Nitzan, A.; Jortner, J.; Kommandeur, J.; Drent, E.
A quantum mechanical analogue of the Stern-Volmer equation.
Chemical Physics Letters, vol.9, no.4, p. 273-8 15 May 1971. PDF
The authors discuss the role of interference effects in intramolecular electronic energy quenching of an excited electronic state of a large molecule. For a small electronic energy gap the Stern-Volmer relation is obtained in the limit of strong coupling, while in intermediate cases the (pressure dependent) quantum yield may exhibit a minimum. This prediction was experimentally verified for the radiative decay of the singlet excited state of biacetyl
3. Nitzan, A.; Jortner, J.
Optical selection stusedies of radiationless decay in an isolated large molecule.
Journal of Chemical Physics, vol.55, no.3, p. 1355-68 1 Aug. 1971. PDF
In this paper the authors present the results of a theoretical study of the nonradiative decay probability of a single vibronic level of a large isolated molecule. Utilizing Feynman's operator techniques a theoretical expression is derived of the dependence of the electronic relaxation rate on the excess vibrational energy in the excited electronic state for a 'harmonic molecule' which is characterized by displaced potential surfaces. For a large effective energy gap the nonradiative decay probability increases with increasing excess vibrational energy, while for a small energy gap the nonradiative decay in higher vibronic levels may be retarded. These rough numerical calculations are found to be consistent with recent experimental data on optical selection studies in the isolated benzene molecule (31 Refs.)
Nitzan, A.; Jortner, J.; Rentzepis, P.M.
Internal conversion in large molecules.
Molecular Physics, vol.22, no.4, p. 585-92 1971. PDF
Considers the problem of internal conversion in a highly excited state of a large molecule in the statistical limit in terms of a consecutive decay problem. The Wigner- Weisskopf approximation was utilized to handle the problem of sequential decay. Elucidates the features of the radiative decay, such as the decay pattern, the decay times and the quantum yields of a 'statistical' second-excited singlet state in different spectral regions.
Nitzan, A.; Jortner, J.
What is the nature of intramolecular coupling responsible for internal conversion in large molecules?
Chemical Physics Letters, vol.11, no.4, p. 458-63 1 Nov. 1971. PDF
The authors discuss the criteria for the specification of a proper basis set for describing electronic relaxation processes in large molecules (16 Refs.)
Nitzan, A.; Jortner, J.; Rentzepis, P.M.
Intermediate level structure in highly excited electronic states of large molecules.
Proceedings of the Royal Society of London, Series A (Mathematical and Physical Sciences), vol.327, no.1570, p. 367-91 1972. PDF
Considers the radiative decay of excited electronic states of a large molecule which corresponds to the dense intermediate level spacing situation, encountered for the second excited singlet state of some aromatic hydrocarbons, which is separated from the first excited singlet state by a small (3000 to 4000 cm/sup -1/) electronic energy gap. Intramolecular interstate coupling and the interaction with the radiation field were handled by a selfconsistent extension of the Wigner-Weisskopf approximation. A general expression is derived for the time and energy resolved decay spectrum of a highly excited state of a large molecule, which yields information concerning the decay pattern, for the fluorescence lifetime(s) and for the corresponding quantum yields, in different spectral regions (43 Refs.)
Nitzan, A.; Jortner, J.
Optical selection studies of radiationless decay in an isolated large molecule. II. Role offrequency changes.
Journal of Chemical Physics, vol.56, no.5, p. 2079-87 1 March 1972. PDF
For pt. I see abstr. A64078 of 1971. The authors provide an extension of the theoretical study of nonradiative decay of a single vibronic level of a large molecule. Theoretical expressions have been derived for the dependence of the electronic relaxation rate on the excess vibrational energy in the excited electronic state of a 'harmonic molecule' which is characterized by displaced and frequency modified potential surfaces. The simple case of displaced potential surfaces was handled by relating the potential surfaces via a simple displacement operator. To handle frequency changes in optical selection the authors have applied Feynman's operator techniques to disentangle exponential operators which involve nonlinear terms. The role of frequency changes in optical selection experiments was elucidated.
Nitzan, A.; Jortner, J.
Intramolecular nonradiative transitions in the 'non-Condon' scheme.
Journal of Chemical Physics, vol.56, no.7, p. 3360-73 1 April 1972. PDF
The nonradiative intramolecular decay of a large molecule is considered utilizing Born-Oppenheimer wavefunctions as a zero order basis, and bypassing the conventional Condon approximation for the calculation of the electronic coupling matrix elements. The electronic adiabatic wavefunctions are expanded in terms of the Wigner-Brillouin perturbation series in the weak electronic vibrational coupling limit. A generalized version of Feynman's operator calculus is applied to derive general expressions for the nonradiative decay probability of a statistical harmonic molecule characterized by displaced potential surfaces. Numerical calculations were performed for the decay of the vibrationless excited electronic state in the 'non-Condon' scheme. The numerical data for the decay rate in a two electronic level system in the weak electronic vibrational coupling limit exceed the results obtained invoking the Condon approximation by 2-3 orders of magnitude. The relevant off resonance coupling terms in the adiabatic representation are shown to be appreciably smaller than the near resonance coupling terms.
Nitzan, A.; Jortner, J.
Line shape of a molecular resonance.
Molecular Physics, vol.24, no.1, p. 109-32 July 1972. PDF
The authors consider some implications of intramolecular electronic relaxation on the optical line shape of large molecules in the statistical limit. General expressions for the line shape were derived utilizing the Green's function formalism which account both for interference with background absorption and for interference between resonances. The energy dependence of the line-width functions were elucidated. They have demonstrated that the line shape for an 'isolated' resonance is a fanian; however, as the line profile index is determined by the ratio of the level spacing to the non-radiative width, the corrections to the lorentzian line shape are small in this case. Thave established the equivalence of the physical description utilizing a three-level crude adiabatic basis and a two- level adiabatic basis. In the case of overlapping resonances the line shape may be recast in terms of a modified Fano- type formula where the line profile index is energy dependent (24 Refs.)
Nitzan, A.; Jortner, J.
Resonance fluorescence from large molecules.
Journal of Chemical Physics, vol.57, no.7, p. 2870-89 1 Oct. 1972. PDF
In this paper the authors apply the T matrix formalism of scattering theory to derive general expressions for the absorption cross sections, the cross sections for resonance fluorescence and the emission quantum yields from large molecules in the statistical limit. In the simple case of an isolated molecular resonance both the absorption line shape and the photon scattering cross section exhibit a Lorentzian distribution on the photon energy, the emission quantum yields are distributed among the ground state vibronic levels according to their radiative widths and, most important, the emission quantum yields are independent of the photon energy and of the spectral width of the exciting light. The authors were able to derive general expressions for the resonance scattering from a pair of overlapping resonances, including radiative corrections to infinite order. The absorption cross section does not vanish in the region of destructive interference but assumes a finite value which depends on the radiative widths.
11. A. Nitzan and J.
Radiationless decay and intrastate energy equilibrium in an isolated large molecule.
J. Chem. Phys. 56, 5200-5201 (1972). PDF
Nitzan, A.; Jortner, J.
Sequence congestion effects in optical selection studies of electronic relaxation.
Chemical Physics Letters, vol.13, no.5, p. 466-72 1 April 1972. PDF
The authors present a theoretical study of the non-radiative decay rate of an 'isolated' large molecule characterized by displaced potential surfaces which will exhibit temperature dependence due to sequence congestion effects (17 Refs.)
Nitzan, A.; Jortner, J.
Preparation of metastable molecular states by optical excitation.
Chemical Physics Letters, vol.14, no.2, p. 177-83 15 May 1972. PDF
The implications of Rhodes 'filtering' process for the reduced density operator of excited molecular states are explored demonstrating that the relaxation characteristics of an isolated resonance in the statistical limit are independent of the excitation mode (6 Refs.)
Nitzan, A.; Jortner, J.
Effects of vibrational relaxation on the optical lineshapes in molecular spectra.
Chemical Physics Letters, vol.15, no.3, p. 350-6 15 Aug. 1972. PDF
The authors derive general expressions for the time dependent optical lineshape of a molecule undergoing vibrational relaxation in a dense medium (11 Refs.)
Nitzan, A.; Jortner, J.
Vibrational relaxation of a molecule in a dense medium.
Molecular Physics, vol.25, no.3, p. 713-37 March 1973. PDF
The authors consider some features of vibrational relaxation of a guest molecule in a host matrix. The model system involves a harmonic molecule interacting with a harmonic medium. Three specific models for the molecule-medium coupling were considered, which involve single phonon decay, vibron-phonon decay and multiphonon decay. Explicit solutions were derived utilizing the Wigner-Weisskopf approximation. This generalized formalism was applied for the study of the time evolution of the distribution, the cooling and the heating processes of the oscillator by a thermal field and for the coupling between vibrational relaxation and infra-red emission (22 Refs.)
Nitzan, A.; Jortner, J.
Effects of vibrational relaxation on molecular electronic transitions.
Journal of Chemical Physics, vol.58, no.6, p. 2412-34 15 March 1973. PDF
The implications are explored of the coupling between nonradiative electronic relaxation and vibrational relaxation in excited electronic states of large molecules. The physical model involved a two electronic level molecular system interacting with a harmonic medium via linear coupling terms in the molecular nuclear coordinates. Two models were advanced for the molecule-medium coupling which involve single phonon decay and alternatively double phonon (or rather phonon-vibron) decay. The functional form of the final results is independent of the specific model adopted for the vibrational relaxation. The molecular Hamiltonian and the intramolecular coupling were recast in terms of second quantization formalism where the nonadiabatic coupling operator was modified by a Franck Condon shift operator.
Nitzan, A.; Jortner, J.
Electronic relaxation of small molecules in a dense medium.
Theoretica Chimica Acta, vol.29, no.2, p. 97-116 1973. PDF
The authors present a theoretical study of radiationless transitions in a small molecule embedded in a dense inert medium. Two extreme situations of the molecule-medium coupling were considered, involving the case of zero displacements of the medium modes between the two electronic states (i.e. the Shpolskii matrix) and the limit of strong molecule-medium coupling. The Fourier transform of the non radiative decay probability of a small molecule in a Shpolskii matrix involves exponential damping, while for the strong coupling situation Gaussian damping is involved. In the case of the Shpolskii matrix the decay rate of a small molecule can be expressed in terms of an infinite series where each term corresponds to a product of an (intramolecular) Poisson distribution and a (medium induced) Lorentzian distribution. The Lorentzian widths were explicitly expressed in terms of the vibrational relaxation widths. The Robinson-Frosch formula can be obtained for the extreme case of near degeneracy in a Shpolskii matrix. In the limit of strong molecule-medium coupling the decay rate of a small molecule can be recast in terms of an infinite sum where each term involves a superposition of a Poisson distribution and a Gaussian distribution. The medium induced Gaussian distribution is determined by intramolecular phonon broadening (32 Refs.)
Nitzan, A.; Jortner, J.
Comments on optical selection studies.
Journal of Chemical Physics, vol.58, no.6, p. 2669-70 15 March 1973. PDF
The authors argue that the scheme proposed by Fong and Wassam (see ibid. vol.58, no.6, 2667, 1973) who derived the nonradiative decay probability of a single vibronic level and its Boltzmann average for a harmonic model (characterised by identical frequencies) where the promoting modes are characterised by finite origin displacements, is of limited applicability for molecular relaxation processes and may be encountered in some large molecules characterised by low symmetry (14 Refs.)
Nitzan, A.; Jortner, J.; Berne, B.J.
Interference effects in sequential decay.
Molecular Physics, vol.26, no.2, p. 281-90 Aug. 1973. PDF
The authors utilize the Green's function method to study sequential decay processes which involve interference effects. The model system involves a zero-order discrete state coupled to a set of continua, which are themselves coupled together, while the coupling matrix elements are energy independent. Interference effects in parallel and consecutive decay involving two continua result in the retardation of the decay rate of the initial state and in the reversal of the branching ratio for the population of the two continua. Finally, a general solution was provided for the problem of sequential decay involving multiple continua (11 Refs.)
Nitzan, A.; Jortner, J.
Non radiative transition probabilities in the statistical limit.
Theoretica Chimica Acta, vol.30, no.3, p. 217-29 1973. PDF
The authors derive a general computational scheme for the calculation of the non radiative decay probability of a polyatomic molecule in the statistical limit. Within the framework of the Harmonic Approximation the relaxation rate of any polyatomic molecule can be expressed in terms of an infinite sum where each term consists of a medium distribution function and an intramolecular term. In the statistical limit the medium induced vibrational relaxation widths do not affect the non radiative decay characteristics. Numerical calculations are reported for the T/sub 1/ to S/sub 0/ intersystem crossing in the benzene molecule (13 Refs.)
Nitzan, A.; Ross, J.
Oscillations, multiple steady states, and instabilities in illuminated systems.
Journal of Chemical Physics, vol.59, no.1, p. 241-50 1 July 1973. PDF
The absorption of light by some but not all species of a chemical reaction, followed by a radiationless transition and ultimate conversion of light into heat on a time scale short compared to the chemical reaction time scale, is shown to give rise to the possibilities of multiple steady states, damped oscillations in state variables, hysteresis and instabilities. All these phenomena are predicted to occur even for the simplest reaction A to or from B, where only A absorbs light, and where the rate equation, with temperature dependent rate coefficients, is coupled nonlinearly to the equation for the rate of change of temperature. The theory is developed for both stationary and transient experiments. For the cyclic reaction mechanism A to or from B to or from C to or from A, where again only A absorbs light, damped oscillations occur under isothermal conditions; the illumination, as described, effectively breaks microscopic reversibility. Both the kinetic and the thermodynamic analysis show the essential role of light in effectively breaking microscopic reversibility analogous to the net flux of reactants and of products across the boundary of an open system.
Photon absorption and scattering in Fano anti-resonances.
Molecular Physics, vol.27, no.1, p. 65-80 Jan. 1974. PDF
The Green's function method is utilized to obtain a modified treatment of Fano's line-shape problem which takes into account the coupling between different states in the continuous (or quasi-continuous) non-radiative manifold due to their interaction with the same radiation field states. A new expression for the absorption line-shape is obtained in the form sigma /sub a/( epsilon ) varies as (( epsilon +qY/sup L/)/sup 2/+(Y/sup L/q/sup 2/+1)(1-Y/sup L/))/( epsilon /sup 2/+1), where epsilon is the reduced energy parameter, q is Fano's line-shape index and Y/sup L/ is the non-radiative quantum yield obtained when the non-radiative manifold is optically forbidden. As Y/sup L/ is always smaller than unity, the absorption never strictly vanishes in contrast to the result obtained in Fano's approximation. In addition, expressions are obtained for the emission line- shape and for the (energy dependent) emission quantum yield within a Fano resonance. The quantum yield so obtained is free from the singular behaviour which characterizes the same quantity obtained in Fano's approximation (12 Refs.)
Nitzan, A.; Ortdeva, P.; Ross, J.
Symmetry breaking instabilities in illuminated systems.
Journal of Chemical Physics, vol.60, no.8, p. 3134-43 15 April 1974. PDF
Instabilities are analysed in chemically non-reactive and reactive systems which are driven far from equilibrium by absorption of illumination. Two types of symmetry-breaking instabilities are identified; the first is where spatial patterning is dictated by container dimensions; the second where it is inherent in the transport properties and kinetics. Examples of a two-component non-isothermal system and a single component gaseous system are considered (16 Refs.)
A.; Ross, J.
A comment on fluctuations around nonequilibrium steady states.
Journal of Statistical Physics, vol.10, no.5, p. 379-90 May 1974.
The authors study fluctuations around nonequilibrium steady states of some model nonlinear chemical systems. A previous result of Nicolis and Prigogine (1971) states that the mean square fluctuation computed from a master equation in the space of internal states of the reacting species is identical to that calculated from Einstein's fluctuation formula. Our analysis of fluctuations based on that master equation leads with the assumption of local equilibrium to a result identical to that obtained from a master equation for the total concentration of the reacting species, which is different from the equilibrium (Einstein relation) result. Nicolis and Prigogine approximated one term in their master equation, and a discussion of this approximation is presented. The master equation without this approximation yields at equilibrium the result expected on the basis of Einstein's formula (9 Refs.)
Nitzan, A.; Mukamel, S.; Jortner, J.
Some features of vibrational relaxation of a diatomic molecule in a dense medium.
Journal of Chemical Physics, vol.60, no.10, p. 3929-34 15 May 1974. PDF
The authors' recently published model of the relaxation of a guest molecule (see abstr. A30229 of 1973) is applied to the case of a diatomic molecule, and the case of relaxation of a polyatomic molecule at its lowest vibrational frequency. Expressions are derived for the dependence of relaxation time on the natural frequency of the molecule and on temperature. A calculation for CO in solid Ar gave fair agreement with literature experimental data (21 Refs.)
On the coupling between vibrational relaxation and molecular electronic transitions.
Molecular Physics, vol.28, no.2, p. 559-69 Aug. 1974. PDF
Vibrational relaxation of a harmonic molecule in contact with its surrounding medium is studied, and its effect on the electronic relaxation rate in such molecules is examined. Results of earlier works which considered harmonic phonon models for the medium are extended to the case of a general thermal bath. The formal expression for the vibrational relaxation rate is modified but the general form of the final results for the electronic and vibrational time evolution is shown to remain intact (9 Refs.)
