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

Abstract

The electronic Husimi distribution (r ជ , p ជ ) is a ''fuzzy'' density in phase space. Sections through this function with a zero momentum variable (p ជ ϭ0), are shown to be indicative of the spatial locations of chemical bonds and ''free electron pairs'' in molecules. The distribution (r ជ ;0) tends to focus on the inter-nuclear regions in position space. The Laplacian ٌ r 2 (r ជ ;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 ជ ϭ0), 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 H 2 , N 2 , CH 4 , H 2 O, C 2 H 4 and C 6 H 6 systems in their Hartree-Fock approximation.

A family of intracules, a conjecture and the electron correlation problem

“…We will not consider these alternatives in this article but it is worth pointing out that the Husimi distribution [19][20][21][22] The n-electron Wigner distribution is a complicated function of 6n coordinates (excluding spin) and it is even less intelligible than the 3n-coordinate wavefunctions to which it is equivalent. However, since our interest lies primarily in the behaviour of pairs of electrons, it is sensible to ask whether a two-electron function can be distilled out of the Wigner distribution.…”

“…We note in passing that, although it is the oldest, the Wigner distribution is not the only possible phase-space distribution and several others have been developed over the years. We will not consider these alternatives in this article but it is worth pointing out that the Husimi distribution [19][20][21][22] is everywhere positive and, in a sense, more Heisenberg-friendly. There are two reasons for preferring the Wigner distribution to the Husimi analogue.…”

Molecular Networks in Position, Momentum, and Phase Space: A Case Study on Simple Hydrocarbons

“…In fact, it is possible to arrive at this network based solely on the “low-momentum electron density” η( r⃗ ;0), which has the desirable property of focusing on slow electrons, i.e. , the ones that are chemically relevant . As a result, we end up with a position-space picture that has as its central parts bond regions rather than nuclei and the connections of the former.…”

“…We investigate this question further in the present paper. For the zero-momentum Husimi distribution, the Laplacian was used to enhance fine features of this function . Here, we use it for the characterization of saddle points.…”

Irreducible charge density matrices for analysis of many‐electron wave functions

“…Attention is concentrated primarily on the one‐particle density matrix (1‐RDM), which determines one‐electron charge and spin distributions, and provides intuitive, pictorial interpretations of quantum chemical data 8, 9. Other useful tools 10–20 for electronic structure analysis can be reduced to the 1‐RDM representation as well. Yet, one‐electron distribution functions alone are not sufficient for description of molecular systems, especially those undergoing chemical reactions and many‐electron rearrangements, such as formation and breaking of bonds.…”