A divide and conquer real-space approach for all-electron molecular electrostatic potentials and interaction energies

Abstract

A computational scheme to perform accurate numerical calculations of electrostatic potentials and interaction energies for molecular systems has been developed and implemented. Molecular electron and energy densities are divided into overlapping atom-centered atomic contributions and a three-dimensional molecular remainder. The steep nuclear cusps are included in the atom-centered functions making the three-dimensional remainder smooth enough to be accurately represented with a tractable amount of grid points. The one-dimensional radial functions of the atom-centered contributions as well as the three-dimensional remainder are expanded using finite element functions. The electrostatic potential is calculated by integrating the Coulomb potential for each separate density contribution, using our tensorial finite element method for the three-dimensional remainder. We also provide algorithms to compute accurate electron-electron and electron-nuclear interactions numerically using the proposed partitioning. The methods have been tested on all-electron densities of 18 reasonable large molecules containing elements up to Zn. The accuracy of the calculated Coulomb interaction energies is in the range of 10(-3) to 10(-6) E(h) when using an equidistant grid with a step length of 0.05 a(0).