Computational Chemistry

This energy difference should be a measure of the C–C bond energy in cyclo-
pentane. These calculations used NBO localization (the result of Boys localization
was messy when visualized) and CASSCF(2,2)/6-31G.
Several starting geometries were explored to obtain a C 5 diradical that was a
relative minimum, but a thorough exploration of the potential energy surface was
not attempted. Starting from a roughly bow-shaped C 1 structure created by con-
straining the end carbons with molecular mechanics to a separation of 4.5 A ̊yielded
aC 1 relative minimum. The visualization step showed that for the input structure
the default active space MOs, MO 20 and 21, the HOMO and LUMO, were the
desired orbitals, localized at the end carbons. However, for cyclopentane the
occupied C–C bonding MO, representing the bond to be broken, was number 10,
while MO 20 was a pure C–H bonding orbital, an unwanted intruder in the active
space; a command to switch orbitals 10 and 20 was therefore given as part of the
optimization input. See Fig.8.12. The diradical and cyclopentane, optimized at
the CASSCF(2,2)/6-31G level, were checked by frequency calculations to ensure
that the structures were relative minima on the potential energy surface and to
obtain the energy parameters below (Gaussian 03 output).

cyclopentane MO 20

1, 5-pentanediyl MO 20 1, 5-pentanediyl MO 21

cyclopentane MO 10 cyclopentane MO 21

Fig. 8.12 The molecular orbitals of 1,5-pentanediyl and cyclopentane, relevant to the C–C
cleavage of the cycloalkane that leads to the acyclic diradical. Calculated with the HF/STO-3G
wavefunction and localized by the NBO method. The cyclopentane C–C bonding orbital, MO 10,
relevant to this reaction, must be switched with MO 20, a pure C–H bonding MO with no relevance
here, to move the C–C MO into the active space. Note that these molecules have 40 electrons

544 8 Some “Special” Topics