configuration interaction method like a complete active space SCF (CASSCF)
calculation (Section 5.4.3). See too Section 8.2.
Although Hartree–Fock calculations are satisfactory for many purposes
(Section 5.5)therearecaseswhereabettertreatment of electron correlation
is needed. This is particularly true for the calculation of relative energies
(Section 5.5.2), although geometries (5.5.1) and some other properties can benefit
from post-Hartree-Fock calculations (Section 5.4). As an illustration of a shortcom-
ing of Hartree–Fock calculations consider an attempt to find the C/C single bond
dissociation energy of ethane by comparing the energy of ethane with that of two
methyl radicals:
H 3 C#CH 3 þEdiss!H 3 C(CH 3Let us simply subtract the energy of two methyl radicals from that of an ethane
molecule, and compare with experiment the results of Hartree–Fock calculations
and (anticipating Section 5.4.2) the post-Hartree–Fock (i.e. correlated) MP2
method. In Table5.5the energies shown for CH 3 (and CH 3 CH 3 are successively
the “uncorrected” ab initio energies (the energy displayed at the end of any
calculation; this is the electronic energyþthe internuclear repulsion), the ZPE,
and the “corrected” energy (uncorrected energy + ZPE); see Section 5.2.3.6.4. The
ZPEs used here are from HF/6–31G* optimization/frequency jobs; these are fairly
fast and give reasonable ZPEs. The ZPEs were all calculated by multiplying by an
empirical correction factor of 0.9135 (this brings them into better agreement with
Table 5.5 The C–C bond energy of ethane calculated by the Hartree–Fock and MP2 methods
Energy
Method/basis CH 3 ( CH 3 CH 3 E(2CH 3 (#CH 3 CH 3 )
HF/6–31G #39.55899 #79.22876 0.09451
0.02829 0.07285 248
#39.53070 #79.15591
HF/6–311þþG(3df,3p2d) #39.57712 #79.25882 0.08831
0.02829 0.07285 232
#39.54883 #79.18597
MP2/6–31G #39.66875 #79.49474 0.14097
0.02829 0.07285 370
#39.64046 #79.42189
MP2/6–311þþG* #39.70866 #79.57167 0.13808
0.02829 0.07285 363
#39.68037 #79.49882
The radical CH 3 (and the closed-shell CH 3 CH 3 were calculated by unrestricted and restricted
methods, respectively: UHF and UMP2, versus RHF and RMP2 – see concluding part of
Section 5.2.3.6.2); the HF method largely ignores electron correlation, while MP2 recovers
about 85% of the electron correlation. The set of three numbers for each species are respectively,
in hartrees, the uncorrected ab initio energy, the corrected (0.9135 factor, see text) HF/6–31G
ZPE, and the corrected ab initio energy (uncorrected energyþZPE). Calculated (by subtraction)
bond energies are in hartrees and kJ mol#^1 (2,626'hartrees). The experimental C–C energy of
ethane has been reported at 377 kJ mol#^1 [ 81 ]. Each species was optimized at the level shown (i.e.
none of these are single-point calculations).
5.4 Post-Hartree–Fock Calculations: Electron Correlation 259