Approximation of Molecular Orbitals in Diatomic Molecules by Diatomic Orbitals

Abstract

The constants necessary for the specification of the exact wave functions of the homonuclear one-electron diatomic molecule have been tabulated for a range of relatively large internuclear distances. A method for determining upper and lower bounds of the constants is presented. The energy of the hydrogen molecule has been calculated for the ground state using the one-electron two-center wave functions as molecular orbitals. The results of a similar calculation by Hylleraas have been confirmed and extended. It is found that the best results are obtained if the effective nuclear charges for the molecular orbital of one electron are different from the effective nuclear charges for the molecular orbital of the second electron. Somewhat less satisfactory results are obtained if the effective nuclear charges are the same in both orbitals. The application of diatomic orbitals in the calculation of the properties of other diatomic molecules is discussed. Calculations of energy appear to be prohibitively laborious; calculations of electric dipole moments and transition probabilities may be feasible.