Computational Chemistry

These calculated geometries do not satisfy even our “fairly good” criterion
(errors in calculated bond lengths, angles and dihedrals of up to 0.02 A ̊,3and
4  respectively) and are well short of being “accurate” (bond lengths about
0.01–0.02 A ̊, bond and dihedral angles about 1–2); the bond lengths are particu-
larly bad. Using the HF method and the 6–311þþG basis (for FOOF, 88 vs 60
basis functions; for O 3 , 66 vs 45 basis functions) we get for calculated geometries
(errors) using (HF/6–311þþG):

FOOF FO length 1.353 A ̊(#0.222)

OO length 1.300 (0.083) A ̊

FOO angle 106.5(#3.0)

FOOF dihedral 85.3(#2.2)

O 3 OO length 1.194A ̊(#0.078)

OOO angle 119.4(2.6)

Thus with a much larger basis, but still using the Hartree–Fock method, the
FOOF geometry is about the same and the O 3 geometry has become even worse
than at the HF/6–31G* level!
In a 2001 paper FOOF was called “the unsolved problem” of structure predic-
tion, and a really good structure was obtained only by DFT with the aid of a
somewhat contrived procedure [ 119 ]. How has the situation changed since then?
Here are the best results for FOOF from two 2007 studies [120, 121] of that and
other small O/F molecules:

O O

F F

1.209

1.211

(1.217) 1.628

1.579

109.2 (1.575)

111.0

(109.5)

OOOF dihedral:

88.7

88.8

(87.5)

CCSD(T)/ aug-cc-pVDZ [118]

G96PW91/ D95(3df) [119]

Experiment

The errors in the CCSD(T) (their DFT results were quite similar) [ 120 ] and the
G96PW91 (a DFT method) [ 121 ] calculations are:

FO length 0.053 [ 120 ]/0.004 A ̊[ 121 ]

OO length #0.008 [ 120 ]/#0.006 A ̊[ 121 ]

FOO angle #0.3[ 120 ]/1.5[ 121 ]

FOOF dihedral 0.2[ 120 ]/1.3[ 121 ]

Here the only problematic parameter is the CCSD(T) FO bond length: the DFT
error was#0.051 A ̊, still a bit outside our imposed 0.01–0.02 A ̊error limits. The
DFT geometry is fully high-quality.

290 5 Ab initio Calculations