Hybrid gausslet/Gaussian basis sets

Abstract

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