Measuring correlated electron motion in atoms with the momentum-balance density

TL;DR

This paper introduces new measures to analyze electron motion in atoms, revealing how Coulomb and Fermi correlations influence electron momentum distributions and local electron behavior.

Contribution

It presents novel measures—equimomentum, antimomentum, and momentum-balance—and applies them to atomic wave functions to distinguish correlation effects on electron motion.

Findings

Coulomb correlation increases equimomentum probability.

Fermi correlation increases antimomentum probability.

Momentum-balance varies with distance from the nucleus.

Abstract

Three new measures of relative electron motion are introduced: equimomentum, antimomentum, and momentum-balance. The equimomentum is the probability that two electrons have the exact same momentum, whereas the antimomentum is the probability their momenta are the exact opposite. Momentum-balance (MB) is the difference between the equimomentum and antimomentum, and therefore indicates if equal or opposite momentum is more probably in a system of electrons. The equimomentum, antimomentum and MB densities are also introduced, which are the local contribution to each quantity. The MB and MB density of the extrapolated-Full Configuration Interaction wave functions of atoms of the first three rows of the periodic table are analyzed, with a particular focus on contrasting the correlated motion of electrons with opposite and parallel spin. Coulomb correlation between opposite-spin electrons leads to a higher probability of equimomentum, whereas Fermi correlation between parallel-spin electrons leads to a higher probability of antimomentum. The local contribution to MB, given an electron is present, is a minimum at the nucleus and generally increases as the distance from the nucleus increases. There are also interesting similarities between the effects of Fermi correlation and Coulomb correlation (of opposite-spin electrons) on MB.