Diradical, MP2¼"195.6895856
Cyclopentane, MP2¼"195.8242116
We can use these energies, with the thermal corrections to the enthalpy (above)
to calculate the sum of electronic and thermal enthalpies starting with the CAS-
MP2 electronic energies:
Diradical,"195.6895856þ0.148403¼"195.54118
Cyclopentane,"195.8242116þ0.156203¼"195.66801
The difference of these represents the room temperature enthalpy of dissociation
of the C–C bond in cyclopentane, i.e. the standard bond energy [ 68 ]: ["195.54118]"
["195.66801]¼0.12683¼333.1 kJ mol"^1. Of the energy-difference values calcu-
lated here, this is the closest to the likely C–C bond energy [ 69 ] of cyclopentane,
which should be about the same as that of butane, for which an experimental value of
363.2'2.5 kJ mol"^1 and calculated values of ca. 367, 378 and 379 kJ mol"^1 have
been reported [ 70 ].
One more example of the CASSCF procedure will be outlined: calculating the
barrier to rotation around the CC double bond in ethene. Step 2, orbital localization,
showed nicely localized orbitals when NBO localization was used, but the orbitals
were harder to identify with Boys localization. For a CAS(2,2)/6-31G optimiza-
tion the active orbitals chosen were thepandp MOs, and for a CAS(4,4)/6-31G
optimization thep,p,sands MOs. The input structures were the normal planar
ethene and perpendicular (90twisted) ethene. Optimization and frequency calcu-
lations gave a minimum for the planar and a transition state for the perpendicular
structures. The energies (without ZPE, for comparison with those calculated with
the GVB method by Wang and Poirier [ 71 ]) were:
CASSCF(2,2):
perpendicular ethene,"77.9630054, planar ethene,"78.0673444;
barrier¼0.10434¼274.0 kJ mol"^1.
CASSCF(4,4):
perpendicular ethene,"77.982972, planar ethene,"78.0852825;
barrier¼0.10231¼268.7 kJ mol"^1.
Wang and Poirier obtained from GVB calculations [ 71 ] a barrier of 263.6 kJ
mol"^1 (65.4 kcal mol"^1 ). The reported experimental value for the barrier ofcis-
ethene-d 2 is 272 kJ mol"^1 [ 72 ]. Hartree–Fock, MP2 and DFT (B3LYP) optimiza-
tions on the perpendicular ethene transition state did give an optimized structure
with one imaginary frequency, but the barriers (6-31G) basis were respectively
540, 572, and 399 kJ mol"^1 (without ZPE, which was only ca. 10–20 kJ mol"^1 ).
More complex than ethene but amenable to a similar attack is the fascinating
molecule orthogonene. This is so named because in this C 14 molecule four C 2
clamps hold the C 6 tetrasubstituted double bond moiety twisted through ca. 90:
546 8 Some “Special” Topics