Molecular electronic distribution functions and correlation holes Theory and application to H2, LiH and BH

The one-electron density functions for the diatomic hydrides H₂, LiH and BH, defined with respect to a limited STO basis set, are partially integrated to yield longitudinal and transverse distribution functions which admit of a simple pictorial representation. The maxima in the longitudinal distribution functions occur in regions conventionally ascribed to core pairs, lone pairs or bond pairs.

The correlation between pairs of electrons of given spin is then analysed in terms of the analogous partially integrated pair density functions and in terms of the associated hole functions. In the case of LiH and BH, the Fermi hole functions are similar in form to the negatives of the one-electron distribution functions for the appropriate singly occupied molecular orbitals; but the differences between the two functions are more marked in BH, where there is increased spatial interpenetration of the valence electron pairs. The results also show, in a simple way, how the electron motion is over-correlated in H₂ when the Heitler-London wavefunction is used.