An efficient basis set representation for calculating electrons in molecules
The method of McCurdy, Baertschy, and Rescigno, is generalised to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules. It uses a basis set of product sinc functions arrayed on a Cartesian grid, and yields 1 kcal/mol precision for valence transition energies with a grid resolution of approximately 0.1 bohr. The Coulomb matrix elements are replaced with matrix elements obtained from the kinetic energy operator. A resolutionoftheidentity approximation renders the primitive one and twoelectron matrix elements diagonal; in other words, the Coulomb operator is local with respect to the grid indices. The calculation of contracted twoelectron matrix elements among orbitals requires only O( Nlog (N)) multiplication operations, not O( N ^{4}), where N is the number of basis functions; N = n ^{3} on cubic grids. The representation not only is numerically expedient, but also produces energies and properties superior to those calculated variationally. Absolute energies, absorption cross sections, transition energies, and ionisation potentials are reported for 1 (He ^{+}, H ^{+} _{2}), 2 (H _{2}, He), 10 (CH _{4}), and 56electron (C _{8}H _{8}) systems.
 Authors:

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 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Univ. of Nevada, Las Vegas, NV (United States)
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Davis, CA (United States)
 Publication Date:
 Grant/Contract Number:
 AC0205CH11231
 Type:
 Accepted Manuscript
 Journal Name:
 Molecular Physics
 Additional Journal Information:
 Journal Volume: 114; Journal Issue: 13; Journal ID: ISSN 00268976
 Publisher:
 Taylor & Francis
 Research Org:
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; sinc function; basis set; electronic structure; resolutionoftheidentity
 OSTI Identifier:
 1379502
Jones, Jeremiah R., Rouet, Francois Henry, Lawler, Keith V., Vecharynski, Eugene, Ibrahim, Khaled Z., Williams, Samuel, Abeln, Brant, Yang, Chao, McCurdy, William, Haxton, Daniel J., Li, Xiaoye S., and Rescigno, Thomas N.. An efficient basis set representation for calculating electrons in molecules. United States: N. p.,
Web. doi:10.1080/00268976.2016.1176262.
Jones, Jeremiah R., Rouet, Francois Henry, Lawler, Keith V., Vecharynski, Eugene, Ibrahim, Khaled Z., Williams, Samuel, Abeln, Brant, Yang, Chao, McCurdy, William, Haxton, Daniel J., Li, Xiaoye S., & Rescigno, Thomas N.. An efficient basis set representation for calculating electrons in molecules. United States. doi:10.1080/00268976.2016.1176262.
Jones, Jeremiah R., Rouet, Francois Henry, Lawler, Keith V., Vecharynski, Eugene, Ibrahim, Khaled Z., Williams, Samuel, Abeln, Brant, Yang, Chao, McCurdy, William, Haxton, Daniel J., Li, Xiaoye S., and Rescigno, Thomas N.. 2016.
"An efficient basis set representation for calculating electrons in molecules". United States.
doi:10.1080/00268976.2016.1176262. https://www.osti.gov/servlets/purl/1379502.
@article{osti_1379502,
title = {An efficient basis set representation for calculating electrons in molecules},
author = {Jones, Jeremiah R. and Rouet, Francois Henry and Lawler, Keith V. and Vecharynski, Eugene and Ibrahim, Khaled Z. and Williams, Samuel and Abeln, Brant and Yang, Chao and McCurdy, William and Haxton, Daniel J. and Li, Xiaoye S. and Rescigno, Thomas N.},
abstractNote = {The method of McCurdy, Baertschy, and Rescigno, is generalised to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules. It uses a basis set of product sinc functions arrayed on a Cartesian grid, and yields 1 kcal/mol precision for valence transition energies with a grid resolution of approximately 0.1 bohr. The Coulomb matrix elements are replaced with matrix elements obtained from the kinetic energy operator. A resolutionoftheidentity approximation renders the primitive one and twoelectron matrix elements diagonal; in other words, the Coulomb operator is local with respect to the grid indices. The calculation of contracted twoelectron matrix elements among orbitals requires only O(Nlog (N)) multiplication operations, not O(N4), where N is the number of basis functions; N = n3 on cubic grids. The representation not only is numerically expedient, but also produces energies and properties superior to those calculated variationally. Absolute energies, absorption cross sections, transition energies, and ionisation potentials are reported for 1 (He+, H+2), 2 (H2, He), 10 (CH4), and 56electron (C8H8) systems.},
doi = {10.1080/00268976.2016.1176262},
journal = {Molecular Physics},
number = 13,
volume = 114,
place = {United States},
year = {2016},
month = {4}
}