Computational Chemistry

indicate them to be minima. The interesting hexaazabenzene (“benzene-N 6 ”) is
predicted to be a minimum at the HF/6–31G level, but a hilltop with two
imaginary frequencies at the MP2/6–31G level [ 115 ]. For transition states, in
contrast to ground states, we don’t have experimental geometries, but correlation
effects can certainly be important for theirenergies(Section 5.5.2.2b), which can be
experimentally probed by kinetics, and MP2/6–31G geometries for transition
states are probably significantly better in general than HF/6–31G ones.
Suppose we want something better than “fairly good” structures? Experienced
workers in computational chemistry have said [ 116 ]

When we speak of “accurate” geometries, we generally refer to bond lengths that are within
about 0.01–0.02 A ̊of experiment and bond and dihedral angles that are within about 1–2
of the experimentally-measured value (with the lower end of both ranges being more
desirable).
Even by these somewhat exacting criteria, MP2/6–31G and even HF/6–31G
calculations are not, in the cases studied here, far wanting; the worst deviations
from experimental values seem to be for dihedral angles, and these may be the least
reliable experimentally. However, since some larger deviations from experiment
are seen in our sample, it must be conceded that HF/6–31G and even MP2/6–31G
calculations cannot bereliedon to provide “accurate” (sometimes called high-
quality) geometries. Furthermore, there are some molecules that are particularly
recalcitrant to accurate calculation of geometry (and sometimes other characteris-
tics); two notorious examples are FOOF (dioxygen difluoride) and ozone (these
have been described as “pathological” [ 117 ]). Here are the HF/6–31G, MP2
(fc)/6–31G and experimental [ 118 ] geometries:

O O

F F

1.367

1.495

(1.575)

105.8

106.9

(109.5)

1.311

1.293

(1.217)

HF /6-31G*

MP2 /6-31G*

Experiment

O

O

O

1.204

1.300

119.0 (1.272)

116.3

(116.8)

F-O-O-F dihedral

84.1

85.8

(87.5)

The errors (calculated – experimental) in the calculated geometries are
(HF/6–31G/MP2/6–31G):

FOOF FO length #0.208/#0.080 A ̊

OO length 0.094/0.076 A ̊

FOO angle #3.7/#2.6

FOOF dihedral #3.4/#1.7

O 3 OO length #0.068/0.028 A ̊

OOO angle 2.2/#0.5

5.5 Applications of the Ab initio Method 289