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Orientational invariance and significance of electron densities obtained with approximate all-valence electron wavefunctions

par Figeys, Hubert ;Geerlings, Pau̧l;Van Alsenoy, Christian
Référence Journal of the Chemical Society. Faraday transactions II, 71, page (1375-1381)
Publication Publié, 1975

Article révisé par les pairs

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Résumé :

The total electron density ρ(R), computed with approximate all-valence electron wavefunctions, at a point defined by the position vector R, should (i) obey the orientational invariance requirement, i.e., be independent of the orientation of the molecule in a general coordinate system provided the position vector R is transformed according to the same "reorientation" matrix as the molecular coordinates, and (ii) satisfy the normalization condition, i.e., ∫ ρ(R) dR = N, where N is the total number of valence electrons. It is shown that with these two restrictions in mind, only two approximations are physically significant: (i) the use of NDO-type wave functions (CNDO/2, INDO, etc.) combined with the evaluation of ρ(R) up to an INDO-level; (ii) the use of wavefunctions obtained either by solving the complete Roothaan equations, i.e., where overlap integrals are explicitly taken into account, or by deorthogonalizing NDO-functions, together with the unapproximated expression for ρ(R). A comparison of the density maps for formaldehyde obtained by these two methods, with ab initio plots obtained with wavefunctions giving an energy close to the Hartree-Fock limit, leads to the conclusion that the second possibility is the more significant.