuous projective measurement of a quantum system often leads to a suppression of the dynamics, known as the Zeno effect. Alternatively, generalized nonprojective, so-called `weak' measurements can be carried out. Such a measurement is parameterized by its strength parameter that can interpolate continuously between the ideal strong measurement with no dynamics-the strict Zeno effect, and a weak measurement characterized by almost free dynamics but blurry observations. Here we analyze the stochastic properties of this uncertainty component in the resulting observation trajectory. The observation uncertainty results from intrinsic quantum uncertainty, the effect of measurement on the system (backaction) and detector noise. It is convenient to separate the latter, system-independent contribution from the system-dependent uncertainty, and this paper shows how to accomplish this separation. The systemdependent uncertainty is found in terms of a quasi-probability, which, despite its weaker properties, is shown to satisfy a weak positivity condition. We discuss the basic properties of this quasi-probability with special emphasis on its time correlation functions as well as their relationship to the full correlation functions along the observation trajectory, and illustrate our general results with simple examples. We demonstrate a violation of classical macrorealism using the fourthorder time correlation functions with respect to the quasi-probability in the two level system.

294. M. Galperin and A. Nitzan                                                                                PDF
Raman scattering and electronic heating in molecular conduction junctions
J. Phys. Chem. Lett. 2, 2110–2113 (2011)
Surface-enhanced Raman scattering (SERS) was recently used to monitor nonequilibrium properties of molecular conduction junctions. Ward et al. (Nat. Nanotechnol. 2011, 6, 33) have used such measurements to estimate heating of the molecular vibrations (indicated by the ratio between Stokes and anti-Stokes Raman peaks) as well as the electronic metal substrate (inferred from the corresponding components of the Raman continuum). The latter observation suggests, contrary to standard assumptions, significant heating of the metal contacts. Here, we discuss this observation by advancing a theory of the electronic Raman scattering background in biased current carrying molecular junctions and using it to estimate the electronic heating, as seen in the Raman signal. We reach the unexpected conclusion that while heating of the electronic background in Raman scattering from biased molecular junctions is indeed observed, this does not necessarily imply an appreciable deviation from thermal equilibrium in the electronic distributions in the leads.

CB28. V. Ben-Moshe, D. N. Beratan, A. Nitzan and  S. S. Skourtis                      PDF
Chiral control of current transfer in molecules
Topics in Current Chemistry
Electron transmission through chiral molecules induced by circularly polarized light can be very different for mirror image structures. This behaviour is described in terms of current transfer: the transfer of both charge and momentum. We review recent theoretical developments on the theory of current transfer and discuss related experimental studies of electron transmission through chiral molecular structures adsorbed on surfaces.

CB27. A. Landau, L. Kronik and A. Nitzan                                                             PDF
Molecular conduction junctions: Intermolecular effects
in Perspectives of Mesoscopic Physics (World Scientific, Singapore, 2010).
Intermolecular interactions can affect the conduction properties of molecular junctions in several ways: Direct and through-substrate electronic interactions affect the spectral properties (density of states) of the conducting junction, intermolecular electrostatic interactions affect the positioning of molecular electronic energies and thereby the nature of interface polarization. Such interactions also influence the screening properties of the junction and consequently the electrostatic potential profile across the biased junction. Other consequences include effects on junction mechanical properties that can be manifested by a different temperature dependence of conduction for a single molecule and for a molecular layer, as well as effects on optical response that may be important, for example, for the junction response associated with light induced switching. This article discusses some of these effects and their implications for the performance of molecular junctions.

293. Circular Currents in Molecular Wires                                             PDF
D. Rai, O. Hod and A. Nitzan
J. Phys. Chem C, 114, 20583-20594 (2010)
We consider circular currents driven by voltage bias in molecular wires with loop substructures studied within simple tight-binding models. Previous studies of this issue have focused on specific molecular structures. Here we address several general issues. First we consider the quantitative definition of a circular current and adopt a definition that identifies the circular component of a loop current as the sole source of the magnetic field induced in the loop. The latter may be associated with the field at the loop center, with the magnetic moment associated with this field or with the total magnetic flux threading the loop. We show that all three measures yield an identical definition of the loop current. Second, we study dephasing effects on the loop current and the associated induced magnetic field. Finally, we consider circular currents in several molecular structuressbenzene, azulene, naphthalene, and anthracenesand show that circular currents occur generically in such structures; can be, in certain voltage ranges, considerably larger than the net current through the molecule; and are furthermore quite persistent to normal thermal dephasing.

292. M. Einax, G. Solomon, W. Dieterich and A. Nitzan                        PDF
Unidirectional hopping transport of interacting particles on a finite chain
J. Chem. Phys. 133, 054102 (2010)   [12 pages]
Particle transport through an open, discrete one-dimensional channel against a mechanical or chemical bias is analyzed within a master equation approach. The channel, externally driven by time-dependent site energies, allows multiple occupation due to the coupling to reservoirs. Performance criteria and optimization of active transport in a two-site channel are discussed as a function of reservoir chemical potentials, the load potential, interparticle interaction strength, driving mode, and driving period. Our results, derived from exact rate equations, are used in addition to test a previously developed time-dependent density functional theory, suggesting a wider applicability of that method in investigations of many particle systems far from equilibrium.

291. P.Schiff and A. Nitzan                                                                    PDF
Kramers barrier crossing as a cooling machine
Chemical Physics
The achievement of local cooling is a prominent goal in the design of functional transport nanojunctions. One generic mechanism for local cooling is driving a system through a local uphill potential step. In this paper we examine the manifestation of this mechanism in the context of the Kramers barrier crossing problem. For a particle crossing a barrier, the local effective temperature and the local energy exchange with the thermal environment are calculated, and the coefficient of performance of the ensuing cooling process is evaluated.

290. V. Ben-Moshe, D. Rai, S. S. Skourtis and A. Nitzan                       PDF
Steady state current transfer and scattering theory
J. Chem. Phys, 133, 054105 (2010)   [9 pages]
The correspondence between the steady-state theory of current transfer and scattering theory in a system of coupled tight-binding models of one-dimensional wires is explored. For weak interwire coupling both calculations give nearly identical results, except at singular points associated with band edges. The effect of decoherence in each of these models is studied using a generalization of the Liouville-von Neuman equation suitable for steady-state situations. An example of a single impurity model is studied in detail, leading to a lattice model of scattering off target that affects both potential scattering and decoherence. For an impurity level lying inside the energy band, the transmission coefficient diminishes with increasing dephasing rate, while the opposite holds for impurity energy outside the band. The efficiency of current transfer in the coupled wire system decreases with increasing dephasing.

289. V. Ben Moshe, A. Nitzan, S. S. Skourtis and D. Beratan                 PDF
Steady-state theory of current transfer
J. Phys. Chem. C, 114, 8005–8013 (2010)
Current transfer is defined as a charge-transfer process where the transferred charge carries information about its original motion. We have recently suggested that such transfer causes the asymmetry observed in electron transfer induced by circularly polarized light through helical wires. This paper presents the steady-state theory of current transfer within a tight binding model of coupled wires systems. The asymmetry in the system response to a steady current imposed in a particular direction on one of the wires is used to define the efficiency of current transfer.

288. G. Li, B. D. Fainberg, A. Nitzan, S. Kohler and Peter Hänggi           PDF
Coherent charge transport through molecular wires: Exciton blocking and current from electronic excitations in the wire
Phys. Rev. B 81, 165310(2010) [14 pages]
We consider exciton effects on current in molecular nanojunctions, using a model comprising a two twolevel sites bridge connecting free-electron reservoirs. Expanding the density operator in the many-electron eigenstates of the uncoupled sites, we obtain a 16x16 density matrix in the bridge subspace whose dynamics is governed by Liouville equation that takes into account interactions on the bridge as well as electron injection and damping to and from the leads. Our consideration can be considerably simplified by using the pseudospin description based on the symmetry properties of Lie group SU(2). We study the influence of the bias voltage, the Coulomb repulsion, and the energy-transfer interactions on the steady-state current and, in particular, focus on the effect of the excitonic interaction between bridge sites. Our calculations show that in case of noninteracting electrons this interaction leads to reduction in the current at high voltage for a homodimer bridge. In other words, we predict the effect of "exciton" blocking. The effect of exciton blocking is modified for a heterodimer bridge and disappears for strong Coulomb repulsion at sites. In the latter case the exciton type interactions can open new channels for electronic conduction. In particular, in the case of strong Coulomb repulsion, conduction exists even when the electronic connectivity does not exist.

287. M. Einax, M. Körner, P Maass and A. Nitzan                                 PDF
Nonlinear hopping transport in ring systems and open channels
Phys. Chem. Chem. Phys. 12, 645-654 (2010)
We study the nonlinear hopping transport in one-dimensional rings and open channels. Analytical results are derived for the stationary current response to a constant bias without assuming any specific coupling of the rates to the external fields. It is shown that anomalous large effective jump lengths, as observed in recent experiments by taking the ratio of the third-order nonlinear and the linear conductivity, can occur already in ordered systems. Rectification effects due to site energy disorder in ring systems are expected to become irrelevant for large system sizes. In open channels, in contrast, rectification effects occur already for disorder in the jump barriers and do not vanish in the thermodynamic limit. Numerical solutions for a sinusoidal bias show that the ring system provides a good description for the transport behavior in the open channel for intermediate and high frequencies. For low frequencies temporal variations in the mean particle number have to be taken into account in the open channel, which cannot be captured in the more simple ring model.

286. H. Nakanishi, K. J. M. Bishop, B. Kowalczyk, A. Nitzan, E. A. Weiss, K. V. Tretiakov, M. M. Apodaca, R. Klajn, J. F. Stoddart and B. A. Grzybowski
Photoconductance and inverse photoconductance in films of functionalized metal nanoparticles                                        PDF
Nature, 460, 371-375 (2009)
In traditional photoconductors1-3, the impinging light generates mobile charge carriers in the valence and/or conduction bands, causing the material's conductivity to increase4. Such positive photoconductance is observed in both bulk and nanostructured5,6 photoconductors. Here we describe a class of nanoparticle-based materials whose conductivity can either increase or decrease on irradiation with visible light of wavelengths close to the particles' surface plasmon resonance. The remarkable feature of these plasmonic materials is that the sign of the conductivity change and the nature of the electron transport between the nanoparticles depend on the molecules comprising the self-assembled monolayers (SAMs)7,8 stabilizing the nanoparticles. For SAMs made of electrically neutral (polar and non-polar) molecules, conductivity increases on irradiation. If, however, the SAMs contain electrically charged (either negatively or positively) groups, conductivity decreases. The optical and electrical characteristics of these previously undescribed inverse photoconductors can be engineered flexibly by adjusting the material properties of the nanoparticles and of the coating SAMs. In particular, in films comprising mixtures of different nanoparticles or nanoparticles coated with mixed SAMs, the overall photoconductance is a weighted average of the changes induced by the individual components. These and other observations can be rationalized in terms of light-induced creation of mobile charge carriers whose transport through the charged SAMs is inhibited by carrier trapping in transient polaron-like states9,10. The nanoparticle-based photoconductors we describe could have uses in chemical sensors and/or in conjunction with flexible substrates.

CB26. B.D. Fainberg, P. Hanggi, S. Kohler and A. Nitzan
Exciton- and Light-induced Current in Molecular Nanojunctions
American Institute of Physics Conference Proceedings 1147, 78-86 (2009)
(ICTOPON-2009 Conference: Transport And Optical Properties Of Nanomaterials)
In isolated organic molecular chain, electron-hole pairs (excitons) possess dipole moments interacting with each other and leading to exciton tunneling along the molecule.  Although this mechanism does not induce a net charge transfer, it nevertheless may influence the electrical current, in particular, if the molecule is subject to laser radiation. We have investigated exciton- and light-induced current in molecular nanojunctions. Using a model comprising a two two-level sites bridge connecting free electron reservoirs we show that the exciton coupling between the sites of the molecular bridge can markedly effect the source-drain current through a molecular junction. In some cases when excited and unexcited states of the sites are coupled differently to the leads, the contribution from electron-hole excitations can exceed the Landauer elastic current and dominate the observed conduction. We have proposed an optical control method using chirped pulses for enhancing charge transfer in unbiased junctions where the bridging molecule is characterized by a strong charge-transfer transition.

285. J. E. Subotnik, T. Hansen, M. A. Ratner and A. Nitzan
Nonequilibrium steady state transport via the reduced density matrix operator
J. Chem. Phys. 130, 144105 (2009)                                                     PDF
We present a very simple model for numerically describing the steady state dynamics of a system interacting with continua of states representing a bath. Our model can be applied to equilibrium and nonequilibrium problems. For a one-state system coupled to two free electron reservoirs, our results match the Landauer formula for current traveling through a molecule. More significantly, we can also predict the nonequilibrium steady state population on a molecule between two out-of-equilibrium contacts. While the method presented here is for one-electron Hamiltonians, we outline how this model may be extended to include electron-electron interactions and correlations, an approach which suggests a connection between the conduction problem and the electronic structure problem.

284. M. Galperin, K. Saito, Al. V. Balatsky and A. Nitzan
Cooling mechanisms in molecular conduction junctions
Phys. Rev. B 80, 115427 (2009) [12 pages]                               PDF
While heating of a current carrying Ohmic conductors is an obvious consequence of the diffusive nature of the conduction in such systems, current-induced cooling has been recently reported in some molecular conduction junctions. In this paper, we demonstrate by simple models the possibility of cooling molecular junctions under applied bias, and discuss several mechanisms for such an effect. Our model is characterized by single electron tunneling between electrodes represented by free electron reservoirs through a system characterized by its electron levels, nuclear vibrations and their structures. We consider cooling mechanisms resulting from  (a) cooling of one electrode surface by tunneling-induced depletion of high-energy electrons; (b) cooling by coherent sub resonance electronic transport analogous to atomic laser-induced cooling and (c) the incoherent analog of process (b)-cooling by driven activated transport. The non-equilibrium Green function formulation of junction transport is used in the first two cases, while a master equation approach is applied in the analysis of the third.

283. A. Landau, L. Kronik and A. Nitzan
Cooperative effects in molecular conduction II: The Semiconductor−Metal Molecular Junction
J. Phys. Chem. A 113, 7451–7460 (2009)                                PDF
Our recent calculation of the effect of intermolecular interactions on molecular conduction (J. Comput. Theor. Nanosci. 2008, 5, 535) is generalized to molecules adsorbed on a model semiconductor surface and in a metal-molecule-semiconductor junction. The metal and semiconductor electrodes are represented by cubic lattices within generic tight binding models, where the semiconductor two-band structure is described by using a simple site-alteration property. A physically motivated choice of parameters for the molecule(s) and the electrodes completes the model definition. The model encompasses direct intermolecular interactions as well as through-metal interactions and can be solved exactly to yield spectral properties (surface density of states) and transport characteristics (transmission coefficients and current-voltage behavior) for single-molecule junctions and molecular layers. The model is applied to analyzing the effect of intermolecular interactions on the predicted negative differential resistance in metal-molecule-semiconductor junctions (recently observed in scanning tunneling microscopy studies of adsorbates on Si(100)).

282. S. Yeganeh, M. Ratner M. Galperin and A. Nitzan
Transport in State Space: Voltage-Dependent Conductance Calculations of Benzene-1,4-dithiol
Nano Let. 9, 1770-74 (2009)                                                   PDF
We implement a method to study transport in a basis of many-body molecular states using the nonequilibrium Hubbard Green's function technique. A well-studied system, a junction consisting of benzene-dithiol on gold, is the focus of our consideration. Electronic structure calculations are carried out at the Hartree-Fock (HF), density functional theory (DFT), and coupled-cluster singles and doubles (CCSD) levels, and multiple molecular states are included in the transport calculation. The conductance calculation yields new information about the transport mechanism in BDT junctions.

281. M. Galperin, M.A. Ratner and A. Nitzan
Raman scattering in current carrying molecular junctions.
J. Chem. Phys. 130, 144109 (2009)                                      PDF
This is a preliminary acount of a theory for Raman scattering by current-carrying molecular junctions. The approach combines a non-equilibrium Green's function (NEGF) description of the non-equilibrium junction with a generalized scattering theory formulation for evaluating the light scattering signal. This generalizes our previous study (Phys. Rev. Lett. 95, 206802 (2005); J. Chem. Phys. 124, 234709 (2006)) of junction spectroscopy by including molecular vibrations and developing machinery for calculation of state-to-state (Raman scattering) fluxes within the NEGF formalism. For large enough voltage bias we find that the light scattering signal contains, in addition to the normal signal associated with the molecular ground electronic state, also a contribution from the inverse process originated from the excited molecular state as well as an interference component. The effect of coupling to the electrodes and of the imposed bias on the total Raman scattering as well as its components are discussed. Our result reduces to the standard expression for Raman scattering in the isolated molecule case, i.e. in the absence of coupling to the electrodes. The theory is used to discuss the charge transfer contribution to surface enhanced Raman scattering for molecules adsorbed on metal surfaces and its manifestation in the biased junction.

280. M. Galperin, M.A. Ratner and A. Nitzan
Raman scattering from non-equilibrium molecular conduction junctions
Nano Lett., 9, 758-762(2009)                                              PDF
We present a theory of Raman scattering from molecular conduction junctions that combines a non-equilibrium Green's function description of the junction with a generalized scattering theory of light scattering.  The scattering flux depends on the bias voltage because of two principal reasons:  First, partial populations in the ground and excited molecular levels give rise to two scattering pathways as well as interference between them.. Secondly, junction heating affects the relative Stokes and anti-Stokes scattering intensities. This suggests Raman scattering as an important future tool in the study of structure, dynamics and thermal properties of non-equilibrium molecular junctions.

