title: The "Fermi hole" and the correlation introduced by the symmetrization or the anti-symmetrization of the wave function.
abstract: The impact of the antisymmetrization is often addressed as a local property of the many-electron wave function, namely that the wave function should vanish when two electrons with parallel spins are in the same position in space. In this paper, we emphasize that this presentation is unduly restrictive: we illustrate the strong non-local character of the antisymmetrization principle, together with the fact that it is a matter of spin symmetry rather than spin parallelism. To this aim, we focus our attention on the simplest representation of various states of two-electron systems, both in atomic (helium atom) and molecular (H2and the π system of the ethylene molecule) cases. We discuss the non-local property of the nodal structure of some two-electron wave functions, both using analytical derivations and graphical representations of cuttings of the nodal hypersurfaces. The attention is then focussed on the impact of the antisymmetrization on the maxima of the two-body density, and we show that it introduces strong correlation effects (radial and/or angular) with a non-local character. These correlation effects are analyzed in terms of inflation and depletion zones, which are easily identifiable, thanks to the nodes of the orbitals composing the wave function. Also, we show that the correlation effects induced by the antisymmetrization occur also for anti-parallel spins since all Mscomponents of a given spin state have the same N-body densities. Finally, we illustrate that these correlation effects occur also for the singlet states, but they have strictly opposite impacts: the inflation zones in the triplet become depletion zones in the singlet and vice versa.
authors: Dipartimento di Scienze Chimiche e Famaceutiche, Universita di Ferrara, Via Fossato di Mortara 17, I-44121 Ferrara, Italy.
authors: Emmanuel
authors: E
authors: Giner
authors: Dipartimento di Scienze Chimiche e Famaceutiche, Universita di Ferrara, Via Fossato di Mortara 17, I-44121 Ferrara, Italy.
authors: Lorenzo
authors: L
authors: Tenti
authors: Dipartimento di Scienze Chimiche e Famaceutiche, Universita di Ferrara, Via Fossato di Mortara 17, I-44121 Ferrara, Italy.
authors: Celestino
authors: C
authors: Angeli
authors: Laboratoire de Chimie et Physique Quantiques, (UMR 5626 of CNRS), IRSAMC, Université Paul Sabatier, 118 route de Narbonne, F-31062 Toulouse Cedex, France.
authors: Jean-Paul
authors: JP
authors: Malrieu