Nitzan, A.; Ortoleva, P.; Deutch, J.; Ross, J.
Fluctuations and transitions at chemical instabilities: the analogy to phase transitions.
Journal of Chemical Physics, vol.61, no.3, p. 1056-74 1 Aug. 1974. PDF
A general analysis is presented of the analogy between phase transitions and instability. Both are modelled as a set of nonlinear partial d.e.'s; the properties of the d.e.'s near the threshold of instability are studied both in the deterministic (time-averaged) and stochastic forms of the equation. An analogy is demonstrated between phase transitions and hard and soft transitions of the d.e.'s; the stochastic form of the d.e.'s is used to analyse the concept of steady state; and the behaviour of a system at a steady state near the margin oinstability is discussed (42 Refs.)
Nitzan, A.; Silbey, R.J.
Relaxation in simple quantum systems.
Journal of Chemical Physics, vol.60, no.10, p. 4070-5 15 May 1974. PDF
Relaxation times of a harmonic oscillator and of a two level system are analysed, and Green's functions and line shape functions are obtained. Expressions for decay rates are obtained and used to establish their temperature difference using Rackovsky models, a phonon bath and of a bath of two- level systems. Radiative relaxation is treated as a particular case of the theory (14 Refs.)
Nitzan, P. Ortoleva and J. Ross
Nucleation in systems with multiple stationary states.
Faraday Symposium of the Chemical Society 9, 241-253 (1974). PDF
Weconsider a reaction diffusion system, far from equilibrium, which has multiple stationary states (phases) for given ranges of external constraints. If two stable phases are put in contact, then in general one phase annihilates the other and in that process there occurs a single front propagation (soliton). We investigate the macroscopic dynamics of the front structure and velocity for two model systems analytically and numerically, and for general reaction-dffusion systems by a suitable perturbation method. The vanishing of the solition velocity establishes the analogue of the Maxwell construction used in equilibrium thermodynamics. The problem of nucleation of one phase imbedded in another is studied by a stochastic theory. We show that if the reactiondynamics is derived from a generalized potential function then the macroscopic steady state are extrema of the probability distribution. Weuse this result to obtain an expression for the critical radius of anucleating phase and confirm the prediction of the stochastic theory by numerical solution of the deterministic macroscopic kinetics for a model system.
Sup Hahn, A. Nitzan, P. Ortoleva and J. Ross
Threshold excitations, relaxation oscillations and effect of noise on an enzyme reaction.
Proc. Nat. Acad. Sci. 71, 4067-4071 (1974). PDF
We study a deprotonation reaction by an enzyme with activity dependent on pH. The rate and transport equations are simpplified with a number of assumptions, are analyzed according to the presence of different time scales, and are solved numerically to show relaxation oscillation and threshold excitation, for different choicesof parameters. The imposition of fluctuations (noise) on the deterministic equations for threshold excitationconditions leads to random occurrence of an exeitation and return to state at low noise level and to large, random variation in concentration at high noise level. At intermediate noise levels (of the order of the threshold excitation), however, we find quasi-periodic concentration oscillations. Thus, critical values of external constraints necessary for oscillations are altered by the presence of noise.
Metiu, H.; Ross, J.; Nitzan, A.
On the theory of time resolved near-resonance light scattering.
Journal of Chemical Physics, vol.63, no.3, p. 1289-94 1 Aug. 1975. PDF
A theory of time resolved near resonance light scattering is presented. A one photon pulse model is first developed. This is then generalized to a pulse of n photons. A equation is derived for the time dependence of the population of the optically active molecular excited state. Time and energy are mutually independent in this equation (9 Refs.)
Nitzan, A.; Mukamel, S.; Jortner, J.
Energy gap law for vibrational relaxation of a molecule in a dense medium.
Journal of Chemical Physics, vol.63, no.1, p. 200-7 1 July 1975. PDF
A new model Hamiltonian for medium induced vibrational relaxation is presented. Some approximate relations for the vibrational relaxation of a guest molecule in a monatomic host lattice is observed where the multiphonon process is of high order. The energy gap law is derived and temperature and isotope effects considered. Expressions for the relaxation of individual vibrational levels and the relaxation of an anharmonic oscillator are given. The effects are also considered at high temperature limits and under strong coupling (38 Refs.)
Stone, J.P.; Nitzan, A.; Ross, J.
Superradiance and energy transfer within a system of atoms.
Physica A, vol.84A, no.1, p. 1-47 1976. PDF
Cooperative effects in energy relaxation and energy transfer for N atoms in a thermal radiation field with superradiance master equations as well as a closed set of coupled moment equations. For small systems nonlinear rate equations for the energy are related to the moment equations. Symmetry of the small system to interchanging atoms is used to incorporate off-diagonal solutions of the superradiance master equation in expressions for the probability of the transfer of energy from one group of atoms to another. The long time excitation probability for initially unexcited atoms is large and strongly correlated. Cooperative processes in a large system include energy loss and transfer terms in the master equation. The energy transfer is oscillatory in time. Energy relaxation is shown by numerical solution to become cooperative in a very sudden manner as the scale of the atomic system is decreased through the resonant wavelength (19 Refs.)
Fujimoto, G.; Nitzan, A.; Weitz, E.
Diffusion of vibrationally excited molecules.
Chemical Physics, vol.15, no.2, p. 217-25 1 July 1976. PDF
A treatment is presented for the effect of intermolecular vibrational energy transfer on the diffusion coefficient of vibrationally excited molecules. An analytic treatment based on random walk statistics and a Monte Carlo type calculation have been performed. Both methods yield very similar results which correlate well with existing experimental studies. A hard sphere collision model is treated extensively with comparisons made to other intermolecular potentials. The results support the involvement of long range energy transfer in V to V interactions. The effect of temperature on the diffusion coefficient of vibrationally excited molecules is calculated, with applications to the Co/sub 2/*- CO/sub 2/ system (20 Refs.)
Ondrechen, M.J.; Nitzan, A.; Ratner, M.A.
A treatment of vibrational relaxation without the rotating wave approximation.
Chemical Physics, vol.16, no.1, p. 49-59 1 Aug. 1976. PDF
A harmonic oscillator weakly coupled to a heat bath is studied without invoking the rotating wave approximation. Corrections to the lorentzian lineshape which characterizes the RWA are derived. An expression for the time evolution of the population of the oscillator which is exact in the van Hove weak coupling limit is also obtained. The results are compared to earlier expressions which were obtained using the rotating wave approximation. In the equation for the population of the oscillator an additional transient term is observed and the time evolution of the population under a variety of conditions is examined. The applicability of the rotating wave approximation is discussed in the light of these results (19 Refs.)
Nitzan, A.; Freed, K.F.; Cohen, M.H.
Renormalisation group and critical localisation.
Physical Review B (Solid State), vol.15, no.9, p. 4476-89 1 May 1977. PDF
Renormalisation group theory is applied to the problem of critical binding of a particle moving in a given potential on an infinite lattice. Nontrivial solutions can be obtained exactly to the renormalisation group transformations and critical exponents and scaling laws are obtained as well as the exact critical value for the binding potential in the Slater-Koster model by taking all irrelevant variables into account. The extension of the method to random potentials is discussed (18 Refs.)
Andresen, B.; Berry, R.S.; Nitzan, A.; Salamon, P.
Thermodynamics in finite time. I. The step-Carnot cycle.
Physical Review A (General Physics), vol.15, no.5, p. 2086- 93 May 1977. PDF
A general variational statement of the problem of finding bounds to process functions, such as heat and work, for finite-time processes, is presented. With one exception, the model problems assume a 'step-Carnot' cycle which is smaller to the reversible Carnot cycle but the external pressure varies in finite steps. The problems analyzed are the maximization of effectiveness and efficiency of the optimal period for such a cycle where the contact with external reservoirs has finite heat conductance. For a continuous Carnot cycle with finite heat conductance between system and thermostats, the maximum power and the rate of obtaining this are determined (13 Refs.)
Bimpong-Bota, E.K.; Nitzan, A.; Ortoleva, P.; Ross, J.
Cooperative instability phenomena in arrays of catalytic sites.
Journal of Chemical Physics, vol.66, no.8, p. 3650-8 15 April 1977. PDF
An analysis is presented of localised nonlinearity sources in regular arrays of catalytic sites. Two cases are considered; AA, where all sites are equivalent; AB where two different types of site alternate. Stability conditions for these lattices in the steady state are derived as functions of local and bulk reactions, inter-site distance and coupling between the sites. The AA analysis is applied to a product-activated enzyme system and to an oscillatory system with Prigogine-Lefever reactions; the AB model is used to study a reaction system dependent on the mutual activation of two species. It is shown in all cases that cooperative instability plays a significant role in catalytic reactions (11 Refs.)
Mukanel, S.; Nitzan, A.
Resonance Raman scattering from a multilevel, thermally relaxing system.
Journal of Chemical Physics, vol.66, no.6, p. 2462-79 15 March 1977. PDF
The process of scattering of low-intensity light from a molecule is modelled in terms of incident and scattered photon streams, a multi-level molecular system with a manifold of optically active levels interacting with heat baths at finite temperature (reversible) or at zero temperature (irreversible). The model is formulated within the Liouville space formalism and is solved to obtain general expressions for absorption and scattering cross sections. Using a system with a single intermediate level as an example the model can be used to obtain insight into relaxation processes involving the excited state (49 Refs.).
Nitzan, A.; Mukamel, S.; Ben-Reuven, A.
On the impact and the separation approximations in the theory of multiphoton interactions with thermally perturbed systems.
Chemical Physics, vol.24, no.1, p. 37-43 15 Aug. 1977. PDF
Criteria are provided for the factorization of thermal averages incurring in the calculation of cross-sections for several-photon processes, into products of independently averaged single-photon processes. These criteria are compared to those involved in the impact approximation for single photon spectra, and are shown to be less restrictive (16 Refs.)
Bondybey, V.E.; Nitzan, A.
Radiationless transitions in small molecules: interstate cascading in matrix isolated CN.
Physical Review Letters, vol.38, no.16, p. 889-92 18 April 1977. PDF
The effects of coupling with medium modes on radiationless transitions in small molecules are discussed. The relaxation of CN in a matrix at low temperature was studied. A time resolved laser two photon technique was used to excite an A/sup 2/ pi state level and measure the population of the ground state level, subsequently. The process is ascribed to interstate cascading, involving A/sup 2/ pi and X/sup 2/ Sigma vibrational levels (8 Refs.)
Shugard, M.; Tully, J.C.; Nitzan, A.
Dynamics of gas-solid interactions: calculations of energy transfer and sticking.
Journal of Chemical Physics, vol.66, no.6, p. 2534-44 15 March 1977. PDF
A model of gas-surface collisions is proposed in which the surface is treated as an assembly of primary and secondary lattice atoms; interaction between these are harmonic. The interactions between gas atoms and the surface are dependent on the positions of the primary lattice atoms. The coupled equations of the model are developed within the generalised Langevin formalism and solved by Monte Carlo sampling of trajectories to obtain values for energy transfer on collision, the extent of sticking, and residence time. Numerical results for energy transfer in the He-W system are in good agreement with results from a quantum mechanical distorted wave calculation (18 Refs.)
Weissman, Y.; Nitzan, A.; Jortner, J.
Quadratic effects in multiphonon transition rates in solids.
Chemical Physics, vol.26, no.3, p. 413-19 15 Dec. 1977. PDF
Investigates the contribution of quadratic impurity-phonon coupling terms on nonradiative multiphonon transition rates in solids. It is demonstrated that the quadratic terms may increase substantially the transition rate and may modify quantitatively the energy gap law. Such effects will be exhibited even when the quadratic coupling is too weak to be observable in the optical spectra (23 Refs.)
Chemical instabilities as critical phenomena.
Physical Review A (General Physics), vol.17, no.4, p. 1513- 28 April 1978. PDF
A detailed study is presented of the analogy between equilibrium phase transitions and chemical instabilities in the vicinity of the critical point of a nonequilibrium reacting diffuse system characterized by multiple homogeneous steady states. The mathematical properties of marginal stability and critical points corresponding to homogeneous transitions are investigated. These properties are shown to be essential in the subsequent reduction of the equations of motion near the critical point. The Ginzberg estimate for the size of the critical region in diffusing reacting chemical systems (1960) is obtained and discussed (29 Refs.)
Shugard, M.; Tully, J.C.; Nitzan, A.
Stochastic classical trajectory approach to relaxation phenomena. I. Vibrational relaxation of impurity molecules in solid matrices.
Journal of Chemical Physics, vol.69, no.1, p. 336-45 1 July 1978. PDF
The authors present a theory of impurity vibrational relaxation in condensed media based on computer simulation of the classical equations of motion of the impurity molecule and a small number of neighboring host atoms. The host atoms are in communication with the remainder of the lattice through the presence of stochastic forces and damping terms that are constructed from knowledge of the phonon spectrum of the solid. Temperature is introduced via the fluctuation-dissipation theorem. The method is applied here to a Cl/sub 2/ impurity molecule imbedded in an argon matrix. The dependence of energy relaxation and dephasing times on interaction parameters is monitored, and comparison is made with recent spectroscopic measurements on this system (43 Refs.)
Nitzan, A.; Shugard, M.; Tully, J.C.
Stochastic classical trajectory approach to relaxation phenomena. II. Vibrational relaxation of impurity molecules in Debye solids.
Journal of Chemical Physics, vol.69, no.6, p. 2525-35 15 Sept. 1978. PDF
For pt.I see ibid., vol.69, no.1, p.336 (1978). The stochastic classical trajectory approach is extended through introduction of a systematic class of phonon mode densities. Convenient algorithms are presented for generating the required random forces and damping integrals corresponding to mode spectra which approach, as closely as desired, the Debye spectrum. Extension to realistic mode densities involving irregular and discontinuous features is discussed. Application to vibrational relaxation of impurities in solids demonstrates that rates can depend sensitively on the structure of the phonon density of states, particularly at low temperature (10 Refs.)
Grimbert, D.; Lavollee, M.; Nitzan, A.; Tramer, A.
Mechanism of collision-induced intersystem crossing in CO.
Chemical Physics Letters, vol.57, no.1, p. 45-9 1 July 1978. PDF
The authors have studied inert-gas pressure effects on the fluorescence decay in CO selectively excited to the nu =0 to 7 vibronic levels of the A/sup 1/ Pi electronic state. It is shown that the dependence of the quenching cross section sigma /sub isc/ on the average value of the S-T mixing coefficient ( beta /sup 2/) has a quasi-logarithmic form. A simple two-level model describing semiquantitatively this behavior is proposed (20 Refs.)
Carmeli, B.; Nitzan, A.
On a random coupling mode for intramolecular dynamics.
Chemical Physics Letters, vol.58, no.2, p. 310-16 15 Sept. 1978. PDF
The time evolution of a system involving separable random coupling between quasi-continuous manifolds is studied. The problem is solved using ensemble averages. In the strong coupling maximum randomness case the continua are found to be effectively uncoupled on the experimentally relevant time scale (13 Refs.)
Carmeli, B.; Nitzan, A.
Kinetic equations for collisionless multiphoton excitation of large molecules.
Chemical Physics Letters, vol.62, no.3, p. 457-61 15 April 1979. PDF
Most of the multiphoton absorption steps in a large molecule excited by an intense radiation field may be viewed as transitions between quasicontinuous manifolds of exact molecular levels. It is shown that the assumption that the radiative coupling varies randomly with level indices leads to simple kinetic schemes. Coherent phenomena are absent if the average coupling vanishes, but may persist otherwise (12 Refs.)
Phenomenology of resonance Raman Scattering from thermally relaxing systems.
Chem. Phys. 41 , 163-181 (1979). PDF
The problem of resonance Raman scattering and resonance fluorescence from thermally relaxing systems is studied. A general expression obtained earlier is rewritten explicitly in the dipole approximation. Numerical computations are performed on simple model systems and reveal the role that thermal relaxation play in the light scattering process. In particular, the effect of thermal relaxation on interference features, the temperature dependence of the absorption and the scattering cross-sections (apart from the effect of the initial level distribution) and the transition from thermal relaxation behavior to an irreversible damping are studied in detail.
Nitzan, A.; Jortner, J.
Inverse electronic relaxation.
Chemical Physics Letters, vol.60, no.1, p. 1-4 15 Dec. 1978. PDF
The authors explore the possibility of detecting fluorescence emission following high-order infrared multiphoton excitation in the ground electronic manifold of polyatomic molecules and formulate the conditions for the experimental observation of such inverse electronic relaxation process (8 Refs.)
Nitzan, A.; Jortner, J.
Theory of inverse electronic relaxation.
Journal of Chemical Physics, vol.71, no.8, p. 3524-32 15 Oct. 1979. PDF
In this paper the authors advance a theory of inverse electronic relaxation (IER) induced by high-order multiphoton excitation of collision-free molecules. The IER process involves spontaneous one-photon radiative decay of molecular eigen sates. These states originate from intramolecular scrambling of vibronic levels corresponding to the ground state electronic manifold with a discrete vibronic level (or a set of such levels) which belong to a low-lying excited electronic state. For a diatomic molecule and for a small polyatomic the molecular eigenstates are excited by a coherent multiphoton excitation process, while for large polyatomic molecules where the low electronically excited state corresponds to an intermediate level structure or to the statistical limit, incoherent multiphoton excitation of the molecular eigenstates of an 'isolated' molecule prevails. Explicit expressions for the rate of IER are derived and the conditions for the observation of this novel phenomenon are established (24 Refs.)
