Computational Chemistry

Ozone is an easier target than FOOF for a high-quality geometry. Some results
for this molecule are [ 122 ]:

O

O

O

1.276

1.277

(1.272)

117.1

118.2

(116.8)

CCSD(T) / aug-cc-pVTZ

BPW91) / aug-cc-pVTZ

Experiment

The errors in the CCSD(T) and BPW91 (a DFT method) calculations easily fall
within our limits:

OO length 0.004 (CCSD(T)/0.005 A ̊(BPW91)

OOO angle 0.3(CCSD(T))/1.4(BPW91)

Other coupled-cluster calculations [ 123 ] and CASPT2 [ 124 ] gave similar results.
The problem with ozone probably arises at least partly from the fact that this
molecule has singlet diradical character (Section 8.2): it is approximately a species
in which two electrons, although having opposite spin, are not paired in the same
orbital [ 125 ]:

O

O O

The Hartree–Fock method works best with normal closed-shell molecules,
because it uses a single Slater determinant, but ozone has open-shell diradical
character: it is, or at least resembles, a species with two half-filled orbitals, one
with a singleaelectron and the other with a singlebelectron. Correlated methods,
which go beyond the HF method by including in the wavefunction determinants
corresponding to states in which electrons have been promoted (“excited”) into
virtual orbitals, handle molecules like ozone better, but can still give problems if we
demand highly accurate geometries (or energies). For some techniques for handling
molecules like this see Foresman and Frisch [ 118 ].
The cause of the problems with FOOF are harder to explain, but fluorine is
known to be a somewhat troublesome element [ 126 ], although some fluoro organics
apparently give good geometries at moderate computational levels [ 127 ].

5.5.2 Energies..........................................................

5.5.2.1a Energies: Preamble

We used the concept of energy in Chapters 2 (potential energy surfaces), 3
(molecular mechanics energies), and 4 (molecular orbital energy levels from simple

5.5 Applications of the Ab initio Method 291