# Relativistic corrections for the ground electronic state of molecular hydrogen

## TL;DR

This paper recalculates relativistic corrections for molecular hydrogen's ground state using high-precision variational methods, revealing discrepancies with experimental data that suggest larger unknown relativistic recoil effects.

## Contribution

It introduces a highly precise computational approach for relativistic corrections in molecular hydrogen, highlighting potential larger recoil effects than previously estimated.

## Key findings

- Achieved 8-digit numerical precision in relativistic correction calculations.
- Discovered discrepancies between theoretical energies and experimental values.
- Indicated possible significance of unknown relativistic recoil corrections.

## Abstract

We recalculate the leading relativistic corrections for the ground electronic state of the hydrogen molecule using variational method with explicitly correlated functions which satisfy the interelectronic cusp condition. The new computational approach allowed for the control of the numerical precision which reached about 8 significant digits. More importantly, the updated theoretical energies became discrepant with the known experimental values and we conclude that the yet unknown relativistic recoil corrections might be larger than previously anticipated.