Chemistry Reference
In-Depth Information
atomic orbital to the molecular orbital wave function. Two atomic orbitals generate
two molecular orbitals, one lower in energy than either
ϕ
2
- the bonding
molecular orbital and one higher in energy - the antibonding molecular orbital.
Replacing a many electron wave function by molecular orbitals consisting of
electron pairs is a significant idealization, but nonetheless a crucial part of the
process of abstraction because it allows one to determine explanatorily relevant
factors by permitting the classification of the relative phase-symmetries of the
molecular orbitals contributing most to the reaction and hence the relative energies
of those orbitals. The signs of the coefficients
c
1
and
c
2
in a bonding molecular
orbital are either both positive or both negative, which means that it is an in-phase,
bonding combination of the atomic orbitals. The coefficients of an antibonding
molecular orbital are of opposite sign, i.e., out-of-phase.
By developing this computational model, one can construct the molecular
orbitals corresponding to the bonds that break and form in the reaction and classify
those molecular orbitals according to their symmetry properties under reflection in
at least one plane. Finally, in order to explain why a reaction occurred in the way
that it did, and to predict the stereochemical course of a reaction, one constructs a
qualitative
orbital correlation model
with the approximate energy levels of the
reactants on one side, those of the product on the other, and the intermediate region
representing the reaction transition state. By correlating the molecular orbitals of
bonds broken and formed during a reaction according to the relative phase sym-
metries of the molecular orbital wave functions, one can determine whether a given
reaction is energetically favourable and allowed (symmetry is conserved) or
whether it is energetically unfavourable or “forbidden” (symmetry is broken)
because it requires the photochemical promotion of electrons to higher energy
antibonding molecular orbitals.
Symmetry is a domain of non-casual dependence that underwrites the kairetic
criterion of difference-making in the quantum chemical explanation of pericyclic
reactions. The orbital correlation model contains those factors - the symmetry of
the molecular orbitals - that make a difference to the explanatory target. It is used to
explain why a reaction occurs in the way that it did occur, or indeed why it did not
occur. By citing the symmetry of molecular orbitals as difference-makers, the
invariance of the symmetry properties of molecular orbitals (the conservation of
orbital symmetry) explains why a particular reaction is allowed and, when symme-
try is broken, why it is forbidden. It should be noted that symmetry is
not
simply a
matter of mathematical explanation wherein the explanandum represents some
domain of abstract mathematical relations. Explanatory relevance is matter of
determining those mathematical structures that make a difference to, and hence
entail (though not
causally
entail), their explanatory targets - regularities and
concrete events in organic chemistry. What we end up with
are
idealized explan-
atory models. But the shift of the domain of dependence “away” from the causal
story results in a model that is not explanatorily illegitimate. The idea that
orbital symmetry is a difference-maker is embodied in Woodward and Hoffmann
ϕ
1
or
s
famous
selection rules
- the Woodward-Hoffmann rules - providing synthetic
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