The computational effort of biomolecular simulations can be significantly reduced by means of implicit solvent models in which the energy generally contains a correction depending on the surface area and/or the volume of the molecule. In this article, we present simple derivation of exact, easy-to-use analytical formulas for these quantities and their derivatives with respect to atomic coordinates. In addition, we provide an efficient, linear-scaling algorithm for the construction of the power diagram required for practical implementation of these formulas. Our approach is implemented in a C++ header-only template library.
Derivatives of molecular surface area and volume: Simple and exact analytical formulas
K. Klenin, F. Tristram, T. Strunk, and W. Wenzel
J. Comp. Chem. 32, 2647-2653