Calculation of Exchange Energies Using Algebraic Perturbation Theory

Abstract

An algebraic perturbation theory is presented for efficient calculations of localized states and hence of exchange energies, which are the differences between low-lying states of the valence electron of a molecule, formed by the collision of an ion \(Y^{+}\) with an atom \( X\). For the case of a homonuclear molecule these are the gerade and ungerade states and the exchange energy is an exponentially decreasing function of the internuclear distance. For such homonuclear systems the theory is used in conjunction with the Herring-Holstein technique to give accurate exchange energies for a range of intermolecular separations \(R\). Since the perturbation parameter is essentially 1/\(R\), this method is suitable for large \(R\). In particular, exchange energies are calculated for \(X_{2}\)\(^{+}\) systems, where \(X\) is H, Li, Na, K, Rb, or Cs.