On the Nature of the Crystal‐Field Approximation. IV. Generalization and Numerical Results

A modified molecular orbital theory was developed by Herzfeld and Goldberg to show the effect of the neglect of the wavefunction overlap and the electron exchange on the results of the conventional crystalfield theory. It was applied by them to calculate the interaction of a hydrogen atom in the 2p state and a hydrogen molecule in the ground state in two different simple nuclear configurations. In one case the atom nucleus was taken to lie on the perpendicular bisector of the molecular axis (T case), and in the other all the three nuclei were taken to lie on a line (L case). The method was generalized for the pⁿ‐atom–H₂‐molecule system (L case) by Goldberg (n  =  1–5). Numerical results were given for the p¹‐atom–H₂‐molecule system (L and T cases) by Berger and Herzfeld. In the present calculation this generalization is further extended to the pⁿ‐atom–H₂‐molecule system (T case) with numerical results given for the L and T cases. It is shown that the generalized crystal‐field theory can account for some of the shortcomings of the conventional crystal‐field theory. In particular, calculation shows how the “center of gravity” rule and the inversion result are modified. It also shows how the degeneracy is lifted in a system consisting of a diatomic molecule and an atom in the pⁿ configuration. The generalization of the Herzfeld–Goldberg method clearly demonstrates that the conventional crystal‐field theory cannot be considered to be a fundamental theory for the description of the wide range of phenomena that as a semiempirical method it has dealt with so well.