Salamon, P.; Nitzan, A.; Andresen, B.; Berry, R.S.
Minimum entropy production and the optimization of heat engines.
Physical Review A (General Physics), vol.21, no.6, p. 2115- 29 June 1980. PDF
The authors consider the problem of minimum entropy production in a heat engine subject only to thermal- resistance losses. For such engines, minimizing the total entropy production is equivalent to minimizing the loss of availability. The authors show for any engine operating with a given cycle time that minimum total entropy production is achieved in a heat engine by operating it so as to keep the entropy production rate constant along each branch. For the limit of slow engine operation, the entropy production rate should be the same constant for all branches of the cycle. The authors obtain an expression for the minimum total entropy production and use this to give a bound on the maximum work which can be produced by such engines. This bound is significantly more realistic than the reversible one. Analogous results are derived for a working fluid which carries arbitrary flows from one potential to another (22 Refs.)
Nitzan, A.; Ortoleva, P.
Scaling and Ginzburg criteria for critical bifurcations in nonequilibrium reacting systems.
Physical Review A (General Physics), vol.21, no.5, p. 1735- 55 May 1980. PDF
Critical conditions are obtained for bifurcation phenomena in nonequilibrium systems (chemical instabilities) which are appropriate for transitions between homogeneous steady states as well as for symmetry-breaking transitions to static structures. In the case of symmetry-breaking instabilities these criteria enable the theory to be applied to systems in any number of spatial dimensions, eliminating a restriction to one-dimensional systems encountered in other treatments. These critical conditions allow for the derivation of time-dependent Ginzburg-Landau (TDGL)-type equations for the critical-mode amplitude (the order parameter) that grows into the new macrostate beyond the critical point. For homogeneous transitions the usual TDGL equation is obtained. For the case of intrinsic symmetry breaking, TDGL equations are found for coupled order parameters corresponding to different directions in k space. In both the intrinsic and the extrinsic cases the TDGL equations are found to have nonlinear transport terms. When the TDGL equations are turned into Langevin equations, Ginzburg criteria (defining the region where mean-field theory breaks down) are derived. The critical dimensionality thus determined is 4 for homogeneous and intrinsic symmetry- breaking transitions, and 6 for the extrinsic symmetry- breaking case (under given mild technical conditions). Expressions for the size of the nonclassical critical regions are obtained for the different transitions in terms of characteristic parameters For chemical instabilities these regions are in principle accessible (17 Refs.)
Carmeli, B.; Schek, I.; Nitzan, A.; Jortner, J.
Numerical simulations of molecular multiphoton excitation models.
Journal of Chemical Physics, vol.72, no.3, p. 1928-37 1 Feb. 1980. PDF
In this paper the authors report the results of numerical simulations of the intramolecular dynamics of a model system for multiphoton excitation of large molecules, where the low energy range is represented by a single discrete state, while the quasicontinuum is mimicked by two or three manifolds of molecular eigenstates. The random coupling model (RCM), where the radiative coupling matrix elements are assumed to be random functions of the level indices, yields conventional rate equations describing consecutive- reversible transitions for the populations with golden rule rates. In addition, numerical simulations were conducted for a constant coupling model (CCM) and for a separable random coupling model (SRCM), confirming the counterintuitive analytical results for these model systems. The time evolution of a RCM system is determined by the distribution function of the coupling elements and not by individual coupling terms, and the intramolecular dynamics is essentially determined by the lower moments (average and variance) of the distribution function. On the basis of numerical simulations the authors have shown that a radiative RCM, based on the molecular eigenstates, is equivalent to an intramolecular RCM founded on a zero-order molecular basis with a small number of optically active modes, random anharmonic coupling, and constant selective radiative interaction terms. Their computer experiments provide evidence for the validity of a strong coupling kinetic master equation for the RCM and suggest that random coupling is essential for the erosion of phase coherence effects in the multiphoton excitation of a molecular quasicontinuum (20 Refs.)
Carmeli, B.; Nitzan, A.
Random coupling models for intramolecular dynamics. I. Mathematical approach.
Journal of Chemical Physics, vol.72, no.3, p. 2054-69 1 Feb. 1980. PDF
Intramolecular dynamics in large molecules is modeled as a problem involving random coupling between manifolds of molecular levels. The random coupling model (RCM) is based on the rapid variations observed in coupling matrix elements involving highly excited bound molecular states, and on the high density of such state encountered in large molecules. The finite time and energy scales involved in real experimental situations lead to the observation that the time evolution and spectral properties characterizing the system do not depend on the detailed arrangement of states and their coupling elements but rather on low order moments of the distribution characterizing these coupling elements. This provides the basis for an approach based on ensemble averages. The coupling V is taken as a superposition V=u+ nu of a smoothly varying component u=(V) and a randomly varying (in state space) component nu =V-(V). The authors introduce a diagrammatic expansion and averaging method to evaluate the diadic Green's function for problems involving absorption line shapes, and a similar approach for the evaluation of the tetradic Green's function used in calculations of time evolution. With these methods they study the time evolution in systems involving discrete states and quasicontinuous manifolds. The solution is relevant for multiphoton excitation of large molecules, and for intramolecular electronic and vibrational transitions. The authors also study the effect of random coupling in absorption line shapes involving interference between resonances of interference between resonance and background absorptions. The mechanism for coherence erosion resulting from the random behaviour of the coupling is elucidated (37 Refs.)
Carmeli, B.; Nitzan, A.
Random coupling models for intramolecular dynamics. II. Kinetic equations for collisionless multiphoton excitation of large molecules.
Journal of Chemical Physics, vol.72, no.3, p. 2070-80 1 Feb. 1980. PDF
For pt.I see ibid., vol.73, no.3, p.2054, 1980. Multiphoton excitation and dissociation of large molecules under collisionless conditions is discussed in terms of an intercontinuum random coupling model. The mathematical approach described in a previous paper is used to obtain the general solution for a system of consecutively coupled discrete states, quasicontinuous manifolds, and continuous (dissociative) manifolds of molecular levels (eigenstates of the total molecular Hamiltonian), where the radiative coupling matrix elements are assumed to be given as a linear combination of smoothly varying and randomly varying (over level indices in the molecular manifolds) components. In the range of discrete molecular levels the time evolution is coherent and described in terms of the optical Bloch equation. In the quasicontinuous and continuous ranges the time evolution may be described in terms of Markoffian kinetic equations for the number of photons absorbed by the molecule, provided that the intramolecular vibrational relaxation widths associated with optically active molecular modes is much larger than the Rabi frequency associated with the excitation of these modes. The kinetic evolution itself consists of direct multiphoton excitation processes (simultaneous transitions from the upper discrete levels to all higher energy molecular manifolds) resulting from the smooth component in the radiative coupling, and a consecutive excitation process described by the Pauli master equation with rates given by the golden rule expression. The interaction which enters into the golden rule expression is the variance in the radiative coupling. The direct excitation component contributes a negligible part of the overall excitation even if the random and smooth radiative coupling components are comparable. The resulting incoherent time evolution of the multiphoton excitation process is consistent with available experimental results (36 Refs.)
Yahav, G.; Haas, Y.; Carmeli, B.; Nitzan, A.
Incubation times in the multiphoton dissociation of polyatomic molecules.
Journal of Chemical Physics, vol.72, no.5, p. 3410-15 1 March 1980. PDF
The incubation period revealed in the multiphoton dissociation of molecules by intense infrared lasers is discussed. It is found experimentally that large excess of added foreign gas affects the incubation period to a much smaller degree than the overall yield. A rate equations model is presented, including both the laser intensity and collisional effects. Exact numerical solution is compared with a simple analytical approximation, based on the passage time moments method. Agreement with experimental results is quite satisfactory, indicating that the role of collisions in the case discussed (tetramethyldioxetane dissociation) is primarily vibrational relaxation of excited molecules (17 Refs.)
Nitzan, A.; Ratner, M.A.; Shriver, D.F.
A coupled-mode model relating Raman line shape to high ionic conductivity.
Journal of Chemical Physics, vol.72, no.5, p. 3320-6 1 March 1980. PDF
A phenomenological model, based on the generalized Langevin equation scheme first developed by Bruesch, Zeller, and co- workers, is employed to calculate the Raman band shapes for metal-halogen stretching modes in ionic conductors of the Ag/sub 2/HgI/sub 4/ class. The observed strong broadening of the Hg-I/sub 4/ stretch mode near 122 cm/sup -1/ is explained as arising from coupling to the mobile ion diffusive mode. Below the beta to alpha phase transition, the Ag-I mode is oscillatory, and the coupling effect is negligible on either Ag-I or Hg-I. In the conducting phase, the long time diffusive character of the Ag-I motion results in a strong effective damping of the Hg-I motion, leading to the observed broadening. The coupling effects are strong only when one of the two modes is indeed diffusive, thus explaining the apparent value of the Raman linewidth as a screening device for possible new ionic conductor crystals (13 Refs.)
Jacobson, S.H.; Nitzan, A.; Ratner, M.A.
A stochastic Langevin dynamics study of correlated ionic motion in one dimensional solid electrolytes.
Journal of Chemical Physics, vol.72, no.6, p. 3712-19 15 March 1980. PDF
The motion of mobile ions in one dimensional ionic conductors is described by stochastic Langevin dynamics. The interactions of the mobile ions with the framework lattice are approximated by a sum of periodic and random potentials, yielding a set of coupled Langevin equations, which are then solved numerically. The parameters in these phenomenological equations of motion include the potential in which the ion moves and the lattice temperature. Correlated motion is considered by including long range (Coulombic) and short range potentials among the mobile ions. Inclusion of these potentials in calculations describing systems with an integral ratio of total sites to mobile ions (commensurate stoichiometry) shifts the frequency dependent conductivity (increase of maximum frequency, decrease of DC conductivity) in a manner indicating that the mobile ions are driven towards their equilibrium positions. The conductivity then decreases with increasing effective charge. However, when the carrier/site ratio is not integral (incommensurate stoichiometry, e.g. potassium hollandite) the long range ion- ion interaction drives the mobile ions into arrays which are distorted near the vacancies. This lowers the effective potential bar, and therefore is responsible for increasing the calculated diffusion coefficient and conductivity. As the strength of the ion-ion interactions is increased this cooperative behavior is enhanced. The results for potassium hollandite are in good agreement with X-ray scattering data (20 Refs.)
Gersten, J.; Nitzan, A.
Electromagnetic theory of enhanced Raman scattering by molecules adsorbed on rough surfaces.
Journal of Chemical Physics, vol.73, no.7, p. 3023-37 1 Oct. 1980. PDF
A theory for surface enhanced Raman scattering (SERS) is developed. Effects due to realistic surface geometry and dielectric properties are included. Three sources of enhanced Raman scattering are noted: the image dipole enhancement effect, the increase of local field ('lightning rod' effect), and the resonant excitation of surface plasmons. The surface is modeled as a hemispheroid protruding from a conducting plane, although other models are considered. The spherical limit is discussed in some detail and molecular orientation effects are considered. Cross sections for Mie, Rayleigh, and Raman scattering are derived (17 Refs.)
High energy photochemistry.
Journal de Chimie Physique et de Physico-Chimie Biologique, vol.77, no.1, p. 51-7 Jan. 1980. PDF
There are as yet few photochemical studies of highly excited molecular systems. The important processes and relevant parameters in such systems are characterized. A brief discussion is given of the observables in the study of molecular photochemical processes. Theoretical models are presented which deal with the problem of coupling between continua of levels, dissociative or otherwise. Predissociation and direct dissociation are considered. Photoisomerization processes are dealt with using multiphonon theory (30 Refs.)
Freed, K.F.; Nitzan, A.
Intramolecular vibrational energy redistribution and the time evolution of molecular fluorescence.
Journal of Chemical Physics, vol.73, no.10, p. 4765-78 15 Nov. 1980. PDF
The authors note the presence of contradictory estimates of intramolecular vibration relaxation rates in the literature where large molecules in high energy states, corresponding to huge densities of vibrational levels, have been ascribed relaxation rates orders of magnitude smaller than those assigned to smaller molecules with much smaller densities of vibrational levels. This unphysical disparity is explained as arising from vague (or undefined) definitions of intramolecular vibrational relaxation and/or from a consideration of quantities which are not directly measured or measurable. A resolution of a portion of the problem is already well known for electronic relaxation, but the application of those results to a description of the time evolution of the molecular fluorescence, produced during the intramolecular vibrational relaxation of the electronically excited molecules, requires a generalization of the electronic relaxation theory to separate and describe the 'unrelaxed' and 'relaxed' emission spectra. The authors provide a general theory of the time variation of the emission spectrum for molecules conforming to both the intermediate and statistical limits of intramolecular vibrational relaxation with emphasis placed upon the distinguishability between these two cases. The intermediate case analysis utilizes egalitarian and random coupling type models with essentially identical conclusions from both. The time evolution and relative yields associated with the emission spectra are described for both continuous and short pulse excitation, and reasons are provided for the absence of observation of time varying emission spectra in the experiments of Smalley and co-workers (1980). Quantum beats are possible in principle in the sparse intermediate case. Their observability depends, however, on the detection method. When the emission spectrum can be resolved, beats are expected only in the frequency integrated intensity (36 Refs.)
Jacobson, S.H.; Ratner, M.A.; Nitzan, A.
Stoichiometry-dependent conductivity in framework ionic conductors.
Physical Review B (Condensed Matter), vol.18,p. 1580-83, 1981. PDF
Stochastic Langevin dynamics simulation of a one-dimensional model for framework ionic conductors shows competing effects of static lattice potential and ion interactions. For commensurate cases, repulsions decrease the conductivity, whereas for incommensurate systems, Coulomb repulsion partly overcomes lattice potential localization, leading to increased conductivity. A new explanation is offered for the observed behavior of NASICON (Na/sub 3/Zn/sub 2/PSi/sub 2/O/sub 12/), based on the important interparticle correlations (10 Refs.)
Nitzan, A.; Brus, L.E.
Can photochemistry be enhanced on rough surfaces?
Journal of Chemical Physics, vol.74, no.9, p. 5321-2 1 May 1981. PDF
It has been shown that at least part of the surface enhanced Raman phenomenon (SERS) is due to the intensified local electromagnetic field which occurs near a surface protrusion (10-10/sup 3/ AA scale) on a rough surface. Incident fields are locally enhanced near the protrusion by image, shape, and plasmon resonance effects. Consequently, all types of electromagnetic interactions should be affected. The authors ask whether photochemical processes may also be enhanced. Enhanced absorption does not necessarily imply enhanced photochemistry because of the existence on the surface of competing routes for molecular energy dissipation. These are (a) radiationless transfer of molecular energy to the surface and (b) thermal and photon induced desorption of adsorbed molecules. It is therefore necessary to study the time scale and the efficiency of the photochemical process relative to these competing channels. It is also necessary to find and model dielectric materials with resonances throughout the IR-UV photochemical range (10 Refs.)
Tramer and A. Nitzan
Collisional effects in electronic relaxation.
Advances in Chem. Phys. 47 , 337-380 (1981). PDF
1. Essential Features of the CoHision-Induced Electronic Relaxation 338
A. General Remarks 338
B. Phenomenological Description of CoUisional Effects 341
II. Model Treatment of the CoUision-Induced Electronic Relaxation 344
A. Outline 344
B. "Primary" Collision Effects 345
C. Time Evolution of the ColfisionaUy Perturbed Molecule 348
D. SmaU-Molecule Weak-Coupling Case 350
E. Intermediate-Size Molecules 357
F. Some Specific Comments 358
III. Review and Analysis of Experimental Data 359
A. Reversibility of Colfision-Induced Electronic Relaxation 360
B. Vibrational Relaxation by Reversible Electronic Relaxation 362
C. Dependence of Colhsional Relaxation Rates on Intramolecular Parameters 363
D. Role of Strongly Mixed States (Problem of "Gates') 366
E. Dependence of CoUisional Relaxation Rates on the Intermolecular Potential. . 368
IV. New Problems and Perspectives 370
A. Electronic Relaxation in van der Waals Complexes 370
B. Electronic Relaxation of Photofragmentation Products 372
C. Magnetic-Field Effects 373
V. Final Conclusions 376
Salamon, P.; Nitzan, A.
Finite time optimizations of a Newton's law Carnot cycle.
Journal of Chemical Physics, vol.74, no.6, p. 3546-60 15 March 1981. PDF
Treats the problem of optimal finite time operations of a heat engine using an arbitrary working fluid and working between two constant temperature heat reservoirs. The authors work in a simplified framework ('Newton's law thermodynamics') which considers only losses associated with the heat exchange processes. The authors find the operations which maximize power, efficiency, effectiveness, and profit and those which minimize the loss of available work and the production of entropy. The authors find that all these optimal operations take place with the working fluid exchanging heat at a constant rate with each reservoir (implying a constant rate of entropy production) and undergoing adiabatic processes instantaneously. The authors define 'Carnot space' to be the set of all operations of the engine which consist of constant rate heat exchanges and instantaneous adiabats. All optimal operations are points in this space which is shown (within the model) to be three dimensional. The different optimal operations with different connotations of 'optimal' as described above are compared within this framework. To further study the economic implication of this model the authors also view the operation of the engine as an economic production process with work as its output. The authors a simple analytical form of the production function and see repeatedly that maximum profit operation is a compromise between operation which maximizes the power and operation which minimizes the loss of available work. The path of maximum profit is obtained as a function of the costs of power and of availability (29 Refs.)
