Electron-electron cusp condition and asymptotic behavior for the Pauli potential in pair density functional theory

Abstract

In the ground state, the pair density n can be determined by solving a single auxiliary equation of a two-particle problem. Electron-electron cusp condition and asymptotic behavior for the Pauli potential of the effective potential of the two-particle equation are presented.

Modeling the Pauli potential in the pair density functional theory

“…However, there are no data for the Pauli potential in the literature, yet. Although recently, the electron-electron cusp condition and asymptotic behavior for the Pauli potential have been derived, 7 much work is called for to completely understand how such a potential could be modelized in analogy with the Kohn-Sham potential in ordinary density functional theory. Considering the present knowledge, this kind of work appears extremely difficult.…”

Explicit form of Pauli potential for direct derivation of pair density from a two-particle differential equation for the quintet state of four electrons with harmonic interparticle interactions

“…More recently, some interest has been focussed on the pair density functional description [3,4]. There, a generalized Pauli potential has been defined in order to write a two-particle differential equation for the pair density amplitude, say χ(r 1 , r 2 ), in an N-electron problem [3,5].…”

New venues in electron density analysis

“…According to Coulomb's law, the accumulation of electron density in the internuclear region should ease the repulsion between the two nuclei and be strongly stabilizing; [1][2][3][4] at the same time, the exact many-body electron density is correlated in terms of spin and electron-electron interactions. 5 In general, it can be said that the deviation from the initial promolecular density is directly related to interactions between atoms. 6 As such, it has become customary to study the electron density via the analysis of its critical points, as popularized in the Quantum Theory of Atoms in Molecules (QTAIM) introduced and developed by Bader and coworkers.…”