Electronically adiabatic reaction field approach to solvation. I. Theoretical formulation via multipole expansion in a fluctuating cavity

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Abstract
A theoretical framework for the solute electronic structure description under nonequilibrium solvation is developed via multipole expansions of a quantum dielectric continuum solvent formulation of Kim and Hynes [J. Chem. Phys. 96, 5088 (1992)]. By employing a spherical cavity for the solute and invoking a Born–Oppenheimer description for the solvent electronic polarization P⃗el, the cavity boundary effects on the solute electric and solvent polarization fields are taken into account exactly. The solute–solvent electronic correlation effects are also included within the dielectric continuum context in the fast P⃗el limit. Another novel feature of the theory includes the cavity size variation with the solute electronic charge distribution and its thermal fluctuations. This effectively accounts for, e.g., electrostriction, largely ignored in many solution-phase quantum chemistry calculations based on the reaction field methods. By employing a coherent state description for P⃗el, we obtain electronically adiabatic free energies as a function of the cavity radius variable that measures the fluctuating cavity size and the solvent coordinates that gauge the nonequilibrium solvent orientational polarization P⃗or. These define multidimensional electronic free energy surfaces, upon which nuclear dynamics occur. Their local structure near equilibrium, along with the solute polarizability effects on the force constant matrix, is analyzed. With a polaron description for the P⃗or kinetic energy, it is found that the frequency relevant for ultrafast inertial solvation dynamics decreases as the Pvec;or multipole character increases. This is in qualitative agreement with recent molecular solvation theory predictions. As for the cavity, the frequency associated with its symmetric breathing mode is examined by analyzing our previous molecular dynamics simulation results via the equipartition principle. It is found that the cavity frequency is comparable to that of P⃗or. The variation of the equilibrium cavity size with the solute charge distribution and its influence on free energetics are also studied. Model calculations in water show that the cavity size decreases with the increasing solute dipole moment. This results in a significant reduction of equilibrium free energy, compared to that obtained with the neglect of the electrostriction effect.