The generalized Heitler-London theory for interatomic interaction and surface integral method for exchange energy

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Abstract
Based on the theory of the permutation group and the Rayleigh-Schrodinger perturbation theory, a systematic procedure is developed for the calculation of interatomic potentials. When this method is applied to the H molecule, the triplet (t) and singlet (s) energies are given by N N E = epsilon + s 1 epsilon, t, s n n x n = n = where epsilon and s are the n th-order polarization energy and overlap integral n n respectively, and epsilon is the exchange energy defined as epsilon = ( E - E ) 2. With N = 1, x x t s this expression is shown to be identical with the usual Heitler-London energy ; therefore this method is called generalized Heitler-London (GHL) theory. When epsilon x is expanded in terms of the Coulomb integral and the exchange integral, many previous symmetry-adapted perturbation theories are shown to be subsets of this expansion. The advantage of the GHL theory is that, instead of using the approximate exchange integrals, the exchange energy calculated from the surface integral method can be used directly. After a careful examination of the surface integral method for H and H, the exchange energy in a multielectron diatomic system is shown to be equal to the exchange energy of a single electron pair times a constant which can be obtained from a simple counting procedure. According to this theory, the energy curves of van der Waals potentials depend only on the known dispersion coefficients, the amplitude of the asymptotic wavefunctions, and the ionization energy of the individual atoms. With a simple analytical expression, potentials of many different diatomic systems are predicted with a high degree of accuracy. The GHL theory is also applied to the triatomic H system. Many previous semiempirical surfaces including the well known London-EyringPolanyi-Sato surface are examined in the light of the present result. In particular, the Cashion-Herschbach surface is shown to encompass far more information than previously recognized. The new theory now contains all the terms needed for an exact calculation.

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