Fernando Raineri | SUNY: Stony Brook University (original) (raw)

Papers by Fernando Raineri

Journal of Chemical Physics, Oct 1, 1994

The familiar generalized Langevin equation (GLE1) of Mori has a variant, the convolutionless gene... more The familiar generalized Langevin equation (GLE1) of Mori has a variant, the convolutionless generalized Langevin equation (GLE2) of Tokuyama and Mori, for which we propose a very simple approximation to calculate time correlation functions. This new method, the reference frequency modulation approximation (RFMA), leads quite straightforwardly to known useful formulas. One is the power law of dynamic solvation due to Maroncelli, Kumar, and Papazyan. Another is a decay-time analog of the Powles–Glarum relation between single-particle and collective dielectric correlation times. A third application gives a relation between single-particle rotational time correlation functions of different tensorial rank recently used by Chang and Castner. The GLE2-RFMA method may be considered as the counterpart of the reference memory function approximation of GLE1 theory.

Berichte der Bunsengesellschaft für physikalische Chemie, Sep 1, 1986

In a detailed theoretical and experimental study it is shown that the initial slope for the depen... more In a detailed theoretical and experimental study it is shown that the initial slope for the dependence of the conductivity of an electrolyte solution with respect to the concentration of an added trace electrolyte is not only determined by the trace ionic conductivity of the non‐common ion added plus the ionic conductivity of the common ion at the concentration of the original (supporting) electrolyte, as has been proposed by H. G. Hertz et al. (J. Chim. Phys. 78, 68 (1981)). It is also determined in a non‐negligible amount by the variation of the equivalent conductivity of the pure supporting electrolyte with concentration as well as by the variation of this conductivity with the composition of the mixture at constant total concentration. The theoretical equations are verified with the complete electric transport data of the system HCl‐KCl‐H2O and careful conductivity measurements for the system NaCl‐KCl‐H2O. It is concluded that the trace ionic conductivity of an ion in a mixture cannot in general be obtained by conductivity measurements alone (transport number determinations are unavoidable) and the proposal due to Hertz et al. is shown to be inadequate. Only in the case of H+ as a trace ion the later two dependences mentioned above can be neglected within an error of 1% at relatively low concentrations of the supporting electrolyte.

Journal of Molecular Liquids, Nov 1, 2018

We consider the solvent-solvent interaction energy change associated with the solvent restructuri... more We consider the solvent-solvent interaction energy change associated with the solvent restructuring in response to a progressive change in the interaction between the solute and the solvent molecules. We derive expressions for this solvent restructuring energy using a new solvent scaling scheme in which the solvent-solvent potential energy is scaled relative to its reference value. We find that we can naturally extend the familiar 1-coupling parameter methodology with a second coupling parameter that controls the solvent-solvent interactions. In doing so we can not only access information about the solvent restructuring energy, but also quantify the statistical correlations between the fluctuations of the solute-solvent and the solvent-solvent interaction energies. Based on these findings we implement a molecular dynamics simulation strategy to evaluate the solvent restructuring energetics associated with turning on the electrostatic interactions between one initially uncharged water molecule dissolved in liquid water, using both the TIP4P-2005 and OPC water models. We also use the theory to explore the dependence of the solvent restructuring energy on solutesolvent coupling, both in general and in the special case in which solute-solvent coupling is accurately described by the linear response approximation.

Journal of Chemical Physics, May 1, 1991

A molecular theory of the liquid junction between two different solutions of the same single bina... more A molecular theory of the liquid junction between two different solutions of the same single binary electrolyte is derived from the statistical mechanical theory of linear response to thermal perturbations. The new theory employs a certain salt representation of the electrolyte solution that involves the transport numbers of the ion constituents. In this representation the solution is formally treated as a binary mixture of nonelectrolytes. The theory leads to expressions for the profiles (distributions through the junction) of charge, electrical potential, and number densities of the ion constituents in terms of the transport numbers and static equilibrium correlation functions formulated at the Born–Oppenheimer level. The implications of the new theory for the liquid junction potential (LJP) at this level remain to be developed. A simple approximation reduces the calculation of these profiles to the McMillan–Mayer level where only the ion–ion equilibrium correlation functions are required. The LJP derived at this level depends on the specific interactions between ions through the short-range part of the ion–ion direct correlation functions. If these interactions are absent (point ions) or if their effect mutually cancels (as in the restricted primitive model) we recover the LJP of classical electrochemistry, a result that is not trivially derived from a molecular theory. Calculations are presented to illustrate the predictions of the theory concerning the charge profile.

Journal of Chemical Physics, Aug 15, 1992

The ‘‘optical’’-like collective mode (OM) in TIP4P model water recently reported by Ricci et al. ... more The ‘‘optical’’-like collective mode (OM) in TIP4P model water recently reported by Ricci et al. is investigated here with a simple dynamical theory, the reference memory function approximation (RMFA), applied to calculate the dynamical dielectric properties of rigid and nonpolarizable interaction site models for water. Our results indicate that the OM is responsible for the high-frequency local charge density fluctuations that are germane to the frequency- and wave vector-dependent longitudinal dielectric function of water. The results for the OM in the TIP4P and SPC/E water models studied here under RMFA are in good agreement with each other as well as with molecular dynamics simulation results of Ricci et al. on the TIP4P model. An interesting connection to ion solvation dynamics is established.

