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Title: An efficient basis set representation for calculating electrons in molecules

Abstract

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 resolution-of-the-identity approximation renders the primitive one- and two-electron matrix elements diagonal; in other words, the Coulomb operator is local with respect to the grid indices. The calculation of contracted two-electron 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 56-electron (C8H8) systems.

Authors:
 [1];  [1];  [2];  [1];  [1];  [1];  [3];  [1];  [3];  [1];  [1];  [1]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  2. Univ. of Nevada, Las Vegas, NV (United States)
  3. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Davis, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1379502
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Molecular Physics
Additional Journal Information:
Journal Volume: 114; Journal Issue: 13; Journal ID: ISSN 0026-8976
Publisher:
Taylor & Francis
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; sinc function; basis set; electronic structure; resolution-of-the-identity

Citation Formats

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., 2016. 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. Wed . "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 resolution-of-the-identity approximation renders the primitive one- and two-electron matrix elements diagonal; in other words, the Coulomb operator is local with respect to the grid indices. The calculation of contracted two-electron 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 56-electron (C8H8) systems.},
doi = {10.1080/00268976.2016.1176262},
journal = {Molecular Physics},
number = 13,
volume = 114,
place = {United States},
year = {2016},
month = {4}
}

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