Electronic Structure Calculations with the Exact Pseudopotential and Interpolating Wavelet Basis

Abstract

Electronic structure calculations are mostly carried out with Coulomb potential singularity adapted basis sets such as STO or contracted GTO. With another basis or for heavy elements, the pseudopotentials may appear as a practical alternative. Here, we introduce the exact pseudopotential (EPP) to remove the Coulomb singularity and test it for orbitals of small atoms with the interpolating wavelet basis set. We apply EPP to the Galerkin method with a basis set consisting of Deslauriers–Dubuc scaling functions on the half-infinite real interval. We demonstrate the EPP–Galerkin method by computing the hydrogen atom 1s, 2s, and 2p orbitals and helium atom configurations He1s2, He1s2s1S, and He1s2s3S. We compare the method to the ordinary interpolating wavelet Galerkin method (OIW–Galerkin), handling the singularity at the nucleus by excluding the scaling function located at the origin from the basis. We also compare the performance of our approach to that of finite-difference approach, which is another practical method for spherical atoms. We find the accuracy of the EPP–Galerkin method to be better than both of the above-mentioned methods.