Journal of Physical Chemistry B, Mar 17, 2005

Potential distribution and coupling parameter theories are combined to interrelate previous solva... more Potential distribution and coupling parameter theories are combined to interrelate previous solvation thermodynamic results and derive several new expressions for the solvent reorganization energy at both constant volume and constant pressure. We further demonstrate that the usual decomposition of the chemical potential into noncompensating energetic and entropic contributions may be extended to obtain a Gaussian fluctuation approximation for the chemical potential plus an exact cumulant expansion for the remainder. These exact expressions are further related to approximate first-order thermodynamic perturbation theory predictions and used to obtain a coupling-parameter integral expression for the sum of all higher-order terms in the perturbation series. The results are compared with the experimental global solvation thermodynamic functions for xenon dissolved in n-hexane and water (under ambient conditions). These comparisons imply that the constantvolume solvent reorganization energy has a magnitude of at most ∼kT in both experimental solutions. The results are used to extract numerical values of the solute-solvent mean interaction energy and associated fluctuation entropy directly from experimental solvation thermodynamic measurements. † Part of the special issue "David Chandler Festschrift".

Journal of Chemical Physics, Feb 15, 1992

The static longitudinal dielectric function εL(k) is calculated for several polar interaction sit... more The static longitudinal dielectric function εL(k) is calculated for several polar interaction site model (ISM) fluids for comparison with related models having arbitrary short-range interactions and a set of one or more lower-order multipole moments at the centers (ΩM models). The requisite averages over the ISM fluids are calculated by the extended reference interaction site method (XRISM) using site–site hypernetted chain (HNC)-like closures modified to reproduce the correct long-range behavior of the site–site pair correlation functions. They are compared with averages over the ΩM models under the RHNC theory taken from the literature or calculated under the mean spherical approximation. We find for fluids of strong enough polarity that εL(k) is negative over a finite range of k, the low end being in agreement with recent computer simulation studies of both ISM and ΩM polar fluids. However, we confirm that the expected large-k behavior εL(k)=1 governs the ISMs, but not the ΩM models. Based on an adaptation of the color charge–color field techniques of molecular dynamics, we develop the concept of the color longitudinal dielectric function; it provides useful information about the role of the spatial extent of the molecular charge distribution on the behavior of εL(k). The ISM fluids we have analyzed include dipolar dumbbells over a wide range of bond length and polarity as well as realistic interaction site models for water and methanol. For the methanol model, we compare our εL(k) with recent computer simulation results and find substantial agreement.

Journal of Chemical Physics, 1990

Molecular dynamics simulations are reported for a solute immersed in a monatomic solvent• systems... more Molecular dynamics simulations are reported for a solute immersed in a monatomic solvent• systems modeled represent monatomic and diatomic solute species (whose atoms are larger' and heavier than the solvent), with varying force constant and bond length for the diatomic. From these simulations, autocorrelation functions, diffusion coefficients (D), and friction coefficients (5) are determined; for the diatomic, these are found for both the center-of-mass ~nd re~ative coordin.ates. ~hese r~su1ts are used to develop simple models for D and 5, mcludmg (for the diatomic relatlve coordinate) their frequency dependence. The models enable D and 5 to be readily determined from properties such as bulk viscosity, potential parameters, etc. These D and 5 can be used to interpret and predict picosecond time scale data for solute dynamics using stochastic models (e.g., the Kramers or Langevin equations) at the mo~ec.ular level; their ~he~retical basis is such that they should apply to many types of solute mOletles (e.g., aromatlc nngs) as well as to the large atoms used in the simulations.

Journal of Chemical Physics, Jan 15, 1991

A recently proposed theory for transport coefficients in ionic solutions can be reinterpreted so ... more A recently proposed theory for transport coefficients in ionic solutions can be reinterpreted so that it becomes applicable to calculating the dielectric relaxation processes in dipolar fluids and in ionic solutions in dipolar solvents. The resulting theory is the same as the Smoluchowski–Vlasov theory which has been derived in various other ways by Munakata, Calef and Wolynes, and Chandra and Bagchi. Here the theory is applied to calculate the time correlation function for the fluctuating polarization density field in simple dipolar fluid, and in an ionic solution in a dipolar solvent. The results are similar to those derived some time ago by Berne using a ‘‘forced diffusion equation’’ as the theory for calculating the response. Comparison is also made with the results of Chandra and Bagchi using the Smoluchowski–Vaslov theory.

