Page 130 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

QUANTUM CHEMISTRY IN FRONT OF SYMMETRY BREAKINGS 115

treatment of the conformational symmetry breaking. Except for intrinsic degeneracies
(leading to conical intersections) the potential energy must have a zero derivative with
respect to the symmetry breaking coordinate (in the symmetrical conformation)

and this will be the case for the energy obtained from a symmetry-adapted approximate
wave function In case of symmetry breaking of the wave function, there exist two
other degenerate solutions and of broken symmetry and lower energy

and if the SA solution is unstable (which is not necessarily the case), one cannot build a
function (δ) tending to when tends to 0. The variational procedure falls on
and one can only find estimates of the potential energy surface around
by stabilization techniques [48].

Thus the potential energy surface does not exist and is reduced to a line for On
the contrary the solutions exist whatever (at least one of them, the
other one may become unstable), but the derivative of the corresponding energy surfaces
are different from zero at

The shape of the potential energy surface obtained by considering the lowest HF energy is
qualitatively wrong near since the resonance between and is not treated
properly. This is evident at but is necessarily remains a problem for If is
biased for the bias is necessarily continuous and exists for Since we have
already mentioned the difficulty to restore symmetry from a symmetry-broken solution, ie
to correct the bias of the starting wave function, it is clear that the calculation of the PES
even near this potential well is questionable if its starts from This is not an academic
comment. One may take as an example the famous problem of bonding alternation in linear
polyenes, first rationalized by Longuet-Higgins and Salem [49]. This interpretation in
terms of Peierls distorsion was purely monoelectronic and led to some contradiction
regarding the r-dependence of the hopping integral and electron correlation must be
invoked. A recent ab initio evaluation of the correlation energy for an infinite chain has
been reported by Stolhoff [50] starting from an HF determinant, and it is clear that a
spurious cusp exists for in this work, which questions its reliability to determine the
value of the bond alternation, ie such that