Relativistic theory of H₂⁺

The Dirac equation for H₂⁺ is reduced to a form similar to that of the Schrödinger equation with some perturbation terms. A first-order perturbation calculation for the 1sσ_g state then reveals that these relativistic effects lower the electronic energy by a small amount of order 0.2α2 for most internuclear separations and thereby make the molecule slightly more stable. The formalism is readily generalized to the isoelectronic sequence of H₂⁺, and the ratio of the relativistic correction to the nonrelativistic energy is found to be of order Z²α². Consequently, the relativistic correction becomes progressively more important as Z increases.