Journal of Physics: Condensed Matter, Aug 22, 2016

The solvation energetics associated with the transformation of a solute molecule at infinite dilu... more The solvation energetics associated with the transformation of a solute molecule at infinite dilution in water from an initial state A to a final state B is reconsidered. The two solute states have different potentials energies of interaction, [Formula: see text] and [Formula: see text], with the solvent environment. Throughout the A [Formula: see text] B transformation of the solute, the solvation system is described by a Hamiltonian [Formula: see text] that changes linearly with the coupling parameter ξ. By focusing on the characterization of the probability density [Formula: see text] that the dimensionless perturbational solute-solvent interaction energy [Formula: see text] has numerical value y when the coupling parameter is ξ, we derive a hierarchy of differential equation relations between the ξ-dependent cumulant functions of various orders in the expansion of the appropriate cumulant generating function. On the basis of this theoretical framework we then introduce an inherently nonlinear solvation model for which we are able to find analytical results for both [Formula: see text] and for the solvation thermodynamic functions. The solvation model is based on the premise that there is an upper or a lower bound (depending on the nature of the interactions considered) to the amplitude of the fluctuations of Y in the solution system at equilibrium. The results reveal essential differences in behavior for the model when compared with the linear response approximation to solvation, particularly with regards to the probability density [Formula: see text]. The analytical expressions for the solvation properties show, however, that the linear response behavior is recovered from the new model when the room for the thermal fluctuations in Y is not restricted by the existence of a nearby bound. We compare the predictions of the model with the results from molecular dynamics computer simulations for aqueous solvation, in which either (1) the solute-solvent electrostatic interactions, or (2) the shorter-range attractive interactions are switched-on in the A [Formula: see text] B process.

Journal of the Chemical Society, 1986

In base of a baricentric expression given by H. Mori and with the introduction of a new set of co... more In base of a baricentric expression given by H. Mori and with the introduction of a new set of collective dynamical variables, the ‘mean molecular velocities’ of the components, new Green–Kubo type expressions for the mass-transport phenomenological coefficients of irreversible thermodynamics in any reference frame are obtained. The dynamical variables involved in the time correlation functions are the mean molecular velocities of the components relative to the corresponding ‘microscopic reference velocity’, which is defined by analogy with the usual macroscopic one. The linear dependence of the relative mean molecular velocities determines that the sets of time correlation functions, their time integrals and the phenomenological coefficients are also linearly dependent. Nevertheless, the Onsager reciprocal relations are valid for each set. As the reference velocity appears explicitly, general transformation formulae among different frames for all these quantities are readily obtained at a microscopic level. As an application the expression by time correlation functions of some empirical transport coefficients such as the electric conductivity, transport numbers and ionic conductivities in mixed electrolyte solutions, and the interdiffusion coefficients in non-electrolyte mixtures, are deduced. The new expressions show explicitly the microscopic interpretation of these transport coefficients and their dependence on the reference frame.

Chemical Physics, Apr 1, 1991

The molecular theory of the frequency-dependent and wavevectordependent longitudinal dielectric f... more The molecular theory of the frequency-dependent and wavevectordependent longitudinal dielectric function eL(k, w) is derived for fluids comprising interaction-site model molecules in which point charges are located on the interaction sites. We find that cc(k, w) is a simple functional of a particular charge susceptibility X,O (k, o), which in turn is related to a collective chargecharge equilibrium time correlation function. The electrostatic part F &,.,,(t) of the time-dependent free energy of salvation of a solute that instantaneously changes its charge state is, on the other hand, determined by a charge susceptibility x$(k, k', w) of the solvent in the presence of the solute molecule in its initial charg state. Using an approximate relation between x$ and x,,,o we expnss FBom(t) in terms of x,,+. The restthing theory is applied to calculate the solvation time correlation function of the solute immersed in a dipolar hard sphere (DS) and in dipolar dumbbell (DD) model solvent; the mean spherical approximation and an extended mean spherical approximation are used to compute the structure of the DS and DD solvent models, respectively. With parameters chosen so that the two models have the same molecular volume and the same electric dipole moment, it is found that they have very nearly the same eL(k, o) except at large wavevector, but significantly different solvation time correlation

Journal of Chemical Physics, Jun 1, 1993

It is customary in the physicochemical literature to define the static transverse dielectric func... more It is customary in the physicochemical literature to define the static transverse dielectric function of a polar fluid according to the relation εT(k) = 1 + 4πβST(k), where β=(kBT)−1 and ST(k) is a measure of the static fluctuations of the Fourier components of the transverse part of the electric polarization field in the fluid. In this work we evaluate εT(k) for models of two classes. (1) In a DS model each molecule is a hard sphere with a point dipole at its center. It is the simplest representative of models in which the long range intermolecular interactions are generated by a set of point multipoles located at a single point in the molecule. In this case ST(k) is SM,T(k), the static correlation function of the transverse part of the dipole polarization density M̂(k). (2) In a ζDS model fluid, comprising nonideal dipolar hard spheres, the long range interactions are accounted for by two opposite partial charges on either side of the sphere’s center and separated by a distance ℓ. The ζDS model is the simplest interaction site model (ISM) of a polar fluid. For an ISM the relevant structure factor ST(k) is SPμ ,T(k), the static correlation of the transverse part of the full electric polarization density vector P̂μ(k). Here we compare εT(k) for DS and ζDS models with the help of the mean spherical approximation for the required structure functions. The ζDS–DS difference in εT(k) at large k is found to parallel the behavior of the static longitudinal dielectric function εL(k). However, εT(k), unlike εL(k), is a damped oscillatory function of k with no poles on the real k axis.

