Computational Chemistry

1,3-Propanediyl, trimethylene.Four different starting geometries were used
(Fig.8.7), with symmetry C 1 ,C 2 ,Cs, and C2v, and each of them was submitted to
a geometry optimization/frequency calculation by the HF, the MP2, and the B3LYP
method (seeChapters 5 and 7for these ab initio methods and this DFT method), for
12 calculations in all. The results are summarized in Table8.3: all but one optimi-
zation, that starting with the C2vstructure, led to closing of the diradical to give
cyclopropane. The C2vstarting structure gave a stationary point resembling the
starting structure, an open-chain species. At the HF/6-31G level this was a hilltop
with a principal imaginary frequency of 668iand a secondary one of 74icm"^1 ,
while at the MP2/6-31G and the B3LYP/6-31G* levels it was a transition state
(imaginary frequencies 191iand 453i,respectively). When the MP2 transition state
was slightly distorted along the imaginary mode (the reaction mode; by visualizing
the vibration, replacing a central CH 2 H by F and subjecting this now-Csstructure to
just two optimization steps, then restoring the hydrogen and optimizing fully) a Cs
potential energy relative minimum (no imaginary frequencies) was obtained, i.e. a
real molecule (caveat: atthislevel). At the HF and B3LYP levels the C2vstructure,
altered to Cs and optimized, each gave a transition state with a central hydrogen

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Energy

Two orbitals of the same or

slightly different energy

Fig. 8.6 A singlet diradical.
Two electrons (usually the
highest-energy ones) are
unpaired but of opposite spin

Cs C2v

C 1 C 2

Fig. 8.7 The input structures
for attempted model
chemistry optimizations on
1,3-propanediyl
(.CH 2 CH 2 CH 2 .). All bond
lengths and angles in these
structures were standard, e.g.
C–C ca. 1.5 A ̊, C–H ca. 1.1 A ̊,
bond angles ca. 110

536 8 Some “Special” Topics