Explicitly correlated Gaussian functions with shifted-center and projection techniques in pre-Born-Oppenheimer calculations

TL;DR

This paper develops numerical projection methods for explicitly correlated Gaussian functions in non-relativistic many-particle systems, improving energy calculations for the H3+ molecular ion by allowing flexible basis functions with rotational and parity quantum numbers.

Contribution

It introduces projection techniques for shifted explicitly correlated Gaussian functions, enhancing the accuracy of pre-Born-Oppenheimer calculations for molecular ions.

Findings

Achieved a substantial improvement in the variational upper bound for H3+ ground-state energy.

Demonstrated the effectiveness of projection methods for flexible basis functions.

Compared results with rovibrational calculations including non-adiabatic effects.

Abstract

Numerical projection methods are elaborated for the calculation of eigenstates of the non-relativistic many-particle Coulomb Hamiltonian with selected rotational and parity quantum numbers employing shifted explicitly correlated Gaussian functions, which are, in general, not eigenfunctions of the total angular momentum and parity operators. The increased computational cost of numerically projecting the basis functions onto the irreducible representations of the three dimensional rotation-inversion group is the price to pay for the increased flexibility of the basis functions. This increased flexibility allowed us to achieve a substantial improvement for the variational upper bound to the Pauli-allowed ground-state energy of the H$_3^+=\{$p$^+,$p$^+,$p$^+,$e$^-,$e$^-\}$ molecular ion treated as an explicit five-particle system. We compare our pre-Born-Oppenheimer result for this molecular ion with rovibrational results including non-adiabatic corrections.