Gersten, J.; Nitzan, A.
Spectroscopic properties of molecules interacting with small dielectric particles.
Journal of Chemical Physics, vol.75, no.3, p. 1139-52 1 Aug. 1981. PDF APPENDIX
Optical properties of small dielectric spheroids with or without adsorbed molecules are studied theoretically. Expressions for the absorption line shapes, the radiative and nonradiative decay rates, and quantum yields are derived. In the case of a molecule near a spheroid the magnitudes differ dramatically from the corresponding case of a molecule near a plane (24 Refs.)
Nitzan, A.; Brus, L.E.
Theoretical model for enhanced photochemistry on rough surfaces.
Journal of Chemical Physics, vol.75, no.5, p. 2205-14 1 Sept. 1981. PDF
A simplified theory of enhanced ultraviolet, visible, and infrared photochemistry near rough dielectric and metallic surfaces is described and numerically investigated. Protrusions on a rough surface are modeled as isolated microscopic spheres. The authors formulate classical equations of motion for molecules interacting with electromagnetic fields and such material spheres. The model incorporates (a) dipole-dipole coupling between absorbing molecules and the large, induced dipoles created in microscopic spheres irradiated near Mie resonances, and (b) dissipative energy transfer from excited molecules to higher order (l>1) multipole resonances in the spheres. Calculations show that substantial enhancements in photochemical yields are possible for relatively slow chemical reactions as well as fast reactions. The similarities and differences between enhanced photochemistry and surface enhanced Raman scattering (SERS) are discussed in detail. Dielectric materials for enhanced infrared photochemistry at CO/sub 2/ laser wavelengths are proposed (20 Refs.)
Aravind, P.K.; Nitzan, A.; Metiu, H.
The interaction between electromagnetic resonances and its role in spectroscopic studies of molecules adsorbed on colloidal particles or metal spheres.
Surface Science, vol.110, no.1, p. 189-204 Sept. 1981. PDF
The authors study the modification of optical properties of two metal spheres brought about by their electromagnetic interactions. They compute the excitation spectrum of the two sphere system and study the shape and the magnitude of the local fields. The relevance of this calculation to surface enhanced spectroscopy and to the study of the Brownian motion in colloidal solutions is discussed (23 Refs.)
Jacobson, S.H.; Nitzan, A.; Ratner, M.A.
Charge carrier correlations in framework solid electrolytes.
Solid State Ion. (Netherlands), Solid State Ionics, vol.5, p. 125-8 Oct. 1981. PDF
Stochastic langevin dynamics is employed to simulate correlated charge carrier diffusion in framework solid electrolytes. The authors include realistic Coulombic ion- ion interactions, as well as static and dynamic effects of the framework lattice. Ionic conductivity and correlation factors are calculated for several model systems. These transport properties characterize the diffusion mechanism as either liquid-like or correlated hopping. For systems in which the charge carrier density is incommensurate with the period of the lattice, ionic motion can be either liquid- like or hopping depending on the system parameters. The transition from correlated hopping to liquid-like diffusion induced by variation of these parameters is discussed (9 Refs.)
Carmeli, B.; Nitzan, A.
First passage times and the kinetics of unimolecular dissociation.
Journal of Chemical Physics, vol.76, no.11, p. 5321-33 1 June 1982. PDF
Approximate solutions for multistep master equations describing the time evolution of product formation in multiphoton or thermal unimolecular reactions are investigated. A method based on fitting the first few moments of the passage time distribution associated with the given stochastic process to proposed simple expressions for the product yield function is studied. Reasonable agreement with the exact numerical solution of the corresponding master equation is obtained with a two parameter fit (using two passage time moments) and an excellent agreement is obtained with a three parameter fit (using three passage time moments). In no case studied does a need arise for more than a three-moment description and the quality of available experimental results makes the simpler two-moment description sufficient in most cases. Analytical solutions for the first and second passage time moments are obtained for simple discrete and continuous master equation models. Expressions for the incubation time and the reaction rate are obtained in terms of these solutions. The validity of discretizing a continuous master equation is studied using both the approximate two-moment solutions and exact numerical solutions. It is concluded that a proper discretization of a continuous master equation may be carried out provided epsilon <<k/sub B/T*, where epsilon is the discretization energy step, k/sub B/ the Boltzmann constant, and T* the effective (density of states weighted) temperature. A larger discretization step can be used if only the incubation time is required. Using the approximately discretized master equation, the authors next calculate the effect of collision on the incubation time and the rate of multiphoton dissociation using a model constructed to correspond to the unimolecular dissociation of tetramethyldioxethane. Incubation times are less sensitive to collisions than the reaction rates. Finally, the authors investigate the applicability of the passage time moments method to describe the time evolution of product formation in a system whose dynamics is determined by a quantum mechanical Liouville equation (38 Refs.)
Kotler and A. Nitzan
Dielectric environment effects on surface enhanced resonant electromagnetic phenomena.
J. Phys. Chem. 86 , 2011-2015 (1982). PDF
when a thick layer of Raman active molecules is deposite on a rough metal surface, on metal colloid particles, or on a metal island film, in a surface enhanced Raman scattering (SERS) experiment, the dielectric properties of the molecular layer should affect the observed scattering. This effect is expected to be large for resonance Raman scattering, where the dielectric function of the molecular layer is appreciably different from unity. This effect is studied within the coat-sphere model. Arich structure is predicted for the frequency dependence of the enhancement ratio in the resonant case. In addition, the coverage dependence of SERS is predicted to be substantially diffrent in the resonant and nonresonant cases.
Carmeli, B.; Nitzan, A.
Non-Markoffian theory of activated rate processes.
Physical Review Letters, vol.49, no.7, p. 423-6 16 Aug. 1982. PDF
The Brownian motion of a general classical anharmonic oscillator is studied in the low-viscosity limit for a general non-Markoffian interaction with a heat bath. Memory effects are shown to have a profound influence on the rate of energy accumulation and relaxation (9 Refs.)
Bergman, D.J.; Nitzan, A.
Averaged local field intensities in composite materials.
Chemical Physics Letters, vol.88, no.4, p. 409-12 14 May 1982. PDF
Averaged local field intensities are calculated for isotropic composites in the Maxwell-Garnett and in the effective medium theories. Exact upper and lower bounds on these intensities are also found. Implications for photophysical properties of molecules embedded in the composites are discussed (14 Refs.)
Jacobson, S.H.; Ratner, M.A.; Nitzan, A.
Correlated ionic motion in solid electrolytes: tests of Smoluchowski dynamics and conductivity relations.
Journal of Chemical Physics, vol.77, no.11, p. 5752-6 1 Dec. 1982. PDF
The conductivity ofa one-dimensional model for solid electrolytes of framework type is calculated using both the Langevin and Smoluchowski equations. The Smoluchowski conductivity is generally larger than that from the (more general) Langevin approach; they become identical only in the strong damping limit. The inversion of computed or observed carrier densities to obtain an effective potential is generally straightforward for one dimension, but the derivation of the conductivity from this potential is easy only in the strong-damping extreme. The vibrational spectra of most ionic conductors indicate that the quantitative validity of the Smoluchowski equation is dubious for them (25 Refs.)
Kotler and A. Nitzan
Averaged local field intensities in composite films.
Surf. Sci 130 , 124-154 (1983). PDF
The photophysical properties of molecules absorbed in composite films (e.g. surface island films) depend on the local electromagnetic field within the film. the ratio between the average field intensity <|E|2> in the film and the intensity |E1|2 associated with the incident field is a measure of the electromagnetic contribution to the surface influence on molecular photophysical phenomena. This ratio depends on the film composition and morphology, on the dielectric properties of the pure components making the film and on the frequency, direction and polarization of the incident radiation. Calculations of this ratio as a function of these parameters for several models of composite films are presented. Image interactions and retardation effects as wellas radiative damping and finite size contributions to the dielectric response of the film are takeninto account. In addition, an estimate of the field inhomogeneity within the filmis obtained by calculating also the ratio <|E|2>shell/|E|2 associated with the field in this shells surrounding the dielectric particles which constitute the film.
Nitzan and J.C. Tully
Stochastic classical trajectory approach to relaxation phenomena III. Comparison of trajectory results to quantum mechanical perturbation theory.
J. Chem. Phys. 78, 3959-3963 (1983). PDF
A simple model representing an impurity oscillator coupled anharmonically to a lattice is examined both by quantum mechanical perturbation theory and by stochastic classical trajectory simulations. Energy relaxation rates are computed as a function of temperature. Classical and quantum relaxation rates are found to agree well at high temperatures but, as expected, diverge drastically at low temperatures. If zero-point motion of the lattice is incorporated into the classical calculation, classical and quantum relaxation rates agree quite well for all temperatures, even for T0. This suggests that the stochastic classical trajectory method can provide an accurate description of relaxation phenomena even at very low temperatures.
Kirson, R.G. Gerber and A. Nitzan
Excitation and emission of metal electrons in atom surface collisions.
Surf. Sci. 124 , 279-296 (1983). PDF
Electron-hole pair excitation and ionization probabilities are calculated for atomic collisions with metal surfaces at high incident energies. The method adopted is based on a Sudden Collision Approximation, and a realistic model is employed for the bound and continuum electronic states involved. The parameters used in the calculations are for Ar, He, H atoms impinging on a Li surface at 300 eV. The main results are: (1) Only single electron-hole pair excitations are important; multiple pair contributions are small. (2) The transitions are dominated by the behavior of the electronic wavefunctions in the tunneling region and may serve as a probe of this regime. (3) The excitation efficiency is in the order H>>Ar>>He, the effectiveness of hydrogen being due to its stronger, longer-range coupling. (4) The maximum excitation probabilities are for electrons ejected with relatively low excess energies. (5) Total transition probabilities are about 0.5 per collision for H, and about 0.1 for Ar, indicating that these are importent, easily detectable processes. Experiments in this field provide importent information on electronic wavefunctions at the metal-gas, and on gas-metal interactions at high energies.
Carmeli and A. Nitzan
Non Markoffian theory of activated rate processes II. Thermal desorption.
Isr. J. Chem. 22 , 360-364 (1982). PDF
A model for thermal desorption, described by a one dimensional classical generalized langevin equation (GLE) for the motion of an adatom, is solved by reducing the GLE to a fokker planck equation in action space. The escape rate is obtained as the inverse mean furst passage time for the particle to achieve a threshold energy (or action).A calculation using parameters corresponding to the desorption of At form W is compared with quantum mechanical results for the same model.
Carmeli, B.; Tulman, R.; Nitzan, A.; Kalos, M.H.
Random coupling models. IV. Numerical investigation of the dependence on the random coupling distribution and on the initial phases. PDF
Chemical Physics, vol.72, no.3, p. 363-9, 1982 (pt.III is No 55: J. Chem. Phys., vol.72, p.1928 (1980)).
Results of numerical simulations of the time evolution associated with hamiltonians characterized by random coupling matrix elements between dense manifolds of states are presented. It is shown that in the statistical limit (averaged magnitude of the coupling larger than the inverse density of states) the time evolution is independent of the detailed nature of the coupling and depends only on the first and second moments of the random coupling distribution, provided that these moments are finite. If these moments do not exist the golden rule is not obeyed. In the symmetric random coupling model the time evolution is independent of the choice of the initial phases (16 Refs.)
Jacobson, M.A. Ratner and A. Nitzan
Motion mechanism in framework solid electrolytes: Correlated hopping and diffusion.
J. Chem. Phys. 78 , 4154-4161 (1983). PDF
Motion mechanisms for ions in framework solid electrolytes are investigated. The results are
obtained from numerical studies on a one-dimensional model system, utilizing the method of
stochastic Langevin dynamics. We find that, for commensurate systems (for which one mobile
ion occurs exactly every l lattice sites), the mechanism always involves correlated hops, and the
ion–ion repulsion decreases (always) the total conductivity. For incommensurate systems, the
conductivity changes from hopping to liquidlike as the interaction forces are increased to
dominate the potential due to the framework lattice. Different assumed ion–ion potentials
produce different correlations, both local and overall; the nearest-neighbor harmonic forces,
such as are assumed in the Frenkel–Kontorova model, will generally produce substantially
different correlation effects from the Coulomb repulsion. The frequency-dependent conductivity
at low frequency is shown to be proportional to the square of the frequency; the proportionality
coefficient is positive for correlated hopping mechanisms. A double-peaked structure in the
frequency-dependent conductivity, due to local oscillation and to long-time, long-range diffusive
behavior, is observed when particle–particle interactions are absent and damping is weak. The
Journal of Chemical Physics is copyrighted by The American Institute of Physics.
Weitz, S. Garoff, J.I. Gersten and A. Nitzan
The enhancement of Raman Scattering, resonance Raman Scattering and fluorescence from molecules adsorbed on rough silver surfaces.
J. Chem. Phys. 78 , 5324-5338 (1983). PDF
The enhancements of normal Raman scattering, resonance Raman scattering, and fluorescence
from molecules adsorbed on identical, well-characterized, silver-island films are reported. The
enhancement arises from the electromagnetic interaction between the molecules and the
electronic plasma resonance of the silver islands. A hierarchy of enhancement ratios is found,
with typical values of 105 for RS, 103 for RRS and 10 – 1 to 10 for fluorescence, depending on
the quantum yield of the molecular fluorescence. A model, developed on heuristic grounds and
substantiated using the density matrix formalism, describes the light scattering processes and the
effects of the plasma resonance. This model presents a unified picture of the surface-induced
enhancement effects and is consistent with the experimental values. The comparison of all the
forms of optical scattering leads to a complete determination of the role of the plasma
resonances in the various portions of the scattering process. The excitation of the electronic
plasma resonance results in an increased local field at the molecules leading to an increased
excitation or absorption rate. Similarly, the excitation of the plasma resonance by the molecular
emission dipole results in an increase in the radiative decay rate. However, the electromagnetic
coupling of the molecule to the plasma resonance also adds an additional damping channel
which can result in a reduction of the absorption or excitation rate as well as the emission yield.
The resultant balance of these processes leads to the hierarchy in the measured enhancements.
The hierarchy of enhancements is also shown to have important spectroscopic consequences.
The Journal of Chemical Physics is copyrighted by The American Institute of Physics.
Carmeli and A. Nitzan
Non Markoffian theory of activated rate processes I. Formalism.
J. Chem. Phys. 79 , 393-404 (1983). PDF
The escape of a particle from a potential well is treated using a generalized Langevin equation
(GLE) in the low friction limit. The friction is represented by a memory kernel and the random
noise is characterized by a finite correlation time. This non-Markovian stochastic equation is
reduced to a Smoluchowski diffusion equation for the action variable of the particle and explicit
expressions are obtained for the drift and diffusion terms in this equation in terms of the
Fourier coefficients of the deterministic trajectory (associated with the motion without coupling
to the heat bath) and of the Fourier transform of the friction kernel. The latter (frequency
dependent friction) determines the rate of energy exchange with the heat bath. The resulting
energy (or action) diffusion equation is used to determine the rate of achieving the critical
(escape) energy. Explicit expressions are obtained for a Morse potential. These results for the
escape rate agree with those from stochastic trajectories based on the original GLE.
Non-Markovian effects are shown to have large effects on the rate of energy accumulation and
relaxation within the well. The Journal of Chemical Physics is copyrighted by The American
Institute of Physics.
Carmeli and A. Nitzan
Theory of activated rate processes: Bridging between the Kramers limits
phys. Rev. Letters 51 , 233-236 (1983). PDF
The Kramers theory for the escape rate of a Brownian particle moving in a potential well is generalized to account for the full viscosity range. An expression for the escape rate, which is valid for all values of the friction and yields the Kramers results in the appropriate limits, is obtained. Physical Review Letters is copyrighted by The American Physical Society.
Druger, S.D.; Ratner, M.A.; Nitzan, A.
Polymeric solid electrolytes: dynamic bond percolation and free volume models for diffusion.
Solid State Ion. (Netherlands), Solid State Ionics, vol.9- 10, pt.2, p. 115-20 Dec. 1983. PDF
Polymeric solid electrolytes offer a difficult problem from the viewpoint of understanding the charge transport mechanism. While quasithermodynamic theories (configurational entropy, free volume) are useful for rationalizing the behaviour of these materials, they do not really amount to a microscopic picture. The authors have developed a dynamic bond percolation (DBP) model to describe ionic conductivity in these materials. The DBP model is based on a master equation describing ion hops among sites. The percolation aspects are included by making the bonds between sites randomly open or closed. The dynamical aspect is due to the configurational motions of the polymer, and results in the variation of the bond assignments as open or closed. The relationship of DBP to free volume theory is sketched; this involves a specific consideration of kinetic effects on free-volume motion (33 Refs.)
Druger, S.D.; Nitzan, A.; Ratner, M.A.
Dynamic bond percolation theory: A microscopic model for diffusion in dynamically disordered systems. I. Definition and one-dimensional case.
