Hartree-Fock instabilities

FSGO Hartree-Fock Instabilities of Hydrogen in External Electric Fields... 

This behaviour is a nice example of the symmetry dilemma in the conventional Hartree-Fock scheme and is intimately connected with the question of Hartree-Fock instability. 

FSGO Hartree-Fock instabilities of hydrogen in external electric fields... 

At this point, it is appropriate to return to the issue of Hartree-Fock instabilities, which are perhaps most easily discussed within this framework. Let us consider the somewhat esoteric perturbation % which is simply a rotation that... 

The assumption here is that if the total many-electron Hamiltonian commutes with various symmetry operations of the group then the Fock operator that leads to F can also be chosen in such a fashion. In such a case each MO will transform as one of the irreducible representations of the group. The ideas presented in the Roothaan paper are very important, and allow factorization of the Roothaan equations into simpler blocks, one for each irreducible representation, but experience has indicated that on occasion there are Hartree-Fock instabilities that destroy the symmetry of the resultant MOs. However, the Fock operator can always be constrained to have the symmetry of the nuclei. 

In all cases where the question concerning the relative stabilities of equidistant versus bond alternating structures arises (polyyne [20,21, polyacetylene 22-27, polymethineimine 28,29 ) the latter are more stable within the framework of the restricted Hartree Fock approximation. For polyyne and polyacetylene this issue is in accord with the well known concept of a Peierls distortion jsoj. The occurence of Hartree Fock instabilities (see e.g. refs. 31,32 ) in the case of the equidistant, metallic structures of polyyne (cumulene) and all-trans polyacetylene points, however, to the need for improved methods going beyond the independent particle model. First efforts in this direction 27 show that at the level of second order Moller-Plesset perturbation theory the alternant configuration of polyacetylene is still preferred energetically although as expected the energy difference to the equidistant structures becomes smaller. 

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