Improving the efficiency and convergence of geometry optimization with the polarizable continuum model: New energy gradients and molecular surface tessellation

Abstract

New equations are derived and implemented for efficient and accurate computation of solvation energy derivatives for the conductor-like polarizable continuum model (C-PCM) and the isotropic integral equation formalism polarizable continuum model (IEF-PCM). Two new molecular surface tessellation procedures GEPOL-RT and GEPOL-AS that generate near continuous potential energy surfaces are proposed for PCM geometry optimization. The combined use of these new techniques leads to efficient and convergent geometry optimizations with the PCMs.

Polarization energy gradients in combined quantum mechanics, effective fragment potential, and polarizable continuum model calculations

“…In this study only the conductorlike C-PCM, which in principle is applicable to conductors with = ϱ, is considered. However, it is common 11,16,17 to use C-PCM for solvents with Ͻϱ via simply scaling the apparent surface charges by a factor, selected to be ͑ −1͒ / in this study. Then, the energy and gradient expressions contain corresponding scaling factors.…”

“…The details of the approximation and simplification can be found in Ref. 17. The approximate PCM solvation energy gradients are sufficient for molecular geometry optimization and Hessian analyses.…”

“…A comparison between the gradients obtained by the approximate equations ͑analytic ones͒ and finite displacement ͑numerical ones͒ can be found in Ref. 17.…”

“…Since various approximations have been introduced in the evaluations of the derivatives of the QM fields 8 and the derivatives of the C matrix elements, 17 both the EFP polarization energy gradient and the PCM solvation energy gradient are approximate. To simplify the computer program development for the solution of two sets of PCM induced charges ͓Eqs.…”

“…It is emphasized that the errors of the approximations in Eqs. ͑46͒ and ͑47͒ are considerably smaller than those introduced in the approximate derivatives of the C matrix elements, 17 as assessed by comparing the numerical gradients obtained from small displacements to the analytic gradients obtained with the approximate equations for both EFP/PCM calculations with and without induced dipoles. There is little benefit to use the rigorous equations ͓Eqs.…”