Springer eBooks, 1992

A reference memory function approximation to the generalized Langevin equation (GLE) is generated... more A reference memory function approximation to the generalized Langevin equation (GLE) is generated by setting the normalized l th memory function of the time correlation function of interest equal to the l th normalized memory function of the time correlation function of a reference dynamical variable. Specializing this general prescription in various ways leads to known approximation schemes. Among them are the Vineyard and Kerr approximations for a simple fluid and their generalization to fluids of polar molecules; the Smoluchowski-Vlasov equations for polar molecules and electrolyte solutions, and especially, the extensions of these theories needed for use with interaction site models.

Journal of the Chemical Society, 1986

... Part 1.—Solution of a single binary electrolyte. Fernando O. Raineri and Ernesto O. Timmerman... more ... Part 1.—Solution of a single binary electrolyte. Fernando O. Raineri and Ernesto O. Timmermann. J. Chem. Soc., Faraday Trans. ... Our expressions have no resemblance to the dynamic variable proposed by Hertz, and a comparison of our procedure with those of Hertz is given. ...

Journal of the Chemical Society, Faraday Transactions, 1990

The new variational principle recently introduced is applied to extend the concept of the mean mo... more The new variational principle recently introduced is applied to extend the concept of the mean molecular velocity of a salt presented earlier for solutions of several electrolytes with a common ion constituent. All the isothermal vectorial transport coefficients of these systems are described in terms of the dissipative motions of the ion constituents, which are built up by two linear fully decoupled contributions. These are (1) a migrational part, associated with the movement of the ion constituent relative to its corresponding salt and (2) a diffusional part, associated to the movement of its salt relative to the solvent. Each salt velocity is dynamically orthogonal to the electric current; this guarantees that diffusion and electrical transport superpose but do not interact. The new formalism is entirely consistent with the formulations of irreversible thermodynamics and of velocity correlation integrals. By means of projection operators it is easily shown that the ionic phenomenological conductance coefficients as well as the ionic velocity correlation coefficients consist of two linear fully decoupled components which correspond to the migrational and the diffusional contributions.

Journal of Physics: Condensed Matter, Oct 9, 2004

We discuss the derivation and use of a key feature of a new version of thermodynamic perturbation... more We discuss the derivation and use of a key feature of a new version of thermodynamic perturbation theory (TPT) that Ben-Amotz and Stell have developed recently---the choice of a hard-core diameter to be used in modelling soft-core systems. We go on to show the way the new version of TPT can be used as input for the self-consistent Ornstein-Zernike approach

Pure and Applied Chemistry, 1991

Brook N. Y. 11794, USA Abstra t-Hydration complexes, lon an object of study in the coordination c... more Brook N. Y. 11794, USA Abstra t-Hydration complexes, lon an object of study in the coordination chemistry field, c : n now be studied more directfy by new and powerful methods. Among the new experimental methods are the refined neutron scattering methods developed by J. E. Enderby, G. Neilson and co-workers. Another is the study of ion-solvent clusters in molecular beams, especially by spectroscopic techniques. Some important new theoretical studies begin with calculating the Born-Oppenheimer potential surfaces for very small ion-water clusters. Then one of the available statistical mechanical techniques is applied to generate solvent-averaged ion-ion pair potentials from which measurable equilibrium solution properties can be calculated. In another new development, the same solvent-averaged models are dressed with bare ionic self diffusion coefficients and with the ion-ion hydrodynamic interactions. From such models one can calculate some of the solution transport coefficients for comparison with real systems. Illustrations of both consistencies and contradictions are found.

Molecular Physics, Nov 10, 2005

We report a number of new exact expressions, within the realm of classical statistical mechanics,... more We report a number of new exact expressions, within the realm of classical statistical mechanics, for the solvation contribution ΔA to the free energy change of a solute that undergoes a transformation between two states that differ in the way they interact with the solvent. Our basic result is a coupling-parameter expression that is equivalent to the usual cumulant expansion

Journal of Chemical Physics, Nov 1, 1989

The theory of the correction for the difference in the fluctuations among the different ensembles... more The theory of the correction for the difference in the fluctuations among the different ensembles is applied to derive the time correlation function formula required to compute the distinct diffusion coefficients in the barycentric reference frame by molecular dynamics. In the process it is found that the dynamical variables in the time correlation function of any mass transport coefficient of any reference frame are the same in the canonical as in the molecular dynamics ensemble. The result agrees with the accepted formulas for computing the kinetic part of the mutual diffusion coefficient in a binary mixture of nonelectrolytes and for computing the electrical conductivity in molten salts and electrolyte solutions. The static velocity correlations in the molecular dynamics ensemble are analyzed without recourse to the other ensembles. In sharp contrast with the ensembles which are not constrained with respect to the total momentum, the laboratory-frame velocities of two different particles at the same time are found to be correlated. The result obtained is equivalent to the initial value of the canonical time correlation function of the barycentric distinct diffusion coefficients derived in the preceding paper.

