K enthalpies were calculated by Gaussian 03 [ 78 ] (except for M06, by Spartan
‘08 [ 71 ]) using a statistical mechanics algorithm and are “appropriate for
calculating enthalpies of reaction” [ 79 ]. Product enthalpies minus reactant
enthalpies give the calculated bond enthalpy; standard, tabulated bond enthalpies
are for 298 K. The experimental bond energy has been reported to be 90.1-0.1 kcal
mol"^1 , i.e. 377-0.4 kJ mol"^1 [ 80 ], and the CBS-APNO value (Section 5.5.2.2b),
with a mean absolute deviation of 2.2 kJ mol"^1 , is 379.3 kJ mol"^1. In Table7.3
we see that the Hartree–Fock bond energy is about 122 kJ mol"^1 too low, the M06
and TPSS values are not bad (8 and 11 kJ mol"^1 too low), and the MP2 and B3LYP
enthalpies are good, within 4 and 2 kJ mol"^1 of what we hold to be the correct bond
energy. Thus all of these electron correlation methods handle homolytic bond
breaking at least tolerably well.
The reaction profiles in Fig.7.3, mentioned above in connection with geometry,
also explore the effect of basis set size on relative energies (barriers and reaction
energies) for the B3LYP functional. As stated in Section7.3.1, these geometries
seem to be reasonably insensitive to basis set, but there are some significant changes
in energies on going from the 6-31G to the 6-311+G or the 6-311++G(2df, 2p)
basis: the reaction energy for the ethenol isomerization rises from ca."67 to ca.
"45 kJ mol"^1 and for the HNC isomerization from ca."69 to ca."57 kJ mol"^1.
The insensitivity of theactivation energiescan be rationalized with the Hammond
postulate [ 81 ], which implies that for an exothermic reaction the reactant resembles
its subsequent transition state; thus the effect of changing the basis set might be
much the same for both reactant and transition state. Why the CH 3 NC and cyclo-
propylidene reaction energies are unperturbed is unclear. The effect of basis set on
the energies of these reactions is discussed further in Section7.3.2.2b, under
kinetics (where some reference is also made to reaction energies).
Table7.4compares with experiment [ 82 ] the effect of functionals and of basis
set size on the reaction enthalpies of the important H 2 /Cl 2 and H 2 /O 2 reactions.
Table 7.3 The C–C bond energy of ethane by HF, MP2(fc), and DFT (B3LYP, M06, and TPSS)
calculations, at 0 and 298 K. The basis set is 6-31G*. Standard, tabulated bond energies are for
dissociation at 298 K. Bond energy¼2(CH 3 radical enthalpy) – (CH 3 CH 3 enthalpy). For the
radical the unrestricted method (UHF etc.) was used. For the 0 K dissociation enthalpy, the HF and
MP2 calculations use energies corrected for ZPE, with the ZPE itself corrected by a factor of
0.9135 (HF) or 0.9670 (MP2) [ 77 ]. The 0 K dissociation enthalpy for the DFT calculations is
uncorrected for ZPE, and the 298 K dissociation enthalpy is from standard statistical thermody-
namics methods [ 79 ]. The experimental C–C energy of ethane has been reported as 90.1-0.1 kcal
mol"^1 , i.e. 377-0.4 kJ mol"^1 [ 80 ]. Calculations are by the author
Method 0 K 298 K
HF 248 255
MP2(fc) 372 381
B3LYP 363 375
M06 380 369
TPSS 357 366
References to the methods: HF, Section5.2.2; MP2, Section5.4.2; B3LYP [ 57 , 58 ]; M06 [ 45 , 65 ];
TPSS [ 73 ].
478 7 Density Functional Calculations