Journal
MOLECULAR PHYSICS
Volume 114, Issue 13, Pages 2014-2028Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00268976.2016.1176262
Keywords
Sinc function; basis set; electronic structure; resolution-of-the-identity
Funding
- US Department of Energy Office of Basic Energy Sciences, Division of Chemical Sciences [DE-AC02-05CH11231]
- US Department of Energy [DESC0007182]
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The method of McCurdy, Baertschy, and Rescigno, J. Phys. B, 37, R137 (2004) [1] is generalised to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronicwave 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(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- (CH4), and 56-electron (C8H8) systems. [GRAPHICS] .
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