ALBERT

Notes: 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 similar in the various cases studied here.

Notes: The spin-lattice relaxation time for nuclei possessing electric quadrupole moments is determined mainly by the electric quadrupolar interactions between the nucleus and its environment. Here we give a microscopic formulation of the nuclear quadrupolar relaxation problem for a nucleus of a monatomic solute dissolved in molecular fluids. Our formulation is based on classical statistical mechanics and the interaction site model representation of the intermolecular potential. We assume that the fluctuating field gradient felt by the nucleus is caused mainly by the charge distribution of the surrounding solvent molecules, modulated by the Sternheimer (anti)shielding factor of the nucleus. In the extreme narrowing condition, the problem reduces to the determination of a time integral of the field gradient time correlation function G(t) on the nucleus position. By separation of G(t) into a static contribution G(t=0) and a normalized time correlation function, we seek microscopic expressions for both G(t=0) and its correlation time τQ. Within certain approximations we express τQ in terms of the wavevector-dependent polarization charge correlation time τμ(k), and G(t=0) in terms of the pure solvent charge structure factor Sμ(k) and an analytical function of the solute cavity radius a. Taking as input τμ(k) from molecular dynamics simulations of the pure solvent and Sμ(k) from the extended reference interaction-site model (XRISM) calculation, we apply the theory to the spin lattice relaxation rate of seven quadrupolar nuclei in acetonitrile solution. The solutes considered cover a wide range of size, charge, and nuclear spin quantum number. With reasonable choices of the solute cavity radii, the theory successfully reproduces the experimentally measured 1/T1 for these solutes. Using molecular dynamics simulation, we also investigate the effects on 1/T1 of neglecting the solute mobility. Our simulated data suggest that the solute mobility can reasonably be neglected for spin relaxation of heavy quadrupolar nuclei such as Kr and Xe. Finally, the dielectric continuum limit of our theory is discussed and compared with the related theory developed by Hynes and Wolynes. © 1998 American Institute of Physics.

Notes: We extend a recent molecular theory of solvation dynamics to accommodate static solvent effects on the energetics of charge transfer (CT) processes. Our theory is based on a simple renormalized linear response development which incorporates nonlinear aspects of equilibrium solvation. It can accommodate polarizable solvent molecules as well as the limiting case represented by electronically rigid interaction site model (ISM) solvent molecules. We focus on the diabatic free energy profiles governing CT processes in solute donor–acceptor systems of chemical interest. By studying CT in ISM solution models we naturally cover both the short range and long range solute-solvent interactions, thereby enabling applications to CT in solvents of higher multipolar as well as dipolar character. We derive expressions for the key energetic parameters of a CT process; the solvent reorganization energy, the solvent contribution to the change in thermodynamic free energy, and the optical absorption and fluorescence frequencies. © 1996 American Institute of Physics.

Notes: We apply the theories developed in the preceding paper (paper I) to calculate various energy quantities of charge transfer (CT) reactions in nine solvents that cover a wide range of polarity, and for which interaction site models (ISM's) may be found in the literature. Besides the two surrogate Hamiltonian theories developed in paper I, the renormalized site-density theory (RST) and the renormalized dielectric theory (RDT), we also investigate a simple harmonic approximation (HXA) for the diabatic free energy profiles, whose characteristic parameters are calculated taking specific advantage of the expression given by the extended reference interaction site method (XRISM) for the free energy of solvation. For each CT process we analyze (a) the solvent reorganization energy λ, (b) the shift of the absorption transition energy due to the solvatochromic effect, and (c) the solvent contribution to the free energy change ΔA. In addition, for a few selected examples, we also report the detailed diabatic free energy profiles. The calculations reported rely on solute–solvent and solvent–solvent pair correlation functions obtained with the XRISM integral equation method applied to nonpolarizable (with fixed mean partial charges) ISM representations of the solute and solvent molecules. To rectify the omission of the solvent electronic degrees of freedom, we correct the dielectric part of the solvent reorganization energy with an additive term designed to compensate for the use of fixed charge ISM models. Contact with theories in which the solvent is represented as a dielectric continuum medium (with or without spatial dispersion) and the solute as a set of charges inside spherical cavities carved out of the dielectric is made straightforwardly within the RDT theory by considering a particularly simple form of the solute–solvent RISM site–site direct correlation functions. Using simple ISM models for several solute species, including Reichardt's betaine-30 dye and a porphyrin-quinone (PQ) "dyad'' recently studied by Mataga and co-workers, we examine the ability of the molecular theories to explain the dependence of charge-transfer energetics on dipolar and nondipolar solvents. We find that the solvatochromic effect on the absorption energy of betaine-30, which forms the basis of the ET(30) empirical solvent polarity scale, is reproduced reasonably well by the RST, RDT, and HXA theories for solvents ranging from carbon tetrachloride to water. In the case of the PQ dyad, we find that the calculated values of λ in dipolar and nondipolar solvents are in good agreement with experimental estimates. Our results indicate that the molecular theories of solvation discussed in this paper can explain the observation that a solvent with vanishing molecular dipole moment, like benzene, can show unmistakable "polarity,'' as reflected by its influence on the energetics of CT reactions. We also present calculations that corroborate the suggestion (Sec. VII of paper I) that, compared with the behavior in dipolar solvents, in nondipolar solvents the dependence of λ with the donor–acceptor separation distance is practically negligible. © 1996 American Institute of Physics.

