What is it about?
An extension of the analysis by Tang et al. (1991) of the ground and excited states of H2(+) is presented which indicates that the dominant terms of the exchange energy in a multielectron diatomic molecular ion can be calculated systematically by using the expansion of the polarized wave function in powers of 1/R in the Holstein-Herring surface integral. Because the expansion coefficients can be obtained by solving inhomogeneous differential equations using variational or other methods, a straightforward procedure is established for calculating the exchange energies of multielectron ionic systems at large internuclear distances.
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Why is it important?
This PRL paper resolved a mystery concerning the convergence issues of the results by Tang et. al concerning the Holstein-Herring method. They thought the polarization wave function (obtained from perturbation theory) converged somewhere in between the two lowest states of H2+. Wrong. Without realizing it, what they had instead was the Herring function! Nonetheless, their treatment lead to the Herring function for H2+ which is why they correctly got the lead term of H_2^+.
Perspectives
Nonetheless, the authors Tang et al. showed that the polarization wave function i.e. the wave function obtained from perturbation theory could be used to get the exchange energy splittings. A potential industry resulted in calculating such an elusive yet important result which is the exchange energy splitting at long internuclear distances, order by order.
Dr Tony Cyril Scott
RWTH-Aachen University
Read the Original
This page is a summary of: Exchange energy ofH2+</mml:mrow..., Physical Review Letters, September 1991, American Physical Society (APS),
DOI: 10.1103/physrevlett.67.1419.
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