Computational Chemistry

species is formed. However, this does not tell us whether this species is an
intermediate or merely a transition state (Fig.9.2). A straightforward way to try
to answer this question would seem to be to calculate the frequencies, at the level
used to optimize the structure, and see if there are any imaginary frequencies – a
relative minimum has none, while a transition state has one (Section 2.5). In a
preliminary investigation [ 3 ] Schaefer and coworkers found that oxirene was
a minimum with the Hartree–Fock (SCF) method, and also when electron correla-
tion was taken into account (Section 5.4) with the CISD and CCSD methods, using
double-zeta basis sets (Section 5.3). However, in going from HF to CISD to CCSD,
the ring-opening frequency fell from 445 to 338 to 262 cm"^1 , which was said to be a
much steeper drop than would be expected. A very comprehensive investigation
with the above (“To be or not to be”) title [ 4 ], in which the frequencies of oxirene
were examined at 46 (!) different levels failed to definitively settle the matter: even
using CCSD(T) calculations with large basis sets the results were somewhat quirky,
and in fact of the six highest levels used, three gave an imaginary frequency and
three all real frequencies. At the two highest levels the ring-opening frequency was
real, but uncomfortably low (139 and 163 cm"^1 ). Although at all of the five DFT

a diazo ketone

R R

N 2 O

oxo carbene a

R R

O

oxirene

a b

O

R R

.

oxo carbene b

R R

O

ketene labelled at the other C

O

R

R

a b

R

R

O

ketene labelled at CO C

Fig. 9.1 Generating an oxo carbene (a “ketocarbene”) from a labelled diazo ketone sometimes
leads to a ketene in which the label is scrambled. This indicates that a species with the symmetry of
oxirene is formed

562 9 Selected Literature Highlights, Books, Websites, Software and Hardware