The Energy of Interaction between Two Hydrogen Atoms

The energy of interaction between two hydrogen atoms at intermediate to large separations is determined by the use of the variational principle applied to a wave function in which both ionic and polarization terms are included. The binding energy is known accurately in the neighborhood of the equilibrium separation from Rydberg's analysis of the experimental vibrational spectrum. At very large separations the van der Waals' energy has been calculated accurately by Pauling and Beach. Our calculations extend from the smallest to the largest internuclear distances. For the normal hydrogen molecule we compute a binding energy of 4.25 ev as compared to the experimental value of 4.74 ev. By comparing our calculations at small separations with Rydberg and at large separations with Pauling and Beach we obtain a most likely potential energy curve for all separations. Similarly we obtain a most likely potential energy curve for the 3Σ excited state of hydrogen by comparing with the accurate results of James, Coolidge, and Present. Many new molecular integrals were evaluated and old ones were recalculated to obtain greater accuracy. Convenient tables of these integrals together with all of the calculational detail is given.