‘‘Low-momentum electrons’’ and the electronic structure of small molecules

Abstract

The electronic Husimi distribution η(r↘,p↘) is a ‘‘fuzzy’’ density in phase space. Sections through this function with a zero momentum variable (p↘;=0), are shown to be indicative of the spatial locations of chemical bonds and ‘‘free electron pairs’’ in molecules. The distribution η(r↘;0) tends to focus on the inter-nuclear regions in position space. The Laplacian ∇2rη(r↘;0), of the function may be used to enhance its diffuse features. The argument is made that the momentum-space Hessian of the Husimi function at the momentum-origin (p↘=0), includes information about the ‘‘flexibility’’ of the electrons and the anisotropy of the latter. The diagonalization of this tensor supplies a pictorial map of preferred directions of electrons in the low-momentum, i.e., ‘‘valence’’ region of momentum space. Examples studied in this paper include the H2, N2, CH4, H2O, C2H4 and C6H6 systems in their Hartree–Fock approximation.