279. S. Tornow, R. Bulla, F. B. Anders and A. Nitzan
Dissipative two-electron transfer: A numerical renormalization group study
Phys. Rev. B 78, 035434 (2008)                                          PDF
We investigate nonequilibrium two-electron transfer in a model redox system represented by a two-site extended Hubbard model and embedded in a dissipative environment. The influence of the electron-electron interactions and the coupling to a dissipative bosonic bath on the electron transfer is studied in different temperature regimes. At high temperatures, Marcus transfer rates are evaluated, and at low temperatures, we calculate equilibrium and nonequilibrium population probabilities of the donor and acceptor with the nonperturbative numerical renormalization group approach. We obtain the nonequilibrium dynamics of the system prepared in an initial state of two electrons at the donor site and identify conditions under which the electron transfer involves one concerted two-electron step or two sequential single-electron steps. The rates of the sequential transfer depend nonmonotonically on the difference between the intersite and on-site Coulomb interaction, which become renormalized in the presence of the bosonic bath. If this difference is much larger than the hopping matrix element, the temperature as well as the reorganization energy, simultaneous transfer of both electrons between donor and acceptor can be observed.

278. S. S. Skourtis, D. N. Beratan, R. Naaman, A. Nitzan and D. H. Waldeck
Chiral control of electron transmission through molecules
Phys. Rev. Let. 101, 238103 (2008)                                      PDF
Electron transmission through chiral molecules induced by circularly polarized light can be very different for mirror-image structures, a peculiar fact given that the electronic energy spectra of the systems are identical. We propose that this asymmetry-as large as 10% for resonant transport-arises from different dynamical responses of the mirrored structures to coherent excitation. This behavior is described in the context of a general novel phenomenon of current transfer (transfer of charge with its momentum information) and accounts for the observed asymmetry and its dependence on structure.

277. B. Fainberg and A. Nitzan
Decaying Rabi oscillations in quantum-dot tunnelling junctions
Phys. Status Solidi A 206, 948–951 (2009)                             PDF
Motivated by the experiments by Zrenner et al. [Nature 418, 612 (2002)], we study the influence of relaxation processes on converting Rabi oscillations in a strongly biased single-quantum-dot photodiode into deterministic photocurrents. We show that the behavior of a quantum dot with different tunnel rates for electron and holes is qualitatively different from that with the equal tunnel rates: in the latter case the current shows attenuating oscillations with the Rabi frequency. In contrast, for different electrons and holes tunnelling rates, the frequency of these oscillations diminishes, and they disappear beyond a definite asymmetry threshold. We give an analytical solution of the problem and a numerical example showing a different behaviour of the transferred charge in the small attenuation limit for equal and different tunnel rates for electrons and holes.

276. M. Galperin, A. Nitzan and M. A. Ratner
The non-linear response of molecular junctions: the polaron model revisited
J. Phys.: Condens. Matter 20, 374107(2008)                           PDF
A polaron model proposed as a possible mechanism for non-linear conductance (Galperin et al
2005 Nano Lett. 5 125–30) is revisited with the focus on the differences between the weak and
strong molecule–lead coupling cases. Within the one-molecule-level model we present an
approximate expression for the electronic Green function corresponding to the inelastic
transport case, which in the appropriate limits reduces to expressions presented previously for
the isolated molecule and for a molecular junction coupled to a slow vibration (static limit). The
relevance of considerations based on the isolated molecule limit to understanding properties of
molecular junctions is discussed.

275. M. Galperin, A. Nitzan and M. A. Ratner
Inelastic transport in the Coulomb blockade regime within a nonequilibrium atomic limit
Phys. Rev. B 78, 125320 (2008)                                     PDF
A method developed by Sandalov et al. Int. J. Quantum Chem. 94, 113 2003 is applied to inelastic
transport in the case of strong correlations on the molecule, which is relatively weakly coupled to contacts. The
ability of the approach to deal with the transport in the language of many-body molecular states as well as to
take into account charge-specific normal modes and nonadiabatic couplings is stressed. We demonstrate the
capabilities of the technique within simple model calculations and compare it to previously published
approaches.

274. Joseph E. Subotnik, Abraham Nitzan
Multibody Scattering, Correlation, Molecular Conduction and the 0.7 Anomaly
J.Chem. Phys. 129, 144107 (2008)                               PDF
We describe a new grid-based (or localized orbital-based) method for treating the effects of exchange and correlation on electronic transmission through a molecular target where there are initially other bound electrons. Our algorithm combines the approaches of (i) solid-state grid-based algorithms using self-energies and (ii) the complex Kohn method from electron-molecule scattering. For the general problem of a molecular target with electrons, our algorithm should ideally solve for electronic transmission with a computational cost scaling as . In this paper, we implement our algorithm to solve three model problems involving two electrons: (i) Single-channel resonant transmission through a double barrier well (DBW), where the target already contains one bound state electron. [Rejec, Ramsak and Jefferson,  Phys. Rev. B.,  67, 075311 (2003)]. (ii) Multi-channel resonant transmission through a DBW, where the incoming electron can exchange energy with the bound electron. (iii) Transmission through a triple barrier well (TBW), where the incoming electron can knock forward the bound-electron, yielding a physical model of electron-assisted electron transfer. This article offers some insight about the role and size of exchange and correlation effects in molecular conduction, where few such rigorous calculations have yet been made. Such multibody effects have already been experimentally identified in mesoscopic electron transport, giving rise to the ``0.7 anomaly'' whereby electrons traveling through a narrow channel pair up as singlets and triplets. We expect the effect of electronic correlation to be even more visible for conduction through molecules, where electrons should partially localize into bonding and anti-bonding orbitals.

273. M. Galperin, M.A. Ratner, A. Nitzan and A. Troisi
Nuclear Coupling and Polarization in Molecular Transport Junctions: Beyond Tunneling to Function
Science, 319, 1056 (2008)                                                                        PDF
Because molecules have strong polarization responses to changing charge state or external field, molecules isolated between two electrodes can show strongly nonlinear current/voltage response.  Much current experimental research on transport in molecular junctions focuses on finite voltages, where such polarization-induced nonlinearities are significant, and may result in technologically-relevant device-type behaviors. This overview will focus on theoretical description of this nonlinear regime. For small applied voltages (up to ~3000 cm-1) the weak response corresponding to inelastic electron tunneling spectroscopy is usually observed. This response, arising from interaction between transporting electrons and molecular vibrations, provides a useful, sensitive probe of the junction.
    At higher voltages and for certain timescale regimes, far stronger coupling effects occur. These include such significant and complicated phenomena as negative differential resistance, dynamical switching, current hysteresis, chemical reactions, heat conduction, noise phenomena, Coulomb blockade and Kondo resonance. Strongly nonlinear current/voltage characteristics are observed. We discuss a general picture for such phenomena, that arise from charging, strong correlation, and polarization (electronic and geometric) effects both in the molecule and at the interface.

272.B. Fainberg, M. Jouravlev and A. Nitzan
Theory of light-induced current in molecular-tunneling junctions excited with intense shaped pulses
Phys. Rev. B 76, 245329  (2007)                                                            PDF
A theory for light-induced current by strong optical pulses in molecular-tunneling junctions is described. We consider a molecular bridge represented by its highest occupied and lowest unoccupied levels, HOMO and LUMO, respectively. We take into account two types of couplings between the molecule and the metal leads: electron transfer that gives rise to net current in the biased junction and energy transfer between the molecule and electron-hole excitations in the leads. Using a Markovian approximation, we derive a closed system of equations for the expectation values of the relevant variables: populations and molecular polarization polarization that are binary, and exciton populations that are tetradic in the annihilation and creation operators for electrons in the molecular states. We have proposed an optical control method using chirped pulses for enhancing charge transfer in unbiased junctions where the bridging molecule is characterized by a strong charge-transfer transition. An approximate analytical solution of the resulting dynamical equation is supported by a full numerical solution. When energy transfer between the molecule and electron-hole excitations in the leads is absent, the optical control problem for inducing charge transfer with linearly chirped pulse can be reduced to the Landau-Zener transition to a decaying level. In the absence of both energy transfer and optical coupling the Landau theory is recovered. The proposed control mechanism is potentially useful for developing novel opto-electronic single-electron devices with optical gating based on molecular nanojunctions.

271. M. Galperin, M.A. Ratner, A. Nitzan                     
Inelastic effects in molecular junction transport: Scattering and self-consistent calculations for the Seebeck coefficient
Molecular Physics, 106, 397-404 (2008)                                                PDF
The influence of molecular vibration on the Seebeck coefficient is studied within a simple model. Results of a scattering theory approach are compared to those of a full self-consistent nonequilibrium Green’s function scheme. We show, for a reasonable choice of parameters, that inelastic effects have non-negligible influence on the resulting Seebeck coefficient for the junction. We note that the scattering theory approach may fail both quantitatively and qualitatively. Results of calculation with reasonable parameters are in good agreement with recent measurements [P. Reddy et al., Science 315, 1568 (2007)] 
 
270. A. Nitzan
Molecules take the heat   (Perspective)                                                     PDF
Science, 317, 759 (2007)
Problems of heating and heat transfer are ubiquitous in everyday life, running from planning efficient airconditioning to dealing with overheated car engines or computer boards. Most people, however, will regards such problems as old science, whose bearing on modern life is an issue of engineering. However, as nanotechnology aims at systems of ever-diminishing size, where heating and heat dissipation on the nanoscale are important factors in system performance and stability, new scientific questions arise. In particular, advances in molecular electronics, where molecules are studied as potential active components in electronic nano-circuits, imply the need to understand and control heating and heat transport on the molecular scale. The study by Z. Wang et al(1) published in this issue of Science constitutes an important step in this direction, in which the authors describe and apply a novel method for measuring the heat conduction properties of a monomolecular layer (MML).

269. A. Landau, L. Kronik and A. Nitzan
Cooperative effects in molecular conduction
J. Comp. Theor. Nanoscience, 5, 535-544 (2008)                                PDF
Current experimental and theoretical studies on the effect of intermolecular interactions on molecular conduction appear to be in conflict with each other. In particular, some experimental results, e.g., the observation of 2-dimensional free-particle character for interface bound electrons indicate strong intermolecular interactions while other observations indicate an additive character of conduction properties. In this paper we use a generic tight binding model with a physically motivated choice of parameters in order to examine this issue. The model encompasses direct intermolecular interactions as well as through-metal interactions and can be solved exactly to yield spectral properties (surface density of states) and transport characteristics (transmission coefficients and current-voltage behaviors) for single molecule junctions, molecular islands and molecular layers. We find linear scaling of conduction properties with the number of conducting molecules in junctions characterized by molecular layers when the probe (STM tip) addresses different numbers of molecules; however, the conduction per molecule can differ significantly from that of an isolated single molecule. When a junction involves finite molecular islands of varying sizes, linear scaling sets in only beyond a certain molecular island size, of the order of a few tens of molecules. Implications for current observation of linear scaling behaviors are discussed.

268. M. Galperin, M.A. Ratner and A. Nitzan                            PDF
Inelastic effects in molecular junctions in the Coulomb and Kondo regimes: Nonequilibrium equation-of-motion approach
Phys. Rev. B 76, 035301 (2007)
Inelastic e_ects in the Coulomb blockade and Kondo regimes of electron transport through molecular junctions are considered within a simple nonequilibrium equation-of-motion (EOM) approach. The scheme is self-consistent, and can qualitatively reproduce the main experimental observations of vibrational features in Coulomb blockade [H. Park et al., Nature 407, 57 (2000)] and Kondo by Meir et al. [Phys. Rev. Lett. 66, 3048 (1991); ibid. 70, 2601 (1993)] are used on the Keldysh contour to account for the nonequilibrium nature of the junction, and dressing by appropriate Franck-Condon (FC) factors is used to account for vibrational features. Results of the equilibrium EOM scheme by Meir et al. are reproduced in the appropriate limit.

267. M. Galperin, M.A. Ratner and A. Nitzan                            PDF
Molecular Transport Junctions:  Vibrational Effects
J. Phys.: Condens. Matter 19, 103201 (2007)
Transport of electrons in a single molecule junction is the simplest problem in the general subject area of molecular electronics. In the past few years, this area has been extended to probe beyond the simple tunnelling associated with large energy gaps between electrode Fermi level and molecular levels, to deal with smaller gaps, with near-resonance tunnelling and, particularly, with effects due to interaction of electronic and vibrational degrees of freedom. This overview is devoted to the theoretical and computational approaches that have been taken to understanding transport in molecular junctions when these vibronic interactions are involved.
After a short experimental overview, and discussion of different test beds and measurements, we define a particular microscopicmodel Hamiltonian. That overall Hamiltonian can be used to discuss all of the phenomena dealt with subsequently. These include transition from coherent to incoherent transport as electron/vibration interaction increases in strength, inelastic electron tunneling spectroscopy and its interpretation and measurement, affects of interelectronic repulsion treated at the Hubbard level, noise in molecular transport junctions, non-linear conductance phenomena, heating and heat conduction in molecular transport junctions and current-induced chemical reactions. In each of these areas, we use the same simple model Hamiltonian to analyse energetics and dynamics.
While this overview does not attempt survey the literature exhaustively, it does provide appropriate references to the current literature (both experimental and theoretical). We also attempt to point out directions in which further research is required to answer cardinal questions concerning the behaviour and understanding of vibrational effects in molecular transport junctions.
1. Introduction………………………………………………….. 2
2. Experimental background – Test beds………………………..8
3. Theoretical approaches……………………………………….10
            3a. A microscopic model……………………………….……10
            3b. The electron-phonon coupling…………………….……...14
            3c. Time and energy scales…………………………….…….15
            3d. Theoretical methods…………….………………….…….19
            3e. Numerical calculations…………………………………....28
4. Incoherent vs. coherent transport…………………………....28
5. Inelastic tunneling spectroscopy…………………….............31
          5a. Experimental background………………………………...31
            5b. Theoretical considerations – the weak coupling limit……....36
            5c. Theoretical considerations – moderately strong coupling..41
            5d. Comparison of approximation schemes…………………...47
            5e. Asymmetry in IETS………………………………………51
            5f. The origin of dips in IETS signals……………………….....53
            5g. Computational approaches……………………………….56
6. Effects of electron-electron (e-e) interactions………………....62
7. Noise………………………………………………………….66
8. Non-linear conductance phenomena……………………….….72
9. Heating and heat conduction………………………………….75
9a. General considerations…………………………………….........75
9b. Heat generation…………………………………………...........79
9c. Heat conduction…………………………………………..........84
9d. Junction temperature……………………………………….......86
10. Current induced reactions…………………………………..89
11. Summary and outlook………………………………............90


266. M. Galperin, M. A. Ratner and A. Nitzan                       PDF
heat conduction in molecular junctions
Phys. Rev. B 75, 155312 (2007)
Heating and heat conduction in molecular junctions are considered within a general NEGF formalism. We obtain a unified description of heating in current carrying molecular junctions as well as the electron and phonon contributions to the thermal flux including their mutual influence. Ways to calculate these contributions, their relative importance and ambiguities in their definitions are discussed. A general expression for the phonon thermal flux is derived and used in a new, a “measuring technique”, to define and quantify ‘local temperature’ in nonequilibrium systems. Superiority of this measuring technique over the usual approach that defines effective temperature using the equilibrium phonon distribution is demonstrated.  Simple bridge models are used to illustrate the general approach with numerical examples.


265. M. Galperin, A. Nitzan, and M. A. Ratner
Inelastic tunneling effects on noise properties of molecular junctions     PDF
Phys. Rev. B 74, 075326 (2006)
The effect of electron-phonon coupling on the current noise in a molecular junction is investigated within a simple model. The model comprises a 1-level bridge representing a molecular level that connects between two free electron reservoirs and is coupled to a vibrational degree of freedom representing a molecular vibrational mode. The latter in turn is coupled to a phonon bath that represents the thermal environment. We focus on the zero frequency noise spectrum and study the changes in its behavior under weak and strong electron-phonon interactions. In the weak coupling regime we find that the noise amplitude can increase or decrease as a result of opening of an inelastic channel, depending on distance from resonance and on junction asymmetry. In particular the relative Fano factor decreases with increasing off resonance distance and junction asymmetry. For resonant inelastic tunneling with strong electron-phonon coupling the differential noise spectrum can show phonon sidebands in addition to a central feature. Such sidebands can be observed when displaying the noise against the source-drain voltage, but not in noise vs. gate voltage plots obtained at low source-drain bias. A striking crossover of the central feature from double to single peak is found for increasing asymmetry in the molecule-leads coupling or increasing electron-phonon interaction. These variations provide a potential diagnostic tool. A possible use of noise data from scanning tunneling microscopy experiments for estimating the magnitude of the electron-phonon interaction on the bridge is proposed.