Journal of Chemical Physics, Oct 1, 1994

The familiar generalized Langevin equation (GLE1) of Mori has a variant, the convolutionless gene... more The familiar generalized Langevin equation (GLE1) of Mori has a variant, the convolutionless generalized Langevin equation (GLE2) of Tokuyama and Mori, for which we propose a very simple approximation to calculate time correlation functions. This new method, the reference frequency modulation approximation (RFMA), leads quite straightforwardly to known useful formulas. One is the power law of dynamic solvation due to Maroncelli, Kumar, and Papazyan. Another is a decay-time analog of the Powles–Glarum relation between single-particle and collective dielectric correlation times. A third application gives a relation between single-particle rotational time correlation functions of different tensorial rank recently used by Chang and Castner. The GLE2-RFMA method may be considered as the counterpart of the reference memory function approximation of GLE1 theory.

Berichte der Bunsengesellschaft für physikalische Chemie, Sep 1, 1986

In a detailed theoretical and experimental study it is shown that the initial slope for the depen... more In a detailed theoretical and experimental study it is shown that the initial slope for the dependence of the conductivity of an electrolyte solution with respect to the concentration of an added trace electrolyte is not only determined by the trace ionic conductivity of the non‐common ion added plus the ionic conductivity of the common ion at the concentration of the original (supporting) electrolyte, as has been proposed by H. G. Hertz et al. (J. Chim. Phys. 78, 68 (1981)). It is also determined in a non‐negligible amount by the variation of the equivalent conductivity of the pure supporting electrolyte with concentration as well as by the variation of this conductivity with the composition of the mixture at constant total concentration. The theoretical equations are verified with the complete electric transport data of the system HCl‐KCl‐H2O and careful conductivity measurements for the system NaCl‐KCl‐H2O. It is concluded that the trace ionic conductivity of an ion in a mixture cannot in general be obtained by conductivity measurements alone (transport number determinations are unavoidable) and the proposal due to Hertz et al. is shown to be inadequate. Only in the case of H+ as a trace ion the later two dependences mentioned above can be neglected within an error of 1% at relatively low concentrations of the supporting electrolyte.

Journal of Molecular Liquids, Nov 1, 2018

We consider the solvent-solvent interaction energy change associated with the solvent restructuri... more We consider the solvent-solvent interaction energy change associated with the solvent restructuring in response to a progressive change in the interaction between the solute and the solvent molecules. We derive expressions for this solvent restructuring energy using a new solvent scaling scheme in which the solvent-solvent potential energy is scaled relative to its reference value. We find that we can naturally extend the familiar 1-coupling parameter methodology with a second coupling parameter that controls the solvent-solvent interactions. In doing so we can not only access information about the solvent restructuring energy, but also quantify the statistical correlations between the fluctuations of the solute-solvent and the solvent-solvent interaction energies. Based on these findings we implement a molecular dynamics simulation strategy to evaluate the solvent restructuring energetics associated with turning on the electrostatic interactions between one initially uncharged water molecule dissolved in liquid water, using both the TIP4P-2005 and OPC water models. We also use the theory to explore the dependence of the solvent restructuring energy on solutesolvent coupling, both in general and in the special case in which solute-solvent coupling is accurately described by the linear response approximation.

Journal of Chemical Physics, May 1, 1991

A molecular theory of the liquid junction between two different solutions of the same single bina... more A molecular theory of the liquid junction between two different solutions of the same single binary electrolyte is derived from the statistical mechanical theory of linear response to thermal perturbations. The new theory employs a certain salt representation of the electrolyte solution that involves the transport numbers of the ion constituents. In this representation the solution is formally treated as a binary mixture of nonelectrolytes. The theory leads to expressions for the profiles (distributions through the junction) of charge, electrical potential, and number densities of the ion constituents in terms of the transport numbers and static equilibrium correlation functions formulated at the Born–Oppenheimer level. The implications of the new theory for the liquid junction potential (LJP) at this level remain to be developed. A simple approximation reduces the calculation of these profiles to the McMillan–Mayer level where only the ion–ion equilibrium correlation functions are required. The LJP derived at this level depends on the specific interactions between ions through the short-range part of the ion–ion direct correlation functions. If these interactions are absent (point ions) or if their effect mutually cancels (as in the restricted primitive model) we recover the LJP of classical electrochemistry, a result that is not trivially derived from a molecular theory. Calculations are presented to illustrate the predictions of the theory concerning the charge profile.

Journal of Chemical Physics, Aug 15, 1992

The ‘‘optical’’-like collective mode (OM) in TIP4P model water recently reported by Ricci et al. ... more The ‘‘optical’’-like collective mode (OM) in TIP4P model water recently reported by Ricci et al. is investigated here with a simple dynamical theory, the reference memory function approximation (RMFA), applied to calculate the dynamical dielectric properties of rigid and nonpolarizable interaction site models for water. Our results indicate that the OM is responsible for the high-frequency local charge density fluctuations that are germane to the frequency- and wave vector-dependent longitudinal dielectric function of water. The results for the OM in the TIP4P and SPC/E water models studied here under RMFA are in good agreement with each other as well as with molecular dynamics simulation results of Ricci et al. on the TIP4P model. An interesting connection to ion solvation dynamics is established.

