Page 131 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

116 J. P. MALRIEU AND J. P. DAUDEY

In our opinion it would be better to avoid the HF step, and to start the CI process from any
unbiased function, symmetrical for as are the Huckel MOs. We think that it is risky
to study the existence and amplitude of a physical symmetry-breaking phenomenon through
a computational sequence involving a symmetry-broken wave function at an intermediate
step, since the use of this function introduces a prejudice and may result in an
overestimation of the geometrical symmetry breaking. In that case the singlet symmetry
breaking goes through an overestimation of the pairing of electrons into bonds (bond-
centered charge density waves) as previously discussed and this overpairing, evident for
necessarily acts for constraining the bond alternation. The approximate CI cannot
repair the defect of this starting point [51].

4. Final comments

Even if symmetry-broken wave functions are difficult to use for higher levels of
computation, their physical content is always instructive about the physical trends of the
problem under study and they deserve interest. Their appearance and the more physical
geometrical symmetry breaking are internally (but not strictly) related. Since they represent
catastrophes on the wave function and/or the energy (or energy derivatives) they should be
studied with attention and our ultranumericist discipline has not paid enough attention to
these critical behaviours. This neglect is perhaps due to some implicit philosophical
"continuism", prevailing in a domain where most instruments are based on variational
procedures and optimizations. The use of computers and algorithms as black-boxes, and
even the systematic plotting of the results through graphic codes using spline interpolations
sometimes lead some quantum chemists of high reputation to miss cusps and intriguing
features in their results [13,37]. Since qualitative explanations or pictures may be obtained
from symmetry-broken wave functions and since funny behaviours are expected around
conformational symmetry breaking, these problems should not be considered as
teratological. Pictorial explanations and qualitative problems are both necessary to balance
the unavoidable and fruitful research of numerical efficiency.

References

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