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

3.2. FURTHER APPROXIMATIONS 17
K. Fukui used a LCAO approach with hybridized valence orbitals (LCVO)
and calculated energies, charge distributions and dipole moments. He used
perturbation theory to develop from there the Frontier Molecular Orbital
Theory (see sect. 3.6) and to calculate reactivities. Further refinements
of EHT were made to account for electron-electron interaction. An iterative
EHT (IEHC) was developed in order to obtain more accurate atomic
charges. Electron-electron correlation is usually completely neglected but
has been approximated by Atom Superposition and Electron Delocalization
Molecular Orbital theory (ASED-MO) [4, 5], thus affording better prediction
of geometries.
3.2 Further approximations
The basis set used for the LCAO is the 1s orbital for hydrogen and hybrid
AOs for carbon, nitrogen and oxygen. Hybrid AOs are linear combinations of
Slater-type orbitals, coefficients depending on the hybridization of the atom.
Tab. 3.1 shows the definition of Slater-type and hybridized orbitals used.
Sulfur and phosphor would also require d-orbitals and their hybrids dsp 3 and
d 2 sp 3 .
Hybrid orbitals are used because we can assume for simplicity that they
are always oriented along bonds, such that for given atom types and hybridizations,
there is always the same overlap. Thus, the corresponding
overlap integral, instead of being calculated repeatedly, can be replaced by
a constant parameter, in analogy to the Tight Binding approximation for
solids [104]. This would not be the case for normal Slater-type orbitals.
A molecule is therefore completely determined by a vertex labeled graph
g, which was introduced by O. Polanski [87]. A graph g = (V, E) is a set of
vertices V and a set of edges E. Vertices are elements v i . Edges are pairs
of vertices (u, v) ∈ V × V defining connected vertices. The vertices of g are
the atom orbitals (labeled by atom type and hybridization); edges denote
overlaps of orbital on adjacent atoms. This orbital graph g is obtained in
an unambiguous way from the chemical structure formula by means of the
rules described in the following. It follows that, in the framework of the Toy
Model, the structure formula already encapsulates the complete information
about the molecule.
The rules for constructing the orbital graph are:
• Overlaps are only non-zero (orbital graph edges exist only) between
orbitals on connected atoms.
• Only the overlaps shown in figs. 3.4, (a) and (b) (direct σ, semi-direct),