Many-Electron Theory of Atoms and Molecules. III. Effect of Correlation on Orbitals

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Abstract
The exact wavefunction of an N‐electron atom or molecule contains, after the Hartree‐Fock (HF) part, correlation terms involving successively one, two, … N electrons at a time. Particularly in closed shells, one‐electron terms f̂i result mainly from pair correlations. The f̂i were previously neglected in the many‐electron theory. Reasons for the smallness of f̂i are summarized. Different types of correlation effects are classified, and methods for estimating each type of f̂i are given. f̂i in closed form, i.e., including infinitely many single excitations is less than 2.8% of the Hartree‐Fock orbital in He with an energy contribution 0.0001 a.u. (63 cal/mole). In the H2 molecule f̂i is negligible for (R/Re) R, as (1σg)2 becomes degenerate with (1σu)2 the f̂i effect increases to ∼0.4 eV at dissociation. However, in such cases and in actual nonclosed shells, these nondynamical f̂i are removed if HF orbitals are obtained after the removal of degeneracies. Dynamical correlation effects give negligible f̂i and so generalized SCF methods are not necessary. Qualitative quantum chemistry can be based on just HF orbitals or approximations to them, though energies include localized pair correlations.