One‐Electron Potential Function for H2

A one‐electron potential function is shown to exist such that the exact energy of the hydrogen molecule can be calculated with only a knowledge of the solution to the one‐electron Schrodinger equation, its eigenvalue and an average, over this solution, of the potential energy of one electron in the mean field of the remaining electron. Hence, given this potential function in advance, the exact energy of H2 can be calculated from the solution of a one‐electron problem. A formula for this potential function is obtained in terms of the exact eigenfunction for H2. The formula can only be applied to accurately calculate the potential function when the hydrogen eigenfunction is known, and hence the formula is useful primarily to demonstrate the existence of the potential. On the basis of the Heitler—London wavefunction, an approximate numerical comparison between this potential function and that suggested by Slater is given. An empirical formula for the potential function is suggested, and an undetermined param...