An efficient basis set representation for calculating electrons in molecules

ABSTRACT

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 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.

KEYWORDS:

• Sinc function
• basis set
• electronic structure
• resolution-of-the-identity

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Erratum

Acknowledgments

We thank the National Energy Research Scientific Computing Center (NERSC) for computational resources.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the US Department of Energy Office of Basic Energy Sciences, Division of Chemical Sciences [Grant Number DE-AC02-05CH11231]; US Department of Energy [Grant Number DESC0007182].