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

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.

References in corpus (6)

• Nonadiabatic corrections to rovibrational levels of H${}_2$
• Nonadiabatic corrections to the wave function and energy
• New representation of orbital motion with arbitrary angular momenta
• Elimination of the Translational Kinetic Energy Contamination in pre-Born-Oppenheimer Calculations
• Accumulation of three-body resonances above two-body thresholds
• Faddeev-Merkuriev equations for resonances in three-body Coulombic systems

Cited by in corpus (14)

• Pre-Born-Oppenheimer Molecular Structure Theory
• All-order relativistic computations for atoms and molecules using an explicitly correlated Gaussian basis
• Effective non-adiabatic Hamiltonians for the quantum nuclear motion over coupled electronic states
• Precise computation of rovibronic resonances of molecular hydrogen: $EF{}^1{\Sigma }_{\mathrm{g}}^{+}$ inner-well rotational states
• Non-adiabatic mass-correction functions and rovibrational states of ${}^4$He${}_2^{+}$ ($X{}^2{\Sigma }_{\text{u}}^{+}$)
• Non-adiabatic mass correction to the rovibrational states of molecules. Numerical application for the H${}_2^{+}$ molecular ion
• The Bethe-Salpeter QED wave equation for bound-state computations of atoms and molecules
• Generalized elimination of the global translation from explicitly correlated Gaussian functions
• H${}_3^{+}$ as a five-body problem described with explicitly correlated Gaussian basis sets
• Pre-Born-Oppenheimer energies, leading-order relativistic and QED corrections for electronically excited states of molecular hydrogen
• Laser-induced dynamic alignment of the HD molecule without the Born-Oppenheimer approximation
• Trilepton and tetralepton bound and resonant states: the QED counterpart of multiquark states
• Gaussians for Electronic and Rovibrational Quantum Dynamics
• Deformed Explicitly Correlated Gaussians