Basis set construction for molecular electronic structure theory: Natural orbital and Gauss-Slater basis for smooth pseudpotentials

TL;DR

This paper introduces a new method for constructing molecular basis sets using atomic natural orbitals and Gauss-Slater primitives optimized for pseudopotentials, improving accuracy and efficiency in electronic structure calculations.

Contribution

The authors develop a general basis set construction approach combining natural orbitals with Gauss-Slater primitives optimized for pseudopotentials, applicable across various electronic structure methods.

Findings

Significant improvements over existing basis sets for elements H to Ar.

Basis sets are compatible with any electronic structure method via Gaussian expansion.

Numerical integral evaluation benefits quantum Monte Carlo applications.

Abstract

A simple yet general method for constructing basis sets for molecular electronic structure calculations is presented. These basis sets consist of atomic natural orbitals from a multi-configurational self-consistent field calculation supplemented with primitive functions, chosen such that the asymptotics are appropriate for the potential of the system. Primitives are optimized for the homonuclear diatomic molecule to produce a balanced basis set. Two general features that facilitate this basis construction are demonstrated. First, weak coupling exists between the optimal exponents of primitives with different angular momenta. Second, the optimal primitive exponents for a chosen system depend weakly on the particular level of theory employed for optimization. The explicit case considered here is a basis set appropriate for the Burkatzki-Filippi-Dolg pseudopotentials. Since these pseudopotentials are finite at nuclei and have a Coulomb tail, the recently proposed Gauss-Slater functions are the appropriate primitives. Double- and triple-zeta bases are developed for elements hydrogen through argon. These new bases offer significant gains over the corresponding Burkatzki-Filippi-Dolg bases at various levels of theory. Using a Gaussian expansion of the basis functions, these bases can be employed in any electronic structure method. Quantum Monte Carlo provides an added benefit: expansions are unnecessary since the integrals are evaluated numerically.