Harold L. Friedman

Brownian dynamics as smart Monte Carlo simulation

A new Monte Carlo simulation procedure is developed which is expected to produce more rapid convergence than the standard Metropolis method. The trial particle moves are chosen in accord with a Brownian dynamics algorithm rather than at random. For two model systems, a string of point masses joined by harmonic springs and a cluster of charged soft spheres, the new procedure is compared to the standard one and shown to manifest a more rapid convergence rate for some important energetic and structural properties.

Integral Equation Methods in the Computation of Equilibrium Properties of Ionic Solutions

Computations have been made for a system of charged hard spheres with parameters chosen to correspond to an aqueous solution of a 1 − 1 electrolyte in the range from 0.001 to 1M. Correlation functions were computed by the analogues of the HNC and PY integral equations due to Allnatt in which the integral equations are constructed after the Mayer resummation has been performed on the expansion of g(r). Activity and osmotic coefficients are computed both by the compressibility and pressure equations and tested for consistency. Based on this test and others, including a comparison with computations published by Carley, it is concluded that the HNC equation gives very accurate results for this primitive model at least up to 1M. The accurate results show that the effect of the excluded volume of the hard‐sphere cores has been considerably underestimated in earlier treatments of the primitive model.

Study of a Refined Model for Aqueous 1‐1 Electrolytes

The hypernetted‐chain integral equation is used to calculate the ion–ion pair correlation functions and the thermodynamic properties of models for aqueous alkali halides based on an ion–ion pair potential function having four terms: the usual Coulomb term, a core repulsion term of order r−9, a well‐known dielectric repulsion term of order r−4, and a “Gurney” term to represent the effect of the overlap of the structure‐modified regions, “cospheres,” about the ions when the ions come close together. The only parameter in the potential which is adjusted to fit excess free energy data for solutions is the coefficient Aij of the Gurney term for the interaction of ions of species i and j. This is scaled so it represents the molar free energy change of water displaced from the cospheres when they overlap. The corresponding entropy change Sij and volume change Vij are adjusted to fit, respectively, heat of dilution and apparent molal volume data. Some thermodynamic problems in this fitting process, due to the und...

Image approximation to the reaction field

The reaction field for a charge at an arbitrary position in a spherical cavity in a medium of dielectric constant e may be expressed in terms of the electrical potential of a certain image charge. For e τ 1 the potential of the reaction field in the cavity is quite accurately the same as the electrical potential of the image charge. These observations form the basis of a rather economical and accurate way to calculate the reaction fields contribution to the interaction potential of particles with electric moments within a cavity within a dielectric. The results promise to be useful in the study of models for polar fluids and solutions by the Monte Carlo and Molecular Dynamics methods.

Brownian dynamics: Its application to ionic solutions

The method of molecular dynamics is applied to a solvent‐averaged model of electrolyte solutions, described by a generalized Langevin equation. For Brownian motion without solute–solute interactions, we recover the characteristic features of an infinitely dilute solution. For interacting brownons, the results exhibit a noticeable dependence of the calculated self‐diffusion coefficients on the influence of the Coulomb forces. The model system exhibits ion association when the Coulomb forces are made strong enough.

A molecular theory of solvation dynamics

The dynamic solvation time correlation function Z(t) is, within linear response, formulated in terms of the intermolecular solute–solvent interactions, without recourse to the intrinsically macroscopic concept of a cavity carved out of a dielectric medium. For interaction site models (ISM) of both the solute and the solvent, the theory relates the fluctuating polarization charge density of the solvent to the fluctuating vertical energy gap that controls Z(t). The theory replaces the factual (or bare) solute charge distribution by a surrogate expressed in terms of the solute–solvent site–site direct correlation functions. Calculations for solute ions in water and in acetonitrile lead to Z(t) and the second moment of the associated spectral density in good agreement with molecular dynamics simulation results in the literature. We also use the theory to calculate Z(t) for model solutes in which the ‘‘sudden’’ change of the charge distribution involves multipoles of higher order. The response is qualitatively...

The theory of the Fe2+–Fe3+ electron exchange in water

The rate constant for the Fe2+–Fe3+ electron exchange is formulated as k23= ∫ 0∞g23(r) k23(r) 4πr2 dr, a form which also is used to analyze the data for the nuclear spin relaxation in Al3+ induced by collision with Ni2+. It is assumed that the equilibrium pair correlation function g23(r) is the same function of ionic composition and temperature in the two cases and that in the spin relaxation process the local rate constant k23(r) has the form that may be deduced from the Solomon–Bloembergen equations. In the case of the exchange reaction the theory of k23(r) is developed with respect to the contributions from slow inner shell or outer shell reorganization (activation) dynamics. It is concluded that in the present case these complications are not important and that the controlling dynamics is the crossing from the reactant to the product diabatic Born– Oppenheimer surface. Neither the exchange nor the spin relaxation data can be accounted for if the smallest metal–metal distance in collisions is that g...

Lewis-Randall to McMillan-Mayer conversion for the thermodynamic excess functions of solutions. Part I. Partial free energy coefficients

Derivations are given for the thermodynamic relations that are needed to compare experimental thermodynamic excess functions of various kinds with the corresponding functions obtained from models for the solutions by calculations made in the framework of the McMillan-Mayer theory. This contribution extends earlier results. The new results are used to elucidate the behavior of the McMillan-Mayer thermodynamic excess functions of solutions which are very nearly ideal on the mole-fraction scale, for example, isotope mixtures. The study of these ideal systems leads to the conclusion that liquid-structure effects associated with the packing of molecules contribute a negative term to the potential of the force between solute particles in the solvent.

Integral Equation Computations for Aqueous 1–1 Electrolytes. Accuracy of the Method

The computations described earlier [J. Chem. Phys. 48, 2742 (1968)] have been carried out for a variety of primitive‐model parameters representative of aqueous 1–1 electrolyte solutions at 25°C. A number of tests, some new, have been applied to assess the accuracy of the results. One test involves a square‐mound model, for which some results are also given. The hypernetted‐chain equation is found to be quite satisfactory for these models up to 1M electrolyte concentration.

Green function theory of charge transfer processes in solution

By using a Green function Q to characterize the linear response of a dielectric body to electric charges, we obtain a theory for the solvent dielectric contribution to relaxation along the reaction coordinate RC(t) in an electron transfer process. For an electron transfer reaction model, in which the ions are embedded in a dielectric continuum, the theory gives, at t=0, the reorganization free energy derived by Marcus in 1956. For the same model the characteristic time τQ associated with RC(t) is evaluated in terms of the dielectric function eω of the medium. How the rate constant ket for an electron transfer process depends on τQ is illustrated for both high‐barrier and low‐barrier cases by approximating RC(t) as a Smoluchowski process on a potential surface. Applying the theory to a molecular model (charged hard sphere ions in a dipolar hard sphere solvent), treated in the mean spherical approximation for the response at any frequency (Wolynes, 1987), indicates that the effects of the molecular structur...