Journal of Physical Chemistry B, Mar 17, 2005

Potential distribution and coupling parameter theories are combined to interrelate previous solva... more Potential distribution and coupling parameter theories are combined to interrelate previous solvation thermodynamic results and derive several new expressions for the solvent reorganization energy at both constant volume and constant pressure. We further demonstrate that the usual decomposition of the chemical potential into noncompensating energetic and entropic contributions may be extended to obtain a Gaussian fluctuation approximation for the chemical potential plus an exact cumulant expansion for the remainder. These exact expressions are further related to approximate first-order thermodynamic perturbation theory predictions and used to obtain a coupling-parameter integral expression for the sum of all higher-order terms in the perturbation series. The results are compared with the experimental global solvation thermodynamic functions for xenon dissolved in n-hexane and water (under ambient conditions). These comparisons imply that the constantvolume solvent reorganization energy has a magnitude of at most ∼kT in both experimental solutions. The results are used to extract numerical values of the solute-solvent mean interaction energy and associated fluctuation entropy directly from experimental solvation thermodynamic measurements. † Part of the special issue "David Chandler Festschrift".

Journal of Chemical Physics, Feb 15, 1992

The static longitudinal dielectric function εL(k) is calculated for several polar interaction sit... more The static longitudinal dielectric function εL(k) is calculated for several polar interaction site model (ISM) fluids for comparison with related models having arbitrary short-range interactions and a set of one or more lower-order multipole moments at the centers (ΩM models). The requisite averages over the ISM fluids are calculated by the extended reference interaction site method (XRISM) using site–site hypernetted chain (HNC)-like closures modified to reproduce the correct long-range behavior of the site–site pair correlation functions. They are compared with averages over the ΩM models under the RHNC theory taken from the literature or calculated under the mean spherical approximation. We find for fluids of strong enough polarity that εL(k) is negative over a finite range of k, the low end being in agreement with recent computer simulation studies of both ISM and ΩM polar fluids. However, we confirm that the expected large-k behavior εL(k)=1 governs the ISMs, but not the ΩM models. Based on an adaptation of the color charge–color field techniques of molecular dynamics, we develop the concept of the color longitudinal dielectric function; it provides useful information about the role of the spatial extent of the molecular charge distribution on the behavior of εL(k). The ISM fluids we have analyzed include dipolar dumbbells over a wide range of bond length and polarity as well as realistic interaction site models for water and methanol. For the methanol model, we compare our εL(k) with recent computer simulation results and find substantial agreement.

Journal of Chemical Physics, 1990

Molecular dynamics simulations are reported for a solute immersed in a monatomic solvent• systems... more Molecular dynamics simulations are reported for a solute immersed in a monatomic solvent• systems modeled represent monatomic and diatomic solute species (whose atoms are larger' and heavier than the solvent), with varying force constant and bond length for the diatomic. From these simulations, autocorrelation functions, diffusion coefficients (D), and friction coefficients (5) are determined; for the diatomic, these are found for both the center-of-mass ~nd re~ative coordin.ates. ~hese r~su1ts are used to develop simple models for D and 5, mcludmg (for the diatomic relatlve coordinate) their frequency dependence. The models enable D and 5 to be readily determined from properties such as bulk viscosity, potential parameters, etc. These D and 5 can be used to interpret and predict picosecond time scale data for solute dynamics using stochastic models (e.g., the Kramers or Langevin equations) at the mo~ec.ular level; their ~he~retical basis is such that they should apply to many types of solute mOletles (e.g., aromatlc nngs) as well as to the large atoms used in the simulations.

Journal of Chemical Physics, Jan 15, 1991

A recently proposed theory for transport coefficients in ionic solutions can be reinterpreted so ... more A recently proposed theory for transport coefficients in ionic solutions can be reinterpreted so that it becomes applicable to calculating the dielectric relaxation processes in dipolar fluids and in ionic solutions in dipolar solvents. The resulting theory is the same as the Smoluchowski–Vlasov theory which has been derived in various other ways by Munakata, Calef and Wolynes, and Chandra and Bagchi. Here the theory is applied to calculate the time correlation function for the fluctuating polarization density field in simple dipolar fluid, and in an ionic solution in a dipolar solvent. The results are similar to those derived some time ago by Berne using a ‘‘forced diffusion equation’’ as the theory for calculating the response. Comparison is also made with the results of Chandra and Bagchi using the Smoluchowski–Vaslov theory.

