Fixed nuclei two-centre problem in quantum mechanics

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Abstract
A special non-crossing rule for the potential curves of one-electron diatomic molecules is proved and then used to correlate united atom and separated atom states. A new technique for finding the asymptotic expansion of the electronic energy W in inverse powers of the internuclear distance R is developed and the expansion of W is found through O(1/R$^{6}$), with the coefficients expressed in terms of the nuclear charges and separated atom quantum numbers. Exponentially small corrections to the asymptotic expansion are evaluated and the g-u homonuclear and quasi-crossing heteronuclear energy splittings are discussed.