On the Calculation of Resonances in Pre-Born-Oppenheimer Molecular Structure Theory

TL;DR

This paper extends a pre-Born-Oppenheimer variational approach with complex coordinate rotation to calculate rovibronic resonances in small molecular systems, providing new resonance energies and widths for positronium and hydrogen molecules.

Contribution

It introduces a novel method combining variational calculations with complex rotation to accurately compute molecular resonances in small quantum systems.

Findings

Calculated resonance energies and widths for Ps$^-$ and Ps$_2$.

Estimated resonance parameters for H$_2$ beyond the $b ext{ }^3 ext{Σ}_ ext{u}^+$ continuum.

Extended the variational approach to include complex coordinate rotation.

Abstract

The main motivation for this work is the exploration of rotational-vibrational states corresponding to electronic excitations in a pre-Born-Oppenheimer quantum theory of molecules. These states are often embedded in the continuum of the lower-lying dissociation channel of the same symmetry, and thus are thought to be resonances. In order to calculate rovibronic resonances, the pre-Born-Oppenheimer variational approach of [J. Chem. Phys. 137, 024104 (2012)], based on the usage of explicitly correlated Gaussian functions and the global vector representation, is extended with the complex coordinate rotation method. The developed computer program is used to calculate resonance energies and widths for the three-particle positronium anion, Ps$^-$, and the four-particle positronium molecule, Ps$_2$. Furthermore, the excited bound and resonance rovibronic states of the four-particle H$_2$ molecule are also considered. Resonance energies and widths are estimated for the lowest-energy resonances of H$_2$ beyond the $b\ ^3\Sigma_\mathrm{u}^+$ continuum.