Chemistry Reference
In-Depth Information
no idealizations. The canonical model implies the same thing as the idealized model
but does so by remaining silent about the causal irrelevances. In other words, it
simply leaves out the irrelevant details. Now Strevens
account is an
ontological
conception of explanation in the sense that difference-makers are those objective
casual facts we draw upon in providing explanations. These causal facts are
what constitute the “setup” of our causal models. A canonical model is just such
a collection of causal facts. However, an
idealized
model is not merely a collection
of causal facts because it contains falsely distorted causal irrelevances as well as
causal facts or difference-makers.
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13.3
Idealization, Pericyclic Reactions,
and Molecular Orbitals
Prima facie, Strevens
account of the explanatory function of idealization seems
amenable to quantum chemistry. Take for example molecular orbital approaches to
the explanation of pericyclic reactions. These reactions take place in a single kinetic
step via a stable transition state in a closed circle of bonds. Pericyclic reactions are
of great significance to synthetic chemistry because they include cycloaddition
reactions including the Diels-Alder reaction and sigmatropic rearrangements like
the Cope rearrangement. Both quantitative and qualitative quantum chemical
models of these reactions have been developed by applying molecular orbital
theory. Fukui
'
s “frontier” molecular orbital approach allows one to use perturbation
theory to calculate the activation energies of two molecules when the reactants
do not differ greatly in their structure from the transition state. Since the perturba-
tion expression is too difficult to solve given the complexity of the systems of
interest to chemists, all terms are neglected except for the one with the smallest
denominator: the highest occupied molecular orbital (HOMO) of one reactant and
lowest unoccupied molecular orbital (LUMO) interaction of the other (i.e., the
“frontier” molecular orbitals). The frontier orbital idealization therefore reduces a
complicated perturbation expression to a single term (Dewar
1989
, pp. 302-303).
Woodward and Hoffmann famously developed the qualitative sibling of the frontier
orbital approach by proposing that the symmetry of the molecular orbital wave
functions corresponding to the bonds broken and formed during a reaction deter-
mines the stereochemical course of the reaction (Hoffmann and Woodward
1968
).
When the symmetry of the molecular orbital wave functions is conserved,
the reaction is “allowed” in the sense that it requires a relatively small input of
energy for the reaction to proceed. And when symmetry is not conserved, greater
energy is required for the photochemical promotion of electrons to higher energy
(non-bonding) molecular orbitals.
Both frontier molecular orbital and orbital symmetry approaches represent a
significant divergence from classical chemical models of pericyclic reactions
(the term “pericyclic reaction” belongs to Woodward and Hoffmann). One of the
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