Computational Chemistry

Chapter 2, Harder Questions, Answers

Q5

Why are chemists but rarely interested in finding and characterizing second-order
and higher saddle points (hilltops)?
The short answer is, because they (the hilltops, not the chemists) don’t do
anything chemically. In a chemical reaction, we have (at least two) minima, and
molecules move between them, passing through transition states, which are first
order saddle points. Although in passing from one minimum to another all mole-
cules do not strictly follow the intrinsic reaction coordinate (IRC) the lowest energy
pathway on a PES that connects the minima, very few molecules are likely to stray
so far outside the IRC that they pass through a hilltop [1].
Although hilltops are rarely deliberately sought, one sometimes obtains them in
an attempt to find a minimum or a transition state. By a little fiddling with a hilltop
one can often convert it to the desired minimum or transition state. For example,
when the geometry of doubly eclipsed (C2v) propane is optimized, one obtains a
hilltop whose two imaginary frequencies, when animated, show that this geometry
wants to relieve both eclipsing interactions. Altering the hilltop structure to a
doubly staggered (ideally also C2v) geometry and optimizing this yields a mini-
mum. Altering the hilltop to a singly eclipsed structure gives a transition state
interconverting minima.

C

C

C

H

H

H

H

H

H

H

H

doubly eclipsed

hilltop

C

C

C

H

H

H

H

H

H

H H

C

C

C

H

H

H

H

H

H

H H

doubly staggered

minimum

singly eclipsed

transition state

Reference

1. Shaik SS, Schlegel HB, Wolfe S (1992) Theoretical aspects of physical organic chemistry: the
   SN2 mechanism. Wiley, New York. See particularly chapters 1 and 2, and pp 50, 51

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