Dielectric boundary smoothing in finite difference solutions of the poisson equation: An approach to improve accuracy and convergence

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Abstract
Finite difference methods are becoming very popular for calculating electrostatic fields around molecules. Due to the large amount of computer memory required, grid spacings cannot be made extremely small in relation to the size of the van der Waals radii of the atoms. As a result, the calculations make a rather crude approximation to the molecular surface by defining grid line midpoints discontinuously as either interior or exterior. We present a method which “smoothes” the boundary, but more accurately models the potential from the analytic solution of the discontinuous dielectric problem and improves convergence in electrostatic energy calculations. In addition, a small improvement in convergence rate is observed.