Hybrid gausslet/Gaussian basis sets
Abstract
We introduce hybrid gausslet/Gaussian basis sets, where a standard Gaussian basis is added to a gausslet basis in order to increase accuracy near the nuclei while keeping the spacing of the grid of gausslets relatively large. The Gaussians are orthogonalized to the gausslets, which are already orthonormal, and approximations are introduced to maintain the diagonal property of the two electron part of the Hamiltonian so that it continues to scale as the second power of the number of basis functions rather than the fourth. We introduce several corrections to the Hamiltonian designed to enforce certain exact properties, such as the values of certain two-electron integrals. We also introduce a simple universal energy correction that compensates for the incompleteness of the basis stemming from the electron–electron cusps based on the measured double occupancy of each basis function. We perform a number of Hartree Fock and full configuration interaction (full-CI) test calculations on two electron systems and Hartree Fock on a ten-atom hydrogen chain to benchmark these techniques. The inclusion of the cusp correction allows us to obtain complete basis set full-CI results for the two electron cases at the level of several micro-Hartrees, and we see similar apparent accuracy for Hartreemore »
- Publication Date:
- Research Org.:
- Univ. of California, Irvine, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF); Simons Foundation
- OSTI Identifier:
- 1978969
- Alternate Identifier(s):
- OSTI ID: 1829534
- Grant/Contract Number:
- SC0008696; DMR-1812 558
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Chemical Physics
- Additional Journal Information:
- Journal Volume: 155; Journal Issue: 18; Journal ID: ISSN 0021-9606
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; electronic structure methods; correlation energy; basis sets; full configuration interaction; wavelet transform; density matrix renormalization group
Citation Formats
Qiu, Yiheng, and White, Steven R. Hybrid gausslet/Gaussian basis sets. United States: N. p., 2021.
Web. doi:10.1063/5.0068887.
Qiu, Yiheng, & White, Steven R. Hybrid gausslet/Gaussian basis sets. United States. https://doi.org/10.1063/5.0068887
Qiu, Yiheng, and White, Steven R. Tue .
"Hybrid gausslet/Gaussian basis sets". United States. https://doi.org/10.1063/5.0068887. https://www.osti.gov/servlets/purl/1978969.
@article{osti_1978969,
title = {Hybrid gausslet/Gaussian basis sets},
author = {Qiu, Yiheng and White, Steven R.},
abstractNote = {We introduce hybrid gausslet/Gaussian basis sets, where a standard Gaussian basis is added to a gausslet basis in order to increase accuracy near the nuclei while keeping the spacing of the grid of gausslets relatively large. The Gaussians are orthogonalized to the gausslets, which are already orthonormal, and approximations are introduced to maintain the diagonal property of the two electron part of the Hamiltonian so that it continues to scale as the second power of the number of basis functions rather than the fourth. We introduce several corrections to the Hamiltonian designed to enforce certain exact properties, such as the values of certain two-electron integrals. We also introduce a simple universal energy correction that compensates for the incompleteness of the basis stemming from the electron–electron cusps based on the measured double occupancy of each basis function. We perform a number of Hartree Fock and full configuration interaction (full-CI) test calculations on two electron systems and Hartree Fock on a ten-atom hydrogen chain to benchmark these techniques. The inclusion of the cusp correction allows us to obtain complete basis set full-CI results for the two electron cases at the level of several micro-Hartrees, and we see similar apparent accuracy for Hartree Fock on the ten-atom hydrogen chain.},
doi = {10.1063/5.0068887},
journal = {Journal of Chemical Physics},
number = 18,
volume = 155,
place = {United States},
year = {Tue Nov 09 00:00:00 EST 2021},
month = {Tue Nov 09 00:00:00 EST 2021}
}
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