An advanced dielectric continuum approach for treating solvation effects: Time correlation functions. I. Local treatment

A local continuum solvation theory, exactly treating electrostatic matching conditions on the boundary of a cavity occupied by a solute particle, is extended to cover time-dependent solvation phenomena. The corresponding integral equation is solved with a complex-valued frequency-dependent dielectric function epsilon(omega), resulting in a complex-valued omega-dependent reaction field. The inverse Fourier transform then produces the real-valued solvation energy, presented in the form of a time correlation function (TCF). We applied this technique to describe the solvation TCF for a benzophenone anion in Debye (acetonitrile) and two-mode Debye (dimethylformamide) solvents. For the Debye solvent the TCF is described by two exponential components, for the two-mode Debye solvent, by three. The overall dynamics in each case is longer than that given by the simple continuum model. We also consider a steady-state kinetic regime and the corresponding rate constant for adiabatic electron-transfer reactions. Here the boundary effect introduced within a frequency-dependent theory generates only a small effect in comparison with calculations made within the static continuum model

Advanced continuum approaches for treating time correlation functions. The role of solute shape and solvent structure

Time correlation functions describing the solvent relaxation around a molecule of coumarin-153 and a benzophenone anion in acetonitrile are calculated using dynamical continuum theories of solvation with an experimental dielectric function epsilon(omega) including the resonance absorption region of the solvent. Apart from the local model with a single molecular-shaped solute cavity of the solute studied previously, a new dynamic local model with a double molecular-shaped cavity and a dynamic nonlocal theory with a spherical cavity are presented, both of which introduce elements of solvent structure. It is shown that both local models, one- and two-cavity, exhibit experimentally unobserved oscillations in the shorter time region t < 1 ps, although the experimental asymptote for t > 1 ps for coumarin is obtained. The dynamics of the two-cavity model are not seen to differ from those of the one-cavity model. The nonlocal dynamic theory is shown to be able to suppress these oscillations, but the long-time asymptote differs markedly from that of the local theories. The nature of this asymptote is studied analytically

An advanced continuum medium model for treating solvation effects: Nonlocal electrostatics with a cavity

The Born-Kirkwood-Onsager (BKO) model of solvation, where a solute molecule is positioned inside a cavity cut into a solvent, which is considered as a dielectric continuum, is studied within the bounds of nonlocal electrostatics. The nonlocal cavity model is explicitly formulated and the corresponding nonlocal Poisson equation is reduced to an integral equation describing the behavior of the charge density induced in the medium. It is found that the presence of a cavity does not create singularities in the total electrostatic potential and its normal derivatives. Such singularities appear only in the local limit and are completely dissipated by nonlocal effects. The Born case of a spherical cavity with a point charge at its centre is investigated in detail. The corresponding one-dimensional integral Poisson equation is solved numerically and values for the solvation energy are determined. Several tests of this approach are presented: (a) We show that our integral equation reduces in the local limit to the chief equation of the local BKO theory. (b) We provide certain approximations which enable us to obtain the solution corresponding to the preceding nonlocal treatment of Dogonadze and Kornyshev (DK). (c) We make a comparison with the results of molecular solvation theory (mean spherical approximation), as applied to the calculation of solvation energies of spherical ions

Nonlocal continuum solvation model with oscillating susceptibility kernels: A nonrigid cavity model

A nonlocal continuum theory of solvation is applied using an oscillating dielectric function with spatial dispersion. It is found that a convergent solution cannot be calculated using a model of a fixed solute cavity inside the solvent continuum. This is attributed to the fact that the dielectric oscillations appear as a result of coupling between polarization and density fluctuations, contradicting the concept of a fixed cavity, The theory is corrected by allowing the cavity size to vary. A cavitation energy and an interaction between the medium reaction field and the cavity size are added to the solvation free energy, and a new theory obtained by a variational treatment. The interaction term enables convergent solutions to become attainable, resulting in an oscillating electrostatic solvation energy as a function of cavity radius, the cavitation term enables these oscillations to be smoothed out, resulting in a regular, monotonic solvation free energy