Atomic basis functions for molecular electronic structure calculations

TL;DR

This paper develops new atomic basis functions, including diffuse functions, to improve the accuracy of molecular electronic structure calculations while reducing computational cost.

Contribution

It introduces a novel approach to generate atomic basis functions with diffuse functions for better molecular property predictions, extending previous correlation-consistent basis sets.

Findings

New atomic basis functions with diffuse functions improve molecular property calculations.

Analytical Gaussian representations achieve microhartree accuracy.

Complete-basis-set extrapolation formulas are developed for better energy convergence.

Abstract

Electronic structure methods for accurate calculation of molecular properties have a high cost that grows steeply with the problem size, therefore, it is helpful to have the underlying atomic basis functions that are less in number but of higher quality. Following our earlier work [Chem. Phys. Lett. 416, 116 (2005)] where general correlation-consistent basis sets are defined, for any atom, as solutions of purely atomic functional minimization problems, and which are shown to work well for chemical bonding in molecules, we take a further step here and define a new kind of atomic polarization functionals, the minimization of which yields additional sets of diffuse functions that help to calculate better molecular electron affinities, polarizabilities, and intermolecular dispersion interactions. Analytical representations by generally-contracted Gaussian functions of up to microhartree numerical accuracy grades are developed for atoms Hydrogen through Nobelium within the four-component Dirac-Coulomb theory and its scalar-relativistic approximation, and also for Hydrogen through Krypton in the two-component nonrelativistic case. The convergence of correlation energy with the basis set size is studied, and complete-basis-set extrapolation formulas are developed.