Recently, Gaussian-based smooth dielectric function has been developed in the DelPhi, which not only provides a surface-free approach for modelling electrostatics, but also can capture the atomic details in the continuum Poisson-Boltzmann (PB) model by using atom-specific heterogeneous dielectric values. In this talk, we will focus on singular point charges of the Gaussian PB model, which are unbounded Dirac delta functions. The usual trilinear interpolation of partial charges is known to introduce large numerical artifact or grid energy. To completely eliminate the grid energy, a novel regularization method is developed. In particular, a dual decomposition of potential and dielectric function is carried out, so that the charge singularities can be analytically captured by the Coulomb potential, while the reaction field potential satisfies a regularized PB equation with a new source term. Mathematical analysis has been conducted to show that a super-Gaussian density, instead of a Gaussian one, is required for the source term being well defined in the sense of distribution. Numerical tests have been conducted to demonstrate the accuracy and robustness of the proposed regularization. This talk is based on joint works with Dr. Emil Alexov (Clemson Univ.) and Dr. Yuanzhen Shao (Univ. of Alabama).

Analytical treatment of singular point charges in the Gaussian dielectric Poisson-Boltzmann model

ACS Spring 2022

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