264. M. Galperin, A. Nitzan, and M. A. Ratner
Resonant inelastic tunneling in molecular junctions
Phys. Rev. B 73, 045314 (2006)                                                    PDF
Within a phonon-assisted resonance level model we develop a self-consistent procedure for calculating electron transport currents in molecular junctions with intermediate to strong electron-phonon interaction. The scheme takes into account the mutual influence of the electron and phonon subsystems. It is based on the second order cumulant expansion, used to express the correlation function of the phonon shift generator in terms of the phonon momentum Green function. Equation of motion _EOM_ method is used to obtain an approximate analog of the Dyson equation for the electron and phonon Green functions in the case of manyparticle operators present in the Hamiltonian. To zero order it is similar in particular cases _empty or filled bridge level_ to approaches proposed earlier. The importance of self-consistency in resonance tunneling situations _partially filled bridge level_ is stressed. We confirm, even for strong vibronic coupling, a previous suggestion concerning the absence of phonon sidebands in the current versus gate voltage plot when the source-drain voltage is small _Mitra et al., Phys. Rev. B 69, 245302 _2004__.

263. E.A. Weiss, G. Katz, R. H. Goldsmith, M. R. Wasielewski, M. A. Ratner, R. Kosloff and A. Nitzan
Electron transfer mechanism and the locality of the system-bath interaction: A comparison of local, semilocal, and pure dephasing models.
J. Chem. Phys. 124, 074501 (2006)                                                      PDF
We simulate the effects of two types of dephasing processes, a nonlocal dephasing of system eigenstates and a dephasing of semilocal eigenstates, on the rate and mechanism of electron transfer _eT_ through a series of donor-bridge-acceptor systems, D-BN-A, where N is the number of identical bridge units. Our analytical and numerical results show that pure dephasing, defined as the perturbation of system eigenstates through the system-bath interaction, does not disrupt coherent eT because it induces no localization; electron transfer may proceed through superexchange in a system undergoing only pure dephasing. A more physically reasonable description may be obtained via a system-bath interaction that reflects the perturbation of more local electronic structure by local nuclear distortions and dipole interactions. The degree of locality of this interaction is guided by the structure of the system Hamiltonian and by the nature of the measurement performed on the system i.e., the nature of the environment_. We compare our result from this “semilocal” model with an even more local phenomenological dephasing model. We calculate electron transfer rate by obtaining nonequilibrium steady-state solutions for the elements of a reduced density matrix; a semigroup formalism is used to write down the dissipative part of the equation of motion. <>

262. M. Galperin, M.A. Ratner and A. Nitzan
Conduction in molecular transport junction: Current from coupling to the electron-hole excitations in the leads
Phys. Rev. Letters, 96, 166803 (2006)                                                   PDF
We show that coupling of the molecular bridge to Electron-hole excitations in the contacts can markedly effect the source-drain current through a molecular junction.We use a simple two-level system to represent the molecule and treat the contacts as reservoirs of free electrons, each at its own equilibrium. The system is treated within the non-equilibrium Green functions approach.We show that in some cases the contribution from electron-hole excitations may be essential as compared to the usual Landauer elastic current. In particular it may dominate the current for asymmetrically coupled junctions and large molecule-lead distances.

261. D. Segal and A. Nitzan
Molecular heat pump
Phys. Rev. E 73, 026109 (2006)                                                          PDF
We propose a molecular device that pumps heat against a thermal gradient. The system consists of a molecular element connecting two thermal reservoirs that are characterized by different spectral properties. The pumping action is achieved by applying an external force that periodically modulates molecular levels. This modulation affects periodic oscillations of the internal temperature of the molecule and the strength of its coupling to each reservoir resulting in a net heat flow in the desired direction. The heat flow is examined in the slow and fast modulation limits and for different modulation wave forms, thus making it possible to optimize the device performance.

260. M. Galperin and A. Nitzan
Optical properties of current carrying molecular wires
J. Chem. Phys. 124, 234709                                                                  PDF
We consider several fundamental optical phenomena involving single molecules in biased metal-molecule-metal junctions. The molecule is represented by its highest occupied and lowest unoccupied molecular orbitals, and the analysis involves the simultaneous consideration of three coupled fluxes: the electronic current through the molecule, energy flow between the molecule and electron-hole excitations in the leads and the incident and/or emitted photon flux. Using a unified theoretical approach based on the non-equilibrium Green function method we derive expressions for the absorption lineshape (not an observable but a useful reference for considering yields of other optical processes) and for the current induced molecular emission in such junctions. We also consider conditions under which resonance radiation can induce electronic current in an unbiased junction. We find that current driven molecular emission and resonant light induced electronic currents in single molecule junctions can be of observable magnitude under appropriate realizable conditions. In particular, light induced current should be observed in junctions involving molecular bridges that are characterized by strong charge transfer optical transitions. For observing current induced molecular emission we find that in addition to the familiar need to control the damping of molecular excitations into the metal substrate the phenomenon is also sensitive to the way in which the potential bias is distributed on the junction.

259. J. Koch, M. Semmelhack, F. von Oppen and A. Nitzan
Current-induced nonequilibrium vibrations in single-molecule devices
Phys. Rev. B,  73, 155306 (2006)                                                        PDF
Finite-bias electron transport through single molecules generally induces nonequilibrium molecular vibrations (phonons). By a mapping to a Fokker-Planck equation, we obtain analytical scaling forms for the nonequilibrium phonon distribution in the limit of weak electron-phonon coupling λ within a minimal model. Remarkably, the width of the phonon distribution diverges as ~ λ-α  when the coupling decreases, with voltage-dependent, non-integer exponents α. This implies a breakdown of perturbation theory in the electron-phonon coupling for fully developed nonequilibrium. We also discuss possible experimental implications of this result such as current-induced dissociation of molecules.

258. M. Galperin and A. Nitzan
Current induced light emission and light induced current in molecular tunneling junctions
Phys. Rev Letters, 95, 206802 (2005)                                                 PDF
The interaction of metal-molecule-metal junctions with light is considered within a simple generic model. We show, for the first time, that light induced current in unbiased junctions can take place when the bridging molecule is characterized by a strong charge-transfer transition. The same model shows current induced light emission under potential bias that exceeds the molecular excitation energy. Results based on realistic estimates of molecular-lead coupling and molecule-radiation field interaction suggest that both effects should be observable.

257. I. Benjamin and A. Nitzan
Path Integral computations of tunneling processes
J. Chem. Phys. 123, 104103 (2005)                                                    PDF
The application of the path integral methodology of Chandler and Wolynes (D. Chandler and P. G. Wolynes, J. Chem. Phys. 74, 4078 (1981)) to the calculation of one-electron tunneling probabilities is revisited. We show that the evaluation of the kink free energy that is related to the tunneling splitting is associated with ‘polymer beads’ distributions over a continuous distributions of scaled   barriers, which makes both the calculation and its physical interpretation relatively difficult. In particular, we find that relative to other available techniques the method converges slowly and suffers from inaccuracies associated with the finite temperature aspect of the calculation, and that past tentative identification of the bead distribution over the barrier with a physical picture of a ‘tunneling path’ should be reassessed

256. D. Segal and A. Nitzan
Heat rectification in molecular junctions
J. Chem. Phys. 122, 194704 (2005)                                                    PDF
Heat conduction through molecular chains connecting two reservoirs at different temperatures can be asymmetric for forward and reversed temperature biases. Based on analytically solvable models and on numerical simulations we show that molecules rectify heat when two conditions are satisfied simultaneously: the interactions governing the heat conduction are nonlinear, and the junction has some structural asymmetry. We consider several simplified models where a two-level system sTLSd simulates a highly anharmonic vibrational mode, and asymmetry is introduced either through different coupling of the molecule to the contacts, or by considering internal molecular asymmetry. In the first case, we present analytical results for the asymmetric heat current flowing through a single anharmonic mode using different forms for the TLS-reservoirs coupling.We also demonstrate numerically, studying a realistic molecular model, that a uniform anharmonic molecular chain connecting asymmetrically two thermal reservoirs rectifies heat. This effect is stronger for longer chains, where nonlinear interactions dominate the transfer process. When asymmetry is related to the internal level structure of the molecule, numerical simulations reveal a nontrivial rectification behavior. We could still explain this behavior in terms of an effective system-bath coupling. Our study suggests that heat rectification is a fundamental characteristic of asymmetric nonlinear thermal conductors. This phenomenon is important for heat control in nanodevices and for understanding of energy flow in biomolecules.

255. O.Durr, W.Dieterich and A. Nitzan
Coupled ion and network dynamics in polymer electrolytes:Monte Carlo study of a lattice model
J. Chem. Phys. 121, 12732-39 (2004)                  PDF
Monte Carlo simulations are used to study ion and polymer chain dynamic properties in a simplified lattice model with only one species of mobile ions.The ions interact attractively with specific beads in the host chains,while polymer beads repel each other.Cross linking of chains by the ions reduces chain mobilities which in turn suppresses ionic diffusion.Diffusion constants for ions and chains as a function of temperature follow the Vogel–Tammann–Fulcher ~VTF! law with a common VTF temperature at low ion concentration,but both decouple at higher concentrations,in agreement with experimental observations.Our model allows us to introduce pressure as an independent variable through calculations of the equation of state using the quasichemical approximation,and to detect an exponential pressure dependence of the ionic diffusion.


 254. M. Galperin, M. A.Ratner and A. Nitzan
Hysteresis, switching, and Negative Differential Resistance in molecular junctions: A polaron model
Nano Letters                                                     PDF
Within a simple mean-field model (self-consistent Hartree approximation) we discuss the possibility of polaron formation on a molecular wire as a mechanism for negative differential resistance (NDR), switching, and/or hysteresis in the I- V characteristic of molecular junctions. This mechanism differs from earlier proposed mechanisms of charging and conformational change. The polaron model captures the essential physics and provides qualitative correspondence with experimental data. The importance of active redox centers in the molecule is indicated.

253. M. Galperin, A. Nitzan, M. A. Ratner  and D. R. Stewart
Molecular Transport Junctions: Asymmetry in Inelastic Tunneling Processes
                                                                                PDF
Inelastic electron tunneling spectroscopy (IETS) measurements are usually carried out in the low-voltage (Ohmic)regime where the elastic conduction voltage characteristic is symmetric to voltage inversion. Inelastic features, normally observed in the second derivative d2I/dV2 are also symmetric (in fact antisymmetric) in many cases, but asymmetry is sometimes observed. We show that such asymmetry can occur due to different energy dependences of the two contact self-energies. This may be attributed to differences in contact density of states (different contact material) or different energy dependence of the coupling (STM like geometry or asymmetric positioning of molecular vibrational modes in the junction). The asymmetry scales with difference between the energy dependence of these self-energies, and disappears when this dependence is the same for the two contacts. Our nonequilibrium Green function approach goes beyond proposed WKB scattering theory [1] in properly accounting for Pauli exclusion, as well as providing a path to generalizations, including consideration of phonon dynamics and higher order perturbation theory.

252. M. Ratner and A. Nitzan
The chemist's view of Nanotechnology: Molecular Electronics
ננוטכנולוגיה בראי הכימיה: אלקטרוניקה מולקולרית
Bulletin of the Israel Chemical Society, Issue 14, p. 3-13 (Dec 2003)   PDF

מאמר זה מהווה סקירה של המצב הנוכחי במחקר בתחום הננו, תוך שימת דגש על תחום האלקטרוניקה המולקולרית. אנו מציינים את התכונות המולקולריות העומדות ביסודו של הפוטנציאל הטמון בשימוש במולקולות כאלמנטים חשמליים, וסוקרים את המבנים המולקולריים שמצאו ומוצאים שימוש בהתקני ננו. תופעות מעבר אלקטרונים דרך מבנים מולקולריים כאלה נסקרות הן באספקט התיאורטי והן במסגרת התוצאות הניסיוניות שהתקבלו עד כה. בפרט אנו מדגישים את התרומות המתחרות של תהליכי מינהור, הולכת פס ואקטיבציה מלווה בזרם קפיצות. אנו מתעכבים על כמה התפתחויות חדשות בתחום זה, כולל שימושים אפשריים בתופעות מגנטיות ואופטיות במערכות מולקולריות, ולבסוף בוחנים את האפשרויות העתידיות בתחום זה.


251. A.W. Ghosh,P.S. Damle,S. Datta,and A. Nitzan
Molecular Electronics: Theory and device prospects
MRS Bulletin, 29, 391-395 (2004)                           PDF
Understanding current flow through molecular conductors involves simulating the contact surface physics,the molecular chemistry ,the device electrostatics,and the quantum kinetics of nonequilibrium transport,along with more sophisticated processes such as scattering and many-body ef fects.We summarize our current theoretical understanding of transport through such nanoscale devices.Our approach is based on self-consistently combining the nonequilibrium Green’s function (NEGF)formulation of transport with an electronic structure calculation of the molecule.W e identify the essential ingredients that go into such a simulation.While experimental data for many of the inputs required for quantitative simulation are still evolving,the general framework laid down in this treatment should still be applicable.W e use these concepts to examine a few prototype molecular devices,such as wires,transistors,and resonant-tunneling diodes.

250. D. Segal  and A. Nitzan
A spin-Boson thermal rectifier                                    PDF
Phys. Rev. Let. 94, 034301 (2005)                     
Following the observation that inherent anharmonicity is required, in addition to structural asymmetry, for rectification of heat transfer in nanojunctions, we analyze this phenomenon within the simplest anharmonic system –a spin-boson nanojunction model. We consider two variants of the model: a linear separable model in which the heat reservoirs contribute additively and a non-separable model suitable for a stronger system-bath interaction. Both model show asymmetric (rectifying) heat conduction when symmetry is removed by taking different couplings to the heat reservoirs.

249. M. Galperin, M. Ratner and A. Nitzan
On lineshapes and linewidths of vibrational features in inelastic electron tunneling spectroscopy
Nano Letters, 4, 1605-1611 (2004)                       PDF 
We addresses the lineshape and linewidths observed in recent inelastic electron tunneling spectroscopy (IETS) experiments. The non-equilibrium Green function (NEGF) formalism is used to analyze the effect of the electron-phonon interaction on the tunneling spectra. We find that IETS lineshapes are sensitive to junction parameters, in particular the position of the bridge electronic resonance and the molecule-lead coupling that may be controlled experimentally. Intrinsic IETS linewidths are found to be dominated by the coupling of molecular vibrations to electron-hole pairs excitations in the lead(s) to which the molecule is bonded chemically. While estimated widths are of similar order of magnitudes as observed in the recent experiment of Wang et al (Nano Letters, 4, 643 (2004)), one cannot rule out inhomogeneous contribution to the linewidth in this monolayer experiment.

248. M. Galperin M. A. Ratner and A. Nitzan
Inelastic electron tunneling spectroscopy in molecular junctions: Peaks and dips
J. Chem. Phys. 121, 11965-11979 (2004)        PDF
We study inelastic electron tunneling through a molecular junction using the  non-equilibrium Green function (NEGF) formalism. The effect of the mutual influence between the phonon and the electron subsystems on the electron tunneling process is considered within a general self-consistent scheme. Results of this calculation are compared to those obtained from the simpler Born approximation and the simplest perturbation theory approaches, and some shortcomings of the latter are pointed out. The self-consistent calculation allows also for evaluating other related quantities such as the power loss during electron conduction. Regarding the inelastic spectrum, two types of inelastic contributions are discussed. Features associated with real and virtual energy transfer to phonons are usually observed in the second derivative of the current I with respect to the voltage   when plotted against ?. Signatures of resonant tunneling driven by an intermediate molecular ion appear as peaks in the first derivative   and may show phonon sidebands. The dependence of the observed vibrationally induced lineshapes on the junction characteristics, and the linewidth associated with these features are also discussed.
 

247. Y. Calev, H. Cohen, G. Cuniberti, A. Nitzan,  and D. Porath
A Tight binding description of the STM image of molecular chains
Israel J. Chem. 44, 133-143 (2004)     PDF
A tight binding model for scanning tunneling microscopy images of a molecule adsorbed on a metal surface is described. The model is similar in spirit to that used to analyze conduction along molecular wires connecting two metal leads and makes it possible to relate these two measurements and the information that may be gleaned from the corresponding results. In particular, the dependence of molecular conduction properties along and across a molecular chain on the chain length, intersite electronic coupling strength and on thermal and disorder effects are discussed and contrasted. It is noted that structural or chemical defects that may affect drastically the conduction along a molecular chain have a relatively modest influence on conduction across the molecular wire in the transversal direction.
 

246. S. Skourtis and A.  Nitzan
Effects of initial state preparation on the distance dependence of electron transfer through molecular bridges and wires
J. Chem. Phys., 119, 6271-6 (2003)      PDF
The dependence of electron transfer rates and yields in bridged molecular systems on the bridge length, and the dependence of the zero-bias conduction of molecular wires on wire length are discussed. Both phenomena are controlled by tunneling across the molecular bridge and are consequently expected to show exponential decrease with bridge length that is indeed often observed. Deviations from this exponential dependence for long bridges, in particular a crossover to a very weak dependence on bridge length were recently observed experimentally and discussed theoretically in terms of thermal relaxation and dephasing on the bridge. Here we discuss two other factors that potentially affect the bridge length dependence of these phenomena.  First, in experiments initiated by an initial preparation of a non-stationary "donor" state the initial energy is not well defined. A small contribution from initially populated eigenstates that are of mostly bridge-level character may dominate transmission for long bridges, resulting in weak or no bridge-length dependence. Secondly, in steady state experiments the distribution of initial states (for example the Fermi distribution at the electrodes in conduction experiments) will cause deviations from exponential dependence on wire length because even a small population in higher energy states will dominate the transmission through long wires. For the first scenario we show that the crossover behavior observed for electron transfer in DNA between G and GGG species separated by AT chains can be largely reproduced just by initial state effects.

