Page 126 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

QUANTUM CHEMISTRY IN FRONT OF SYMMETRY BREAKINGS 111

where a and b are the atomic orbitals of the carbon atoms of The resonance
between the two VB forms and is the interatomic exchange integral Kab. The
repulsion between the two groups tends to rotate the bond, and to put the a and b
orbitals in perpendicular orbitals. Then the Kab integral becomes very weak, and we have
again a weak resonance between two VB components. But these two forms tend to polarize
the frame in two opposite directions. The electronic relaxation energy is large and
prevails on the resonance. So that for highly twisted ethylene the singlet closed shell HF
function will be symmetry-broken and will give two and solutions,

polarized. Allowing then the group to pyrimidalize leads to a stable
structure. This phenomenon, discovered by Salem et al. [34], has given raise to a great
interest in the early seventies under the name of "sudden polarization" but its suddeness has
been questionned when the potential energy surface has been more extensively studied
[35].

2.6. DENSITY FUNCTIONAL AND SYMMETRY BREAKING

As long as it maintains the single determinant picture, the density functional function does
not dissociate properly the chemical bonds, and is thus the subject of symmetry breaking at
large interatomic distances. We may equivalently say that the correlation potential (i.e. the
difference between the exact exchange and the exchange correlation potential) diminishes
the electronic repulsion or that it increases the delocalization. Turning to the VB formulation
of the HF instability, this implies that the symmetry breaking will occur at larger
interatomic distances in DF calculations than in HF ones,

Then an interesting question would be : for molecules which present strong HF symmetry
breaking at equilibrium distance, such as Be2 or cyclic (and eventually are
the symmetry-adapted LDF solutions stable at these distances ? If they are not, one will
face an embarrassing problem ; since the calculated dissociation energies, are already
correct when using the SA, solution at short distance and the separated atoms energies what
should one think of the lower UHF solutions ? Let remember that most LDF calculations
on organometallic systems or metallic clusters are LSD (Local Spin Density) calculations
(i.e. performed in the UHF formalism). Why should one accept the symmetry (closed
shell) constraint in some cases and not in others ?