Journal of Chemical Physics, vol.79, no.6, p. 3133-42 15 Sept. 1983. PDF
A dynamic bond percolation model is defined and studied. The model is intended to describe diffusion of small particles (ions, electrons) in a medium which is statistically disordered (as in ordinary bond percolation), but which is also undergoing dynamic rearrangement processes on a timescale short compared to the observation time. The model should be applicable to polymeric solid electrolytes, where the orientational motions of the polymer (which are responsible for configurational entropy) cause the dynamic motion of the medium (polymer) in which the small particles (alkali ions) diffuse. The model is characterized by three parameters: an average hopping rate w which appears in the master equation for hopping, a percentage of available bonds f, and a mean renewal time tau /sub ren/ for dynamic motion of the medium to rearrange the assignments of closed and open bonds. The authors show that the behavior is always diffusive for observation times long compared to tau /sub ren/, in agreement with experiment on polymeric solid electrolytes. They also derive a closed-form expression for the diffusion coefficient. For observation times smaller than the renewal time there is no diffusion, again in accord with the behavior of polymeric solid electrolytes below the glass transition temperature. The diffusion coefficient is a monotonically increasing function of the inverse renewal time and hence of the free volume, the configurational entropy, and the temperature (20 Refs.)
Carmeli, B.; Nitzan, A.
Non-Markovian theory of activated rate processes. III. Bridging between the Kramers limits.
Physical Review A (General Physics), vol.29, no.3, p. 1481- 95 March 1984. PDF
For pt.II see Phys. Rev. Let., vol.51, no.4, p.233 (1983) Kramers' theory of activated processes yields expressions for the steady-state escape rate in the large and small- friction limits and for Markovian dynamics. The present work extends this theory to non-Markovian dynamics and to the whole friction range. Kramers' results are recovered in the appropriate limits (28 Refs.)
Carmeli, B.; Nitzan, A.
Non-Markovian theory of activated rate processes. IV. The double well model.
Journal of Chemical Physics, vol.80, no.8, p. 3596-605 15 April 1984. PDF
The transition rates associated with a particle moving in a double potential well under the influence of thermal noise and friction is considered as a generalization of Kramer's theory of activated rate processes. The authors obtain expressions for these transition rates which are valid for all friction and for a general (non-Markovian) interaction between the particle and its thermal environment. Nonthermal equilibrium effects in the steady state distribution in the well as well as effects of trajectories returning unrelaxed from the far wall are explicitly taken into account. The results reduce to all the previously obtained results of the single well model. The authors use the theory to analyze the experimental results of Hasha et al. (1981) (25 Refs.)
Gersten, J.I.; Nitzan, A.
Resonance optical response of small dielectric clusters.
Physical Review B (Condensed Matter), vol.29, no.7, p. 3852- 62 1 April 1984. PDF
The optical response of small clusters made of two-level molecules is investigated with particular emphasis on the near-resonance region. It is seen that the dielectric- function concept is still useful for describing first-order properties such as particle polarizability and particle- absorption profile; however, near resonance the dielectric response is strongly affected by dephasing and by the energy- level shifts resulting from clustering of molecules in space. Finite-size effects on the dielectric response are also more pronounced near resonance. Second-order response (light scattering) cannot be described by the dielectric function if dephasing processes are important (as they usually are near resonance) and different response functions must be used for different observables. For a cluster of N molecules the light-scattering cross section is made of two contributions: a coherent part (proportional to N/sup 2/) which may be described by the dielectric-function concept and an incoherent part (proportional to N). Implications for surface effects on the optical properties of molecules adsorbed on such clusters arconsidered (22 Refs.)
Gersten, J.I.; Nitzan, A.
Accelerated energy transfer between molecules near a solid particle.
Chemical Physics Letters, vol.104, no.1, p. 31-7 27 Jan. 1984. PDF
The Forster-Dexter theory of energy transfer between molecules is generalized to include the effects of a nearby solid state particle. It is found that the energy transfer rate between a donor and acceptor molecule may be enhanced by many orders of magnitude when the molecular transition frequencies lie in the vicinity of the resonance frequency of the particle and when the particle possesses sharp features. Due to increased damping near the particle, however, this may or may not lead to increased acceptor molecule radiation (6 Refs.)
Carmeli, B.; Nitzan, A.
Theory of activated rate processes: position dependent friction.
Chemical Physics Letters, vol.102, no.6, p. 517-22 9 Dec. 1983. PDF
The non-markoffian generalization of Kramers' theory of activated rate processes is further generalized to the case of position dependent friction in the low-friction limit. A Smoluchowski equation for the action (or energy) of a particle moving in a potential under the influence of position dependent noise and damping kernel is derived and is used to obtain the escape rate (15 Refs.)
Carmeli, B.; Nitzan, A.
Theory of activated rate processes: coupled modes.
Chemical Physics Letters, vol.106, no.4, p. 329-32 27 April 1984.
The thermally activated escape rate of a classical particle out of a potential well is studied in a simple model which includes coupling between the escape (reactive) coordinate and another coordinate. The main effect of the non-reactive coordinate is to open a new (non-markovian) channel between the reactive coordinate and the thermal bath (19 Refs.)
Kirson, Z.; Gerber, R.B.; Nitzan, A.; Ratner, M.A.
Dynamics of metal electron excitation in atom-surface collisions: a quantum wave packet approach.
Surface Science, vol.137, no.2-3, p. 527-50 Feb. 1984. PDF
Electron-hole pair excitations upon atom impact on a metal surface are studied in a framework of a one-dimensional independent-electron model. The method employed treats electron dynamics quantum mechanically and the atom motion classically, and the two are coupled through the time- dependent self-consistent field (TDSCF) approximation. A variational method is used to calculate the time evolution of the electronic wave packet. Calculations were carried out for the colliders, He, Ar and H; the surface parameters were chosen to model Li. Some of the results obtained are: (1) Electron excitation by H is much more efficient than for a rare-gas collider. Experimental search for hole-pair excitations should thus be best pursued with H as a collider. (2) At 0K surface temperature Delta E/E, the fraction of collision energy converted to hole-pair excitations, decreases as the collision energy increases for energies up to approximately 1 eV. At collision energy E=0.01 eV, the fraction of energy transferred is approximately 0.2% for He and approximately 10% for H. (3) Atom trapping due to energy transfer to electrons occurs with high probability (50-100%) at sufficiently low collision energies. Ar trapping takes place at energies below 1K and H trapping below 20K. (4) The calculations show a pronounced transition from atom de-excitation to atom excitation by electron-hole pairs as surface temperature increases. (5) Perturbation theory is tested against the present method. It breaks down mainly for trapping and for temperature effects (32 Refs.)
Liver, N.; Nitzan, A.; Gersten, J.I.
Local fields in cavity sites of rough dielectric surfaces.
Chemical Physics Letters, vol.111, no.4-5, p. 449-54 9 Nov. 1984. PDF
The results of recent experiments which indicate that surface-enhanced Raman scattering from molecules adsorbed on coldly evaporated silver films is associated with cavity sites is interpreted as an electromagnetic field enhancement in regions enclosed by several silver grains. No such enhancement is obtained for a wedge geometry. Cavity sites are seen to be also strong enhancement centers for resonance optical phenomena such as fluorescence and photochemical yield (10 Refs.)
Unimolecular reactions in condensed phases: is the turnover in the viscosity dependence of the rate observable?
Journal of Chemical Physics, vol.82, no.3, p. 1614-16 1 Feb. 1985. PDF
Theoretical studies of unimolecular rate processes in condensed phases predict an initial growth of the rate with solvent viscosity at very low viscosity, then a turnover and a decreasing rate with further increase of viscosity. Hasha et al. (1982) observed this turnover in the rate of ring inversion in cyclohexane solutions. In contrast, such behavior is not observed in the photochemical isomerization of diphenyl butadiene (DPB) even going in solvent viscosity down to 0.04 cp Courtney et al. (1984) recently observed that the rate of DPB photoiosomerization is approximately the same in room temperature liquid ethane and in an isolated (in supersonic jet) molecule having excess energy equal to the thermal energy. This implies rapid intramolecular energy transfer between reactive and nonreactive modes. It has been argued that failure to observe the turnover predicted by the one-dimensional Kramers theory may result from the rapid energy relaxation in large molecules. The present author quantifies this idea within a non-Markovian theory of activated rate processes. The final result is a generalization of the Kramers rate expression which contains the number N of strongly interacting modes as an additional parameter (10 Refs.)
Druger, S.D.; Ratner, M.A.; Nitzan, A.
Generalized hopping model for frequency-dependent transport in a dynamically disordered medium, with applications to polymer solid electrolytes.
Physical Review B (Condensed Matter), vol.31, no.6, p. 3939- 47 15 March 1985. PDF
Protonic diffusion in hydrogen-bonded networks, ionic conduction in polymeric solid electrolytes, and other processes in which the carrier transport mechanism involves motion of the host medium on a time scale comparable to that of the carrier motion itself require generalization of the usual models based on carrier hopping in a static medium. Under the assumption that this concurrent motion of the host can be modeled by a random reassignment (or 'renewal') of hopping probabilities, with a constant probability lambda per unit time for renewal to occur, the effects of host motion on the frequency-dependent diffusion coefficient D( omega ) are now considered. The authors consider both the dynamic bond-percolation model (in which the site-to-site hopping probability is randomly assigned either the value omega or the value 0) and the more general model based on a possibly continuous distribution of hopping rates randomly assigned between different pairs of sites. Under these assumptions, the diffusion coefficient D( omega ) with renewal is shown to be obtainable from D( omega ) without renewal through the formal substitution i omega to lambda +i omega . For the omega =0 limit, an expression is obtained for the time-dependent mean-square displacement with renewal in terms of the mean-square displacement without renewal. These general formal results are applied to the one- dimensional dynamic percolation model, forwhich specific exact analytic results are thereby obtained, and D( omega ) is calculated and studied for this case (44 Refs.)
Liver, N.; Nitzan, A.; Freed, K.F.
Radiative and nonradiative decay rates of molecules adsorbed on clusters of small dielectric particles.
Journal of Chemical Physics, vol.82, no.8, p. 3831-40 15 April 1985. PDF
The authors develop a formalism which extends previous calculations of lifetimes of excited molecular states near planar dielectric surfaces and near single small dielectric particles to situations where the molecule is adsorbed on a cluster made of several dielectric spherical grains. The nonradiative relaxation rate is seen to be relatively weakly dependent on the cluster structure and, if the molecule is adsorbed on one of the grains, is well approximated by the single grain result. The radiative decay rate and hence the quantum yield are much more sensitive to the geometry of the cluster which determines the position (in frequency) of the dielectric resonances of the cluster. The formalism developed here may be used to evaluate local field intensities at different positions within a cluster of dielectric grains under the influence of an external incident field (23 Refs.)
Gersten, J.I.; Nitzan, A.
Photophysics and photochemistry near surfaces and small particles.
Surf. Sci. (Netherlands), Surface Science, vol.158, no.1-3, p. 165-89 July 1985. PDF
The optical response of molecules adsorbed at or near interfaces are known to be strongly modified relative to those of the free molecules. Surface-enhanced Raman scattering is the most prominent example, however practically all molecular optical properties are affected. The authors review the electromagnetic theory of these phenomena with particular emphasis on resonance processes. They discuss lifetimes of excited molecular states, absorption, resonance Raman and fluorescence cross-sections, light scattering and emission yields, energy transfer between adsorbed molecules and photochemical processes. The electromagnetic theory of these phenomena incorporates the surface effect on the local electromagnetic field intensity with the surface-induced radiative and nonradiative decay rates to give working expressions for cross-sections, rates and yields of surface optical processes in terms of the incident beam direction, polarization and frequency, geometry and optical properties of the substrate and its environment and of the optical properties, location and orientation (relative to the substrate) of the adsorbed molecule. Available experimental results are in good qualitative or semiquantitative agreement with the theory. In addition they consider the role of cavity sites in surface-enhanced optical processes. They discuss two models for cavity sites, the conical wedge and enclosures between small particles. The latter are shown to be associated with particularly large enhancements both of the local field intensity and of the surface-induced radiative and nonradiative decay rates. Finally they dwell on the optical properties of small molecular particles which, near the molecular resonance, may give rise to strong local field enhancement provided that the molecules respond coherently to the incident radiation field. They show that the overall response depends on the rate of dephasing processes, which act to drive molecules out of phase with each other. The actual enhancements depend on this rate and on the particle size and shape (59 Refs.)
Kirson, Z.; Gerber, R.B.; Nitzan, A.; Ratner, M.A.
Dynamics of metal electron excitation in molecular dipole- surface collisions.
Surface Science, vol.151, no.2-3, p. 531-42 March 1985. PDF
Electron-hole pair excitation in low energy collisions of dipolar molecules with metal surface are studied in the framework of one-dimensional independent electron model. The motion of the incoming (rigid) molecule is treated classically and is coupled to the electron dynamics, which is treated quantum mechanically through the time dependent self-consistent field (TDSCF) approximation. Model calculations were carried out for NO and HCl molecules colliding with surface of Li and Al. The average fraction of collision energy converted to electron-hole pair excitation ( Delta E)/E and the probability for trapping due to this process were evaluated for collision energies in the range 0.01-10 eV. The effects of the pure dipolar electron- molecule interaction is compared to that of the short range interaction. It is concluded that the (screened) long range dipolar part of the electron-molecule interaction can play an important role in the collisional energy transfer between dipolar molecules and metal surfaces (4 Refs.)
X.M. Hua, J.I. Gersten and A. Nitzan
Theory of Energy Transfer between molecules near solid state particles.
J. Chem. Phys. 83 , 3650-3659 (1985). PDF
The theory of energy transfer between a donor molecule and an acceptor molecule near a solid
state particle is developed. The particle is modeled as a spheroidal shape and the molecules are
allowed to be at arbitrary positions in space. It is found that there exist zones of activity in
which the molecules display significantly enhanced energy transfer. We develop a formalism
which allows us to describe nonradiative and radiative decay and energy transfer in a unified
manner. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.
Nitzan, A.; Persson, B.N.J.
Vibrational dephasing by the exchange mechanism: some new results.
Journal of Chemical Physics, vol.83, no.11, p. 5610-18 1 Dec. 1985. PDF
The exchange model of vibrational phase relaxation is studied. The vibrational line profile is obtained analytically in various limiting cases such as high temperature and large friction. Expressions for the first and second moments of the line profile are also presented (9 Refs.)
Sawada, S.-I.; Nitzan, A.; Metiu, H.
Mean-trajectory approximation for charge and energy- transfer processes at surfaces.
Physical Review B (Condensed Matter), vol.32, no.2, p. 851- 67 15 July 1985. PDF
The authors discuss electronic energy and charge-transfer processes at surfaces in terms of curve-crossing models. They suggest that at low kinetic energies the trajectory approximation should be replaced by a mean-trajectory approximation (MTA), in which the nuclear motion gets feedback from and adjusts to the curve-crossing dynamics. They discuss two derivations of MTA by using an eikonal approximation and a path-integral method. The effects of phonon or electron-hole pair excitations on the charge- transfer process are also incorporated (58 Refs.)
Carmeli, B.; Nitzan, A.
Non-Markovian theory of activated rate processes. V. External periodic forces in the low-friction limit.
Physical Review A (General Physics), vol.32, no.4, p. 2439- 54 Oct. 1985. PDF
For pt.IV see ibid., vol.80, p.3596 (1984). The escape of a particle from a potential well under the influence of both thermal (generalized Langevin) noise and friction and an external periodic driving force is studied in the low- friction limit. The authors consider three models: (a) additive thermal noise and a completely coherent driving force; (b) additive thermal noise and a phase-diffusing driving force; (c) coherent driving force and multiplicative random noise. The last two models are characterized by dephasing which affects the escape dynamics both qualitatively and quantitatively. In all three cases the escape rate is resonantly enhanced; however, while the first case is characterized by a finite energy peak in the steady- state distribution function, the presence of strong dephasing in the other two cases leads to a generalized Boltzmann distribution with an effective temperature which depends resonantly on the external pumping. The relevance of this work to recent experimental results on the resonant activation of a Josephson junction out of its zero-voltage state is discussed (24 Refs.)
Hellsing, B.; Nitzan, A.; Metiu, H.
A fast Fourier transform method for calculating the equilibrium density matrix.
Chemical Physics Letters, vol.123, no.6, p. 523-7 31 Jan. 1986. PDF
The authors calculate the low-temperature quantum density matrix by integrating numerically the Bloch equation. The initial condition is the classical high-temperature value of the density matrix. The integration method uses short 'time' propagators computed by a fast Fourier transform method (19 Refs.)
Whaley, K.B.; Nitzan, A.; Gerber, R.B.
Quantum diffusion of hydrogen on metal surfaces.
Journal of Chemical Physics, vol.84, no.9, p. 5181-95 1 May 1986. PDF
A quantum mechanical theory is presented for the low temperature diffusion of atomic hydrogen on metal surfaces, based on a band model for the hydrogen motion. The theory is applicable to the diffusion of many interacting particles obeying quantum statistics. At low coverage the hydrogen band motion is limited by collisions between adsorbates, giving rise to a decrease of the diffusion constant with concentration. Other aspects of the hydrogen-hydrogen interaction are introduced to explain the coverage dependence at higher adsorbate concentrations. Comparison with recent low temperature diffusion measurements for H, D, and T on W(110) show that the above model reproduces satisfactorily the main features of the experimental coverage dependence of diffusion. The usefulness and limitations of band treatment for heavy particle diffusion are discussed in the light of these results (48 Refs.)