245. S.Zilberman, T.Becker, F.Mugele, B.N.J.Persson and A.Nitzan
Dynamics of squeeze-out:Theory and experiments
J. Chem. Phys., 118, 1160 (2003)                                          PDF
We consider the dynamics of squeeze-out of a molecularly thin confined two-dimensional ~2D liquidlike layer.The squeeze-out is described by a generalized 2D Navier–Stokes equation which is solved exactly for the limiting case where the squeeze-out nucleates at the center of the contact area, and where the ~perpendicular! three-dimensional pressure profile is Hertzian.We also present numerical results for the case where the nucleation is off-center.The theoretical results are in good agreement with recent experimental data by two of us for octamethylcyclotetrasiloxane.In light of our theoretical model calculations,we also discuss the spatially resolved diffusion experiments of Mukhopadhyay et al.(Phys.Rev.Lett.89,136103 ~2002).Here,we obtain a puzzling disagreement between theory and experiment which requires more investigation.
 
 

244. P. Graf, M. G. Kurnikova, R. D. Coalson and A. Nitzan
Comparison of Dynamic Lattice Monte-Carlo Simulations and Dielectric Self Energy Poisson-Nernst-Planck continuum theory for model ion-channels                                                    PDF
Simulations of ion permeation through narrow model cylindrical channels are carried out using a dynamic lattice Monte Carlo (DLMC) algorithm (equivalent to high friction Langevin dynamics) for the time-evolution of the ions in the system, based on a careful evaluation of the electrostatic forces acting upon each particle.  To mimic the process of ion transport through protein channels, the cylindrical channel is embedded in a dielectric slab (representing a lipid bilayer membrane).  The protein/membrane structure is taken to be rigid, and the water solvent is treated as a dielectric continuum.  Results of these simulations are compared to corresponding results obtained via Poisson-Nernst-Planck (PNP) theory.  In the PNP approach, the mobile ions are treated as a continuous charge density, and the electrostatic force on each ion is treated in an approximate fashion.  Significant differences between DLMC and PNP results are found, with the degree of discrepancy increasing as the radius of the ion channel is reduced.  A major source of error is traced to the neglect in the effective PNP potential of the Dielectric Self Energy (DSE), which is due to interaction of each permeant ion with the dielectrically inhomogeneous environment provided by the water/channel/membrane system.  When this static single-particle potential is pre-calculated and added to the effective potential used in PNP theory, substantial improvement in the quality of the results for current voltage curves and steady-state concentrations is obtained. In fact, the results obtained by this approach, termed Dielectric Self Energy Poisson-Nernst-Planck (DSEPNP) theory, agree nearly quantitatively with DLMC simulation results over the entire range of channel radii (4-12A) studied.

243. D. Segal, A. Nitzan and P. Hanggi
Thermal conductance through molecular wires
J. Chem. Phys. 119, 6840-6855 (2003)                                      PDF
We consider phononic heat transport through molecular chains connecting two thermal reservoirs. For relatively short molecules at normal temperatures we find, using classical stochastic simulations, that heat conduction is dominated by the harmonic part of the molecular force-field. We develop a general theory for the heat conduction through harmonic chains in 3-dimensions. Our approach uses the standard formalism that leads to the generalized Langevin equation for a system coupled to a harmonic heat bath, however the driving and relaxation terms are considered separately in a way that leads directly to the steady state response and the heat current under non-equilibrium driving. A Landauer-type expression for the heat conduction is obtained, in agreement with other recent studies. We used this general formalism to study the heat conduction properties of alkane. We find that for relatively short (1-30 carbon molecules) the length and temperature dependence of the molecular heat conduction results from the balance of three factors: (i) The molecular frequency spectrum in relation to the frequency cutoff of the thermal reservoirs, (ii) the degree of localization of the molecular normal modes and (iii) the molecule-heat reservoirs coupling. The fact that molecular modes at different frequency regimes have different localization properties gives rise to intricate dependence of the heat conduction on molecular length at different temperatures. For example, the heat conduction increases with molecular length for short molecular chains at low temperature. Isotopically substituted disordered chains are also studied and their behavior can be traced to the above factors together with the increased mode localization in disordered chain and the increase in the density of low frequency modes associated with heavier mass substitution. Finally, we compare the heat conduction obtained from this microscopic calculation to that estimated by considering the molecule as a cylinder characterized by a macroscopic heat conduction typical to organic solids. We find that this classical model overestimates the heat conduction of single alkane molecules by about an order of magnitude at room temperature. Implications of the present study to the problem of heating in electrically conducting molecular junctions are pointed out.

242. M. Galperin and A. Nitzan
NEGF-HF method for molecular junction properties calculations
Annals of the NY Academy of Science,   in press                        PDF
Electron-electron interaction is an essential issue in predicting the properties of molecular conduction junction. An accurate treatment requires taking proper account of the potential distribution across the junction as well as for the change in electronic structure under the external voltage drop. Another important point is the necessity to treat molecules as open quantum systems. In the present work we address these issues within the framework of the non-equilibrium Green’s function formalism at the Hartree-Fock level (NEGF-HF), which permits self-consistent treatment of the problem. We apply the method to study the experimentally observed asymmetry in the I/V curves with respect to polarity of voltage bias in Hg-Au junctions containing bilayers of alkanethiols of different chain length. The origin of the effect is suggested to be the asymmetric behavior of the character of the highest occupied molecular orbital (HOMO) of the junction at opposite biases, which leads to different effective barriers for electron transfer across the junction at opposite signs of the voltage drop. The calculated potential profile shows the capacitor-like nature for the junction with the weak link.

241. A. Troisi, M.A. Ratner and A. Nitzan
A Rate Constant Expression for Charge Transfer through Fluctuating Bridges
J. Chem. Phys.                                             PDF
A rate constant expression for charge transfer reactions mediated by flexible bridges is presented as a series of terms of decreasing importance. The leading term corresponds to the static limit obtained under the Condon approximation. Corrections due to finite time fluctuations are evaluated explicitly, assuming a Gaussian shape of the coupling autocorrelation function and the Marcus model with a one-dimensional harmonic thermal bath. The use of this model for the interpretation of the experimental data is discussed.

240. A. Nitzan and Mark Ratner
Electron transport in molecular wire functions: Models and Mechanisms
Science, 300, 1384-1389 (2003)              PDF
Molecular conductance junctions, in which single molecules or small groups of molecules act as conductors of electrical current between two electrodes, have become an area of intense activity.  This overview focuses on theoretical formulation and interpretation of the problem of molecular conductance.  We consider how to formulate the problem of molecular conductance junctions, and the calculation of their current/voltage characteristics.  We discuss different approaches and mechanisms, the relationship between conductance and the fundamental chemical kinetics of electron transfer and some of the challenging areas not yet properly addressed.

239. A. Troisi, M.A. Ratner and A. Nitzan
Vibronic effects in off-resonance molecular wire conduction
J. Chem. Phys. 118, 6072-6082 (2003)           PDF
A model for the calculation of the inelastic contribution to the low-bias electron transport in molecular junctions is presented. It is an extension to the inelastic case of the Green's function approach to the calculation of the conduction of such systems. The model is suited for the calculation in the off resonance regime (where molecular levels are far from the Fermi energy) and in the low bias limit, a typical situation encountered in inelastic electron tunneling measurements. The presentation of a general model is followed by the introduction of several approximations that make the calculation feasible for many systems of interest. Ab initio calculations of the vibronic coupling that leads to inelastic contribution to the conductance are performed for several molecules (butadiene, biphenyl, dipyrrole and dithiophene), representative of possible molecular wires. The role of inelastic conduction is then quantified without empirical parameters and the vibrational modes that dominate the process are identified. The situations where the inelastic mechanism is particularly relevant are considered. The limits of this approach for the resonant case are also discussed.

238. V. Mujica, A. Nitzan, S. Datta, M. A. Ratner and C. P. Kubiak
Molecular Wire Junctions: Tuning the Conductance
J. Phys. Chem., 107, 91-95 (2003)              PDF
Junctions consisting of two electrodes and a single molecule acting as a wire can be investigated by scanning probe conductance measurements. The conductance for low temperature, short wire structures can be characterized by the elastic scattering of the electrons, as described by general Landauer formulas. Tuning the bridge energy levels either by field effect transistor (FET)- like behavior (charging) or by chemical bond formation can raise or lower the conductance by moving the poles of the molecular Green’s function. For small molecular structures with particular HOMO/ LUMO characteristics, functionalization might be a more effective means than Coulomb charging by external gates.

237. A. Nitzan
The relationship between electron transfer rate and molecular conduction. 2. The sequential hopping case
Israel Journal of Chemistry, 42, 163-166 (2002)       PDF
This note discusses the relationship between a given bridge assisted electron transfer rate and the corresponding zero bias molecular conduction of the same molecular species, in the limit where both process occur by sequential hopping. It follows a previous publication (A. Nitzan, J. Phys. Chem. A 105, 2677-2679(2001)) in which the same issue was discussed for coherent tunneling transfer.

236. S. Pleutin,  H. Grabert,  G. L. Ingold and A. Nitzan
The electrostatic potential profile along a biased molecular wire: A model quantum
mechanical calculation
J. Chem. Phys. 118, 3756-3763 (2003)                              PDF
We study the electrostatic potential of a molecular wire bridging two metallic electrodes in the limit of weak contacts. With the use of a tight-binding model including a fully three-dimensional treatment of the electrostatics of the molecular junction, the potential is shown to be poorly screened, dropping mostly along the entire molecule. In addition, we observe pronounced Friedel oscillations that can be related to the breaking of electron-hole symmetry. Our results are in semi-quantitative agreement with recent state-of-the-art ab-initio calculations and point to the need of a three-dimensional treatment to properly capture the behavior of the electrostatic potential. Based on these results, current-voltage curves are calculated within the Landauer formalism. It is shown that Coulomb interaction partially compensates the localization of the charges induced by the electric field and consequently tends to suppress zones of negative differential resistance.

235. M. Galperin, A. Nitzan, S. Sek and M. Majda
Asymmetric Electron Transmission across Asymmetric Alkanethiol Bilayer Junctions
J. Electroanalytical Chemistry, in press             PDF
Asymmetric i/V curves with respect to the polarity of the voltage bias were observed in the Hg-Au junctions containing bilayers of alkanethiols of different chain length.  Larger current resulted when a negative bias was applied to the metal carrying a longer chain alkanethiol monolayer. This behavior is simulated using a single molecule junction model, within the frameworks of the extended Hückel (EH) model and the nonequilibrium Green's function formalism at the Hartree Fock level (NEGF-HF). Qualitative agreement with the experimental results with respect to the magnitude and sign of this asymmetry is obtained. On the basis of the NEGF-HF calculation, the origin of the effect is suggested to be the asymmetric behavior of the character of the junction highest occupied molecular orbital (HOMO) at opposite biases. This change of character leads to different effective barriers for electron transfer for opposite signs of the voltage drop across the junction.

234. J. Lehmann, S. Kohler, P. Hanggi and A. Nitzan
Rectification of laser-induced electronic transport through molecules
J. Chem. Phys.   118, 3283-3293 (2003)         PDF
We study the in uence of laser radiation on the electron transport through a molecular wire weakly coupled to two leads. In the absence of a generalized parity symmetry, the molecule rectifes the laser induced current resulting in directed electron transport without any applied voltage. We consider two generic ways of dynamical symmetry breaking: mixing of different harmonics of the laser eld and molecules consisting of asymmetric groups. For the evaluation of the nonlinear current, a numerically effcient formalism is derived which is based upon the Floquet solutions of the driven molecule. This permits a treatment in the non-adiabatic regime and beyond linear response.

233. A. Nitzan, M. Galperin, G-L. Ingold and H. Grabert
On the electrostatic potential profile in biased molecular wires
J. Chem. Phys., 117, 10837-41 (2002)                              PDF
The potential profile across a biased molecular junction is calculated within the framework of a simple Thomas-Fermi type screening model. In particular, the relationship between this profile and the lateral molecular cross section is examined. We find that a transition from a linear potential profile to a potential that drops mainly near the molecule-metal contacts occurs with increasing cross-section width, in agreement with numerical quantum calculations.

232. A. Mamonov, R. D. Coalson, A. Nitzan, and M. G. Kurnikova
The role of the dielectric barrier in narrow biological channels: a novel composite approach to modeling single channel currents
Biophysical Journal,  84, 3646-61 (2003)                          PDF              
A novel composite continuum theory to calculate ion currents through the channel of known structure that incorporates dynamic molecular information is proposed. The approach is applied and tested to predict current through the Gramicidin A ion channel, a narrow pore in which the applicability of the conventional continuum theories is uncertain. The proposed approach utilizes a modified version of Poisson-Nernst-Planck (PNP) theory, termed Potential of-Mean-Force-Poisson-Nernst-Planck (PMFPNP) theory, to compute ion currents. As in standard PNP, ion permeation is modeled as a continuum drift-diffusion process in a self-consistent electrostatic potential. In PMFPNP, however, the free energy of inserting a single ion into the channel i.e., the potential of mean force (PMF) along the permeation pathway, is calculated using methods of molecular modeling at equilibrium. Therefore, the information about the dynamic relaxation of a protein and other surrounding media is incorporated into the model of ion permeation, i.e. the dynamic flexibility of the channel environment is accounted for via the PMFPNP prescription. The PMF profile of the ion along the GA channel is obtained by combining an equilibrium molecular dynamics (MD) simulations to sample dynamic protein configurations with ion(s) in the channel, with continuum electrostatics calculation of the free energy. The diffusion coefficient of a potassium ion within the channel was also calculated using the MD trajectory. Therefore, no direct fitting parameters are required in our model.  The results of our study revealed that equilibrium fluctuations of the GA channel molecule produce significant electrostatic stabilization of an ion inside the channel. The dielectric-self energy of the ion remains essentially unchanged in the course of the MD simulation, indicating that no substantial changes in the protein geometry occur as the ion passed through it. Also, the model accounted for the experimentally observed saturation of ion current with increase of the electrolyte concentration, in contrast to the predictions of standard PNP theory.

231. B.N.J. Persson, V.N. Samoilov, S. Zilberman and A. Nitzan
Phenomenology of Squeezing and Sliding of molecularly thin Xe, CH4 and C16H34 lubrication films between smooth and rough curved solid surfaces with long-range elasticity
J. Chem. Phys. 117, 3897-3914 (2002)                         PDF
The properties of Xe, CH4 and C16H34 lubricant confined between two approaching solids are investigated by a model that accounts for the curvature and elastic properties of the solid surfaces. We consider both smooth surfaces, and surfaces with short- scale roughness. In most cases we observe well defined molecular layers develop in the lubricant film when the width of the film is of the order of a few atomic diameters, but in some cases atomic scale roughness inhibit the formation of these layers, and the lubricant exhibit liquid- like properties. An external squeezing- pressure
induces discontinuous, thermally activated changes in the number n of lubricant layers. We observe that the layering transition tends to nucleate in disordered or imperfect regions in the lubrication film. We also present and discuss results of sliding dynamics for Xe and C16H34 lubrication films.

230. J. Lehmann, S. Kohler, P. Hanggi and A. Nitzan
Molecular Wires Acting as Coherent Quantum Ratchets
Phys. Rev. Letters, 88, 228305 (2002).                             PDF
The effect of laser fields on the electron transport through a molecular wire being weakly coupled
to two leads is investigated. The molecular wire acts as a quantum ratchet if the molecule is composed of periodically arranged, asymmetric groups. This setup presents a quantum rectifier with a finite dc-response in the absence of a static bias. The nonlinear current is evaluated in closed form within the Floquet basis of the isolated, driven wire. The current response reveals multiple current reversals together with a nonlinear dependence (reflecting avoided quasi-energy crossings) on both the amplitude and the frequency of the laser field. The current saturates for long wires at a nonzero value, while it may change sign upon decreasing its length.

229. M. Galperin, A. Nitzan and I. Benjamin
Numerical simulations of electron tunneling currents in water
J. Phys. Chem. 106, 10790-96 (2002).                                           PDF                           
This paper presents results of numerical simulations of electron tunneling through water that extend our previous calculations on such systems in several ways. First, a tip-substrate configuration is used; second, calculations are carried in the presence of an external potential bias; third, the image potential that reflects the interaction of the electron with the mobile metal electrons is taken into account in the static image approximation. Finally, all-to-all transmission probability calculations are performed in order to get an order-of-magnitude estimate of the current-voltage characteristics of this junction model. The computed currents are within the range of the few available experimental observations on scanning tunneling microscope (STM) currents in water, indicating that our calculation may have taken into account all the important physical attributes of such systems. In addition we examine the effect of the water medium on the spatial distribution of the tunneling flux. We find that while different water configurations scatter the tunneling electron in different ways, on the average the water affected loss of resolution is rather small in the deep tunneling regime but can be substantial in energy regimes where the tunneling is strongly affected by water-supported resonance structures.

228. V. Mujica, M. Ratner and A. Nitzan
Molecular rectification: Why is it so rare?
Chem. Phys. 281, 147-150( 2002).                     PDF
Although conductance measurements of single molecule and few molecules junctions are currently being reported, there is a striking rarity of molecular rectification in these reports. Molecular rectification can be defined as the absence of inversion symmetry, I(V)=-I(-V), where I and V are the measured current and applied voltage. In molecular junctions of the form metal/molecule/metal, there is generally an absence of structural mirror symmetry. One might then expect rectification arising from this asymmetrical structure. We suggest here that molecular rectification in tunneling junctions is generally dificult to achieve, essentially because deformation of the structure in the presence of finite voltage will result in effectively symmetric voltage profiles for forward and reverse biases.

