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

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 diatomic hydrogen molecules, the basis set generated by this formalism exhibits efficient approximation and systematic convergence for both the ground-state energy and electron density on the Hartree–Fock level. Finally, we test our even-tempered formalism on several tetra-atomic hydrogen molecules and identify its current limitations and potential improvements.