Rosenberg, R.O.; Boughaleb, Y.; Nitzan, A.; Ratner, M.A.
Effective potentials from Langevin dynamic simulations of framework solid electrolytes.
Solid State Ion. Diffus. React. (Netherlands), Solid State Ionics, Diffusion & Reactions, vol.18-19, pt.1, p. 127-35 Jan. 1986. PDF
Ionic motion in framework solid electrolytes constitutes a special sort of classical many-body problem. In such electrolytes, the conductivity is due to the motion of interacting mobile ions modulated by the presence of an essentially immobile framework sublattice. Here, a one- dimensional model of interacting particles, governed by Langevin's equations of motion in a sinusoidal potential, is used to calculate particle distribution functions and effective potentials. The effective potential V/sub eff/(x), is then defined through the density distribution, rho (x), rho (x) varies as e( beta V/sub eff/(x)) where beta =1/kT. The Langevin dynamics simulation is used to calculate rho (x), which in turn gives V/sub eff/(x). The DC conductivity and the other distribution functions can be used to investigate commensurability effects, pinning effects, and screening effects. Comparisons can then be made between correct numerical many-body results and various analytical approximations (42 Refs.)
Harris, C.S.; Nitzan, A.; Ratner, M.A.; Shriver, D.F.
Particle motion through a dynamically disordered medium: the effects of bond correlation and application to polymer solid electrolytes.
Solid State Ion. Diffus. React. (Netherlands), Solid State Ionics, Diffusion & Reactions, vol.18-19, pt.1, p. 151-5 Jan. 1986. PDF
The authors study the effect that correlated renewals have on the transport behavior of the model. Simulations were done on a 1-D lattice and a diffusion coefficient calculated. The values of the diffusion coefficients from the two systems (with and without correlated renewal) are studied and their behaviour as a function of the fraction of available bonds, f, and the renewal time is compared. For both correlated and uncorrelated renewals, the systems were diffusive. The diffusion coefficients, in both cases, increased with increasing f and decreasing tau /sub ren/, corresponding to an increase in the free volume, the configurational entropy, the temperature of the polymer systems. The diffusion coefficient from the correlated systems were always smaller than those from the uncorrelated systems, except for the limit f=100% and tau /sub ren/<< tau /sub hop/. The ratio of the diffusion coefficients for the correlated and uncorrelated systems was studied as a function of tau /sub ren/ and f. This ratio falls off to a constant value as tau /sub ren/ is increased and reaches minimum value at f=50%. This behavior of the ratio as a function of f can be explained by considering the diffusion of the bonds in the lattice for the correlated case (14 Refs.)
Boughaleb, Y.; Rosenberg, R.O.; Ratner, M.A.; Nitzan, A.
Correlation effects on ionic motion in framework solid electrolytes
Solid State Ion. Diffus. React. (Netherlands), Solid State Ionics, Diffusion & Reactions, vol.18-19, pt.1, p. 160-8 Jan. 1986. PDF
The authors investigate the static and dynamic properties of a one-dimensional system composed of Brownian particles subject to a periodic potential by using Langevin dynamics simulation. In addition to different types of interaction between the mobile particles, They study the effect of the coupling of the diffusing particle with the crystalline cage. For each kind of interaction potential, they also discuss how the bulk frequency-dependent conductivity is affected by the correlated motion of the particles (24 Refs.)
Druger, S.D.; Ratner, M.A.; Nitzan, A.
Applications of dynamic bond percolation theory to the dielectric response of polymer electrolytes.
Solid State Ion. Diffus. React. (Netherlands), Solid State Ionics, Diffusion & Reactions, vol.18-19, pt.1, p. 106-11 Jan. 1986.
The authors' recently-developed dynamic bond percolation model is extended and applied to polymer electrolytes by assuming an approximate form for the relaxation of the carrier mean-square displacement to its asymptotic value below the percolation threshold, with similar assumptions for the short-range motion of the ionic charges bound to the polymer host. The parameters characterizing the long-range- motion part of the carrier response are shown to be fully determined in terms of the bond percolation parameters, thereby allowing comparison with the exact analytic solution presently available only in one dimension. The behavior of the dielectric response based on the assumed functional form of <r2/sup >//sub 0/(t) (the mean-square carrier displacement from its initial position in a frozen lattice) is shown to be given by a sum of Debye dielectric loss peaks, and is compared with frequency-dependent data for PEO.NaSCN (11 Refs.)
Non-Markovian theory of activated rate processes. VI. Unimolecular reactions in condensed phases.
Journal of Chemical Physics, vol.86, no.5, p. 2734-49 1 March 1987. PDF
For pt.V see Phys. Rev. A, vol.32, p.2439 (1985).The non- Markovian theory of activated rate processes developed by Carmeli and Nitzan (1984) is applied to investigate unimolecular reactions in condensed phases with particular emphasis on the molecular size (number of internal degrees of freedom) dependence of the effect of solvent friction on the reaction rate. The model consists of one reaction coordinate coupled to n-1 nonreactive modes. The molecule solvent interaction is treated within the context of the generalized Langevin equation. The reaction dynamics may be roughly described as two consecutive processes: the well (energy diffusion) dynamics where it is assumed that fast intramolecular vibrational relaxand slower overall molecular energy diffusion dominate the process, and the barrier dynamics where it is assumed that the motion along the reaction coordinate is only weakly coupled to the nonreactive modes. This model leads to a result for the reaction rate which, as in the one-dimensional case, is obtained as the inverse of the sum of two times: the barrier crossing time and the energy diffusion time. The latter is very sensitive to molecular size and becomes extremely short for large molecules. Correspondingly, the Kramers turnover region is predicted to occur for low molecular weight solvent in the high pressure gas phase, as was found in recent experiments. For higher viscosities the rate is dominated by the barrier crossing time with a large (larger for larger molecules) transition state rate plateau and with a falloff for high viscosities. Recent interesting results by Straub et al. (1986) which have pointed out the dominance of spatial diffusion in the well for extremely high viscosities (overdamped well motion) are argued to be irrelevant for most molecular situations (76 Refs.)
Gersten, J.I.; Nitzan, A.
Path integral approach to electrostatic problems.
Journal of Chemical Physics, vol.86, no.6, p. 3557-64 15 March 1987. PDF
A theory that is able to account for electrostatic effects in microscopic situations is formulated in terms of the path integral method. The theory relates the solution of the Poisson equation to the propagator of the diffusion equation. Applications are made to some typical problems of interest, such as the solvation energy of an ion in a solution and to the electrical properties of a diffuse surface (7 Refs.)
Gersten, J.I.; Nitzan, A.
Path-integral approach to electromagnetic phenomena in inhomogeneous systems.
Journal of the Optical Society of America B (Optical Physics), vol.4, p. 293-8 Feb. 1987. PDF
The authors derive a path-integral expression for the time- evolution operator associated with the Maxwell's equations in an inhomogeneous medium and show that its asymptotic behavior for large light velocity corresponds to geometrical optics. They also describe a path-integral approach to the solution of the Laplace equation in an inhomogeneous medium. This approach leads to new numerical methods for the solution of Laplace and Poisson equations in inhomogeneous media of irregular shape. An expression for the image potential near a surface with continuously changing dielectric function is also derived (1 Refs.)
Activated rate processes in condensed phases, the Kramers theory revisited
Adv. Chem. Phys. 70 489-555 (1988). PDF
11. The Kramers Treatment
A. Moderate to Large Damping
B. Low Damping
111. The Need for Generalization of the Kriiiiers Theory
IV. The Generalized Kramers Model
V. Non-Markovian Effects in the One-Diiiiciisional Case
VI. The Escape Rate of a Non-Markov Multidimensional Process
A. Barrier Dynamics
B. Well Dynamics
C. The Combined Solution
VIT. Escape in the Presence of External Periodic Force: The Low-Friction Limit
A. Phase-Diffusing Driving Field
B. External Oscillating Force in the Fast Thermal Dcphasing Limit
VIII. Numerical Results and Applications
Apr,cndix A. Evaluation of the Reactive Mo(le Well Distribution Appendix B. Evaluation of T (Eqs. (6.51)]
Nitzan, A.; Druger, S.D.; Ratner, M.A.
Random walk in dynamically disordered systems.
Philos. Mag. B, Phys. Condens. Matter Electron. Opt. Magn. Prop. (UK), Philosophical Magazine B (Physics of Condensed Matter, Electronic, Optical and Magnetic Properties), vol.56, no.6, p. 853-9 Dec. 1987.
The theory of carrier transport in a disordered system has to be modified when the host medium undergoes microscopic structural changes on a time-scale comparable with or shorter than the observation time. This paper reviews the results obtained to date for models that take into account the dynamic nature of the disorder, and their application to ionic motion in polymeric ionic conductors (11 Refs.)
Makov, G.; Nitzan, A.; Brus, L.E.
On the ionization potential of small metal and dielectric particles.
Journal of Chemical Physics, vol.88, no.8, p. 5076-85 15 April 1988. PDF
The ionization potential of small metal and dielectric spheres is considered in different frameworks: classical, semiclassical, and quantum mechanical density functional approach. Classical calculations give conflicting results, and the generally accepted result for the ionization potential of a metal sphere of radius R:W/sub I/(R)=bulk work function+(3/8)q/sup 2//R is shown to be wrong, resulting from the classical image potential too close to the metal surface. Using appropriate cutoff to the image potential, the result W/sub I/(R)=bulk work function+(1/2)q/sup 2//R (previously obtained from solvation energy considerations) is recovered. Experimental results on relatively large particles are in agreement with the latter result. For very small clusters, deviations of experimental results from this classical behavior are shown by a density functional calculation to arise from quantum mechanical effects. These are first the spilloff of the electronic wave functions beyond the cluster edge and secondly from exchange and correlation contributions (22 Refs.)
Liver, N.; Nitzan, A.; Amirav, A.; Jortner, J.
The effect of small cluster environment on molecular oscillator strengths and spectra.
Journal of Chemical Physics, vol.88, no.6, p. 3516-23 15 March 1988. PDF
The authors present an electrostatic theory of the effect of small atomic cluster environment on molecular oscillator strength and spectra. The molecular dipole is represented by a classical oscillating charge distribution and the cluster atoms by spherical polarizable particles. From the general theoretical results, the authors calculate the effect of cluster size and geometry on the molecular radiative lifetime and the spectral shift. These properties exhibit a considerable sensitivity to the cluster and molecular geometry, i.e., the cluster size and structure, the molecule- atom(s) distance(s), the spatial size of the molecular transition dipole, and molecular orientation within the cluster. The reduced plot of the relative change in the oscillator strength vs. the relative frequency shift seems to have universal character and is useful in analyzing and predicting experimental trends. Available experimental results are consistent with the theoretical predictions (14 Refs.)
Kotler, Z.; Nitzan, A.
Traversal time for tunneling: local aspects.
Journal of Chemical Physics, vol.88, no.6, p. 3871-8 15 March 1988. PDF
The relationship between inelastic tunneling processes and the traversal time for tunneling is studied with emphasis on the local aspects of the tunneling time. Viewed in this framework, the local tunneling time is shown to be a dominant factor in determining the inelastic tunneling probability. It is shown that the Buttiker-Landauer semiclassical formalism (1982, 1985) when generalized to the case of local interactions and applied to the calculation of inelastic tunneling probabilities, gives results identical to other perturbation theory calculations such as the Bardeen formula. Analytical results derived for square potential barrier are shown to hold also for strongly biased barriers. Application to inelastic tunneling in typical scanning tunneling microscope configuration are discussed (19 Refs.)
Matkowsky, B.J.; Nitzan, A.; Schuss, Z.
Does reaction path curvature play a role in the diffusion theory of multidimensional activated rate processes?
Journal of Chemical Physics, vol.88, no.8, p. 4765-71 15 April 1988. PDF
The two-dimensional Kramers' barrier crossing problem in the overdamped (diffusion) limit is investigated with particular attention given to possible effects of the geometry of the potential surface on the rate. Previous work ascribes corrections to the two-dimensional Kramers' formula to curvature of the reaction path. In contrast, the authors find that these corrections are due to the anharmonicity of the potential surface at the saddle and may become appreciable for small windowfrequency, i.e. flat potential surface at the saddle in the direction perpendicular to the reaction path. A general formalism to calculate such corrections is described (28 Refs.)
Barnett, R.N.; Landman, U.; Nitzan, A.
Dynamics and excitations of a solvated electron in molecular clusters.
Physical Review A (General Physics), vol.38, no.4, p. 2178- 81 15 Aug. 1988. PDF
A method for investigations of the ground and excited states and the dynamical evolution of coupled quantum-classical systems is presented. A time-dependent self-consistent-field procedure is used where the time evolution of the wave function is evaluated with use of fast Fourier transforms and the coupled classical motion is treated via classical molecular dynamics. Different modes of simulations are demonstrated for electron attachment to NaCl and water clusters (16 Refs.)
Barnett, R.N.; Landman, U.; Nitzan, A.
Dynamics and spectra of a solvated electron in water clusters.
Journal of Chemical Physics, vol.89, no.4, p. 2242-56 15 Aug. 1988. PDF
The dynamics and spectra of negatively charged water clusters, containing a single excess electron, are investigated. The atomic water constituents of the clusters are treated classically while the excess electron is described quantum mechanically using the fast Fourier transform algorithm to solve the Schrodinger equation. Information about ground and excited electronic states corresponding to the equilibrium, finite temperature, ground- state ensemble configurations can be obtained by solving for these states for given nuclear configurations generated via quantum mechanical path-integral molecular dynamics simulations. As an alternative, more efficient way, the authors introduce the adiabatic simulation method which consists of propagating the nuclei in real time while concurrently annealing the electronic wave functions to their correct values corresponding to the instantaneous, dynamically generated nuclear configurations. The resulting trajectories can be used for analyzing nuclear motion in the ground electronic state as well as for calculating energy distributions for the ground and excited electronic states and the (vertical) excitation line shape. They study the cluster size effect on these quantities, and in particular, by comparing results for (H/sub 2/O)/sub 64//sup -/ and (H/sub 2/O)/sub 128//sup -/, the authors conclude that the vertical ionization potential increases while the vertical excitation energy to the bound excited state decreases for larger cluster sizes. For the smallest negatively charged water cluster (H/sub 2/O)/sub 2//sup -/, where adiabatic separation of electronic and nuclear motion does not hold, they simulate the time evolution in the TDSCF approximation. The dynamics reveals the close correlation between the electronic binding energy and the cluster dipole, and provides information on intramolecular and intermolecular vibrational motion (56 Refs.)
Ratner, M.A.; Nitzan, A.
Fast ion conduction: some theoretical issues.
Solid State Ion. Diffus. React. (Netherlands), Solid State Ionics, Diffusion & Reactions, vol.28-30, pt.1, p. 3-33 Sept. 1988. PDF
Recent progress in the theoretical understanding of fast ion conduction in solids is discussed, with emphasis paced on mechanistic behavior and on the characteristic features of particular sorts of solid electrolytes. The authors consider soft framework materials such as alpha -Ag, and hard framework materials such as beta "-alumina. In each case, they discuss which theoretical methods have been used to investigate mechanisms of conductivity and diffusion and some of the physical insights which have been gleaned on the mechanism of ionic conductivity. Comments are also made on glassy conductors such as glassy lithium aluminosilicate, and polymeric ionic conductors such as polyethylene oxide/lithium triflate. Since different characteristic timescales, and characteristic energies, are appropriate for these different classes of materials, varying theoretical methods have been used, and should be used, to understand the ionic motion. Particular concepts, such as dynamic percolation in polymer electrolytes strong memory effects in soft framework materials, strongly correlated liquid-like diffusion in hard framework materials and disorder-induced weakening of correlations ion glassy materials are pointed out. They speculate briefly on the role of very strong interionic correlation in causing possible domain-wall conduction, a process that goes well beyond any hopping description. They briefly discuss some special behavior observed in certain classes of solid electrolytes, such as fractal behavior, 'universal dielectric response', the mixed alkali effect in glasses, and the 'Liang effect', which is the enhancement of ionic conductivity by inclusion of an insulating second phase. Remarks are ventured both on theoretical methodology and on the usefulness of models for understanding, predicting and designing solid electrolyte behavior (139 Refs.)
Granek, R.; Nitzan, A.; Druger, S.D.; Ratner, M.A.
Dynamics of ionic motion in polymeric ionic conductors.
Solid State Ion. Diffus. React. (Netherlands), Solid State Ionics, Diffusion & Reactions, vol.28-30, pt.1, p. 120-8 Sept. 1988. PDF
Carrier transport in disordered systems is often treated theoretically using random hopping models. When the host medium is a polymer above its glass transition temperature, such theories have to be modified to account for microscopic structural changes in the polymer on the experimental timescale. This paper describes the results obtained to date for models that take into account this dynamic nature of the disorder, and their applications to ionic motion in polymeric ionic conductors (24 Refs.)
Kurizki, G.; Nitzan, A.
Theory of stimulated emission processes in spherical microparticles.
