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

3.2. FURTHER APPROXIMATIONS 21
are also scaled by factors. This reflects the weakness of “banana-bonds” in
constrained rings. The factor 3-ring applies to all bonds in a three-membered
ring. The factor 4-ring applies only to other bonds in four-membered rings,
in order to reflect that bridging bonds, i.e. bonds contained in two rings, are
as strained as bonds in three-membered rings (more precise data is available
from [11]).
The hybridization of a particular atom is determined using valence-shell
electron pair repulsion (VSEPR) theory [53]. VSEPR is a simple method to
predict the geometry of compounds. The only thing needed is the connectivity
of the compounds, which is given by definition by the graph representation
of the molecule. The VSEPR theory assumes that the valence-shell electron
pairs of any atom in the molecule are arranged in a fashion that minimizes
electrostatic repulsion. Electron pairs are represented by the bonds, i.e. edges
of the molecular graph, and by lone electron pairs, whose number depends
only on what element the atom is. Every bond, be it simple, double or triple,
counts as one electron pair. The geometry of atoms depends in the end on
the number of electron pairs, in bonds and in lone pairs. A total of 2 leads
to linear geometry and sp hybridization, 3 to trigonal geometry and sp 2 hybridization,
and 4 to tetrahedral geometry and sp 3 hybridization. The atom
on which VSEPR is applied is called the central atom. Tab. 3.4 summarizes
the results and gives examples for neutral atoms and a charged central atom.
To account for resonance structures, a few more rules are added. Resonance
structures occur when more than one Lewis structure can be drawn
for a molecule. The most common situations are adjacent π bonds, and a
lone pair adjacent to a π bond [86, sect. 6.3]. The former has been taken
care of by always establishing π interactions between adjacent sp 2 atoms (see
tab. 3.2). The latter corresponds to the situation where, when drawing alternative
Lewis structures, lone pairs and π bonds are converted into each
other. In fact, the electrons are delocalized.
Thus the hybridization of an atom with lone pairs depends on its neighbors,
namely those who are not sp 3 hybridized. The current implementation
Table 3.3: Scaling factors for calculating remaining overlaps from the overlaps
in Tab. A.2
indirect hyper- banana
all H conjugation symmetric 3-ring 4-ring
0.1 0.0 0.8 0.0 0.7 0.8