Ab initio determination of bond length dependence of the correlated valence shell Hamiltonian of CH: Comparison with semiempirical theories

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Abstract
The exact ab initio effective valence shell Hamiltonian , which is mimicked by semiempirical theories of valence, is calculated for CH at 11 bond lengths using quasidegenerate many‐body perturbation theory to incorporate extensive correlation contributions. Least squares fits of the bond length dependence of the calculated CH matrix elements provide simple formulas which are compared with the intuitive forms introduced into semiempirical theories. Some of the semiempirical formulas, e.g., one‐center, one‐electron integrals and two‐center, two‐electron integrals, are in good agreement with our correlated ab initio calculations, while others display substantial departures. For example, the bond length dependence of one‐center, two‐electron integrals, which are assumed to be independent of bond length in semiempirical theories, is substantial but physically understandable. Corrections are found to the assumed proportionality of resonance and overlap integrals. The bond length dependence of nonclassical three‐electron integrals is presented along with the hybrid and exchange integrals that are ignored in zero differential overlap methods.