Page 122 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

QUANTUM CHEMISTRY IN FRONT OF SYMMETRY BREAKINGS 107
and one sees that all VB components in terms of localized orbitals (obtained from the
occupied MOs and a proper definition of antibonding valence

have equal coefficients, from the neutral ones to the triply ionic ones, which is especially
absurd. All effective symmetry breakings lower the energy by reducing the components on
the most ionic VB components. For instance in a singlet type symmetry-broken solution of
of the type

x concentrates on atom A while y concentrates on atom B so that the occurence of
and situations is dramatically reduced. This reduction is even stronger in the
UHF solution

where the spin MOs concentrate on atom A and the spin MOs concentrate on atom B.
This increases not only the neutral VB character of the wave function but also the
component on the atomic ground states, satisfying the atomic Hund's rules.
As an example of the interest to scrutinise the UHF solution, one may quote the
problem [19]. The bond is weak but it takes place at short interatomic distance and is
definitely not the dispersion well which one might expect from two closed shell atoms (and
which occurs in and heavier compounds). Quantum chemical calculations only
reproduce this bond when using large basis sets and extensive CI calculations [20]. It is
amazing to notice that the UHF solution gives a qualitatively correct behaviour, and
suggests a physical interpretation of this bond since in

the two a spin MOs concentrate an atom A and have respectively a 2s and dominant
character (the same being true for the spin MOs on atom B). The creation of that weak
bond would be due to an atomic promotion to the lowest excited state of the atoms. This
suggestion would deserve a verification by defining natural MOs from the full CI wave
function and their appropriate localizing transformations.

2.4. EXTENDED SYSTEMS
HF symmetry breaking for polyatomic molecules have the same origin, i.e. the reduction of
the components on highly ionic VB situations. If one considers a strongly localizable
electronic system such as a molecule built of covalent bonds like the cubic (12 P-P
single bonds), each bond is weakly correlated but there are equal mixtures of neutral and
ionic contents. So that each atom being involved in three bonds, the occurence of and
situations is completely exaggerated. Moreover, among the initial situations, the spin