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19.11.2014

"Permutation Symmetry and Non-Dynamic Correlation Energy"

Prof. Marco Antonio Chaer Nascimento
(Institute of Chemistry, Federal University of Rio de Janeiro, Brazil)
Kleiner Hörsaal, 16:30 Uhr

Abstract: 

One of the most important differences between classical and quantum systems of identical particles is that the quantum identical particles are indistinguishable. The fact that identical nuclei of a molecule and the electrons of atoms or molecules are indistinguishable imposes certain restrictions to the wave functions describing such systems.

For some molecules containing identical nuclei it is possible to find symmetry operators (rotation axis, planes etc.) which leave the Hamiltonian invariant. In these cases we say that the Hamiltonian exhibits point group symmetry. One immediate consequence is that the eigenfunctions (not the molecular orbitals!) of the Hamiltonian of the molecule must transform like one of the irreducible representations of its point group.

This kind of symmetry is quite useful but less than 10% of the known molecules exhibit point group symmetry. On the other hand, the Hamiltonian of ALL atoms and molecule with more than one electron exhibits permutation symmetry. Because electrons are indistinguishable one may define a set of operators, Pij v i,j , which permute any pair (i,j) of electrons, leaving the hamiltonian invariant. This set of operators together with the identity operator from a permutation (or symmetric) group of order N ( SN) where N is the total number of electrons.

In this talk we will discuss the restrictions imposed to the eigenfunctions of the Hamiltonian when this type of symmetry is present and the consequences of the permutation symmetry, in particular to the physical meaning of the so-called “non-dynamic correlation energy”.