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Title: 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. As a result, we also introduce diagonal approximations that dramatically reduce the computational scaling of two-electron Coulomb terms in the Hamiltonian.

Authors:
ORCiD logo [1]
  1. Univ. of California, Irvine, CA (United States)
Publication Date:
Research Org.:
Univ. of California, Irvine, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1511036
Alternate Identifier(s):
OSTI ID: 1414610
Grant/Contract Number:  
SC0008696; SC008696
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 147; Journal Issue: 24; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

White, Steven R. Hybrid grid/basis set discretizations of the Schrödinger equation. United States: N. p., 2017. Web. doi:10.1063/1.5007066.
White, Steven R. Hybrid grid/basis set discretizations of the Schrödinger equation. United States. doi:10.1063/1.5007066.
White, Steven R. Fri . "Hybrid grid/basis set discretizations of the Schrödinger equation". United States. doi:10.1063/1.5007066. https://www.osti.gov/servlets/purl/1511036.
@article{osti_1511036,
title = {Hybrid grid/basis set discretizations of the Schrödinger equation},
author = {White, Steven R.},
abstractNote = {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. As a result, we also introduce diagonal approximations that dramatically reduce the computational scaling of two-electron Coulomb terms in the Hamiltonian.},
doi = {10.1063/1.5007066},
journal = {Journal of Chemical Physics},
number = 24,
volume = 147,
place = {United States},
year = {2017},
month = {12}
}

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