Computational Chemistry

advanced post-Hartree–Fock methods suggest it is a true minimum on the potential
energy surface, but its disconcerting tendency to display an imaginary (Section 2.5)
calculated ring-opening vibrational mode at some of the highest levels used leaves
the judicious chemist with no choice but to reserve judgement on its being. The
nature of a series ofsubstitutedoxirenes, studied likewise at high levels, appears to
be clearer [ 53 a].
Another system that has yielded results which are dependent on the level of
theory used, but which unlike the oxirene problem provides a textbook example of a
smooth gradation in the nature of the answers obtained, is the ethyl cation
(Fig. 5.17). At the Hartree–Fock STO-3G and 3–21G(*) levels the classical

H

H H

H

H

+

H

H

H H

H

+

H

HH

H

H

+

H

HH

H

H

+

H

H

H H

H

+

H

H

H H

H

+

H

H

H H

H

+

bridged

6-31G*

MP2 / 6-31G*

STO-3G 47 kJ mol–1

3-21G 32 kJ mol–1

classical

0 kJ mol–1

classical

0 kJ mol–1

classical

0 kJ mol–1

5.0 kJ mol–1

bridged

3.4 kJ mol–1

bridged; the classical ion is not

a stationary point at this level

Fig. 5.17 The ethyl cation problem at various levels. At the three Hartree–Fock levels the
classical cation is a minimum, but at the post-Hartree–Fock (MP2/6–31G) level only the
symmetrical bridged ion is a minimum. The HF/6–31G results are calculations by the author
(ZPE ignored), the other three levels are taken from ref. [ 75 ]

254 5 Ab initio Calculations