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 waveletlike 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 atomcentered Gaussian bases. As a result, we also introduce diagonal approximations that dramatically reduce the computational scaling of twoelectron Coulomb terms in the Hamiltonian.
 Authors:

 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)
 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 00219606
 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 waveletlike 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 atomcentered Gaussian bases. As a result, we also introduce diagonal approximations that dramatically reduce the computational scaling of twoelectron 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}
}
Web of Science
Works referenced in this record:
Exact Tensor Hypercontraction: A Universal Technique for the Resolution of Matrix Elements of Local FiniteRange $N$ Body Potentials in ManyBody Quantum Problems
journal, September 2013
 Parrish, Robert M.; Hohenstein, Edward G.; Schunck, Nicolas F.
 Physical Review Letters, Vol. 111, Issue 13
Ab initio quantum chemistry using the density matrix renormalization group
journal, March 1999
 White, Steven R.; Martin, Richard L.
 The Journal of Chemical Physics, Vol. 110, Issue 9
Impact of electron–electron cusp on configuration interaction energies
journal, July 2001
 Prendergast, David; Nolan, M.; Filippi, Claudia
 The Journal of Chemical Physics, Vol. 115, Issue 4
OneDimensional Continuum Electronic Structure with the DensityMatrix Renormalization Group and Its Implications for DensityFunctional Theory
journal, August 2012
 Stoudenmire, E. M.; Wagner, Lucas O.; White, Steven R.
 Physical Review Letters, Vol. 109, Issue 5
Realspace mesh techniques in densityfunctional theory
journal, October 2000
 Beck, Thomas L.
 Reviews of Modern Physics, Vol. 72, Issue 4
Multiresolution quantum chemistry: Basic theory and initial applications
journal, December 2004
 Harrison, Robert J.; Fann, George I.; Yanai, Takeshi
 The Journal of Chemical Physics, Vol. 121, Issue 23
Tensor hypercontraction. II. Leastsquares renormalization
journal, December 2012
 Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.
 The Journal of Chemical Physics, Vol. 137, Issue 22
The Density Matrix Renormalization Group in Quantum Chemistry
journal, May 2011
 Chan, Garnet KinLic; Sharma, Sandeep
 Annual Review of Physical Chemistry, Vol. 62, Issue 1
An efficient basis set representation for calculating electrons in molecules
journal, April 2016
 Jones, Jeremiah R.; Rouet, FrançoisHenry; Lawler, Keith V.
 Molecular Physics, Vol. 114, Issue 13
Efficient tree tensor network states (TTNS) for quantum chemistry: Generalizations of the density matrix renormalization group algorithm
journal, April 2013
 Nakatani, Naoki; Chan, Garnet KinLic
 The Journal of Chemical Physics, Vol. 138, Issue 13
Reference electronic structure calculations in one dimension
journal, January 2012
 Wagner, Lucas O.; Stoudenmire, E. M.; Burke, Kieron
 Physical Chemistry Chemical Physics, Vol. 14, Issue 24
Colloquium : Area laws for the entanglement entropy
journal, February 2010
 Eisert, J.; Cramer, M.; Plenio, M. B.
 Reviews of Modern Physics, Vol. 82, Issue 1
Sliced Basis Density Matrix Renormalization Group for Electronic Structure
journal, July 2017
 Stoudenmire, E. Miles; White, Steven R.
 Physical Review Letters, Vol. 119, Issue 4
Density matrix formulation for quantum renormalization groups
journal, November 1992
 White, Steven R.
 Physical Review Letters, Vol. 69, Issue 19
Finiteelement method for electronic structure
journal, March 1989
 White, Steven R.; Wilkins, John W.; Teter, Michael P.
 Physical Review B, Vol. 39, Issue 9
Adaptivecoordinate realspace electronicstructure calculations for atoms, molecules, and solids
journal, April 1997
 Modine, N. A.; Zumbach, Gil; Kaxiras, Efthimios
 Physical Review B, Vol. 55, Issue 16
Daubechies wavelets for linear scaling density functional theory
journal, May 2014
 Mohr, Stephan; Ratcliff, Laura E.; Boulanger, Paul
 The Journal of Chemical Physics, Vol. 140, Issue 20
Multiresolution quantum chemistry in multiwavelet bases: excited states from timedependent Hartree–Fock and density functional theory via linear response
journal, January 2015
 Yanai, Takeshi; Fann, George I.; Beylkin, Gregory
 Physical Chemistry Chemical Physics, Vol. 17, Issue 47
An area law for onedimensional quantum systems
journal, August 2007
 Hastings, M. B.
 Journal of Statistical Mechanics: Theory and Experiment, Vol. 2007, Issue 08
Works referencing / citing this record:
Quantum computational chemistry
journal, March 2020
 McArdle, Sam; Endo, Suguru; AspuruGuzik, Alán
 Reviews of Modern Physics, Vol. 92, Issue 1
A review on non‐relativistic, fully numerical electronic structure calculations on atoms and diatomic molecules
journal, May 2019
 Lehtola, Susi
 International Journal of Quantum Chemistry, Vol. 119, Issue 19
Basis set convergence of Wilson basis functions for electronic structure
journal, August 2019
 Brown, James; Whitfield, James D.
 The Journal of Chemical Physics, Vol. 151, Issue 6
Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity
journal, October 2018
 Babbush, Ryan; Gidney, Craig; Berry, Dominic W.
 Physical Review X, Vol. 8, Issue 4