Local density approximations to moments of momentum of diatomic molecules with Hartree–Fock–Roothaan quality electron distributions

Abstract

By generalizing local density arguments for atoms it is found that the mth moment of momentum for molecules 〈pm〉 is proportional to ∫ρ(r)1+(1/3)mdr, where ρ(r) is the electron density. This relation is tested for m=−1, 1, and 2 using wave functions of Hartree–Fock–Roothaan quality: 〈pm〉 is computed directly and the density integrals are evaluated using ρ(r) generated from these wave functions. Eleven neutral diatomic systems and two singly charged positive ions are considered. Apart from changes in the proportionality constants, the local density approximation is vindicated; for m=−1, 1, and 2 the magnitudes of the changes in the predicted constants are less than ∼10%. Finally, 〈p〉, which is proportional to the Dirac–Slater exchange energy, is compared with the appropriate self-consistent Hartree–Fock–Roothaan energy terms and, again, a linear relationship emerges.