Journal of Physics: Condensed Matter, Aug 22, 2016

The solvation energetics associated with the transformation of a solute molecule at infinite dilu... more The solvation energetics associated with the transformation of a solute molecule at infinite dilution in water from an initial state A to a final state B is reconsidered. The two solute states have different potentials energies of interaction, [Formula: see text] and [Formula: see text], with the solvent environment. Throughout the A [Formula: see text] B transformation of the solute, the solvation system is described by a Hamiltonian [Formula: see text] that changes linearly with the coupling parameter ξ. By focusing on the characterization of the probability density [Formula: see text] that the dimensionless perturbational solute-solvent interaction energy [Formula: see text] has numerical value y when the coupling parameter is ξ, we derive a hierarchy of differential equation relations between the ξ-dependent cumulant functions of various orders in the expansion of the appropriate cumulant generating function. On the basis of this theoretical framework we then introduce an inherently nonlinear solvation model for which we are able to find analytical results for both [Formula: see text] and for the solvation thermodynamic functions. The solvation model is based on the premise that there is an upper or a lower bound (depending on the nature of the interactions considered) to the amplitude of the fluctuations of Y in the solution system at equilibrium. The results reveal essential differences in behavior for the model when compared with the linear response approximation to solvation, particularly with regards to the probability density [Formula: see text]. The analytical expressions for the solvation properties show, however, that the linear response behavior is recovered from the new model when the room for the thermal fluctuations in Y is not restricted by the existence of a nearby bound. We compare the predictions of the model with the results from molecular dynamics computer simulations for aqueous solvation, in which either (1) the solute-solvent electrostatic interactions, or (2) the shorter-range attractive interactions are switched-on in the A [Formula: see text] B process.

Journal of the Chemical Society, 1986

In base of a baricentric expression given by H. Mori and with the introduction of a new set of co... more In base of a baricentric expression given by H. Mori and with the introduction of a new set of collective dynamical variables, the ‘mean molecular velocities’ of the components, new Green–Kubo type expressions for the mass-transport phenomenological coefficients of irreversible thermodynamics in any reference frame are obtained. The dynamical variables involved in the time correlation functions are the mean molecular velocities of the components relative to the corresponding ‘microscopic reference velocity’, which is defined by analogy with the usual macroscopic one. The linear dependence of the relative mean molecular velocities determines that the sets of time correlation functions, their time integrals and the phenomenological coefficients are also linearly dependent. Nevertheless, the Onsager reciprocal relations are valid for each set. As the reference velocity appears explicitly, general transformation formulae among different frames for all these quantities are readily obtained at a microscopic level. As an application the expression by time correlation functions of some empirical transport coefficients such as the electric conductivity, transport numbers and ionic conductivities in mixed electrolyte solutions, and the interdiffusion coefficients in non-electrolyte mixtures, are deduced. The new expressions show explicitly the microscopic interpretation of these transport coefficients and their dependence on the reference frame.

Chemical Physics, Apr 1, 1991

The molecular theory of the frequency-dependent and wavevectordependent longitudinal dielectric f... more The molecular theory of the frequency-dependent and wavevectordependent longitudinal dielectric function eL(k, w) is derived for fluids comprising interaction-site model molecules in which point charges are located on the interaction sites. We find that cc(k, w) is a simple functional of a particular charge susceptibility X,O (k, o), which in turn is related to a collective chargecharge equilibrium time correlation function. The electrostatic part F &,.,,(t) of the time-dependent free energy of salvation of a solute that instantaneously changes its charge state is, on the other hand, determined by a charge susceptibility x$(k, k', w) of the solvent in the presence of the solute molecule in its initial charg state. Using an approximate relation between x$ and x,,,o we expnss FBom(t) in terms of x,,+. The restthing theory is applied to calculate the solvation time correlation function of the solute immersed in a dipolar hard sphere (DS) and in dipolar dumbbell (DD) model solvent; the mean spherical approximation and an extended mean spherical approximation are used to compute the structure of the DS and DD solvent models, respectively. With parameters chosen so that the two models have the same molecular volume and the same electric dipole moment, it is found that they have very nearly the same eL(k, o) except at large wavevector, but significantly different solvation time correlation

Journal of Chemical Physics, Jun 1, 1993

It is customary in the physicochemical literature to define the static transverse dielectric func... more It is customary in the physicochemical literature to define the static transverse dielectric function of a polar fluid according to the relation εT(k) = 1 + 4πβST(k), where β=(kBT)−1 and ST(k) is a measure of the static fluctuations of the Fourier components of the transverse part of the electric polarization field in the fluid. In this work we evaluate εT(k) for models of two classes. (1) In a DS model each molecule is a hard sphere with a point dipole at its center. It is the simplest representative of models in which the long range intermolecular interactions are generated by a set of point multipoles located at a single point in the molecule. In this case ST(k) is SM,T(k), the static correlation function of the transverse part of the dipole polarization density M̂(k). (2) In a ζDS model fluid, comprising nonideal dipolar hard spheres, the long range interactions are accounted for by two opposite partial charges on either side of the sphere’s center and separated by a distance ℓ. The ζDS model is the simplest interaction site model (ISM) of a polar fluid. For an ISM the relevant structure factor ST(k) is SPμ ,T(k), the static correlation of the transverse part of the full electric polarization density vector P̂μ(k). Here we compare εT(k) for DS and ζDS models with the help of the mean spherical approximation for the required structure functions. The ζDS–DS difference in εT(k) at large k is found to parallel the behavior of the static longitudinal dielectric function εL(k). However, εT(k), unlike εL(k), is a damped oscillatory function of k with no poles on the real k axis.

