Encoding electronic ground-state information with variational even-tempered basis sets

TL;DR

This paper introduces a novel basis-set design using even-tempered functions to efficiently encode electronic ground-state information, achieving high accuracy with lower computational cost and better scalability.

Contribution

It presents a reduced formalism and a symmetry-adapted approach for even-tempered basis sets, improving accuracy and efficiency in molecular ground-state calculations.

Findings

Hydrogen energy accuracy comparable to conventional methods

Dissociation curve aligns more with high-level basis sets

Effective for tetra-atomic hydrogen molecules

Abstract

We propose a system-oriented basis-set design based on even-tempered basis functions to variationally encode electronic ground-state information into molecular orbitals. First, we introduce a reduced formalism of concentric even-tempered orbitals that achieves hydrogen energy accuracy on par with the conventional formalism, with lower optimization cost and improved scalability. Second, we propose a symmetry-adapted, even-tempered formalism specifically designed for molecular systems. It requires only primitive S-subshell Gaussian-type orbitals and uses two parameters to characterize all exponent coefficients. In the case of the diatomic hydrogen molecule, the basis set generated by this formalism produces a dissociation curve more consistent with cc-pV5Z than cc-pVTZ at the size of aug-cc-pVDZ. Finally, we test our even-tempered formalism against several types of tetra-atomic hydrogen molecules for ground-state computation and point out its current limitations and potential improvements.