# Precise computation of rovibronic resonances of molecular hydrogen: $EF\ ^1\Sigma_\mathrm{g}^+$ inner-well rotational states

## TL;DR

This paper accurately computes the rovibronic resonances of molecular hydrogen's $EF$ state using advanced variational methods, achieving near-exact energies and refining theoretical predictions to match experimental data.

## Contribution

It introduces an energy-tracking optimization for basis representation, significantly improving the precision of resonance calculations in the four-body hydrogen molecule.

## Key findings

- Non-relativistic energies converged within a few nano Hartree
- Relativistic and QED corrections align theory with experiments
- Predissociative widths are negligible at high accuracy

## Abstract

Selected states of the $EF\ ^1\Sigma_\mathrm{g}^+$ electronic manifold of the hydrogen molecule are computed as resonances of the four-body problem. Systematic improvement of the basis representation for the variational treatment is achieved through an energy-tracking optimization procedure. The resulting non-relativistic energy is converged within a few nano Hartree, while the predissociative width is found to be negligible at this level of accuracy. The four-particle non-relativistic energies are appended with relativistic and quantum electrodynamics corrections which close the gap between the experimental observations and earlier theoretical work.