Page 121 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

106 J. P. MALRIEU AND J. P. DAUDEY
t being the hopping integral and the on-site effective bielectronic
repulsion, while the radius of convergence of the Rayleigh Schrodinger perturbation theory
from the RHF single determinant is

For the relevant perturbation consists in perturbing the covalent (or neutral) VB
structures by their interaction with the ionic ones; this is the strongly correlated or magnetic
domain. So that the Hartree Fock symmetry breaking occurs in a zone which covers the
whole magnetic domain and a significant part of the "weakly" correlated domain

2.3. THE MULTIPLE BOND

For more complex problems such as multiple bonds and Metal-
Metal bonds [15-17]) or extended systems ( the system of cyclic polyenes, among
others), the symmetry-breakings may take several forms since one may leave different
space-and spin-symmetry constraints independently or simultaneously. For for
instance, the RHF symmetry adapted solution is of character while
one may find at much lower energy a solution of closed shell character (a pure
singlet) which has broken the symmetry between the x and bonds. A UHF solution lies
much below, which has a dominant VB character

at short interatomic distances and a correct asymptotic content

at large interatomic distances.
The multiplicity of symmetry breakings have been explored in details in where they
occur near the equilibrium interatomic distance [12].
The fact that symmetry breaking occurs at shorter interatomic distances for multiple bonds
than for single bonds may be understood within two different languages. One refers to the
instability conditions of the symmetry-adapted solution. In multiple bonds some bonding
electron pair are strongly delocalized and would not break the symmetry (for instance the
while the p bonds are weaker and enter more rapidly into the :

regime (this criterion is only weakly modified for multiple bonds [12] ). Of course in a
sextuple bond, as the bonds are so weak that they induce a strong symmetry
breaking [18].
In the other approach one looks at the VB content of the symmetry adapted) wave function,
for instance for