A Toy Model of Chemical Reaction Networks - TBI - Universität Wien

3.2. FURTHER APPROXIMATIONS 19
Figure 3.2: π-overlap between p orbitals.
3.2, and 3.3 (π, hyperconjugation and fictitious) are implemented. The
other possible overlaps between hybridized orbitals, see fig. 3.4, (c) and
(d) (indirect), are set to zero as they are in average as low as 0.1 .
• In the style of [89] and [86, ch. 6.4], the term hyperconjugation is used
for overlaps between a p orbital and a neighboring, but “indirect” oriented
sp 3 orbital. Only one of the three sp 3 is randomly chosen for an
overlap proportional to the π overlap of the corresponding atoms. The
other two “indirect” oriented overlaps are set to zero. In order to avoid
choosing randomly an orbital, but to keep the σ-MOs and the π-system
coupled, a second factor is defined for the overlap between the p orbital
and the “direct” oriented sp 3 orbital. This factor may be used instead
of the hyperconjugation factor. The overlap is dubbed “fictitious”.
• The set of overlaps is determined by the hybridization of the two atoms
involved in the bond. Tab. 3.2 shows all the possible combinations of
hybridizations and ensuing overlaps. The set of overlaps only depends
on the type and orientation of the orbitals.
Thus the energy calculation in the Toy Model is parametrized in terms
Table 3.2: Sets of overlaps depending of hybridization on bonding atoms.
number of overlaps
Hybridization of (see figs. 3.2, 3.3 and 3.4)
atom 1 atom 2 σ semi. π hyper. fictitious
sp 3 1 6 0 0 0
sp 3 sp 2 1 5 0 1 1
sp 1 4 0 1 1
sp 2 sp 2 1 4 1 0 0
sp 1 3 1 0 0
sp sp 1 2 2 0 0