Continuous surface charge polarizable continuum models of solvation. I. General formalism

Scalmani, Giovanni; Frisch, Michael J.

doi:doi:10.1063/1.3359469

Continuum solvation models are appealing because of the simplified yet accurate description they provide of the solvent effect on a solute, described either by quantum mechanical or classical methods. The polarizable continuum model (PCM) family of solvation models is among the most widely used, although their application has been hampered by discontinuities and singularities arising from the discretization of the integral equations at the solute-solvent interface. In this contribution we introduce a continuous surface charge (CSC) approach that leads to a smooth and robust formalism for the PCM models. We start from the scheme proposed over ten years ago by York and Karplus and we generalize it in various ways, including the extension to analytic second derivatives with respect to atomic positions. We propose an optimal discrete representation of the integral operators required for the determination of the apparent surface charge. We achieve a clear separation between “model” and “cavity” which, together with simple generalizations of modern integral codes, is all that is required for an extensible and efficient implementation of the PCM models. Following this approach we are now able to introduce solvent effects on energies, structures, and vibrational frequencies (analytical first and second derivatives with respect to atomic coordinates), magnetic properties (derivatives with respect of magnetic field using GIAOs), and in the calculation more complex properties like frequency-dependent Raman activities, vibrational circular dichroism, and Raman optical activity.

Article Outline

INTRODUCTION
GENERAL FORMALISM AND BASIC INTEGRAL OPERATORS
CONTINUOUS SURFACE CHARGE FORMALISM
1. The York–Karplus dicretization scheme
2. Separation of model and cavity in the energy expression
3. Discrete representation of the PCM integral equations
4. Optimal choice of the ζ_i exponents and the f_i and g_i self-factors
5. Separation of model and cavity in the energy derivative expression
  1. First derivatives
  2. Second derivatives
  3. Third derivatives
6. Implementation and efficiency considerations
CONCLUSIONS