Physical Review A (General Physics), vol.38, no.1, p. 267-70 1 July 1988. PDF
A semiclassical theory of stimulated processes in dielectric spherical particles is formulated. The theory applies to the small-signal regime and to isotropic (but radially nonuniform) pumping. Iterative treatment of the pumped- medium susceptibility by scattering theory demonstrates the basic features observed experimentally by Chang and co- workers (H.M. Tzeng, K.F. Wall, M.B. Long, and R.K. Chang, Opt. Lett. vol.9, p.499 (1984); S.X. Qian and R.K. Chang, Phys. Rev. Lett. vol.56, p.926 (1986)), namely, the drastic reduction of the threshold for lasing and multiorder stimulated Raman processes, and the frequency pulling from Mie resonances of the inactive medium (15 Refs.)
Kotler, Z.; Nitzan, A.; Kosloff, R.
Multiconfiguration time-dependent self-consistent field approximation for curve crossing in presence of a bath. A fast Fourier transform study.
Chemical Physics Letters, vol.153, no.6, p. 483-9 30 Dec. 1988.
The applicability of the multiconfiguration time-dependent self-consistent field approximation (MCTDSCF) for the dynamics of curve crossing processes under the influence of 'external' degrees of freedom is tested on a simple model. The fast Fourier transform (FFT) algorithm for solving the time-dependent Schrodinger equation is used to solve the exact equations of motion and the corresponding approximate ones. Good agreement is obtained in adiabatic as well as in nadiabatic situations (10 Refs.)
Granek, R.; Nitzan, A.; Weitz, E.
Vibrational energy transfer in solutions: from diffusive to impulsive binary collisions.
Journal of Chemical Physics, vol.89, no.9, p. 5589-97 1 Nov. 1988. PDF
The effect of diffusion on energy transfer from excited donor to acceptor molecules in liquid solutions is studied with particular attention focused on vibrational energy transfer between solute molecules in dilute solutions. Such processes are often discussed in the independent binary collision (IBC) framework and diffusion effects are assumed to be negligible. The authors introduce the concept of diffusive collisions (encounters between acceptor and donor molecule within an effective energy transfer range) and investigate the conditions under which the cross section for the energy transfer process may be affected by the cross section for the diffusive collision as opposed to the more common fast diffusion limit where the energy transfer is dominated by direct binary collisions. They conclude that while in most common situations vibrational energy transfer is indeed dominated by binary collision events, pronounced diffusion effects should exist at moderately high pressures. Explicit estimates are provided for the HCl/Xe system (26 Refs.)
Barnett, R.N.; Landman, U.; Nitzan, A.
Dynamics of electron localization, solvation, and migration in polar molecular clusters.
Physical Review Letters, vol.62, no.1, p. 106-9 2 Jan. 1989. PDF
The time evolution of electron localization, migration, and solvation in water and ammonia clusters is investigated via computer simulations. The attachment of an electron to a cold molecular cluster in a diffuse weakly bound surface state, the dynamics of solvation, the nonhopping mechanism of migration leading to the formation of an internally solvated state, and the spectral manifestation of these processes are demonstrated (17 Refs.)
Matkowsky, B.J.; Nitzan, A.; Schuss, Z.; Larson, R.S.
Comment on the role of reaction path curvature in diffusional barrier crossing processes (and reply).
Journal of Chemical Physics, vol.90, no.2, p. 1292-3 15 Jan. 1989. PDF
For original paper see Matkowsky, Nitzan and Schuss ibid., vol.88, p.4765 (1988). Matkowsky et al. (MNS) examined the 2D version of Kramers theory of activated rate processes in the high-friction limit. Larson comments that he feels the interpretation of MNS is rather misleading and that some of their equations are incorrect, Matkowsky et al. reply to these comments and point out that their disagreement with Larson concerns not the results but their interpretation (9 Refs.)
Granek, R.; Nitzan, A.
Correlated dynamic percolation: many bond effective-medium theory.
Journal of Chemical Physics, vol.90, no.7, p. 3784-94 1 April 1989. PDF
The authors study the diffusion (and conductivity) associated with the random walk of noninteracting particles on a disorder lattice characterized by bond disorder, temporal rearrangement, and spatial correlations. The paper extends previous works on dynamic bond percolation processes to situations where spatial correlations in the rearrangement process are important. Many bond effective- medium theory is used to obtain the effective diffusion coefficient D/sub eff/ ( omega ) in such systems. The resulting D/sub eff/ ( omega ) depends on the frequency through combinations of the form omega -i/ tau /sub j/ where tau /sub j/ are characteristic relaxation times associated with the rearrangement process. They analyze in detail a model combining single bond renewal with a two bond exchange process. The resulting DC ( omega =0) diffusion coefficient shows a new percolation threshold for the bond exchange model (in the absence of single bond renewal which eliminates the threshold altogether), and a crossover between the different limiting behaviors is seen as the different kinds of renewal process are switched on and off. Implications for ionic transport in polymeric ionic conductors are discussed (25 Refs.)
Klosek-Dygas, M.M.; Hoffman, B.M.; Matkowsky, B.J.; Nitzan, A.; Ratner,
M.A.; Schuss, Z.
Diffusion theory of multidimensional activated rate processes: the role of anisotropy.
Journal of Chemical Physics, vol.90, no.2, p. 1141-8 15 Jan. 1989. PDF
The authors consider an anisotropic multidimensional barrier crossing problem in the Smoluchowski (diffusion) limit. The anisotropy arises from either or both the shape of the potential energy surface and anisotropic diffusion. In such situations, the separatrix, which separates reactant and product regions of attraction, does not coincide with the ridge of the potential surface, which separates reactant and product wells, thus giving rise to a complicated time evolution. In the asymptotically long time limit, the time evolution is governed by crossing the separatrix and is exponential with a rate which may be obtained as a generalization of Kramer's theory to the anisotropic situation. In contrast, in long, though not asymptotically long times, the time evolution is dominated by repeated crossings of the ridge, and is nonexponential. Such nonexponential time evolution has been observed in many biochemical reactions, where many degrees of freedom and anisotropic diffusion processes lead to complicated dynamical behavior. The author's model provides a simple prototype of such situations (14 Refs.)
Berezhkovskii, A.M.; Zitserman, V.Yu.; Klosek, M.M.; Hoffman, B.M.;
B.J.; Nitzan, A.; Ratner, M.A.
Comment on: Diffusion theory of multidimensional activated rate processes: the role of anisotropy (and reply).
Journal of Chemical Physics, vol.95, no.2, p. 1424-6 15 July 1991. PDF
Noise-induced particle escape from a multidimensional potential well in an anisotropic situation was simultaneously treated by Klosek et al. and in the authors' papers. However, some of the results obtained in these papers differ significantly. The authors show that some of the results obtained by Klosek et al. are incorrect (14 Refs.)
R.N. Barnett, U. Landman and A. Nitzan
Relaxation dynamics following transitions of solvated electrons.
J. Chem. Phys. 90, 4413-4422 (1989). PDF
Relaxation dynamics following an electronic transition of an excess solvated electron in clusters and in bulk water is studied using an adiabatic simulation method. In this method the solvent evolves classically and the electron is constrained to a specified state. The coupling between the solvent and the excess electron is evaluated via the quantum expectation value of the electron–water molecule interaction potential. The relaxation following excitation (or deexcitation) is characterized by two time scales: (i) a very fast (~ 20–30 fs) one associated with molecular rotations in the first solvation shell about the electron, and (ii) a slower stage (~ 200 fs), which is of the order of the longitudinal dielectric relaxation time. The fast relaxation stage exhibits an isotope effect. The spectroscopical consequences of the relaxation dynamics are discussed. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.
Doan, K.E.; Druger, S.D.; Shriver, D.F.; Ratner, M.A.; Nitzan, A.
Coulomb trapping effects in polymer solid electrolytes: a simulation study of stoichiometry dependence.
Mol. Cryst. Liq. Cryst. (UK), Molecular Crystals and Liquid Crystals, vol.160, p. 311-19 1988.
The effects of interionic attractive interactions on the diffusion of a tracer ion in polyelectrolytes are studied using a one-dimensional hopping model. In this model the tracer cation is assumed to interact with anions placed at regular distances apart, but all inter-cation repulsions are ignored. The effects of both anion density and temperature on the diffusion of the tracer were evaluated through simulation. The tracer is found no longer to undergo simple diffusion, but to display two different diffusion rates, one for local diffusion near an anion, and another slower rate for long-range diffusion. The local diffusion rate varies little with either stoichiometry or temperature, whereas the long-range diffusion is highly correlated to these variables. These behaviors are relevant to ion-pair trapping in polymer electrolytes (21 Refs.)
U. Landman W.D. Luedtke and A. Nitzan
Dynamics on Tip-substrate Interactions in Atomic Force Microscopy
Surf. Sci. Letters 210 L177-L184 (1989). PDF
Dynamical interactions between a scanning tip and a silicon substrate are investigated using molecular dynamics simulations of both the constant-height and constant-force scan modes. Localized temporary and permanent modifications of the substrate occur, depending on tip-substrate separation and scan geometry. Implications for resolving structural and force characteristics in scanning tip spectroscopies, employing atomically sharp as well as large ordered of disordered tips are discussed.
Barnett, R.N.; Landman, U.; Nitzan, A.
Dynamicsof excess electron migration, solvation, and spectra in polar molecular clusters.
Journal of Chemical Physics, vol.91, no.9, p. 5567-80 1 Nov. 1989. PDF
The dynamics of excess electron localization, migration, and solvation in water and ammonia clusters, and the time- resolved spectroscopic consequences of these processes, are investigated via computer simulations. In these simulations, the solvent evolves classically and the electron propagates in the ground state. The coupling between the polar molecular cluster and the electron is evaluated via the quantum expectation value of the electron-molecule interaction potential. Starting from an electron attached to a cold molecular cluster in a diffuse weakly bound surface state, temporal stages of the electron solvation and migration processes, leading to the formation of an internally solvated state, and the associated variations in the excitation spectra are described. The migration of the excess electron during the penetration is characterized by a nonhopping, polaronlike mechanism (58 Refs.)
M.A. Ratner and A. Nitzan
Conductivity in Polymer Ionics: Dynamic Disorder and Correlations
Faraday Discuss. Chem.Soc. 88,19-42(1989). PDF
Theoretical constructs are developed for discussing diffusivityand conductivity in polymer ionic materials. Such meterials are characterized by extensive disorder, either static (lack of long-range order) or static and dynamic (lack of long-range order with short-range order evolving with time). Beginning with a dynamic percolation model, we show that, in general, so long as the mean-square displacement of the charged particle obeys a certain growth law, the observed charged-particle motion willbe diffusive, both in the ballistic regime, corresponding to electronic motion with strong scattering, and in the ionic-hopping regime, corresponding to dynamic disorder renewal of the hopping situation. Some general behaviour for transport under these conditions is predicted, including definite statments about the frequency dependence of the conduction, the relationship between the growth law in a single interval and the growth law for observation times long compared to scattering or renewal times, and the behaviour in the neighbourhood of the percolation threshold for the static problem. Interpretations are suggested both for ion and electron-hopping situations.
A statistical thermodynamic model is developed for analysis of contact ion pair formation and its effect on conductivity in ion-conducting polymer systems. In this model, the energy (due to solvation and polarization) favouring formation of a homogeneous complex in which the cations are solvated by the polymer host, competes with an entropic term favouring the seperated strctures (free polymer and contact ion pairs). we derive general conditions for this phage separation, and an expression for the number of polymer-bound, homogeneously solvated ions. we show that this number will, in general, decrease monotonically with increase in temperature, due to entropic favouring of the phase-separated material, this is reminiscent of the lower consolute temperature phenomenon in liquid mixtures.
M.A.Ratner S.D.Druger and A.Nitz/B
Polymeric electrolytes and polyelectrolytes: Salt concentration and domain effects on conductivity.
Mat.Res Soc.Symp.Proc. 135,13-25(1989)
Solvent-free polmer electrolytes and polyelectrolytes are usually studied at quite high ionic concentrations, (into the range above 1M). Under these conditions, correlations, effects arising from ion-polymer and ion-ion interactions are expected to be important in the mechanism of conductivity. We sketch some specific ionic effects, separating those scting on the mobility from those effecting carrier concentration. Mobility effects include reduction of thefluidity due to the effective cross-linking by cations, screening of applied fields due to high ionic concentrations, frictional drag due to counterion motion, and in some polymer hosts, lowered local availability of cation solvation sites due to reduction of the number of coordinating basic oxygens. Reduction of the carrier density from its stoichiometric value can be discussed in terms of a generalized ion-pairing model. Though the concentration usually studied are so high that Dybye-Huckel theory is invalid and the stoichiometric average cation-anion separation is smaller then the Bjerrum length (a situation in which ordinary electrolyte theory considers all ions paired), nevertheless consideration in terms of contact ion pairs, solvent seperated ion pairs and mean stoichiometric separation can be used to compute the effective concentration of carriers. Estimates based on an electrostatic continuum, cavity model for the binding energy of a pair describe the reduction of effective carriernumber observaed in poly (propylene oxide) materials.
Barnett, R.N.; Landman, U.; Dhar, S.; Kestner, N.R.; Jortner, J.;
Quantum simulations and ab initio electronic structure studies of (H/sub 2/O)/sub 2//sup -/.
Journal of Chemical Physics, vol.91, no.12, p. 7797-808 15 Dec. 1989. PDF
The energetics of the negatively charged water dimer (H/sub 2/O)/sub 2//sup -/, is studied using quantum-simulation techniques and ab initio electronic structure calculations. Using the RWK2-M potentials for water and a pseudopotential for the interaction of an electron with a water molecule in the ground state, consisting of Coulomb, adiabatic polarization, exclusion, and exchange contributions, it was found via the quantum path-integral molecular dynamics and the coupled quantum-classical time-dependent self-consistent field methods that while the minimum energy of (H/sub 2/O)/sub 2//sup -/ corresponds to a nuclear configuration similar to that found for the neutral (H/sub 2/O)/sub 2/ cluster, other nuclear configurations are also exhibited at finite temperature, characterized by a higher total molecular cluster dipole moment and a larger magnitude of the excess electron binding energy. Quantitative agreement is found between the results obtained by the quantum simulations, employing the excess electron-molecule pseudopotential, and those derived, for selected nuclear configurations, via ab initio calculations, employing the Gaussian 86 code with the basis set for the water molecules supplemented by a large diffuse set located at the midpoint of the two oxygens and in addition by a diffuse set for the excess electron (61 Refs.)
Druger, S.D.; Ratner, M.A.; Nitzan, A.
Charge carrier mobility in polymer materials: mechanisms in polymer electrolytes, and relationships to electronic conductors.
Mol. Cryst. Liq. Cryst. (UK), Molecular Crystals and Liquid Crystals, vol.190, p. 171-83 1990.
Generalized renewal (or continuous-time random walk) models provide a systematic way to describe the dependence of conductivity in polymer systems upon the dynamical motions of the host material. For polymer electrolytes, dynamic disorder hopping models, or dynamic percolation models, provide an attractive kinetic description of the transport. In this picture, the mobility of an (assumed independent) ionic carrier is proportional to the inverse mean renewal time, or structural relaxation time, of the host material. Since structural relaxation times generally display WLF type behavior, so does the ionic conductivity in polymer electrolytes. In electronically conductive redox polymers, the mobility is determined by a hopping process, and should to lowest order be independent of microscopic renewal and relaxation times of the host material. In band type electronically conductive polymers, the renewal time can be identified with the scattering time, and more rapid renewal results in decreased carrier mobilities. Some formal results, and interpretations of ionic conductivity in polymer electrolytes, are stressed (37 Refs.)
Granek, R.; Nitzan, A.
Dynamic percolation theory for diffusion of interacting particles.
Journal of Chemical Physics, vol.92, no.2, p. 1329-38 15 Jan. 1990. PDF
The recently developed dynamic percolation theory is used to solve the problem of diffusion of interacting particles in lattice-gas models within an effective medium approximation. The approach is based on the observation that the motion of a tracer particle in a system of (similar or different) particles can be viewed as particle motion in a changing random environment. This makes it possible to use effective medium theory (EMT) solutions to the latter problem. The main conceptual problem of this approach is to relate the characteristic microscopic times for the evolution of the disordered background to the macroscopic diffusion. The authors discuss and compare several possible ansatzs for this relation and conclude that relating these times to the chemical diffusion rate is the most reasonable simple choice. Using this ansatz, they obtain EMT approximations for the tracer diffusion coefficient in the noninteracting lattice-gas (NILG, blocking interactions only) model and an approximate EMT relation between the chemical and the tracer diffusion coefficients in a lattice gas with nearest- neighbor interactions. Agreement with available simulation results is good whenever single bond EMT is expected to be reliable (39 Refs.)
R.N.Barnett, U.Landman, G.Rajagopal and A.Nitzan
Dynamics, spectra and relaxation phenomena of excess electrons in clusters.
Israel J.Chem., 30,85-105(1990). PDF
In this paper, we review quantum simulation methods for studies of coupled quantum-classical systems and their applications in investigations of dynamics, spectra, and relaxation phenomena of excess electrons in polar molecular and ionic clusters.
M.A.Ratner, A.Nitzan and D.W.Skinner
Frequency-dependent diffusion in a spherical cavity: The effects of domain structure on ionic conduction in polymer electrolytes.