Springer eBooks, 1992

A reference memory function approximation to the generalized Langevin equation (GLE) is generated... more A reference memory function approximation to the generalized Langevin equation (GLE) is generated by setting the normalized l th memory function of the time correlation function of interest equal to the l th normalized memory function of the time correlation function of a reference dynamical variable. Specializing this general prescription in various ways leads to known approximation schemes. Among them are the Vineyard and Kerr approximations for a simple fluid and their generalization to fluids of polar molecules; the Smoluchowski-Vlasov equations for polar molecules and electrolyte solutions, and especially, the extensions of these theories needed for use with interaction site models.

Journal of the Chemical Society, 1986

... Part 1.—Solution of a single binary electrolyte. Fernando O. Raineri and Ernesto O. Timmerman... more ... Part 1.—Solution of a single binary electrolyte. Fernando O. Raineri and Ernesto O. Timmermann. J. Chem. Soc., Faraday Trans. ... Our expressions have no resemblance to the dynamic variable proposed by Hertz, and a comparison of our procedure with those of Hertz is given. ...

Journal of the Chemical Society, Faraday Transactions, 1990

The new variational principle recently introduced is applied to extend the concept of the mean mo... more The new variational principle recently introduced is applied to extend the concept of the mean molecular velocity of a salt presented earlier for solutions of several electrolytes with a common ion constituent. All the isothermal vectorial transport coefficients of these systems are described in terms of the dissipative motions of the ion constituents, which are built up by two linear fully decoupled contributions. These are (1) a migrational part, associated with the movement of the ion constituent relative to its corresponding salt and (2) a diffusional part, associated to the movement of its salt relative to the solvent. Each salt velocity is dynamically orthogonal to the electric current; this guarantees that diffusion and electrical transport superpose but do not interact. The new formalism is entirely consistent with the formulations of irreversible thermodynamics and of velocity correlation integrals. By means of projection operators it is easily shown that the ionic phenomenological conductance coefficients as well as the ionic velocity correlation coefficients consist of two linear fully decoupled components which correspond to the migrational and the diffusional contributions.

Journal of Physics: Condensed Matter, Oct 9, 2004

We discuss the derivation and use of a key feature of a new version of thermodynamic perturbation... more We discuss the derivation and use of a key feature of a new version of thermodynamic perturbation theory (TPT) that Ben-Amotz and Stell have developed recently---the choice of a hard-core diameter to be used in modelling soft-core systems. We go on to show the way the new version of TPT can be used as input for the self-consistent Ornstein-Zernike approach

Pure and Applied Chemistry, 1991

Brook N. Y. 11794, USA Abstra t-Hydration complexes, lon an object of study in the coordination c... more Brook N. Y. 11794, USA Abstra t-Hydration complexes, lon an object of study in the coordination chemistry field, c : n now be studied more directfy by new and powerful methods. Among the new experimental methods are the refined neutron scattering methods developed by J. E. Enderby, G. Neilson and co-workers. Another is the study of ion-solvent clusters in molecular beams, especially by spectroscopic techniques. Some important new theoretical studies begin with calculating the Born-Oppenheimer potential surfaces for very small ion-water clusters. Then one of the available statistical mechanical techniques is applied to generate solvent-averaged ion-ion pair potentials from which measurable equilibrium solution properties can be calculated. In another new development, the same solvent-averaged models are dressed with bare ionic self diffusion coefficients and with the ion-ion hydrodynamic interactions. From such models one can calculate some of the solution transport coefficients for comparison with real systems. Illustrations of both consistencies and contradictions are found.

Molecular Physics, Nov 10, 2005

We report a number of new exact expressions, within the realm of classical statistical mechanics,... more We report a number of new exact expressions, within the realm of classical statistical mechanics, for the solvation contribution ΔA to the free energy change of a solute that undergoes a transformation between two states that differ in the way they interact with the solvent. Our basic result is a coupling-parameter expression that is equivalent to the usual cumulant expansion

Journal of Chemical Physics, Nov 1, 1989

The theory of the correction for the difference in the fluctuations among the different ensembles... more The theory of the correction for the difference in the fluctuations among the different ensembles is applied to derive the time correlation function formula required to compute the distinct diffusion coefficients in the barycentric reference frame by molecular dynamics. In the process it is found that the dynamical variables in the time correlation function of any mass transport coefficient of any reference frame are the same in the canonical as in the molecular dynamics ensemble. The result agrees with the accepted formulas for computing the kinetic part of the mutual diffusion coefficient in a binary mixture of nonelectrolytes and for computing the electrical conductivity in molten salts and electrolyte solutions. The static velocity correlations in the molecular dynamics ensemble are analyzed without recourse to the other ensembles. In sharp contrast with the ensembles which are not constrained with respect to the total momentum, the laboratory-frame velocities of two different particles at the same time are found to be correlated. The result obtained is equivalent to the initial value of the canonical time correlation function of the barycentric distinct diffusion coefficients derived in the preceding paper.