227. U. Peskin, M. Galperin and A. Nitzan
Traversal times for resonant tunneling
J. Phys. Chem. B, 106, 8306-8312 (2002).             PDF
The tunneling time of particle through given barrier is commonly defined in terms of "internal clocks" which effectively measure the interaction time with internal degrees of freedom of the barrier. It is known that this definition of the time scale for tunneling is not unique in the sense that it depends on the clock used to define it. For the case of resonance tunneling, a particular choice that in the limit of a high/broad square barrier yields the original result of Büttiker and Landauer (Phys. Rev. Lett. 1982, 49, 1739 ) is correlated to the lifetime of the resonance state. This is illustrated for analytically solvable one-dimensional double barrier models and for a realistic model of electron tunneling through a static water barrier. The latter calculation constitutes a novel application of this concept to a 3-dimensional model, and the observed structure in the energy dependence of the computed traversal time reflects the existence of transient tunneling resonances associated with instantaneous water structures. These models, characterized by the existence of shape resonances in the barrier, make it possible to examine different internal clocks that were proposed for measuring tunneling times in situations where a "clock independent" intrinsic time scale (the resonance life time) for the tunneling time exists. It is argued that this time may be used in order to estimate the relative importance of dynamical barrier processes that affect the tunneling probability.

226. M. Galperin, S. Toledo and A. Nitzan
Numerical computation of tunneling fluxes
J. Chem. Phys. 117, 10817-26 (2002).                PDF
The computation of tunneling probabilities in three dimensions is a numerical challenge, because the small transition probabilities associated with the overlap of exponentially vanishing wavefunction-tails require large computational accuracy. In scattering situations arising, e.g., in electron tunneling in metal-molecule-metal junctions, this is compounded by the need to provide a proper truncation procedure at the numerical boundaries of the computed system and by the need to account for electrostatic fields and image interactions. This paper describes a numerical methodology to deal with these problems. A pseudo-potential that describes the underlying system is assumed given. Electrostatic fields and image interactions are evaluated for the given boundary conditions from numerically solving Laplace and Poisson equations. Tunneling probabilities are computed using a grid-based absorbing boundary conditions Green's function method. An efficient and exact way to implement the absorbing boundary conditions by using the exact self-energy associated with separating the scattering system from the rest of the infinite space is described. This makes it possible to substantially reduce the size of the grid used in such calculations. Two applications, an examination of the possibility to resolve the spatial structure of an electron wavefunction in an electron cavity by scanning tunneling microscopy, and a calculation of electron tunneling probabilities through water, are presented.

225. D. Segal and A. Nitzan
Heating in current carrying molecular junctions
J. Chem. Phys. 117, 3915-3927 (2002).              PDF
A framework for estimating heating and expected temperature rise in current carrying molecular junctions is described. Our approach is based on applying the Redfield approximation to a tight binding model for the molecular bridge supplemented by coupling to a phonon bath. This model, used previously to study thermal relaxation effects on electron transfer and conduction in molecular junctions, is extended and used to evaluate the fraction of available energy, i.e. of the potential drop, that is released as heat on the molecular bridge. Classical heat conduction theory is then applied to estimate the expected temperature rise. For a reasonable choice of molecular parameters and for junctions carrying currents in the nA range, we find the temperature rise to be a modest few degrees. It is argued, however, that using classical theory to describe heat transport away from the junction may underestimate the heating effect.

224. D. Segal and A. Nitzan
Conduction in molecular junctions: Inelastic effects
Chem. Phys. 281, 235-256  (2002).                  PDF
The effect of a thermal environment on electron (or hole) transfer through molecular bridges and on the electron conduction properties of such bridges is studied. Our steady state formalism based on an extension of the Redfield theory (D. Segal et al, J. Phys. Chem. B 104 (2000) 3817; Chem. Phys. 268 (2001) 315) is extended in two ways: First, a better description of the weak coupling limit, which accounts for the asymmetry of the energy dependence of the quasi-elastic component of the transmission is employed. Secondly, for strong coupling to the thermal bath the small polaron transformation is employed prior to the Redfield expansion. It is shown that the thermal coupling is mainly characterized by two physical parameters: The reorganization energy that measures the coupling strength and the correlation time (or its inverse - the spectral width) of the thermal bath. Implications for the observed dependence of the bridge-length dependence of the transmissions are discussed. It is argued that in the intermediate regime between tunneling behavior and site-to-site thermally induced hopping, the transport properties may depend on the interplay between the local relaxation rate and the transmission dynamics.

223. O. Duerr, T. Volz, W. Dieterich and A. Nitzan
Dynamic percolation theory for particle diffusion in a polymer network  
J. Chem. Phys. 117, 441 (2002).         PDF PS
Tracer diffusion of small molecules through dense systems of chain polymers is studied within an athermal lattice model, where hard-core interactions are taken into account by means of the site exclusion principle. An approximate mapping of this problem onto dynamic percolation theory is proposed. This method is shown to yield quantitative results for the tracer correlation factor of the molecules as a function of density and chain length provided the non-Poisson character of temporal renewals in the disorder configurations is properly taken into account.

222. O. Duerr, W. Dieterich P. Maas and A. Nitzan
Effective medium theory of conduction in stretched polymer electrolytes     
J. Phys. Chem. B, 106, 6149-6155 (2002).         PDF
Recent experimental observations of anisotropic conductivity in stretched polymer electrolytes films of the polyethylene oxide family are discussed. The main experimental observations, enhancement of the ionic diffusion and conductivity in the stretch direction and decrease in these transport coefficients in the normal direction are interpreted in terms of an effective two-phase model. This two-phase model is based on the idea that a highly conducting phase is associated with oriented molecular structures which are surrounded by poorly conducting boundary regions. This model is evaluated within the framework of differential effective medium theory (DEMT). Under stretching these regions change from spherical to prolate-spheroidal shapes. The computed dependence of the DC conductivity tensor and its AC counterpart on the stretch parameters is in good agreement with experimental results.

221. F. Mugele, B.N.J. Persson, S. Zilberman, A. Nitzan and M. Salmeron
Frictional Properties of Chain Alcohols and the Dynamics of Layering Transitions
Tribology Letters, 12, 123-129, (2002).          PDF
We used a surface forces apparatus to investigate layering transitions and frictional properties of chain alcohol films. All but the last two monolayers, strongly bound to each mica surface can be removed by squeezing. Unlike other systems however, chain alcohol films of undecanol and octanol were found to retain their bulk- like lubrication properties down to a thickness of only one (bi) layer. The transition
where this last molecularly thin liquid layer is expelled from the gap proceeds in less than one second. From two- dimensional snapshots of the contact area during the expulsion process, we find that the boundary line between the areas of initial and final film thickness bends and roughens as it moves across the contact area. In the final state, we frequently find pockets of trapped liquid. Both the bending and roughening
of the boundary line and the trapped pockets are due to a dynamic instability that we describe with a two- dimensional hydrodynamic model. The length scale of the roughening is determined by an elastic line tension.

220. S. Zilberman, B.N.J. Persson, A. Nitzan
Theory and Simulations of Squeeze-out Dynamics in Boundary Lubrication
J. Chem. Phys., 115, 11268 (2001).        PDF
The dynamics of expulsion of the last liquidlike monolayer of molecules confined between two surfaces ~measured recently for the first time [J. Chem. Phys. 114, 1831 (2001)] has been analyzed by solving the two- dimensional Navier– Stokes equation combined with kinetic Monte Carlo simulations. Instabilities in the boundary line of the expelled film produce a rough boundary for all length scales above a critical value. The squeeze- out of liquid is shown to result from the 2D- pressure gradient in the lubrication film in the contact area. The Monte Carlo simulations agrees well with experiments, reproducing most qualitative and quantitative features. In particular it shows the formation of small islands, which ~in the absence of pinning mechanism! drift slowly to the periphery of the contact area. We calculate the drift velocity analytically as a function of the distance of the island to the periphery of the contact area. Experiments indicate that some kind of pinning mechanism prevails, trapping fluid pockets for very long times. When including such pinning areas in the simulations, three distinct squeeze phases and time scales were observed: (1) initial fast squeeze of most of the fluid; (2) slower squeeze of unpinned fluid pockets; (3) long term pinning of fluid pockets. We also show that a distribution of small pinning areas may produce a synergistic effect, slowing down the second phase of the squeeze, compared to a small number of big pinning areas. The paper presents a new stochastic numerical approach to problems of moving boundaries
which naturally accounts for thermal fluctuations and their effect in unstable dynamics.

CB21. O. Durr, P. Pendzig, W. Dieterich, A. Nitzan
Model studies of diffusion in glassy and polymer ion conductors
Solid State Ionics: Science & Technology Proc. 6-th Asian Conf. on Solid State Ionics,
edited by B. V. R. Chowdari and S. Chandra (World Scientific Publ. Co., Singapore, 1998) p. 33     PDF
Ion-conducting glasses and polymer systems show several characteristic peculiarities in their composition-dependent diffusion properties and in their dynamic response. First we give a brief review of the current understanding of the ion dynamics in network glasses in terms of stochastic theories. Secondly, a model for PEO(polyethylene-oxide)-based polymer electrolytes is described. The equation of state is calculated from the quasichemical approximation. Using this information together with Monte Carlo simulations of diffusion at constant volume, we obtain constant-pressure results for polymer chain and ion diffusion as a function of ion concentration. This theory allows us to make comparison with experiments which are carried out at constant pressure.

CB20. O. Durr, W. Dieterich, A. Nitzan
Charge Transport in Polymer Ion Conductors: a Monte Carlo Study
NATO Science Series III. Computer and Systems Sciences, 177, 288-292 (2001).      PDF
Diffusion of ions through a fluctuating polymeric host is studied both by Monte Carlo simulation of the complete system dynamics and by dynamic bond percolation (DBP) theory. Comparison of both methods suggests a multiscale-like approach for calculating the diffusion coefficients of the ions

219. O. Duerr, W. Dieterich and A. Nitzan
Diffusion in polymer electrolytes and the dynamic percolation model
Solid State Ionics, 149, 125-130 (2002).          PDF
A semi-microscopic description of ionic transport in polyethylene oxide-type electrolytes is presented, which is based on discrete stochastic moves of individual rnolecular units. Diffusion coefficients for ions and for the center of mass motion of chains are calculated by Monte Carlo simulation as a function of various model parameters, with emphasis on the incorporation of pressure effects. Within an even more coarse-grained description of diffusion in an athermal system of point-like particles and chains we provide a quantitative verification of the concept of dynamic percolation.

218. M. Galperin and A. Nitzan
Inelastic effects in electron tunneling through water layers
J. Chem. Phys. 115, 2681-2694 (2001).          PDF
Calculations of tunneling matrix elements associated with electron transfer through molecular environments are usually done for given frozen nuclear configurations; the underlying assumption being that nuclear motions are slow relative to the timescale of a tunneling event. This paper examines this issue for the case of electron tunneling through water. The motivation for this study is a recent calculation [Peskin et al, J. Chem. Phys. 111, 7558 (1999)] that indicates that electron tunneling through water may be enhanced by tunneling resonances in the range of ~1eV below the vacuum barrier, and finds that the lifetimes of such resonances are in the 10fs range, same order as OH stretch periods. Our calculation is based on the absorbing-boundary-conditions-Green's-function (ABCGF) method and proceeds in two steps. First we consider the effect of a single symmetric OH-stretch mode on electron tunneling in an otherwise frozen water environment and establish that the inelastic tunneling probability is small enough to justify an approach based on perturbation theory limited to single phonon transitions. Next we note that on the short timescale of a tunneling event, even under resonance conditions, water nuclear dynamics may be represented in the instantaneous normal modes picture. We generalize the ABCGF method to take into account low order inelastic scattering from a continuum of such harmonic normal modes. We find that near resonance the total inelastic transmission probability is of the same order as the elastic one, and may lead to an additional ~20-40% enhancement of the overall transmission in the range of up to 1eV below the vacuum barrier. The absolute energy exchange is small, of the order of 1% of the incident electron energy. Surprisingly, we find that the main contribution to the inelastic transmission is associated with energy transfer into the rotational-librational range of the water instantaneous normal mode spectrum.

217. D. G. Wu, D. Cahen, P. Graf, R. Naaman, A. Nitzan and D. Shvarts
Direct Detection of Low Concentration NO in  Physiological Solutions by a New GaAs-Based Sensor
Chem. Eur. J. 7, 1743-1749(2001).          PDF
Nitric oxide (NO) acts as a signal molecule in the nervous system, as a defense against infections, as a regulator of blood pressure and a gate keeper of blood flow to different organs. In vivo it is suggested to have a lifetime of few seconds. Therefore, its direct de-tection at low concentrations is difficult. We report on a new type of hybrid organic-semiconductor electronic sensor, which makes detection of nitric oxide in physiological solution possible. The mode of action of the device is described to explain how its elec-trical resistivity changes as a result of NO binding to a layer of native hemin molecules.  These molecules are self-assembled on a GaAs surface to which they are attached via a carboxylate binding group. The new sensor provides a fast and simple method to directly detect NO at concentrations down to1 mM in physiological aqueous (pH=7.4) solution at room temperature.

216. S. Zilberman, B. N. J. Persson, A. Nitzan, F. Mugele, and M. Salmeron
Boundary Lubrication: Dynamics of Squeeze-Out
Phys. Rev. E, 63, 055103R-(1-4) (2001).          PDF
The dynamics of the expulsion of the last liquid monolayer of molecules conned between two surfaces (measured recently for the rst time) has been analyzed by solving the two-dimensional Navier-Stokes equation combined with kinetic Monte Carlo simulations. Instabilities in the boundary line of the expelledlm were observed. We show that the instabilities produce a rough boundary for all length scales above a critical value and a smooth boundary for shorter lengths. The squeezing out of all but a few trapped islands of liquid is shown to be the result of the pressure gradient in the contact area.

215. A. Nitzan
A relationship between electron transfer rates and molecular conduction.
J. Phys. Chem. A, 105, 2677-9 (2001).          PDF
This note discusses the relationship between a given intramolecular bridge assisted electron transfer rate and the corresponding zero bias molecular conduction of the same molecular species.
 

214. D. Segal and A. Nitzan
Steady state quantum mechanics of thermally relaxing systems.
Chem. Phys.268, 315-335 (2001).          PDF
A theoretical description of quantum mechanical steady states is developed. Applications for simple quantum mechanical systems described in terms of coupled level structures yield a formulation equivalent to time independent scattering theory. Applications to steady states of thermally relaxing systems leads to time independent scattering theory in Liouville space that is equivalent to the tetradic Green's function formalism. It provides however a direct route to derive the particular form of the Liouville equation applicable in steady state situations. The theory is applied to study the conduction properties in the super-exchange model of a metal-molecule-metal contact weakly coupled to the thermal environment. The energy resolved temperature dependent transmission probability, as well as its coherent (tunneling) and incoherent (activated) parts are calculated using the Redfield approximation. These transmissions have a coherent (tunneling) and an incoherent (activated) components that depend differently on the energy gap (or barrier), on the temperature and on the bridge length. The coherent component is most important at low temperatures, large energy gaps and small chain lengths. The incoherent component dominates in the opposite limits. The overall (integrated) transmission provides a generalization of the Landauer conduction formula for small junctions in the presence of thermal relaxation.
 

213. A. Nitzan
Electron transmission through molecules and molecular interfaces
Annual Reviews of Physical Chemistry, 52, 681-750 (2001).         
                PDF(original version)                      PDF (Published, somewhat shorter, version)
Electron transmission through molecules and molecular interfaces has been a subject of intensive research due to recent interest in electron transfer phenomena underlying the operation of the scanning tunneling microscope (STM) on one hand, and in the transmission properties of molecular bridges between conducting leads on the other. In these processes the traditional molecular view of electron transfer between donor and acceptor species give rise to a novel view of the molecule as a current carrying conductor, and observables such as electron transfer rates and yields are replaced by the conductivities, or more generally by current-voltage relationships, in molecular junctions. Such investigations of electrical junctions, in which single molecules or small molecular assemblies operate as conductors constitutes a major part of what has become the active field of molecular electronics.
 In this paper I review the current knowledge and understanding of this field, with particular emphasis on theoretical issues. Different approaches to computing the conduction properties of molecules and molecular assemblies are reviewed, and the relationships between them are discussed. Following a detailed discussion of static junctions models, a review of our current understanding of the role played by inelastic processes, dephasing and thermal relaxation effects, is provided. The most important molecular environment for electron transfer and transmission is water, and our current theoretical understanding of electron transmission through water layers is reviewed. Finally, a brief discussion of overbarrier transmission, exemplified by photoemission through adsorbed molecular layers or low energy electron transmission through such layers is provided. Similarities and differences between the different systems studied are discussed.
THIS TABLE OF CONTENTS REFERS TO ORIGINAL VERSION:
Abstract 1
1. Introduction 2
2. Theoretical approaches to molecular conduction 5
_____2.1. Standard electron transfer theory 5
_____2.2. Transmission between conducting leads  9
_____2.3. The Landauer Formula  12
_____2.4. Molecular conduction  15
_____2.5. Relation to electron transfer rates  17
_____2.6. Quantum chemical calculations  19
_____2.7. Spatial-grid based pseudopotential approaches  22
_____2.8. Density functional calculations  24
_____2.9. Potential profiles  26
_____2.10. Rectification  28
_____2.11. Carrier-carrier interactions  28
_____2.12. Some open issues  30
3. Dephasing and relaxation effects  32
_____3.1. Tunneling traversal times 33
_____3.2. Nuclear relaxation during electron transmission 36
_____3.3. Thermal interactions in molecular conduction  40
_____3.4. Reduced density matrix approaches  44
4. Electron tunneling through water  53
5. Overbarrier transmission  62
6. Conclusions and outlook  66

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212. M. Galperin, A. Nitzan and Uri Peskin
Traversal time for electron tunneling in water
J. Chem. Phys. 114, 9205-8 (2001).          PDF
The traversal time for tunneling is a measure of the time during which the transmitted particle can be affected by interactions localized in the barrier. The Büttiker-Landauer approach, which estimates this time by imposing an internal clock on the system, has been applied so far for relatively simple 1-dimensional models. Here we apply this approach to estimate the traversal time for electron tunneling through a realistic 3-dimensional model of a water layer. Observed structure in the energy dependence of times computed reflects the existence of transient tunneling resonances associated with instantaneous water structures.

