Hybrid gausslet/Gaussian basis sets

TL;DR

This paper presents hybrid gausslet/Gaussian basis sets that improve accuracy near nuclei while maintaining computational efficiency, demonstrated through Hartree Fock and full-CI calculations on small systems.

Contribution

It introduces a novel hybrid basis set combining gausslets and Gaussians, with orthogonalization and corrections to enhance accuracy and computational scaling.

Findings

Achieved microHartree accuracy in two-electron full-CI calculations.

Demonstrated improved near-nucleus accuracy with the hybrid basis.

Maintained quadratic scaling of the Hamiltonian with basis size.

Abstract

We introduce hybrid gausslet/Gaussian basis sets, where a standard Gaussian basis is added to a gausslet basis in order to increase accuracy near the nuclei while keeping the spacing of the grid of gausslets relatively large. The Gaussians are orthogonalized to the gausslets, which are already orthonormal, and approximations are introduced to maintain the diagonal property of the two electron part of the Hamiltonian, so that it continues to scale as the second power of the number of basis functions, rather than the fourth. We introduce several corrections to the Hamiltonian designed to enforce certain exact properties, such as the values of certain two-electron integrals. We also introduce a simple universal energy correction which compensates for the incompleteness of the basis stemming from the electron-electron cusps, based on the measured double occupancy of each basis function. We perform a number of Hartree Fock and full configuration interaction (full-CI) test calculations on two electron systems, and Hartree Fock on a ten-atom hydrogen chain, to benchmark these techniques. The inclusion of the cusp correction allows us to obtain complete basis set full-CI results, for the two electron cases, at the level of several microHartrees, and we see similar apparent accuracy for Hartree Fock on the ten-atom hydrogen chain.