Analytical energy derivatives for a realistic continuum model of solvation: Application to the analysis of solvent effects on reaction paths

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Abstract
Analytical expressions for the first and second derivatives of the Hartree–Fock energy have been derived in case of a solvated system simulated by a multipolar charge distribution embedded in a cavity of arbitrary shape and a solvent represented by a dielectric continuum. A computer code has been written on these bases. It allows geometry optimizations and more generally the determination of the critical points of the potential energy surface for a molecular system interacting with a solvent as easily as in the case of an isolated molecule. The use of this code is illustrated by the computation of the main features of the reaction path of a Menshutkin‐type reaction in various solvents. The results compare pretty well with those obtained by a full Monte Carlo simulation of the solvent by Gao. This agreement supports the idea that solvents, including water, can be safely modeled by a continuum. The advantage of such models rests in the fact that they allow refined computations on the solute at a minimum computational expense.