=======================================
2.
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.)
=======================================
4.
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.
=======================================
5.
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.)
=======================================
6.
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.)
=======================================
7.
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.
=======================================
8.
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.
=======================================
9.
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.)
=======================================
10.
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.
Jortner
Radiationless decay and
intrastate
energy equilibrium in an isolated large molecule.
J. Chem. Phys. 56, 5200-5201
(1972).
PDF
12.
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.)
=======================================
13.
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.)
=======================================
14.
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.)
=======================================
15.
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.)
===============================
16.
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.
=======================================
17.
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.)
=======================================
18.
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.)
=======================================
19.
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.)
=======================================
20.
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.)
=======================================
21.
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.
=======================================
22.
Nitzan, A.
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.)
=======================================
23.
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.)
=======================================
24.Nitzan,
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.)
=======================================
25.
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.)
=======================================
26.Nitzan,
A.
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.)
=======================================
27.
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.)
=======================================
28.
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.)
=======================================
29.
A.
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.
===============================
30.
Hong
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.
=======================================
31.
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.)
=======================================
32.
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.)
=======================================
33.
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.)
=======================================
34.
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.)
=======================================
35.
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.)
=======================================
36.
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.)
=======================================
37.
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.)
=======================================
38.
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.)
=======================================
39.
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.).
=======================================
40.
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.)
=======================================
41.
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.)
=======================================
42.
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.)
=======================================
43.
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.)
=======================================
44.
Nitzan, A.
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.)
=======================================
45.
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.)
=======================================
46.
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.)
=======================================
47.
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.)
===============================
48.
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.)
=======================================
49.
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.)
=======================================
50.
A.
Nitzan
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.
===============================
51.
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.)
=======================================
52.
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.)
=======================================
53.
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.)
=======================================
54.
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.)
=======================================
55.
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.)
=======================================
56.
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.)
=======================================
57.
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.)
=======================================
58.
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.)
=======================================
59.
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.)
=======================================
60.
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.)
=======================================
61.
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.)
=======================================
62.
Nitzan, A.
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.)
=======================================
63.
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.)
=======================================
64.
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.)
=======================================
65.
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.)
=======================================
66.
A.
Tramer and A. Nitzan
Collisional effects in
electronic
relaxation.
Advances in Chem. Phys. 47 ,
337-380
(1981).
PDF
CONTENTS
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
Acknowledgments 377
References 377
===============================
67.
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.)
=======================================
68.
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.)
=======================================
69.
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.)
=======================================
70.
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.)
=======================================
71.
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.)
=======================================
72.
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.)
=======================================
73.
Z.
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.
===============================
74.
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.)
=======================================
75.
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.)
=======================================
76.
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.)
=======================================
77.
Z.
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.
=======================================
78.
A.
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.
=======================================
79.
Z.
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.
===============================
80.
B.
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.
=======================================
81.
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.)
=======================================
82.
S.H.
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.
=======================================
83.
D.A.
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.
=======================================
84.
B.
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.
=======================================
86.
B.
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.
=======================================
87.
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.)
=======================================
88.
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.)
=======================================
89.
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.)
=======================================
90.
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.)
=======================================
91.
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.)
=======================================
92.
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.)
=======================================
93.
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.)
=======================================
94.
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.)
=======================================
95.
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.)
=======================================
95a.
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.)
=======================================
96.
Nitzan, A.
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.)
=======================================
97.
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.)
=======================================
98.
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.)
=======================================
99.
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.)
=======================================
100.
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.)
=======================================
101.
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.
===============================
102.
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.)
=======================================
103.
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.)
=======================================
104.
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.)
=======================================
105.
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.)
=======================================
106.
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.)
=======================================
107.
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.)
=======================================
108.
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.)
=======================================
109.
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.)
=======================================
110.
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.)
=======================================
111.
Nitzan, A.
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.)
=======================================
112.
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.)
=======================================
113.
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.)
=======================================
114.
A. Nitzan
Activated rate processes
in
condensed phases, the Kramers theory revisited
Adv. Chem. Phys. 70 489-555
(1988).
PDF
CONTENTS
1. Introduction
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)]
References
===============================
115.
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.)
======================================
116.
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.)
=======================================
117.
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.)
=======================================
118.
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.)
=======================================
119.
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.)
========================================
120.
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.)
=======================================
121.
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.)
=======================================
122.
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.)
=======================================
123.
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.)
=======================================
124.
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.)
=======================================
125.
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.)
=======================================
126.
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.)
=======================================
127.
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.)
=======================================
128.
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.)
=======================================
129.
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.)
=======================================
130.
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.)
=======================================
130a.
Berezhkovskii, A.M.; Zitserman, V.Yu.; Klosek, M.M.; Hoffman, B.M.;
Matkowsky,
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.)
=======================================
131.
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.
===============================
132.
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.)
=======================================
133.
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.
===============================
134.
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.)
=======================================
135.
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.
===============================
136.
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.
===============================
137.
Barnett, R.N.; Landman, U.; Dhar, S.; Kestner, N.R.; Jortner, J.;
Nitzan,
A.
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.)
=======================================
138.
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.)
=======================================
139.
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.)
=======================================
140.
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.
===============================
141.
S.D.Druger,
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.
===============================
142.
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.)
=======================================
G.Rajagopal, R.N.Barnett, A.Nitzan and U.Landman===============================
144.
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.)
=======================================
145.
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.)
=======================================
146.
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.)
=======================================
147.
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.)
=======================================
148.
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.)
=======================================
149.
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.)
=======================================
150.
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.
===============================
151.
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.)
=======================================
152.
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.
===============================
153.
J.Gersten
and A.Nitzan
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.
===============================
154.
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.)
=======================================
155.
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.)
=======================================
156.
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.)
=======================================
157.
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.)
=========================================