Computation of Atomic Solvent Accessible Surface Areas and Gradients for the Calculation of Solvation Energy and Forces on Molecules

Many models for the calculation of solvation energy and forces on a molecule involve atomic solvent accessible surface areas and their gradients. We present analytical formulas for such areas and gradients which utilize the Delaunay tetrahedrization of a molecule and its subset called the $\alpha$-complex. These formulas have been implemented in a fast computer program in conjunction with a solvation approach called \emph{Semi Explicit Assembly (SEA)}, and has shown to produce quick and physically accurate results.