Notes: Molecular dynamics (MD) simulations of εL(k,ω), the frequency (ω) and wave vector (k) dependent longitudinal component of the dielectric permittivity tensor, a quantity of importance in several theories of solvation dynamics and charge transfer reactions, is reported for three molecular liquids: CH3CN, CO2, and C6H6, represented by nonpolarizable model potentials. In order to study dielectric properties of nondipolar fluids we use, instead of the conventional approach which relates εL(k,ω) to longitudinal dipole density fluctuations, a more general approach of Raineri and co-workers which expresses this quantity in terms of charge density fluctuations. The two formulations are compared in the case of acetonitrile to assess the model dependence of εL(k,ω). We find that at finite k, 1/εL(k), where εL(k)=εL(k,0) is the static longitudinal permittivity, exhibits several similar features for all three liquids: A partial cancellation between single-molecule and pair charge density fluctuation correlations at small k, their constructive interference at intermediate k and the lack of molecular pair correlation contributions at large k. We also find that the extended reference interaction site model (XRISM) integral equations provide an excellent approximation to εL(k) of all three liquids. We use the fact 1/εL(k) is a polynomial in k2 at small k to determine the static dielectric constant ε0=εL(k=0) of acetonitrile and obtain a value in good agreement with ε0 evaluated by more conventional methods. We find that intermolecular correlations contribute the most to the dielectric properties of CH3CN and the least to those of CO2. In the range of k most relevant to solvation (k(approximately-less-than)1 Å−1), the pair component of the charge–charge time correlation function Φqq(k,t) is negative, partially cancelling the positive single-molecule component. The extent of cancellation varies with k and the strength of intermolecular electrostatic interactions, leading to significant qualitative differences in the behavior of Φqq(k,t) for polar and nondipolar liquids: In this k range, Φqq(k,t) in acetonitrile decays more slowly as k increases, while the opposite k-ordering is seen in the two nondipolar liquids. We use our results for εL(kmin,ω), where kmin is the smallest wave vector accessible in our simulation, to calculate the far-IR (infrared) absorption coefficient α(ω) of acetonitrile and find that it agrees well with α(ω) obtained from the transverse permittivity component, εT(kmin,ω), indicating that the bulk limit for this quantity has been reached. © 1999 American Institute of Physics.

Notes: Abstract We explore a recently developed theory of solvation dynamics that analyzes the molecular response of the solvent to a sudden change of the charge distribution of a solute particle immersed in it. We derive an approximate nonequilibrium distribution functionf ∑ h (Γ, t) for a “surrogate” Hamiltonian description of the solvation dynamics process. The surrogate Hamiltonian is expressed in terms of renormalized solute-solvent interactions, a feature that allows us to introduce a simple reduction scheme in the many-body dynamics problem without losing essential solute-solvent static correlations that rule the equilibrium solvation. Withf ∑ h (Γ, t) in hand we calculate the solvation time correlation function in two ways. The first one, previously reported, is basically a “dielectric formulation” in which the local polarization charge density of the solvent is the primary dynamical variable that couples to the field of the solute. In the new development reported here, the “site number density formulation,” the primary dynamical variables comprise the set of local solvent site number densities. We find that the dielectric formulation is embedded in the solvent site number density formulation as shown, for example, by comparing the respective time correlation functions of the solvation dynamics. An important feature of our approach is that at every stage the coupling between the solute and solvent is formulated in terms of the solute-solvent intermolecular interactions, rather than some sort of cavity construction. Furthermore, both the solute and the solvent molecules are represented by interaction site models. Applications of the dielectric theory are illustrated with calculations of the solvation dynamics of a cation in water and an exploration of the effect of the details of the charge distribution on the solvation dynamics of a benzenelike solute in acetonitrile.