211. P. Graf and A. Nitzan, M. G. Kurnikova and R. D. Coalson
A dynamic lattice Monte Carlo model of ion transport in inhomogeneous dielectric
environments: Method and implementation
J. Phys. Chem. 104, 12324-12338 (2000).          PDF
ABSTRACT: A dynamic lattice Monte Carlo (DLMC) simulation approach to the description of ion transport in dielectric environments is presented. Conventional approaches using periodic boundary conditions are inefficient for non-equilibrium situations in inhomogeneous systems. Instead the simulated system is embedded in a bigger system that determines the average electrostatic potential and the ionic concentrations at its boundaries. Two issues are of special importance: implementing the given boundary conditions in the treatment of dynamical processes at and near the boundaries, and efficient evaluation of ion-ion interaction in the heterogeneous dielectric medium during the Monte Carlo simulation. The performance of the method is checked by comparing numerical results to exact solutions for simple geometries, and to mean field (Poisson-Nernst-Planck, PNP) theory in a system where the latter should provide a reasonable description. Other examples in which the PNP theory fails in various degrees are shown and discussed.  In particular, PNP cannot account for the characteristics of ion transport through narrow membrane channels.

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210. A. A. Kornyshev and A. Nitzan
Effect of overscreening on the localization of hydrated electrons
Zeitschrift für Physikalische Chemie, 215, 701 (2001).          PDF
The problem of the ground state of hydrated electron is revisited with a focus on the effects due to nonlocal dielectric response of water. The standard variational analysis is performed. It takes into account - in addition to nonlocal polarization of nuclear modes - the electron repulsion from the closed shells of water molecules, a possibility to form a cavity around the electron and the interaction of the hydrated electron with the high frequency electronic degrees of freedom of water. The classical dielectric continuum limit, shown for a reference, gives the ground state hydration energy that is 2.5 times smaller than the experimental value. The situation alters dramatically if one accounts for the nonlocal dielectric response of water. If one takes literally the existing MD simulation data for the static wave-vector dependent dielectric response function (with an "over-screening" resonance at k ~3A-1), the hydration energy becomes 3 times larger than the experimental one. Thus, an over-screening may have a dramatic effect on the formation of the hydrated electron. For a reduced height of the “over-screening peak”, the ground state energy reduces to the measured value. At the same time, over-screening enhances the localization of electrons. The undamped resonance gives rise to an unphysically small localization radius. A reduced resonance, that provides the correct ground stage energy, is better in this respect but it still gives very compact localization: 2/3 of the Bohr radius. It is thus concluded that either the defect structure of water around the electron suppresses the resonance, or the models of bulk water, which predict a high peak in the response function, are inadequate. The study paves the way to future molecular or phenomenological multi-order parameter models, in which the density and polarization of molecular dipoles and charge density distributions of the solvated electron were considered on the same footing. Such models might reveal the reduction of over-screening near the excess electron.

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209. A. Nitzan and J. Jortner, J. Wilkie, A. L. Burin and M. A. Ratner
Tunneling Time for Electron Transfer Reactions
J. Phys. Chem. B, 104, 5661-5665 (2000) PDF
ABSTRACT: The tunneling time for non-adiabatic electron transfer reactions described within the superexchange model is estimated using a Büttiker type internal clock: the electron is taken to posses two internal spin states that are weakly coupled on the bridge. By studying the transition probability between these channels during the tunneling process the traversal time through the bridge can be estimated. Like the Büttiker-Landauer result it is linear in the bridge length, but its dependence on the barrier energy UB approaches the Büttiker-Landauer form only in the limit of strong interstate coupling (broad band). In the 'normal' super-exchange (weak coupling) limit it is inversely proportional to the barrier energy.

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208. D. Segal, A. Nitzan, W. B. Davis and M.A. Ratner
Activated conductionin microscopic molecular junctions
J. Phys. Chem., 104, 2790-2793 (2000).          PDF
ABSTRACT: We analyze the connection between the electron transfer (ET) rate through a given molecular bridge, and the conduction of a junction based on the same bridge between two metals. The Landauer relation between the conduction of a junction and its transmission properties is generalized to yield a relation between conduction and ET rate, including transfer processes dominated by thermal activation. The relation between the orders of magnitude of these observables involves an additional length parameter, of the order of the range of the donor wavefunction. We find that the functional dependence of these observables on the bridge length (N) and on the temperature (T) changes from the exponential and temperature independent, exp(-?N) for small N, to algebraic and thermally activated form, [1/(alpha1+alpha2*N)]*exp(-beta*E/kT), as N increases. An intermediate range of apparent independence on N exists if alpha1>>alpha2. This behavior is the analog to the quantum Kramers (barrier crossing) problem, analyzed with respect to the barrier length.

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207.  D. Segal, A. Nitzan, W. B. Davis, M.R. Wasielewski and M.A. Ratner
Electron transfer rates in bridged molecular systems 2. A steady state analysis of coherent tunneling and thermal transitions
J. Phys. Chem. B, 104, 3817-3829 (2000).          PDF
ABSTRACT: The effect of dephasing and relaxation on electron transfer in bridged molecular systems is investigated using a simple molecular model. The interaction between the molecular system and the thermal environment is described on the level of the Redfield theory, modified when needed for the description of steady state situations. Noting that transient as well as steady state measurements are possible in such system, we discuss the relation between the rates obtained from these different types of experiments, in particular the conditions under which these rates are the same. Also, a formal relation between the steady state rate for electron transfer across a molecular bridge, and the conductance of this bridge when placed between two metal contacts is established. The effect of dephasing and relaxation on the electron transfer is investigated and new observations are made with regard to the transition from the superexchange to the thermal (hopping through bridge) regime of the transfer process. In particular, the rate is temperature independent in the superexchange regime and its dependence on the bridge-length (N) is exponential,  . The rate behaves like   beyond a crossover value of N, where ?E is the energy gap between the donor/acceptor and the bridge levels, and where ?1 and ?2 are characteristic times for activation onto the bridge and diffusion in the bridge, respectively. We find that in typical cases ?1»?2, and therefore a region of very weak N dependence is expected before the Ohmic behavior, N-1, is established for large enough N. In addition, a relatively weak exponential dependence, exp(-?N), is expected for long bridges if competing processes capture electrons away from the bridge sites. Finally, we consider ways to distinguish experimentally between the thermal and the tunneling routes.

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206. Uri Peskin, Ake Edlund, Ilan Bar-On, Misha Galperin and Abraham Nitzan
Transient Resonance  Structures in Electron Tunneling Through Water
J. Chem. Phys. 111, 7558-66 (1999).          PDF

 The mechanism of electrons tunneling through a narrow water barrier between two Pt(100) metal surfaces is studied.  Assuming an adiabatic picture in which the water configuration is static on the time scale of the electron motion, the tunneling probabilities are found to increase non-monotonically as a function of incident electron energy.  A numerical investigation of single electron scattering wavefunctions suggests that the tunneling is enhanced by resonances, associated with molecular cavities in which the electron is trapped between repulsive oxygen cores.  The lifetimes of these resonances are calculated using a novel filter diagonalization scheme, based on a converging high order perturbative expansion of the single-electron Green’s function, and are found to be of order   10 fs.  The possibility that transient resonance supporting structures contribute to the enhancement of tunneling through water is discussed.

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205. A. Nitzan and I. Benjamin
Electron transmission through molecular layers: Numerical simulations and theoretical considerations
Accounts of Chemical Research, 32, 854-861 (1999).          PDF

Electron transmission through molecular layers takes place in all intermolecular electron transfer processes in condensed phases. It can also be monitored directly in STM experiments in liquid environments, in photoemission through adsorbed molecular layers and in low energy electron transmission (LEET) with electron incident from the gas phase on metals covered with such layers. Finally, such processes are encountered in molecular electronic devices, which combine molecular ‘resistors’ with metal or semiconductor contacts. This paper reviews recent computational approaches to electron transmission through water and other environments, emphasizing the strong correlation between layer composition and structure and its transmission properties.

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204. A. Nitzan
Ultrafast relaxation in water [News and views commentary]
Nature, 402, 472-475 (1999).          PDF

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203. Misha Galperin, Dvira Segal and Abraham Nitzan
Perturbation theory approach to tunneling: Direct and resonance transmission in super-exchange models
J. Chem. Phys., 111, 1569-1579 (1999).          PDF

In this paper we examine, within simple models, different approaches to computing tunneling probabilities in super-exchange models of electron transfer. The relationship between tunneling calculations that use scattering theory type formalisms and approaches based on standing waves, which are more closely related to electron transfer between bound donor and acceptor states, is established. Transmission probabilities computed by using truncated basis representations are compared to exact analytical or numerical results for 1 and 2-dimensional models. We find that while resonance tunneling is well approximated by truncated basis approaches, computing deep tunneling using such basis sets can lead to large errors. Implications for calculations of bridge assisted electron transfer are discussed.

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202. W. Dieterich, O. Durr, P. Pendzig, A. Bunde and A. Nitzan
Percolation concepts in Solid State Ionics
Physica A, 266, 229-237(1999).          PDF

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201. Maria G. Kurnikova, Rob D. Coalson, Peter Graf and Abraham Nitzan
A Lattice Relaxation Algorithm for 3D Poisson-Nernst-Planck Theory with Application to Ion Transport Through the Gramicidin A Channel
Biophys. Journal, 76, 642-656(1999).  PDF
Abstract: A lattice relaxation algorithm is developed to solve the Poisson-
Nernst-Planck (PNP) Equations for ion transport through arbitrary three
dimensional volumes. Calculations of systems characterized by simple par-
allel plate and cylindrical pore geometries are presented in order to calibrate
the accuracy of the method. A study of ion transport through Gramicidin
A dimer is carried out within this PNP framework. Good agreement with
experimental measurements is obtained. Strengths and weaknesses of the
PNP approach are discussed.

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200. P. Pendzig, W. Dieterich and A. Nitzan
Monte-Carlo study of diffusion in polymer electrolytes
J. Non-Crystalline solids, 235, 748(1998).          PDF

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199. O. Durr, P. Pendzig, W. Dieterich and A. Nitzan
Model studies of diffusion in glassy and polymer ionic conductors
Solid State Ionics, 'Science and technology', p. 33-41(1998)

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198. R. Naaman, R. Haran, A. Nitzan, D. Evans and M. Galperin
Electron transmission through molecular layers
J. Phys. Chem. B 102, 3658-3668(1998).          PDF
[Feature Article]
Contents
1. Introduction
2. Experimental Background
3. Theoretical Background
4. Experimental Methods
5. Computational Methods
6. Experimental Results
7. Some Numerical Results
8. Discussion
    a. Dimensionality
    b. Band structure effects
abstract
 This article discusses general issues associated with electron transmission through thin molecular films. On the experimental side we emphasize recent investigations of photoemission through organized organic films adsorbed on metal surfaces. Theoretical and numerical approaches to transmission and tunneling through such films are discussed. We focus on the relation between the structure of the film and its transmission properties. In the experimental work these are controlled by varying the organic layer, by changing its thickness and by inducing disorder via thermal heating and by depositing mixtures of two molecular types. In numerical simulations of simple model systems we consider the dimensionality of the process, effect of molecular ordering and the relation between electronic band structure in the film and its transmission properties. It is shown that electron transmission through thin molecular layersconstitutes a sensitive tool for investigating molecular film properties in addition to providing a convenient prototype system for the study of electron transport in molecular electronic devices.

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197. P. Graf and Abraham Nitzan
Numerical simulations of solvation in simple polar fluids: Dependence on the thermodynamic state below and above the critical point
Chemical Physics, 235, 297-312(1998).          PDF

The phenomenology of electron solvation in polar solvents is studied by investigating the characteristics of
electron solvation in a model polar solvent, a Stockmayer liquid characterized by a combination of
and dipolar intermolecular interactions which interacts with the electron with a combination Lennard-Jones of short
range repulsive and of electrostatic (dipole-charge) interactions. Energetics and dynamical properties of the
solvated electron are studied as functions of the solvent density and of solvent molecular parameters which
determine the electron solvent interaction and the solvent dynamical response. We find that electron localization
in this solvent is caused primarily by the repulsive part of the electron-solvent interaction. Upon increasing
the solvent molecular dipole from zero, the electron becomes more localized; however, this effect seems to
saturate at moderate solvent polarities, and further increase of the polarity changes the ground (and excited)
state energies without affecting strongly the electron size. In this regime the electron behaves approximately
like a classical charge distribution as far as the dependence of its solvation energy on the solvent polarity is
concerned. The dynamical response of the solvent to the solvated electron is investigated by studying the
solvent- induced fluctuations of the electron’s energy levels. As expected we find that fluctuations in the
ground and excited state energies are dominated by the electrostatic part of the electron-solvent interaction,
and their dynamics therefore reflects the solvent rotational motion. Surprisingly, however, the electrostatic
contributions mostly cancel in the fluctuations of the gap between the ground and first excited state.
Consequently the gap fluctuations are dominated by the solvent translational motions. The implications of
these observations on the dynamics of electron solvation are discussed.
 

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196. D.G. Evans, A. Nitzan and M.A. Ratner
Photo-induced electron transfer in mixed-valence compounds: Beyond the golden rule regime
J. Chem. Phys. 108, 6387-6393(1998).          PDF

The short- time charge transfer evolution following photoexcitation in mixed valence compounds is
studied using path integral calculations. Due to the large nonadiabatic coupling, path integral
calculations using direct path summation techniques are inadequate, and charge transfer dynamics
can only be computed using a transfer matrix technique developed by Makri and Makarov. The
resulting relaxation is considerably slower than that predicted by low- order perturbation theory. The
effects of the solvent on the decay process, and the validity of the golden rule to predict the
dynamics of the decay process are investigated. The effects of preparing an initial state that is not
a rovibrational state of the acceptor potential energy surface is also examined. These exact
calculations show that the large electronic mixing gives rise to very fast oscillations in the electronic
state population as the wave function oscillates coherently between the donor and acceptor. This is
followed by a slower relaxation induced by the coupling to the dissipative solvent modes, which
occurs on time scales <100 fs. This information provides insight into the mechanism for
oscillations observed in time- resolved transient spectra of these compounds, and suggests
substantial limitations of the golden rule picture.

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195. D. Rostkier-Edelstein, P. Graf and A. Nitzan
Computing vibrational energy relaxation for high frequency modes in condensed phases.
J. Chem. Phys. 107, 10470 (1997).         PDF

ABSTRACT: In this paper we consider vibrational relaxation of high frequency impurity modes in condensed environments as a computational problem. Linear response theory provides convenient routes for this computation: The vibrational relaxation rate is obtained as a Fourier transform of a force-force time correlation function. However, numerical difficulties arise for processes characterized by a direct relaxation of high frequency modes into an environment characterized by a relatively low cutoff frequency. It is shown that modern signal processing procedures can significantly enhance the efficiency and accuracy of the needed computation. Since the relevant ‘signal’ can be very small, the computation can be very sensitive to boundary conditions, and care must be taken to avoid artifacts. The computation may be facilitated by using the expected functional form, exponential dependence on the impurity frequency for high frequency, and fitting the parameters of this form from the simulation. It is emphasized that this exponential dependence seems to be the correct functional form, in spite of theoretical arguments in favor of a Gaussian dependence.
The main difficulty in the numerical evaluation of the relaxation rate of high frequency modes results from the fact that at low temperature the dynamical behavior of such modes is essentially quantum-mechanical. We demonstrate this issue by considering vibrational relaxation of an impurity CO molecule in a low-temperature Ar matrix. The results obtained for this system by estimating the quantum correction to the classical force-force correlation function are consistent with experimental results, which indicate that under these conditions the relaxation of the vibrationally excited CO is dominated by radiative decay.

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194. W. B. Davis, M.R. Wasielewski, M.A. Ratner, V. Mujica annd A. Nitzan
Electron transfer rates in bridged molecular systems: A phenomenological approach to relaxation.
J. Phys. Chem. A101, 6158-6164 (1997).          PDF

ABSTRACT: A model for bridge-assisted, long range electron transfer in a molecule interacting with a dissipative external bath is presented.  The effects of the system-bath interaction are included phenomenologically in the evolution of the system density matrix as energy dephasings on the bridge sites.  When the bridge dephasings are small, the steady state ET rate in this model is found to be the sum of two competing terms;  the first is a McConnell-type rate arising from direct tunneling from donor to acceptor, and the second is a dephasing-dependent, length-independent scattering channel through the bridge sites.  In the limit of large dephasings, an incoherent channel dominates the dynamics and leads to ET rates which can become only weakly dependent (k ~ 1 / N) on the number of bridge sites in the system, for multisite bridges.

