mFES: A Robust Molecular Finite Element Solver for Electrostatic Energy Computations.

We present a robust method for the calculation of electrostatic potentials of large molecular systems using tetrahedral finite elements (FE). Compared to the finite difference (FD) method using a regular simple cubic grid to solve the Poisson equation, the FE method can reach high accuracy and efficiency using an adaptive grid. Here, the grid points can be adjusted and are placed directly on the molecular surfaces to faithfully model surfaces and volumes. The grid point density decreases rapidly toward the asymptotic boundary to reach very large distances with just a few more grid points. A broad set of tools are applied to make the grid more regular and thus provide a more stable linear equation system, while reducing the number of grid points without compromising accuracy. The latter reduces the number of unknowns significantly and yields shorter solver execution times. The accuracy is further enhanced by using second order polynomials as shape functions. Generating the adaptive grid for a molecular system is expensive, but it pays off, if the same molecular geometry is used several times as is the case for pKA and redox potential computations of many charge variable groups in proteins. Application of the mFES method is also advantageous, if the molecular system is too large to reach sufficient accuracy when computing the electrostatic potential with conventional FD methods. The program mFES is free of charge and available at http://agknapp.chemie.fu-berlin.de/mfes .