Molecular Orbital Treatment of Hydrogen with Central Potentials and Modified Boundary Conditions

A model is proposed for a homonuclear diatomic molecule in which each electron is treated as moving in the field which would prevail for an isolated atom but with boundary conditions which require that either the one electron eigenfunction, or its normal derivative, vanishes along a plane perpendicular to the line of centers and passing through the midpoint. The model is tested by applying it to molecular hydrogen. The assumed potential is compared to that computed from a Heitler‐London function, using a suggestion of Slater, and the energy of the ground state of hydrogen is computed as a function of internuclear distance. Employing the model throughout (i.e., without averaging the exact Hamiltonian) a dissociation energy of 5.65 ev is obtained and an equilibrium internuclear distance of 1.7 a.u. is predicted.