Hybrid grid/basis set discretizations of the Schrödinger equation

White, Steven R.

doi:10.1063/1.5007066

Hybrid grid/basis set discretizations of the Schrödinger equation

Journal Article · Fri Dec 22 00:00:00 EST 2017 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.5007066· OSTI ID:1511036

^[1]

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

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.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of California, Irvine, CA (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

Grant/Contract Number:: SC0008696

OSTI ID:: 1511036

Alternate ID(s):: OSTI ID: 1414610

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 24 Vol. 147; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (25)

Sliced Basis Density Matrix Renormalization Group for Electronic Structure Stoudenmire, E. Miles; White, Steven R. Physical Review Letters, Vol. 119, Issue 4 https://doi.org/10.1103/physrevlett.119.046401	journal	July 2017
Reference electronic structure calculations in one dimension Wagner, Lucas O.; Stoudenmire, E. M.; Burke, Kieron Physical Chemistry Chemical Physics, Vol. 14, Issue 24 https://doi.org/10.1039/c2cp24118h	journal	January 2012
Multiresolution quantum chemistry in multiwavelet bases: excited states from time-dependent Hartree–Fock and density functional theory via linear response Yanai, Takeshi; Fann, George I.; Beylkin, Gregory Physical Chemistry Chemical Physics, Vol. 17, Issue 47 https://doi.org/10.1039/c4cp05821f	journal	January 2015
Impact of electron–electron cusp on configuration interaction energies Prendergast, David; Nolan, M.; Filippi, Claudia The Journal of Chemical Physics, Vol. 115, Issue 4 https://doi.org/10.1063/1.1383585	journal	July 2001
Multiresolution quantum chemistry: Basic theory and initial applications Harrison, Robert J.; Fann, George I.; Yanai, Takeshi The Journal of Chemical Physics, Vol. 121, Issue 23 https://doi.org/10.1063/1.1791051	journal	December 2004
Tensor hypercontraction. II. Least-squares renormalization Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J. The Journal of Chemical Physics, Vol. 137, Issue 22 https://doi.org/10.1063/1.4768233	journal	December 2012
Ab initio quantum chemistry using the density matrix renormalization group White, Steven R.; Martin, Richard L. The Journal of Chemical Physics, Vol. 110, Issue 9 https://doi.org/10.1063/1.478295	journal	March 1999
Efficient tree tensor network states (TTNS) for quantum chemistry: Generalizations of the density matrix renormalization group algorithm Nakatani, Naoki; Chan, Garnet Kin-Lic The Journal of Chemical Physics, Vol. 138, Issue 13 https://doi.org/10.1063/1.4798639	journal	April 2013
Daubechies wavelets for linear scaling density functional theory Mohr, Stephan; Ratcliff, Laura E.; Boulanger, Paul The Journal of Chemical Physics, Vol. 140, Issue 20 https://doi.org/10.1063/1.4871876	journal	May 2014
An efficient basis set representation for calculating electrons in molecules Jones, Jeremiah R.; Rouet, François-Henry; Lawler, Keith V. Molecular Physics, Vol. 114, Issue 13 https://doi.org/10.1080/00268976.2016.1176262	journal	April 2016
An area law for one-dimensional quantum systems Hastings, M. B. Journal of Statistical Mechanics: Theory and Experiment, Vol. 2007, Issue 08 https://doi.org/10.1088/1742-5468/2007/08/p08024	journal	August 2007
Finite-element method for electronic structure White, Steven R.; Wilkins, John W.; Teter, Michael P. Physical Review B, Vol. 39, Issue 9 https://doi.org/10.1103/physrevb.39.5819	journal	March 1989
Adaptive-coordinate real-space electronic-structure calculations for atoms, molecules, and solids Modine, N. A.; Zumbach, Gil; Kaxiras, Efthimios Physical Review B, Vol. 55, Issue 16 https://doi.org/10.1103/physrevb.55.10289	journal	April 1997
One-Dimensional Continuum Electronic Structure with the Density-Matrix Renormalization Group and Its Implications for Density-Functional Theory Stoudenmire, E. M.; Wagner, Lucas O.; White, Steven R. Physical Review Letters, Vol. 109, Issue 5 https://doi.org/10.1103/physrevlett.109.056402	journal	August 2012
Exact Tensor Hypercontraction: A Universal Technique for the Resolution of Matrix Elements of Local Finite-Range N -Body Potentials in Many-Body Quantum Problems Parrish, Robert M.; Hohenstein, Edward G.; Schunck, Nicolas F. Physical Review Letters, Vol. 111, Issue 13 https://doi.org/10.1103/physrevlett.111.132505	journal	September 2013
Density matrix formulation for quantum renormalization groups White, Steven R. Physical Review Letters, Vol. 69, Issue 19 https://doi.org/10.1103/physrevlett.69.2863	journal	November 1992
Real-space mesh techniques in density-functional theory Beck, Thomas L. Reviews of Modern Physics, Vol. 72, Issue 4 https://doi.org/10.1103/revmodphys.72.1041	journal	October 2000
Colloquium : Area laws for the entanglement entropy Eisert, J.; Cramer, M.; Plenio, M. B. Reviews of Modern Physics, Vol. 82, Issue 1 https://doi.org/10.1103/revmodphys.82.277	journal	February 2010
Ten Lectures on Wavelets Daubechies, Ingrid CBMS-NSF Regional Conference Series in Applied Mathematics https://doi.org/10.1137/1.9781611970104	book	January 1992
The Density Matrix Renormalization Group in Quantum Chemistry Chan, Garnet Kin-Lic; Sharma, Sandeep Annual Review of Physical Chemistry, Vol. 62, Issue 1 https://doi.org/10.1146/annurev-physchem-032210-103338	journal	May 2011
An Area Law for One Dimensional Quantum Systems Hastings, M. B. arXiv https://doi.org/10.48550/arxiv.0705.2024	text	January 2007
One-dimensional Continuum Electronic Structure with the Density Matrix Renormalization Group and Its Implications For Density Functional Theory Stoudenmire, E. M.; Wagner, Lucas O.; White, Steven R. arXiv https://doi.org/10.48550/arxiv.1107.2394	text	January 2011
An efficient basis set representation for calculating electrons in molecules Jones, Jeremiah R.; Rouet, Francois-Henry; Lawler, Keith V. arXiv https://doi.org/10.48550/arxiv.1507.03324	text	January 2015
Real-Space Mesh Techniques in Density Functional Theory Beck, Thomas L. arXiv https://doi.org/10.48550/arxiv.cond-mat/0006239	text	January 2000
Impact of Electron-Electron Cusp on Configuration Interaction Energies Prendergast, David; Nolan, M.; Filippi, Claudia arXiv https://doi.org/10.48550/arxiv.cond-mat/0102536	text	January 2001

