and a PES scan (Fig.2.14) indicated that there are indeed six such species.
Examination of this PES shows that the global minimum is structure 1 and that
there is a relative minimum corresponding to structure 4. Geometry optimization
starting from an input structure resembling 1 gave a minimum corresponding to 1 ,
while optimization starting from a structure resembling 4 gave another, higher-
energy minimum, resembling 4. Transition-state optimizations starting from appro-
priate structures yielded the transition states 2 and 3. These stationary points were
all characterized as minima or transition states by second-derivative calculations
(Section2.5) (the species 5 and 6 were not located). The calculated IR spectrum of 1
(using the ab initio HF/6–31G* method –Chapter 5) was in excellent agreement
with the observed spectrum of the putative propenol.
This illustrates a general principle: the optimized structure one obtains is that
closest in geometry on the PES to the input structure (Fig.2.15). To be sure we have
found aglobalminimum we must (except for very simple or very rigid molecules)
searcha potential energy surface (there are algorithms that will do this and locate
the various minima). Of course we may not be interested in the global minimum; for
example, if we wish to study the cyclic isomer of ozone (Section2.2) we will use as
Fig. 2.14 The 1-propen-2-ol potential energy surface (calculated by the AM1 method) (see
Fig.2.13)
2.4 Geometry Optimization 25