A generalized Heitler–London theory of the chemical bond in H+2

Abstract

The perturbation theory for the total energies of the 1sσg and 2pσu states of H+2 is reformulated in a manner which avoids problems resulting from symmetrization. First a new set of localized wave functions are defined and calculated from polarization perturbation theory. After symmetrization of these wave functions, a generalized Heitler–London energy, which can be expanded to all orders, is obtained. In second order the result agrees with the Murrell–Shaw Musher–Amos expression. An expansion of the expectation value of the energy is also carried out and provides similar results. Many symmetry-adapted perturbation results are obtained simply and directly from the present localized wave-function approach. The present theory suggests a novel interpretation of the terms contributing to the total potential energy and helps to rearrange them to give improved results.