Cited By (6)

A review on non‐relativistic, fully numerical electronic structure calculations on atoms and diatomic molecules Lehtola, Susi International Journal of Quantum Chemistry, Vol. 119, Issue 19 https://doi.org/10.1002/qua.25968	journal	May 2019
Basis set convergence of Wilson basis functions for electronic structure Brown, James; Whitfield, James D. The Journal of Chemical Physics, Vol. 151, Issue 6 https://doi.org/10.1063/1.5094295	journal	August 2019
Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity Babbush, Ryan; Gidney, Craig; Berry, Dominic W. Physical Review X, Vol. 8, Issue 4 https://doi.org/10.1103/physrevx.8.041015	journal	October 2018
Quantum computational chemistry McArdle, Sam; Endo, Suguru; Aspuru-Guzik, Alán Reviews of Modern Physics, Vol. 92, Issue 1 https://doi.org/10.1103/revmodphys.92.015003	journal	March 2020
Quantum computational chemistry McArdle, Sam; Endo, Suguru; Aspuru-Guzik, Alan arXiv https://doi.org/10.48550/arxiv.1808.10402	text	January 2018
Basis set convergence of Wilson basis functions for electronic structure Brown, James; Whitfield, James D. arXiv https://doi.org/10.48550/arxiv.1812.09335	text	January 2018

Similar Records

Hybrid gausslet/Gaussian basis sets

Journal Article · Mon Nov 08 19:00:00 EST 2021 · Journal of Chemical Physics · OSTI ID:1978969

Multisliced gausslet basis sets for electronic structure

Journal Article · Sun Feb 10 19:00:00 EST 2019 · Physical Review. B · OSTI ID:1611139

Related Subjects

97 MATHEMATICS AND COMPUTING

Hybrid grid/basis set discretizations of the Schrödinger equation

Citation Formats

References (25)

Cited By (6)

Similar Records

Related Subjects