Chemistry Reference
In-Depth Information
capable of predicting the stereochemical course of organic reactions. But there was
also a crucial development in the kind of explanations that came with those rules.
Woodward and Hoffmann
s approach provided the means to go beyond causal
explanation. In fact, one did not provide an explanation of pericyclic reactions
without doing so.
Woodward and Hoffmann
'
s approach was an essentially “qualitative” applica-
tion of molecular orbital theory to the study of organic reactions. Care is required in
the interpretation of the term “qualitative”. It does not mean an absence of math-
ematics. Drawing on Hoffmann
'
s own sense of the term, Weisberg (
2004
, p. 1071)
argues that “qualitative” expresses the extent of approximations and idealizations
employed in modelling rather than a lack of numbers. This is important because
Woodward and Hoffmann
'
s crucial insight was that the relative phase
symmetries
of the molecular orbitals representing the bonds broken and formed during a
reaction
make a difference
to whether a reaction is thermally allowed or forbidden.
In order to explain why a given pericyclic reaction takes place in a single kinetic
step and bond breaking and formation occurs simultaneously, one idealizes by, for
example, ruling out the explanatory relevance of the bonds comprising the carbon
skeleton, and then applies the molecular orbital theory to the idealized causal
model. This is a “bottom-up” (driven by experiment) as much as a “top-down”
(theory-driven) process. It is not that one begins with the domain of physical causal
influence and then one distils a standalone explanation shorn of causal irrelevances.
Rather, one begins with framework relative, black boxed causal mechanical expla-
nations which are idealized in the sense that they distort the causal story. While this
might sound as if we have moved beyond the bounds of veridical explanation
according to the kiaretic account, one must look at the aim of the modelling strategy
employed in the explanation of pericyclic reactions. One moves from a causal-
mechanical representation of a reaction to the construction of molecular orbitals,
classifying their symmetry properties, and then following the dynamics of the
reaction through in the model, as it were, by correlating energy levels of like
symmetry.
The procedure is effectively a matter of explanatory model construction that
begins with a simple idealized model of the geometry of approach of the reagents
relative to a given plane or planes of symmetry. One then considers the symmetry of
the orbitals contributing most to the reaction (the “frontier” molecular orbitals)
under groups of transformations such as reflection or rotation with respective those
planes of symmetry. In order to determine the symmetry of the molecular orbitals,
one solves the Schr¨dinger equation via the linear combination of atomic orbitals
(LCAO) approximation, which replaces a many-electron wave function with a
molecular orbital consisting of electron pairs:
'
ψ
¼
c
1
ϕ
1
þ
c
2
ϕ
2
where
ϕ
2
the wave functions of the
atomic orbitals, and
c
1
and
c
2
the coefficients expressing the mutual contributions of
ψ
is the molecular orbital wave function,
ϕ
1
and
