Relativistic corrections for the ground electronic state of molecular hydrogen

We recalculate the leading relativistic corrections for the ground electronic state of the hydrogen molecule using the variational method with explicitly correlated functions that satisfy the interelectronic cusp condition. The computational approach allowed for the control of the numerical precision, which reached about eight 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.