Relativistic correction to equilibrium bond lengths for heavy, almost spherical molecules

The relativistic correction to the limiting bond length found by Pucci and March for heavy, almost spherical molecules typified by the series ${\mathrm{CH}}_4$,...,${\mathrm{PbH}}_4$ is calculated as a function of the fine-structure constant α by means of relativistic Thomas-Fermi theory. The correction is found to remain nonzero in the limit as the atomic number of the central atom X in the X${\mathrm{H}}_4$ series tends to infinity. However, putting α=(1/137), the numerical change in bond length is extremely small.