Computational Chemistry

gives a conformation C which has no eclipsing interactions and is therefore a
minimum. There are no lower-energy structures on the C 3 H 8 PES and so C is the
global minimum.
The geometry of propane depends on more than just two dihedral angles, of
course; there are several bond lengths and bond angles and the potential energy will
vary with changes in all of them. Figure2.9was calculated by varying only the
dihedral angles associated with the C1–C2–C3–C4 bonds, keeping the other
geometrical parameters the same as they are in the all-staggered conformation. If
at every point on the dihedral/dihedral grid all the other parameters (bond lengths
and angles) had been optimized (adjusted to give the lowest possible energy, for
that particular calculational method;Section 2.4), the result would have been a
relaxedPES. In Fig.2.9this was not done, but because bond lengths and angles
change only slightly with changes in dihedral angles the PES would not be altered
much, while the time required for the calculation (for thepotential energy surface
scan) would have been greater. Figure2.9is a nonrelaxed or rigid PES, albeit not
very different, in this case, from a relaxed one.
Chemistry is essentially the study of the stationary points on potential energy
surfaces: in studying more or less stable molecules we focus on minima, and
in investigating chemical reactions we study the passage of a molecule from a

A, hilltop

B, transition state

C, minimum

400

300

200

200

300

400

500

100

100

0

0

–100 –100

H--C

1 --C

2 --C

3 dihedral

H--C

3 --C

--C 2

dihedra 1

l

B

A

C

Fig. 2.9 The propane potential energy surface as the two HCCC dihedrals are varied (calculated
by the AM1 method,Chapter 6). Bond lengths and angles were not optimized as the dihedrals
were varied, so this is not a relaxed PES; however, changes in bond lengths and angles from
one propane conformation to another are small, and the relaxed PES should be very similar to
this one

2.2 Stationary Points 19