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An efficient basis set representation for calculating electrons in molecules

Journal Article · · Molecular Physics
 [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)
+ Show Author Affiliations
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.
Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1379502
Journal Information:
Molecular Physics, Journal Name: Molecular Physics Journal Issue: 13 Vol. 114; ISSN 0026-8976
Publisher:
Taylor & FrancisCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (4)

Probing vibrational coupling via a grid‐based quantum approach—an efficient strategy for accurate calculations of localized normal modes in solid‐state systems journal October 2018
Hybrid grid/basis set discretizations of the Schrödinger equation journal December 2017
Low-Depth Quantum Simulation of Materials journal March 2018
A Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using Randomization journal June 2016

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Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
basis set
electronic structure
resolution-of-the-identity
sinc function