Computational Chemistry

locating a transition state is often referred to specifically as a transition state
optimization. Geometry optimizations are done by starting with an input structure
that is believed to resemble (the closer the better) the desired stationary point and
submitting this plausible structure to a computer algorithm that systematically
changes the geometry until it has found a stationary point. The curvature of the
PES at the stationary point, i.e. the second derivatives of energy with respect to the
geometric parameters (Section 2.2) may then be determined (Section 2.5) to
characterize the structure as a minimum or as some kind of saddle point.
Let us consider a problem that arose in connection with an experimental study.
Propanone (acetone) was subjected to ionization followed by neutralization of the
radical cation, and the products were frozen in an inert matrix and studied by IR
spectroscopy [ 13 ]. The spectrum of the mixture suggested the presence of the enol
isomer of propanone, 1-propen-2-ol (Reaction 2.2):

C

Reaction 2

O

C

OH

H 3 CHCH 3 2 C CH 3

To confirm (or refute) this the IR spectrum of the enol might be calculated (see
Section 2.5and the discussions of the calculation of IR spectra in subsequent
chapters). But which conformer should one choose for the calculation? Rotation
about the C–O and C–C bonds creates six plausible stationary points (Fig.2.13),

O O

O O

O

2 3

(^54)
6
H
H
H H
H
H
H
H
H H
H H
H
H H
O
(^1) H
H
H
H
H
H
H
H
H
Fig. 2.13 The plausible
stationary points on the
propenol potential energy
surface. A PES scan
(Fig.2.14) indicated that 1 is
the global minimum and 4 is a
relative minimum, while
2 and 3 are transition states
and 5 and 6 are hilltops. AM1
calculations gave relative
energies for 1 , 2 , 3 and 4 of 0,
0.6, 14 and 6.5 kJ mol%^1 ,
respectively ( 5 and 6 were not
optimized). Thearrows
represent one-step (rotation
about one bond) conversion
of one species into another
24 2 The Concept of the Potential Energy Surface