On the Nature of the Crystal Field Approximation. II. Numerical Results

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Abstract
Herzfeld and Goldberg developed a modified molecular orbital technique to show the effect of the neglect of wavefunction overlap and electron exchange on the results of crystal field theory. They gave formal results for the interaction of a hydrogen atom in a 2p state and a hydrogen molecule in the ground state for two different nuclear configurations. In one case, the atom nucleus lies on the perpendicular bisector of the molecule axis, and in the other all three nuclei lie on a line. These results have been evaluated analytically and numerically for a wide range of internuclear distances. Values for crystal field splitting parameters obtained by the new MO method cross over those obtained by crystal field theory at a distance between the atom and perturbing molecule of about 4‐bohr radii (2A). At this distance, the result of the modified MO calculation is primarily determined by overlap and exchange contributions. At larger distances, where exchange and overlap go to zero, both methods give the classical expression for the interaction of two quadrupoles.

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