 

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193. Benjamin, I.; Evans, D.; Nitzan, A.
Asymmetric tunneling through ordered molecular layers
Journal of Chemical Physics, vol.106, p. 1291-3(1997).          PDF
ABSTRACT. Electron tunneling through ordered molecular barriers is found to depend on the tunneling direction. In particular, the transmission probability of an electron incident in the normal direction on a 10 AA water layer strongly polarized in the tunneling direction is 4-5 orders of magnitude larger when it enters from the positive (hydrogen) face than from the negative (oxygen) face, in contrast to continuum dielectric model prediction. This emphasizes the importance of the discrete multidimensional nature of the barrier structure and suggests possible rectifying properties of such barriers, beyond the linear regime (14 Refs.)
 
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192. A. Haran, K. Kadyshevitch, H. Cohenn, R. Naaman, D. Evans, T. Seidman and A. Nitzan
Electron transmission through band structure in organized organic thin films
Chem. Phys. Letters, 268, 475-480(1977).          PDF


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191. Benjamin, I.; Evans, D.; Nitzan, A.
Electron tunneling through water layers: effect of layer structure and thickness
Journal of Chemical Physics, vol.106 p. 6647-54(1997).          PDF

ABSTRACT: The effect of thickness and molecular structure on the probability of electron tunneling through water layers is investigated using a recently developed method. Water configurations of 1-4 layers are prepared between two parallel slabs of the Pt(100) surface, using equilibrium molecular dynamics and the polarizable simple point charge water model. Electron tunneling probabilities through the different water layers are computed as functions of energy using the absorbing boundary conditions Green function method and employing either an effective two-body water-electron interaction or a many-body polarizable water-electron potential. As long as the electron incident energy is below the barrier and far from a resonance state, the tunneling probabilities can be reasonably fitted to a one-dimensional rectangular-barrier model. However, near and over-barrier transmission probabilities cannot be reasonably described using a one-dimensional model, and the three-dimensional discrete structure of the water plays an important role. In all systems, the many-body electronic polarizability of the water significantly affects the transmission probability. The role played by the first adsorbed water layer is also discussed (35 Refs.)
 
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190. Pendzig, P.; Dieterich, W.; Nitzan, A.
Constant pressure simulations of lattice gas models
Journal of Chemical Physics, vol.106, p. 3703-9(1997).          PDF
ABSTRACT: A method for constant pressure Monte Carlo simulations in
lattice gas models is described. The simulation box is placed between two hard walls with fluctuating distance, and periodic boundary conditions are applied in the perpendicular directions. Continuous volume fluctuations in the bounded direction are made possible by introducing a generalized volume, which interpolates between the discrete values that correspond to the given lattice. This is achieved by using a surface potential variable which makes the lattice surface layer next to the hard wall gradually less accessible to particle occupation. The method is applied to the equation of state of noninteracting lattice gas models, where exact results are available for comparison, and also to less trivial models of interacting point-particles and athermal lattice chains, for which the quasichemical approximation (QCA) provides reliable results to compare with. For the chain simulations the method can be used in conjunction with the configuration biased Monte Carlo procedure in order to enhance its performance. However, since the Monte Carlo moves can be chosen to fit any desired kinetic model, our method can be used not only to generate constant pressure equilibrium ensembles, but also in the context of dynamic Monte Carlo studies. The center of mass diffusion in dense systems of athermal chains is investigated as an example. In all our static applications the method performs very well in comparison with exact or with QCA results, provided that the system size is large enough in the bounded direction. For small systems finite size effects are observed and analyzed, suggesting potential applications in the study of confined systems.
 
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189. A. Mosyak, P. Graf, I. Benjamin and A. Nitzan
Electron tunneling through water layers: Effect of polarizability
J. Phys. Chem. A, 101, 429-433(1997).          PDF
ABSTRACT: In a recent work (A. Mosyak et al, J. Chem. Phys. 104, 1549(1996)), we have investigated numerically electron tunneling through water layers confined between two solid walls. In the present paper the effect of some of our model assumptions and parameters on the tunneling behavior is studied. In particular we focus on the role played by the water electronic polarizability. We find that the tunneling behavior computed with water configurations prepared with a polarizable SPC water model is very similar to that obtained with configurations prepared using the non-polarizable RWK2-M water model used previously, provided that the same electron-water pseudo-potential is invoked. On the other hand, including the self-consistent many-body potential associated with the water electronic polarizability in the model for the electron-water interaction has a profound effect on the tunneling behavior, making the tunneling probability ~2 orders of magnitude larger than calculated with the non-polarizable model. This rectifies the disagreement found before between the tunneling behavior computed with the non-polarizable water model and experimental results. The strong effect of including the many-body polarizability interactions found in the present study stands in marked contrast to the relatively weak effect found in the context of electron hydration and hydrated electron spectroscopy. The origin of this effect is traced to properties of the lowest excess electron states found for neutral water configurations in the two models: The states asssociated with the polarizable model are of lower energy, yet more extended than the corresponding levels found for the non-polarizable model. We suggest that the existence of these lower, more extended electronic states in the polarizable model plays a decisive role in the observed lower effective barrier to tunneling through water as compared with vacuum.

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188. Persson, B.N.J.; Nitzan, A.
Linear sliding friction: on the origin of the microscopic friction for Xe on silver
Surface Science, vol.367, no.3, p. 261-75(1996).          PDF
ABSTRACT: We have performed a computer simulation study of the force
required to slide xenon monolayer and bilayers on a silver surface. With information about the adsorbate-substrate interaction potential deduced from experimental data, we find that for the compressed incommensurate monolayer film the observed sliding friction is very close to the parallel microscopic friction which acts on the individual adsorbates, which is of mainly electronic origin. For the bilayer him a small fraction of the observed sliding friction may arise from internal excitations in the film, and the rest from the direct energy transfer to the substrate via the electronic friction.
 
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187. Graf, P.; Nitzan, A.; Diercksen, G.H.F.
Phenomenology of electron solvation in polar fluids
Journal of Physical Chemistry, vol.100, p. 18916-23(1996).          PDF
ABSTRACT: The phenomenology of electron solvation in polar solventsis studied by investigating the characteristics of electron solvation in a model polar solvent. A Stockmayer liquid characterized by a combination of Lennard-Jones and dipolar intermolecular interactions which interacts with the electron with a combination of short range repulsive and of electrostatic (dipole-charge) interactions. Energetics and dynamical properties of the solvated electron are studied as functions of the solvent density and of solvent molecular parameters which determine the electron solvent interaction and the solvent dynamical response. We find that electron localization in this solvent is caused primarily by the repulsive part of the electron-solvent interaction. Upon increasing the solvent molecular dipole from zero, the electron becomes more localized; however, this effect seems to saturate at moderate solvent polarities, and further increase of the polarity changes the ground(and excited) state energies without affecting strongly the electron size. In this regime the electron behaves approximately like a classical charge distribution as far as the dependence of its solvation energy on the solvent polarity is concerned. The dynamical response of the solvent to the solvated electron is investigated by studying the solvent-induced fluctuations of the electron's energy levels. As expected we find that fluctuations in the ground and excited state energies are dominated by the electrostatic part of the electron-solvent interaction, and their dynamics therefore reflects the solvent rotational motion. Surprisingly, however, the electrostatic contributions mostly cancel in the fluctuations of the gap between the ground and first excited state. Consequently the gap fluctuations are dominated by the solvent translational motions. The implications of these observations on the dynamics of electron solvation are discussed (25 Refs.)
 
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186. Mosyak, A.; Nitzan, A.; Kosloff, R.
Numerical simulations of electron tunneling in water
Journal of Chemical Physics, vol.104,p. 1549-59(1996).          PDF
ABSTRACT: Electron tunneling through molecular layers has long been
under study in conjunction with electron tunneling microscopy. More recently solvent effects on the tunneling matrix elements associated with electron transfer problems and with "underwater" electron tunneling microscopy have come under discussion. This paper describes the results of computer simulations of electron tunneling through frozen water layers. A water layer (~10 AA) is confined between two electrodes, and is equilibrated and evolved in time in order to generate an ensemble of barrier configurations. The electron-(classical) water interaction is represented by a suitable pseudopotential. It is assumed that the water dynamics is negligible on the time scale of the tunneling process, so tunneling is studied for the resulting group of frozen c. Several numerical methods for evaluating the transmission through such disordered barriers are described and compared. It is shown that tunneling probabilities as low as 10/sup -10/ can be calculated with sufficient accuracy. We find that tunneling in this system cannot be described by averaging over one-dimensional paths. Furthermore, in contrast to common practice which assumes that the barrier to tunneling may be estimated by lowering the bare (vacuum) barrier by a magnitude associated with the electronic dielectric response of water taken as a dielectric continuum, the simulations show that transmission is strongly reduced due to the fact that much of the physical barrier space is blocked by the practically impenetrable oxygen cores. The tunneling probability significantly depends on the water configuration in the barrier, in particular on the orientational distribution of the water molecules. These observations suggest that external variables such as temperature and electric field will affect the tunneling through their effect on the water density and orientation, in addition to the effect of these variables on the bare (vacuum) tunneling (28 Refs.)
 
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185. Olender, R.; Nitzan, A.; Knodler, D.; Dieterich, W.
Lattice theory of solvation in macromolecular fluids. III. Monte Carlo simulations
Journal of Chemical Physics, vol.103, p. 6275-82 (1995).          PDF
Monte Carlo simulations are used to calculate the energy, free energy, and entropy of solvation in a lattice model of polymer host. The solute particle interacts with specific beads in the host chain at nearest neighbor sites. The results are used to check the accuracy of the quasichemical approximation (QCA) recently used (Olender and Nitzan, J. Chem. Phys. 101, 2338 (1994)) to study ion solvation and ion pair dissociation in polymer hosts. For noninteracting chains we find that the QCA is very accurate when the solvent consists of homogeneous chains (all beads interact equally with the impurity), and give errors of up to 20% when nonhomogeneous chains (with some of the beads interacting with the impurity) are used. For interacting chains this trend is reversed and the QCA works better for nonhomogeneous chains. Deviations of the QCA prediction from the "exact" numerical results are traced to three-body and higher order correlations. The success of the QCA for interacting solvents of nonhomogeneous chains is associated with cancellation of opposing effects of such correlations.
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184. Lonergan, M.C.; Nitzan, A.; Ratner, M.A.; Shriver, D.F.
Dynamically disordered hopping, glass transition, and polymer electrolytes
Journal of Chemical Physics, vol.103, p. 3253-61(1995).          PDF

ABSTRACT: The central parameter of the dynamically disordered hopping (DDH) model, the renewal time, is correlated with the characteristic time constant of the glass transition relaxation in polymer-salt complexes. With this identification, the frequency-dependent permittivity of these materials can be quite adequately described. In particular, experimental evidence for a high-frequency relaxation predicted by the DDH model is presented. This relaxation corresponds to the polarization of ions in their local percolation clusters as they wait for a renewal event to occur. In light of information on the renewal time, the direct current properties of polymer-salt complexes are used to calculate the size of these local clusters. These calculations suggest that the motion of an ion in the absence of renewal (polymer segmental motion) corresponds to displacements within its local coordination "cage" rather than hopping between several available coordination sites (89 Refs.)
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183. Vijayadamodar, G.V.; Nitzan, A.
On the application of instantaneous normal mode analysis to long time dynamics of liquids
Journal of Chemical Physics, vol.103, p. 2169-77(1995).          PDF

ABSTRACT: While the applicability of instantaneous normal mode (INM) analysis of liquids to short time dynamics is in principle obvious, its relevance to long time dynamics is not clear. Recent attempts by Keyes and co-workers to apply information obtained from this analysis to self-diffusion in supercooled liquid argon is critically analyzed. By extending the range of frequencies studied we show that both imaginary and real branches of the density of modes are represented better, for large omega , by ln( rho ( omega )) approximately omega /sup 2//T than by ln( rho ( omega )) approximately omega /sup 4//T/sup 2/ as advocated by Keyes (J. Chem. Phys. 101, 5081(1994)). However, since in the relevant frequency range the two fits almost overlap, the numerical results obtained by Keyes, showing good agreement with the simulation results for self-diffusion in supercooled liquid argon, remain valid even though implications for the frequency dependence of the barrier height distribution change. We also explore other possibilities for extracting information from the INM analysis: (1) The density of "zero force modes", defined as the distribution of normal modes found at the bottom or top of their parabolic potential surfaces, can be computed with no appreciable additional numerical effort. This distribution provides a better representation than the total density of modes for the normal mode distribution at well bottoms and at saddles, however, we find that it makes little difference in quantitative analysis. (2) We suggest that the ratio rho /sub u/( omega )/ rho /sub s/( omega ) between the density of modes in the unstable and stable branches provide an estimate for the averaged barrier height distribution for large omega. Using this estimate in a transition state theory calculation of the average hopping time between locally stable liquid configurations and using the resulting time in a calculation of the self-diffusion coefficient yields a very good agreement with results of numerical simulation.
 
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182. O. Cheshnovsky, R. Giniger, G. Markovich, G. Makov, A. Nitzan and J. Jortner
Surface and Internal Anion Solvation in water clusters.
J. de Chimie. Physique, 92, 397-408(1995)
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181. Olender, R.; Nitzan, A.
Solvation dynamics in dielectric solvents with restricted molecular rotations: polyethers
Journal of Chemical Physics, vol.102, p. 7180-96(1995).          PDF

ABSTRACT: Molecular dynamics simulations are used to study solvation
and solvation dynamics of a classic charge in a series of ethers of increasing molecular weights, CH/sub 3/(CH,OCH/sub 2/)/sub n/H with n=1, 2, and 4. Equilibrium structures of the solvated species, ion mobility, linear response solvation functions, and nonequilibrium solvation are studied and compared with the corresponding results for a simple (Stockmayer) fluid. For a typical positive ion, Na/sup +/, solvation in these systems is found to belong to the nonlinear response regime; the nonlinear behavior is associated with the specific binding of the cation to the negative oxygen sites. Solvation dynamics in the timescale studied (t<0.5 ns) is found to be essentially bimodal, with short composimilar in duration and magnitude to that found in simpler solvents. However, except for the simplest system studied (ethyl methyl ether) the short time componentis not Gaussian (i.e., its Gaussian part is limited to insignificantly short times) and cannot be interpreted as inertial free streaming of solvent molecules in the potential field of the solute. Instead we suggest that it originates from damped solvent vibrations about solvent inherent structures. The character of the solvent motions that drive the solvation process changes as the molecular size increases: from overall molecular rotations in the monoether, to intramolecular segmental motions in the larger solvents. It is suggested that solvation dynamics (studied, e.g., by laser induced fluorescence) can be used as a probe for the dynamics of such segmental motions in polymer electrolytes (44 Refs.)
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180. Lonergan, M.C.; Nitzan, A.; Ratner, M.A.
Ionic diffusion in dynamically-disordered materials: motion on a renewing, percolative lattice
Journal of Molecular Liquids, vol.60, p. 269-88(1994)

ABSTRACT: Diffusion in concentrated ionic solutions involves ionic motion subject both to interionic Coulomb forces and to the fluctuating potentials arising from solvent motion. To study how these reflect themselves in the ion transport, we examine a problem in which Coulomb particles hop on a lattice that is percolative (some jumps are forbidden) and renewing (the forbidden jumps evolve in time). Diffusivity and tracer correlation are both effected by both renewal and Coulomb interaction. Coulomb effects can destroy the validity of the dynamic percolation result that the diffusivity is proportional to the renewal rate; non-exponential decay of the energy fluctuation correlation function is observed (60 Refs.)

