Page 120 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

QUANTUM CHEMISTRY IN FRONT OF SYMMETRY BREAKINGS 105
The space symmetry would only be restored by superposing the degenerate and
solutions in
Such phenomena do not occur in heavier alkaline earth atoms due to a poorer differential
overlap between the valence s and p orbitals (smaller Ksp integrals) as explained by
Kutzelnigg [9].
Another well-known atomic HF symmetry breaking is the problem but it is more
artificial since in this unbound state, two electrons leave the atom oppositely in two diffuse
orbitals [10].

2.2. THE WEAK SINGLE BOND
The most popular use of the UHF solutions concerned the single bond breaking, since it
was rapidly understood that while the RHF solution of

with

imposed a constant ratio of ionic/neutral VB components whatever the interatomic distance

and therefore a spurious asymptote at (IP-EA)/2 above the dissociation into neutral atoms,
the UHF solution

with

authorized one electron to concentrate on atom A while the second one concentrates an atom
B. The detailed conditions for the appearance of the UHF solution have been explicited a
long time ago as a special application of the Thouless' relations [2]. This relation analyzes
the stability of the symmetry-adapted HF solution, using symmetry-adapted MOs [11]. The
transcription of these conditions in Valence Bond terms is easy to derive, [12] and one may
show that the symmetry breaking takes place when

where in the element of the Fock operator between the valence AOs a and b and
is the energy difference between the neutral and the ionic VB determinants. The
solid state physicists would say that