Hybrid grid/basis set discretizations of the Schrödinger equation

White, Steven R.

doi:10.1063/1.5007066

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:

^[1]

Univ. of California, Irvine, CA (United States)

Publication Date:: Fri Dec 22 00:00:00 EST 2017

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 0021-9606

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING

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                    White, Steven R. Hybrid grid/basis set discretizations of the Schrödinger equation.  United States: N. p., 2017. 
Web.  doi:10.1063/1.5007066.

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                    White, Steven R. Hybrid grid/basis set discretizations of the Schrödinger equation.  United States.  https://doi.org/10.1063/1.5007066

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                    White, Steven R. Fri .  
"Hybrid grid/basis set discretizations of the Schrödinger equation".  United States.  https://doi.org/10.1063/1.5007066.  https://www.osti.gov/servlets/purl/1511036.

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@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         = {Fri Dec 22 00:00:00 EST 2017},

  month        = {Fri Dec 22 00:00:00 EST 2017}

}

Copy to clipboard

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Works referenced in this record:

Exact Tensor Hypercontraction: A Universal Technique for the Resolution of Matrix Elements of Local Finite-Range $N$ -Body Potentials in Many-Body Quantum Problems
journal, September 2013

Parrish, Robert M.; Hohenstein, Edward G.; Schunck, Nicolas F.
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One-Dimensional Continuum Electronic Structure with the Density-Matrix Renormalization Group and Its Implications for Density-Functional Theory
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Stoudenmire, E. M.; Wagner, Lucas O.; White, Steven R.
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Annual Review of Physical Chemistry, Vol. 62, Issue 1
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Efficient tree tensor network states (TTNS) for quantum chemistry: Generalizations of the density matrix renormalization group algorithm
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Nakatani, Naoki; Chan, Garnet Kin-Lic
The Journal of Chemical Physics, Vol. 138, Issue 13
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Reference electronic structure calculations in one dimension
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Wagner, Lucas O.; Stoudenmire, E. M.; Burke, Kieron
Physical Chemistry Chemical Physics, Vol. 14, Issue 24
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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
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White, Steven R.; Wilkins, John W.; Teter, Michael P.
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Daubechies wavelets for linear scaling density functional theory
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Hastings, M. B.
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Hastings, M. B.
arXiv
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text, January 2011

Stoudenmire, E. M.; Wagner, Lucas O.; White, Steven R.
arXiv
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An efficient basis set representation for calculating electrons in molecules
text, January 2015

Jones, Jeremiah R.; Rouet, Francois-Henry; Lawler, Keith V.
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text, January 2000

Beck, Thomas L.
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text, January 2001

Prendergast, David; Nolan, M.; Filippi, Claudia
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journal, July 2017

Stoudenmire, E. Miles; White, Steven R.
Physical Review Letters, Vol. 119, Issue 4
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Works referencing / citing this record:

A review on non‐relativistic, fully numerical electronic structure calculations on atoms and diatomic molecules
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Lehtola, Susi
International Journal of Quantum Chemistry, Vol. 119, Issue 19
DOI: 10.1002/qua.25968

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journal, August 2019

Brown, James; Whitfield, James D.
The Journal of Chemical Physics, Vol. 151, Issue 6
DOI: 10.1063/1.5094295

Quantum computational chemistry
text, January 2018

McArdle, Sam; Endo, Suguru; Aspuru-Guzik, Alan
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DOI: 10.48550/arxiv.1808.10402

Basis set convergence of Wilson basis functions for electronic structure
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Brown, James; Whitfield, James D.
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DOI: 10.48550/arxiv.1812.09335

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Title: Hybrid grid/basis set discretizations of the Schrödinger equation

Abstract

Citation Formats

Exact Tensor Hypercontraction: A Universal Technique for the Resolution of Matrix Elements of Local Finite-Range N -Body Potentials in Many-Body Quantum Problems journal, September 2013

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An efficient basis set representation for calculating electrons in molecules journal, April 2016

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Exact Tensor Hypercontraction: A Universal Technique for the Resolution of Matrix Elements of Local Finite-Range $N$ -Body Potentials in Many-Body Quantum Problems
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Ab initio quantum chemistry using the density matrix renormalization group
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Impact of electron–electron cusp on configuration interaction energies
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Multiresolution quantum chemistry: Basic theory and initial applications
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Ten Lectures on Wavelets
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Tensor hypercontraction. II. Least-squares renormalization
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The Density Matrix Renormalization Group in Quantum Chemistry
journal, May 2011

An efficient basis set representation for calculating electrons in molecules
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Efficient tree tensor network states (TTNS) for quantum chemistry: Generalizations of the density matrix renormalization group algorithm
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Reference electronic structure calculations in one dimension
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Sliced Basis Density Matrix Renormalization Group for Electronic Structure
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Daubechies wavelets for linear scaling density functional theory
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An area law for one-dimensional quantum systems
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Real-Space Mesh Techniques in Density Functional Theory
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