J.Chem.Phys. 92,4491-4500(1990). PDF
The effects of domain structure on the low-frequency conductivity response of a polymer electrolyte having low carrier concentration are investigated by modeling the domains as spheres. For zero leakage (no dc conductivity), the diffusion equation is solved exactly. The results are also extended approximately to the case of small but nonzero leakage by imposing physically reasonable approximate boundary conditions together with an ad hoc procedure for treating the diffusion in the less conductive exterior. Interaction between charge carriers in different domains is taken into account in the Maxwell–Garnet approximation and found to have only a small effect for physically reasonable parameter values. The predicted diffusive behavior is studied and the results are applied to examine the predicted behavior of the frequency-dependent conductivity. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.
Penner, A.; Amirav, A.; Jortner, J.; Nitzan, A.; Gersten, J.
Solvation effects on molecular pure radiative lifetime and absorption oscillator strength in clusters.
Journal of Chemical Physics, vol.93, no.1, p. 147-58 1 July 1990. PDF
The solvation effects on the molecular pure radiative lifetime, its absorption line shape, oscillator strength, and spectral red shift are studied for 9, 10- dichloranthracene embedded in clusters of argon, krypton, and xenon. The clusters are synthesized in a supersonic free- jet coexpansion of the organic molecule with the rare gas. Cluster size is controlled by the nozzle backing pressure and its pure radiative lifetime is obtained by measuring both the fluorescence lifetime and the absolute emission quantum yield. For small (jet atom) clusters the pure radiative lifetime is increased by subsequently adding rare gas atoms. For up to two rare gas atoms this increase correlates with the atomic polarizabilities and with the spectral red shift. For Ar and Kr this trend of increasing radiative lifetime continues up to clusters of six rare gas atoms. These results are in good agreement with calculations based on classical electromagnetic theory using point polarizable dipoles for the atom and a simplified charge distribution for the molecule. For large clusters of Ar (up to approximately 1000 atoms) both the spectral red shift and the lifetime become cluster size independent. This is also in agreement with classical electromagnetic theory using a model of a point (molecular) dipole embedded in a dielectric (rare gas) sphere. Both experiment and theory indicate that the radiative lifetime in this limit is still larger than that of the free molecule, which in itself is longer than that expected in the bulk solvent. This implies that a further cluster size evolution of this quantity is expected upon increasing the cluster size above the radiation wavelength. The authors also report on a sudden lineshape broadening and a slight spectral blue shift that accom the growth of large molecule-argon clusters and which they interpret as originating from a possible transition towards the surface of the molecule in order to minimize growth strain (25 Refs.)
Barnett, R.N.; Landman, U.; Makov, G.; Nitzan, A.
Theoretical studies of the spectroscopy of excess electrons in water clusters.
Journal of Chemical Physics, vol.93, no.9, p. 6226-38 1 Nov. 1990. PDF
Variational calculation based on a continuum dielectric model, and numerical simulations based on the RWK2-M water potential and on a pseudopotential for the electron-water interaction, are used to evaluate excitation energies and optical spectra for bound interior states of an excess electron in water clusters and in bulk water. Additionally, optical data for surface states are obtained from numerical simulations. The simulation approach uses adiabatic dynamics based on the quantum-classical time-dependent self- consistent field (TDSCF) approximation and the fast-Fourier transform (FFT) algorithm for solving the Schrodinger equation. Both approaches predict very weak or no cluster size dependence of the excitation spectrum for clusters that support interior solvated electron states. For an electron attached to the cluster in a surface localization mode, bound excited states exist for most nuclear configurations of clusters down to (H/sub 2/O)/sub 18//sup -/, and the corresponding excitation energy is strongly shifted to the red relative to that associated with stable internal states in larger clusters. Binding and excitation energies associated with surface states are about half the value of these quantities for interior states. The present variational continuum dielectric theory is in relatively good agreement with the simulation results on the size dependence of the relative stability of interior states. However, it strongly underestimates the vertical excitation energy of the solvated electron. It is suggested that optical spectroscopy of excess electrons in water clusters could serve as a sensitive probe of the transition from surface to interior localization modes as the number of water molecules in the cluster is increased (60 Refs.)
Granek, R.; Nitzan, A.
Dynamic bond percolation theory for diffusion of interacting particles: tracer diffusion in a binary mixture lattice gas.
Journal of Chemical Physics, vol.93, no.8, p. 5918-34 15 Oct. 1990. PDF
Dynamic percolation theory is used to obtain the tracer diffusion coefficient in binary mixtures of 'noninteracting' lattice gas (with only the blocking interactions, i.e., double occupancy of a lattice site is forbidden) within the effective medium approximation (EMA). The author's approach is based on regarding the background particles as a changing random environment. The result is expressed in terms of two fluctuation time parameters which they attempt to determine self-consistently. They compare two possible choices for these parameters which are consistent with our former results for the single component system. The resulting tracer diffusion coefficient for both choices compares well with numerical simulations whenever single bond EMA is expected to be reliable. Comparison is also made with the theoretical results of Sato and Kikuchi (Phys. Rev. B 28, 648 (1983)) and discrepancies between both theories are discussed (49 Refs.)
Barnett, R.N.; Landman, U.; Nitzan, A.
Primary events following electron injection into water and adsorbed water layers.
Journal of Chemical Physics, vol.93, no.9, p. 6535-42 1 Nov. 1990. PDF
The initial stages of the evolution of an electron injected into bulk water (at 300 K) and into thin water films (1-4 monolayers) adsorbed on a Pt(111) substrate at 50 K are investigated. It is shown that for electrons injected into bulk water with an initial translational kinetic energy between 1.54 and 6.18 eV (i.e. subexcitation energies), the electron momentum time-correlation function (p(0)p(t)), decays to zero on a time scale of less than 1 fs, reflecting strong backscattering of the electron by the water molecules. On this time scale the electron propagation in the medium is dominated by elastic processes. Furthermore, during this initial stage the system is well represented by a static aqueous medium. Transmission of electrons injected into thin films of adsorbed water is also dominated by elastic scattering. The dependence of the electron transmission probability on the film thickness and the initial injection energy are in accord with experimental results of photoinjected electrons into adsorbed water films (34 Refs.)
Silverberg, M.; Ratner, M.A.; Granek, R.; Nitzan, A.
Tracer diffusion of interacting particles on incomplete lattices: effective medium approximation.
Journal of Chemical Physics, vol.93, no.5, p. 3420-6 1 Sept. 1990. PDF
Dynamic percolation theory is adapted to obtain diffusion coefficients for particles with blocking interactions on incomplete lattices, within an effective medium approximation (EMA). The substrate lattices have static bond disorder. The motion of a tracer particle among identical background particles is regarded as particle motion in a fluctuating random environment superimposed on the statically disordered lattice; the fluctuations result from the motion of the background particles. Several schemes for incorporating the effect of the background particles are discussed, all relating their motion in different ways to the macroscopic diffusion. Comparisons with Monte Carlo simulations are performed for two-dimensional simple square and three-dimensional simple cubic lattices. In the range where single bond EMA is thought to be reliable, good agreement with the simulation is achieved (15 Refs.)
Barnett, R.N.; Landman, U.; Nitzan, A.
Excess electron transport in water.
Journal of Chemical Physics, vol.93, no.11, p. 8187-95 1 Dec. 1990. PDF
The properties of excess hydrated electrons in liquid water, at room temperature, are studied via coupled quantum- classical simulations. In these simulations, the system evolves dynamically on the adiabatic potential energy surface with the electron maintained in the ground state throughout the process. The diffusion constant of the hydrated electron under field-free conditions is found to be the same as that obtained, via the Nernst-Townsend-Einstein relation, from the electron mobility simulated for a system under an electric field of 3.2*10/sup 6/ V/cm, acting on the electron. For larger electric fields, the electron mobility is found to be field dependent. The mode of migration of the excess electron is polaronic in nature and the influence of the intramolecular degrees of freedom of the water molecules on the hydrated electron transport properties is investigated. It is shown that the electron diffusion constant obtained in simulations under field-free conditions with rigid-water molecules (D/sub e//sup O/=(3.7+or- 0.7)*10/sup -5/ cm/sup 2//s) is larger than that obtained from simulations where a flexible-water model potential is employed (D/sub e//sup O/=(1.9+or-0.4)*10/sup -5/ cm/sup 2//s) and smaller than the experimental estimated value obtained from conductivity measurements (4.9*10/sup -5/ cm/sup 2//s). The difference between the diffusion constants calculated for the two models is correlated with a marked enhancement of the probability of reversal of the direction of motion of the migrating electronin flexible water. The self-diffusion constant of water using the rigid-molecules model (D/sub 5/=(3.6+or-0.4)*10/sup -5/ cm/sup 2//s) is also larger than that found for the flexible-water molecule model (D/sub s/=(2.3+or-0.2)*10 /sup -5/ cm/sup 2//s), with the latter in agreement with the experimental value (D/sub s/=2.3*10/sup -5/ cm/sup 2//s). Structural and dynamical aspects of hydrated electron transport are discussed (31 Refs.)
Barnett, R.N.; Landman, U.; Nitzan, A.; Rajagopal, G.
Born-Oppenheimer dynamics using density-functional theory: equilibrium and fragmentation of small sodium clusters.
Journal of Chemical Physics, vol.94, no.1, p. 608-16 1 Jan. 1991. PDF
The properties of small neutral and positively charged sodium clusters and the fragmentation dynamics of Na/sub 4//sup ++/ are investigated using a simulation technique which combines classical molecular dynamics on the electronic Born-Oppenheimer ground-state potential surface with electronic structure calculations via the local spin- density functional method. Results for the optimal energies and structures of Na/sub n/ and Na/sub n//sup +/ (n<or=4) are in quantitative agreement with previous studies and experimental data. Fission of Na/sub 4//sup ++/ on its ground state Born-Oppenheimer potential-energy surface, following sudden ionization of selected configurations of an Na/sub 4//sup +/ (or Na/sub 4/) cluster, whose vibrational energy content corresponds to 300 K, is found to occur on a picosecond time scale. The preferred fission channel is found to be Na/sub 3//sup +/+Na/sup +/, with an interfragment relative translational kinetic energy of approximately 2 eV, and a vibrationally excited Na/sub 3//sup +/. The dynamics of the fragmentation process is analyzed (56 Refs.)
B.Carmeli, V.Mujica and A.Nitzan
Dynamics of multidimensional barrier crossing in the overdamped limit.
Berichte der Bunsenges. Phys. Chem., 95, 319-326(1991). PDF
Two methods for numerical solution of multidimensional diffusion problems are presented and applied to the two dimensional barrier crossing problem in the overdamped linit. One of these methods is based on evaluating the smallest non-vanishing eigenvalue of the Smoluchowski equation, and the other is based on an adaption of Chandler's steady state correlation function approach. Both methods make use of the fast Fourier transform algorithm for solving a transform version of the smoluchowski equation. Thenumerical solutions are compared to results based on the Kramers theory and some observations concerning effects of the dynamics of barrier crossing problems are made.
Kotler, Z.; Neria, E.; Nitzan, A.
Multiconfiguration time-dependent self-consistent field approximations in the numerical solution of quantum dynamical problems.
Computer Physics Communications, vol.63, no.1-3, p. 243-58 Feb. 1991.
The use of the time-dependent self-consistent field approximation (TDSCF) in the numerical solution of quantum curve crossing and tunneling dynamical problems is investigated. Particular emphasis is given to multiconfiguration TDSCF (MCTDSCF) approximations, which are shown to perform considerably better with only a small increase in computational effort. The authors investigate a number of simple models in which a 'system' characterized by two electronic potential surfaces evolves while interacting with a 'bath' mode described by an harmonic oscillator, and compare exact numerical solutions to one and two- configuration TDSCF approximations. They also introduce and investigate a semiclassical approximation in which the 'bath' mode is described by semiclassical wavepackets (one for each electronic state) and show that for all models investigated this scheme works very well in comparison with the fully quantum MCTDSCF approximation (15 Refs.)
M.A.Ratner and A.Nitzan
Polyelectrolytes: Hopping, domain structures and frequency - deconductivity.
Mat.Res.Soc.Symp.Proc., Vol 210,109-117, 1991.
The dynamic bond percolation model was developed to deal with dynamic disorder, treating ion mobility by a percolation model in whichthe assignment of any site-to-site jump as allowed or forbidden changes on a timescale related to the local reorganizational dynamics of the polymer segments (the renewal time). Here we discuss the special casses of high-frequancy spectra and partially crystalline electrolytes. At high frequencies, the present hopping model yields unphysical behavior (frequancy-independent response); we trace this back to the incorrect treatment of short-time dynamics, and show how it can be corrected. For partially crystalline meterials, we show that a rollover feature in the spectrum, in the microwave range, can be expected when ions are trapped in isolated regions of high conductivity, such as amorphous in largely crystalline PEO.
Radiative properties of solvated molecules in dielectric clusters and small particles.
J.Chem.Phys., 95, 686-699(1991). PDF
The radiative lifetime of molecules solvated in finite size clusters and particles is studied as a function of size. Four regimes of behavior are indicated by our present and previous theoretical results and by the available experimental data: The microscopic regime (up to a few tens of solvent molecules), where the lifetime is sensitive to microscopic structural details of the cluster; the electrostatic regime (up to sizes ~ 0.1, where is the radiation wavelength in the cluster), where the lifetime follows the predictions of classical electrostatics of dielectric environments; the electromagnetic regime (sizes of the order of ), where the behavior is dominated by electromagnetic resonances in the particles; and the bulk regime (sizes much larger than ). In the last three regimes the radiative lifetime may be approximated as a product of a cavity factor and a solvent factor. The first depends on the shape of the microscopic cavity surrounding the molecule and the second depends on the shape and size of the solvent particle. For spherical particles and for spherical or mildly spheroidal cavities, the lifetime changes from being longer than that of the free molecule in the electrostatic regime to being shorter in the bulk regime, in agreement with recent experimental results. The transition region occurs in the electrodynamic size regime. In the ``bulk regime'' (very large particles) molecules near the particle surface (within ~ one wavelength) are strongly affected by electromagnetic Mie resonances and show strong size-dependent deviation from the bulk behavior which characterizes molecules in the interior. The size dependence of the radiative lifetime stands in marked qualitative contrast to the size dependence of the solvent induced frequency shift, which approaches its bulk limit much earlier—when the cluster size becomes much larger than the microscopic cavity size. Finally, the ratio between the integrated absorption profile and the radiative decay rate does not depend on the cluster size. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.
Nitzan, A.; Granek, R.; Ratner, M.
Mechanical properties of dynamically disordered networks. PDF
J. Non-Cryst. Solids (Netherlands), Journal of Non- Crystalline Solids, vol.131 no.2, pt.2, p. 1018-21 1991.
Ionic motion in polymeric ionic conductors has been recently described in the framework of dynamic percolation theory (DPT) or, more generally, dynamic disorder hopping (DDH). In these models the polymer network above the glass transition is modelled as a random bond network in which the random bond distribution evolves in time with rate characteristic to the polymer motion. The present paper deals with the mechanical properties of such networks. The authors present a simple analysis of the viscosity of such dynamically disordered networks, thus relating a characteristic network relaxation time to the local (microscopic) viscosity of the polymer. If the same time is assumed to govern ionic transport, they obtain a relation between the ionic diffusion rate and the polymer viscosity. Estimates of the ionic diffusion based on this model are consistent with experimental observations (7 Refs.)
Neria, E.; Nitzan, A.; Barnett, R.N.; Landman, U.
Quantum dynamical simulations of nonadiabatic processes: solvation dynamics of the hydrated electron.
Physical Review Letters, vol.67, no.8, p. 1011-14 19 Aug. 1991. PDF
A new method for simulating nonadiabatic quantum processes is presented. It is suitable for transitions which are not dominated by near crossing of potential surfaces. The method is applied to the calculation of the radiationless transition rate of the hydrated electron from its lowest excited level to the ground state. The results are consistent with recent experimental indications that this process dominates the solvation dynamics of the electron in water (16 Refs.)
Makov, G.; Nitzan, A.
On the nonclassical asymptotic behavior of electronic properties in metal clusters.
Journal of Chemical Physics, vol.95, no.12, p. 9024-7 15 Dec. 1991. PDF
The ionization potential I(R) of small metal spheres (of radius R) as well as the electronic chemical potential mu (R) in such particles are considered within a three- parameter variational local-density-functional calculation. The asymptotic (R to infinity ) deviations of I(R) and mu (R) from their bulk values behave as C/R and C/sub mu //R, respectively, where within the computational accuracy C+C/sub mu /=0.5. These results are quantitatively similar to those obtained from a recent variational calculation by Engel and Perdew (EP) (1991), and identify the origin of the deviation of C from its classical value of 0.5 in the size dependence of mu (R). While EP show that this size dependence originates from the gradient terms in the energy functional, the authors find that its magnitude results from a delicate balance between different contributions. The classical limit C=0.5 is approached when both Z and R are large, where Z is the number of electrons involved in the transition. These results also lead to the resolution of an apparent paradox recently described by van Staveren et al. (1987) (10 Refs.)
Neria, E.; Nitzan, A.
Simulations of solvation dynamics in simple polar solvents.
Journal of Chemical Physics, vol.96, no.7, p. 5433-40 1 April 1992. PDF
The authors describe 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. They 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. They find that even in this structureless solvent, as in the more structured 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 (38 Refs.)