Chemistry Reference
In-Depth Information
combination of all these symmetry operators is the highest possible symmetry of the
transition state. All subgroups are also valid candidates. Equations (
3
) and (
4
)of
Bone et al. [
253
], and Theorems I and II of McIver and Stanton [
268
,
270
] may
serve as tests to eliminate some options. The next step of a theoretical study is to
find the stationary point with this point group by symmetry constrained geometry
optimization. Note that the optimization may be constrained to the totally symmet-
ric subspace [
270
]. Furthermore, in the case where the symmetry operator
corresponding to the process is part of the point group, a minimum in this subspace
has to be found [
270
]. This will make the computations much more efficient,
particularly when the highly symmetric conformations are considered first. Vibra-
tional frequencies should be calculated to verify that the conformation found is a
bona fide transition state with one and only one imaginary frequency. It may turn
out to be a local energy minimum (i.e., an intermediate conformation with no
imaginary frequency) or a higher order saddle point (with more than one imaginary
frequency). In the case where a higher order saddle point is found, the symmetry
species of the imaginary modes may give useful information. One mode points
towards educt and product, while the other mode(s) indicate(s) the point group(s) of
the (possible) true transition state(s) and the distortions leading thereto. This
information may aid in selecting the next point group to be considered.
In the case where a local minimum was found, this may be an intermediate on the
pathway from educt to product. The process in question proceeds in two steps. In
this case a new transition state on the way from the original educt to this interme-
diate product has to be found, and a second transition state on the pathway from the
intermediate to the original product. If the original educt and product are symmetry
related, the second transition state leading from the intermediate to the original
product should be symmetry equivalent to the first transition state.
Even if a bona fide transition state has been found, this may not be the only
transition state on this pathway from educt to product. There is the possibility of a
multi-step pathway via several intermediates and transition states. This cannot be
decided by symmetry considerations. It may be checked by calculating the reaction
path with an intrinsic reaction coordinate (IRC) calculation, which will follow the
minimum energy pathways from the transition state to the minima corresponding to
its immediate educt and product [
274
,
275
]. This technique allows a computational
check of the connectivity of transitions states and the corresponding minima, and
also the detailed study of the reaction mechanism by providing a continuous series
of transient structures along the pathways from the transition state to the
corresponding educt and product. Energetic and conformational changes along
the reaction path can thus be studied in small steps.
3.7 Bifurcating Pathways
Another complication that may occur along a reaction path is the case that a steepest
descent path from a transition state TS1 leads, by symmetry, to another transition