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179. A. D. Hammerich, A. Nitzan and M. A. ratner
Fourier analysis, correlation functions and non-adiabatic electron transfer: wave- packets and exact representations,
Theoretica Chimica Acta, 89, 383-399 (1994).                        PDF
 

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178. Knodler, D.; Dieterich, W.; Lonsky, C.; Nitzan, A.
Nonlinear relaxation and solvation dynamics in a Coulomb lattice gas
Journal of Chemical Physics, vol.102, p. 465-70(1995).          PDF

ABSTRACT: The transient response of ions upon sudden creation or removal of a local, external charge in a one-component Coulomb lattice gas is investigated by Monte Carlo simulations. Our model can be regarded as a simplified description of solvation dynamics processes in electrolyte systems. Effects of the nonlinearity of the relaxation are pointed out and are contrasted with predictions from linear (Debye-Huckel and Debye-Falkenhagen) theories (14 Refs.)
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177. M. D. Todd, A. Nitzan, M.A. Ratner and J. T. Hupp
Electron transfer rates from time dependent correlation functions: Wavepacket dynamics, solvent effects and applications.
J. of Photochemistry and Photobiology, 82, 87-101(1994)                                  PDF

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176. Coalson, R.D.; Evans, D.G.; Nitzan, A.
A nonequilibrium golden rule formula for electronic state population in nonadiabatically coupled systems
Journal of Chemical Physics, vol.101, p. 436-48(1994).          PDF
ABSTRACT: A formula for computing approximate leakage of population from an initially prepared electronic state with a nonequilibrium nuclear distribution to a second nonadiabatically coupled electronic state is derived and applied. The formula is a nonequilibrium generalization of the familiar golden rule, which applies when the initial nuclear state is a rovibrational eigenstate of the potential energy surface associated with the initially populated electronic state. Here, more general initial nuclear states are considered. The resultant prescription, termed the nonequilibrium golden rule formula, can be evaluated via semiclassical procedures and hence applied to multidimensional, e.g., condensed phase systems. To illustrate its accuracy, application is made to a spin-boson model of "inner sphere" electron transfer. This model, introduced by Garg et al. (J. Chem. Phys. 83, 4491 (1985)) for the nonadiabatic transition out of a thermal distribution of states in the initial (donor) electronic level, is extended to include nonequilibrium, nonstationary initial nuclear states on the donor surface. The predictions of the nonequilibrium golden rule are found to agree well with numerically exact path integral results for a wide range of initial distortions of the initial nuclear wave packet from its equilibrium configuration (28 Refs.)
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175. A. Nitzan and Z. Schuss
Multidimensional barrier crossing
in: The Barrier Crossing Problem, edited by G.R. Fleming and P. Hänggi (World Scientific, 1994)

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174. Rostkier-Edelstein, D.; Urbakh, M.; Nitzan, A.
Electron tunneling through a dielectric barrier
Journal of Chemical Physics, vol.101, p. 8224-37(1994).          PDF

ABSTRACT: Electron tunneling through a dielectric barrier is considered with special attention given to questions relevant for STM experiments in dielectric liquids. The effect of the barrier dielectric response on the tunneling probability is studied using the effective Hamiltonian formalism for the polarization dynamics in the barrier, and two different theoretical approaches for the calculation of the tunneling probability: A generalization of the Bardeen's formalism to inelastic tunneling and the quasiclassical of Brink, Nemes, and Vautherin (1983) as expanded by Sumetskii (1985). Although based on different approximations, both approaches yield similar results in the slow barrier limit, where their ranges of validity coincide. The approach based on the Bardeen's formalism relies on the adiabatic approximation and fails for fast barrier dynamics. The overall effect of the barrier dielectric response is to
enhance the tunneling probability relative to the rigid barrier case. The enhancement factor is larger for thicker barrier, higher temperature and faster barrier dynamics. Both the elastic and inelastic components of the tunneling current show these trends in the relevant range of parameters (25 Refs.)
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173. Nitzan, A.; Ratner, M.A.
Conduction in polymers: dynamic disorder transport
Journal of Physical Chemistry, vol.98, p. 1765-75(1994)   (Feature Article).          PDF

ABSTRACT: Hopping and diffusion models are extremely useful for describing processes occurring in extended systems, on time scales far longer than some underlying molecular time, such as a characteristic solvent vibrational time or (for crystals) an inverse Debye frequency. Most applications of hopping models to problems in chemistry and materials science assume the presence of two time scales, a residence time and hopping time, and that the time of residence is far longer than the time involved in hopping from one site to another. We describe a generalization of this model to deal with systems in which the underlying structure exhibits dynamical disorder-that is, in which in addition to the species undergoing hopping motions, the lattice itself is reorganizing in time. An important example is glass-forming liquids above their glass transition temperature, especially polymeric materials. In its simplest realization, this multiple time scale hopping model involves only two times a hopping time and a renewal time tau /sub R/ characterizing the average relaxation time of the underlying lattice motions. One then is faced with the analysis of a problem involving motion on these two time scales, and with the application of that model to-a number of systems. Experimentally, a model was originally developed to deal with polymer electrolyte materials, in which ionic diffusion occurs in polymer hosts well above their glass transition temperatures. In this case, the renewal time can be roughly correlated with the glass transition relaxation in the neat polymer host. The dynamic disorder hopping model, or dynamic bond percolation model, is closely related to other models used in solid-state theory, such as the continuous time random walk of Scher and Lax, or the stirred percolation model used in the study of microemulsions. It has a very simple chemical interpretation, since only two times are defined. We describe the nature of the dynamic disorder models, their solutions in particular cases, and their application to a number of physical systems. Particularly important results include formal proofs that, when dynamic disorder is present, percolation thresholds disappear and the system is always diffusive over times long compared to the renewal time. One can also derive generalized analytic continuation results relating the frequency-dependent diffusion in the dynamically renewing lattice to the frequency-dependent diffusion in the static lattice. While the model was originally developed to deal with ionic transport in polymer media, a number of interesting applications in other areas, including polymer viscosity and polymer dynamics, are also briefly discussed (73 Refs.)
 
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172. Olender, R.; Nitzan, A.
Lattice theory of solvation and dissociation in macromolecular fluids. II. Quasichemical approximation
Journal of Chemical Physics, vol.101, p. 2338-49(1994).          PDF

ABSTRACT: Solvation and association of ions in polymer solvents used for polymer electrolytes is studied in the framework of the Guggenheim quasichemical approximation using a lattice model. The pure solvent is described using the mean-field approximation of Sanchez and Lacombe. The model accounts for the short range part of the ion-polymer interaction, in particular at specific interaction sites (such as the cation-oxygen attraction in polymer hosts), while long range dielectric effects are added as in the Born theory of solvation. We obtain expressions which relate thermodynamic quantities of solvation (free energy, entropy, enthalpy, and volume) to properties of the pure solvent. From these, the equilibrium constant for the ion pairing can be obtained as a function of temperature, pressure, and solvent properties. A consistent fit to the experimental data in poly(propylene oxide) (PPO) can be obtained if specific interaction sites for the cations are assumed. Dependence of the solvation and the equilibrium constant on the polymer chain length which is seen in the short chain limit saturates and disappears beyond a few monomer sizes. The relative roles of short range and of dielectric interactions is discussed (28 Refs.)
 
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171. G. Makov and A. Nitzan
SOLVATION AND IONIZATION NEAR A DIELECTRIC SURFACE.          PDF
J. Phys. Chem. 98, 3459 (1994)

Abstract: Solvation and ionization energies of ions and neutral atomic solutes near planar and  spherical  (cluster) surfaces were calculated using continuum dielectric theory.  For  highly  polarized solvents, the magnitude of the solvation energy at the surface is   similar   to  that  in  the  bulk,  while  the  reorganization  energy  and  the  photodetachment  energy  of  an electron from a negative ion are found to be slightly larger  for  solutes  located  at  the  surface.   The cluster size dependence of the solvation and ionization energies is found to be determined only by the properties of the  solvent,  in good agreement with experimental data, and to be insensitive to the location  of  the solute in the cluster.  Implications for the size dependence of the photodetachment  energies  from  negative  ions  in  water  and  ammonia clusters are discussed.   In particular it is suggested that the observed photodetachment energies from  small  (NH )   clusters  are  compatible  with  the  dielectric predictions for electron solvation in solid ammonia.

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170. A. Mosyak and A. Nitzan
Electron solvation: Quantum and classical aspects.
in: Reaction Dynamics in Clusters and Condensed Phases, edited by B. Pullman, J. Jortner and R.D. Levine (Kluwer, Amsterdam,1994), p.557.
 

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169. Neria, E.; Nitzan, A.
Numerical simulations of solvation dynamics in electrolyte solutions
Journal of Chemical Physics, vol.100, p. 3855-68(1994).         PDF

ABSTRACT: Recent experimental studies of solvation dynamics in electrolyte solutions indicate the existence of a slow dynamical component associated with the salt ions. This contribution cannot be accounted for by the Debye-Falktenhagen theory of ionic atmosphere response. Molecular dynamics simulations of solvation dynamics in a simple model (Stockmayer solvent containing spherical ions) of electrolyte solution are presented. The simulations confirm the interpretation that the slow dynamical component is primarily an outcome of ion exchange between the first solvation shell about the solute and the solution bulk. The simulations also indicate the highly correlated motion between the salt ions and the solvent molecules (26 Refs.)

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168. Neria, E.; Nitzan, A.
Numerical evaluation of golden rule rates for condensed phase processes
Chemical Physics, vol.183, p. 351-63(1994)                            PDF
ABSTRACT: Our recently proposed method for the numerical evaluation of golden rule rates of non-adiabatic transitions in condensed phases is generalized. As before, the method is based on propagating Gaussian wavepackets on the initial and final electronic potential surface. In the present paper these Gaussians are thermal wavefunctions obtained by thermal propagation of eigenfunctions of the position operator using either the high temperature limit of the propagator or the local harmonic approximation to it. The high T limit is essentially equivalent to our previously proposed procedure, but is more rigorously defined. The local harmonic approximation makes it possible to extend the method to low temperature situations. The performance of the method relative to other available procedures is examined by model calculations (26 Refs.)
 
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167. Olender, R.; Nitzan, A.
Lattice theory of solvation and dissociation in macromolecular fluids. I. Mean field approximation
Journal of Chemical Physics, vol.100, p. 705-18(1994).         PDF
ABSTRACT: This paper analyzes solvation and association in macromolecular solvents using mean-field theory applied to several lattice-gas models. The thermodynamic functions of solvation and the equilibrium constant for association is calculated in terms of the temperature, pressure, and solvent molecular size. Applications to ion association in polymer electrolytes are discussed and the advantages and flaws of the model are critically analyzed. Exact results for a simple one dimensional model are also obtained and discussed (41 Refs.)

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166. M.C. Longergan, A. Nitzan and M. Ratner
Ionic diffusion in dynamically-disordered materials: Motion on a renewing percolative lattice.
J. Mol. Liquids, (1994).

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165. E. Neria and A. Nitzan
Numerical Studies of Solvation Dynamics in Electrolyte Solutions in "Ultrafast
Phenomena in Condensed Molecular Systems
Edited by Y Guaduel and P. Rossky, Am. Phys. Soc. (1993)

Recent experimental works on solvation dynamics in polar solvent containing added
salt indicate the existence of a contribution to the solvation process associated
with the salt ions. This contribution can not be described by the linearized
Poisson Boltzmann equation, i.e. the Debye Folkehagen theory. Numerical
simulations on a model system (a Stockmayer solvent containing spherical ions)
show that the primary contribution to this dynamics comes from ion-solvent
exchange at the first solvation shell surrounding the solute. The fast time
scales associated primarily with the solvent response are only slightly dependent
on the presence and properties of the electrolyte in the concentration range
studied.

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164. G. Makov and A. Nitzan
Electronic Properties of Finite Metallic Systems.
Phys. Rev. B, 47, 2301 (1993).         PDF

The relationship between the surface geometry and certain electronic properties
is considered for neutral metal systems. For systems enclosed by surfaces of
constant curvature, the total energy, the surface energy, and the chemical
potential are found to depend linearly on the surface curvature. Explicit
expressions are found for the coefficients of this dependence, in particular for
the curvature energy. It is shown that for systems with surfaces of varying
curvature a surface charge distribution is formed (and therefore an electric
potential varying across the surface), to ensure a constant chemical potential.
Implications for the ionization potentials of finite and infinite systems of
finite curvature (e.g., spheroids and thin wires) are discussed.

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163. E. Neria and A. Nitzan
Semiclassical Evaluation of Nonadiabatic Rates in Condensed
Phases.
J. Chem. Phys, 99, 1109 (1993).         PDF

A procedure for calculating nonadiabatic transition rates in the semiclassical
limit is implemented and tested for models relevant for condensed phase
processes. The method is based on evaluating the golden rule rate expression
using a quantum description for the electronic subsystem and a semiclassical
propagation for the nuclear degrees of freedom, similar to Heller's calculation
of absorption and Raman spectra. In condensed phase processes, the short
lifetimes of the relevant correlation functions make it possible to implement the
procedure within the frozen Gaussian method. Furthermore, because of the large
density of states involved, which implies fast dephasing, incoherent
superpositions of frozen Gaussian trajectories may be used for the evaluation of
the rate. The method is tested using two simple exactly soluble models. One of
them, consisting of two coupled electronic potential surfaces, harmonic and
linear, is also used for testing and comparing a recently proposed algorithm by
Tully. The other, the well-known displaced harmonic potentials model, is a
prototype of many condensed processes. Finally, the method is applied for
calculating the nonadiabatic raditionless relaxation of the solvated electron
from its first excited state to the fully solvated ground state.

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162. M.D. Todd, A. Nitzan and M.A. Ratner
Electron Transfer via Superexchange; A Time-Dependent Approach.
J. Phys. Chem., 97, 29-33 (1993).         PDF

The superexchange model for the facilitation of electron
transfer between donors and acceptors by means of intermediate bridges is recast
in a time-dependent framework. We develop a model in which three electronic
states (donor, bridge, and acceptor) are considered and vibronic levels are
included on the donor and acceptor. An explicitly time-dependent formulation, in
which the golden rule is rewritten in the form of an integral over a
timedependent correlation function, is used to calculate the rate. Simple example
calculations for model three-systems are given; inverted region behaviour and
reasonable values are obtained. The model is a general one and should be useful
for interpretation of superexchange-assisted transfer based on the experimental
observations of frequencies and displacements (such as the information that can
be obtained with Raman spectroscopy). The model can be generalized to include
effects such as dephasing, relaxation, solvent dynamics, and anharmonicities, as
well as breakdown of the Condon approximation.

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161 R. Granek and A. Nitzan
Comment on: Self-consistent theory of polymer dynamics in melts
J.Chem.Phys. 97,3873-3874(1992).         PDF

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160. R. Olender and A. Nitzan
Ion Solvation and Association in Complex Solvents: Theoretical Considerations
Electrochemia Acta. Vol 37, 1505-1509 (1992).                      PDF
We discuss some theoretical issues concerning ion association in complex hosts.
In particular the effect of temperature and pressure on ion pairing is discussed
in relation to recent experimental observations in polymer ionic conductors.

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159. N. Liver and A. Nitzan
Redox Properties of Small Semiconductor Particles.
J. Phys. Chem, 96, 3366-3373 (1992).         PDF

In this paper we study the equilibrium properties of the semiconductor particles
of intermediate sizes (_Debye length) in contact with an electrolyte solution
containing a given redox pair. We focus on the size dependence of electrical and
thermodynamical quantities associated with such particles. The equilibrium
distribution of the potential and of the charge in the particle and in the
surrounding electrolyte is obtained analytically in limiting cases and computed
in the general case using the nonlinear PoissonBoltzmann equation, assuming
Boltzmann statistics for carrier distributions in the semiconductor. A simple
relation for the sizedependent redox potential of a semiconductor sphere
characterized by its radius and charge is proposed and is found to provide a good
approximation for a broad range of electrolyte concentrations. This leads to an
expression for the "equilibrium constant" for the semiconductor/electrolyte
system, which relates the concentrations of the electrolytic redox components to
the concentration, size, and charge of the semiconductor particles.

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158. G. Makov and A. Nitzan
Association of Ion Pairs in Clusters of Dielectric Solvents.
J. Phys. Chem., 96,2965-2967 (1992).         PDF

The association of ion pairs in clusters is studied in an extended Bjerrum model
using both a Coulombic potential and a potential of mean force calculated from
molecular dynamicssimulations. Association is found to increase rapidly as the
cluster size decreases until a critical size is reached, below which the ions are
in the paired state. For NaCl in water this is estimated at 12 water molecules
for contact ion pairs. It is also found that the short-range details of the
potential are important and that replacing them with a Coulombic assumption leads
to a large overestimate of the critical size.

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157. E. Neria and A. Nitzan
Simulations of Solvation Dynamics in Simple Polar Solvents.
J. Chem. Phys. 96, 5433-5440 (1992).         PDF

The paper describes the results of computer simulations of charge solvation dynamics in a Stockmayer solvent (Lennard-Jones spheres with point dipoles at their centers). The solvent molecules are characterized by mass and moment of inertia which can be varied independently, thus providing the possibility to study the separate effects of the rotational and translational solvent motions on the solvation process. We focus on the role played by these degrees of freedom, and on the contributions of different solvation shells around the solute to the solvation process in order to check the validity of recently proposed theories of
solvation dynamics. We find that even in this structureless solvent, as in the more structures solvents studied earlier, inertial effects dominate the solvation process, and dielectric solvation theories which do not take into account these effects cannot describe the observed dynamics. The dynamic mean spherical approximation and generalized diffusion theories cannot account for the observed dynamics even when solvent translations are frozen.

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CB16. Lonergan, M.C.; Shriver, D.F.; Nitzan, A.; Ratner, M.A.
The mechanism and modeling of conductivity in polymer electrolytes
Solid State Ionics IV. Symposium, p. xiii+715, 245-62 (Solid State Ionics IV. Symposium, Boston, MA, USA; 1994)
ABSTRACT: The progress of dynamically disordered hopping (DDH) in modelling charge transport in polymer electrolytes is reviewed. The DDH model successfully describes many of the salient features of polymer electrolytes, most notably, the frequency and temperature dependence of the conductivity. Furthermore, analyses and simulations based on the DDH model provide rich mechanistic information. The general picture of charge transport that emerges from the DDH model is one in which two classes of charge carriers exist in thermal equilibrium: quasi-free and bound. The quasi-free carriers dominate the conductivity response and diffuse freely over short distances (=IAA) with longer range diffusion requiring local segmental motions, renewal in the language of DDH, of the polymer solvent. The bound carriers, which are likely polymer solvated ion clusters, are immobile on the time-scale of renewal and contribute relatively little to the conductivity (90 Refs.)
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