Hybrid grid/basis set discretizations of the Schrödinger equation

Abstract

We present a new kind of basis function for discretizing the Schrödinger equation in electronic structure calculations, called a gausslet, which has wavelet-like features but is composed of a sum of Gaussians. Gausslets are placed on a grid and combine advantages of both grid and basis set approaches. They are orthogonal, infinitely smooth, symmetric, polynomially complete, and with a high degree of locality. Because they are formed from Gaussians, they are easily combined with traditional atom-centered Gaussian bases. We also introduce diagonal approximations which dramatically reduce the computational scaling of two-electron Coulomb terms in the Hamiltonian.

arXiv comment16 pages, 9 figures

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