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

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.

15 pages, 14 figures, 5 tables, 2 algorithms

References in corpus (5)

• Recent developments in the PySCF program package
• A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry
• Communication: Curing basis set overcompleteness with pivoted Cholesky decompositions
• Hydrogen molecule spectrum by many-body GW and Bethe-Salpeter equation
• Basis set generation and optimization in the NISQ era with Quiqbox.jl