7.3.2 Energies..........................................................
7.3.2.1 Energies: Preliminaries
Usually, we seek from a DFT calculation, as from an ab initio or semiempirical one,
geometries (preceding section) and energies. Like an ab initio energy, a DFT energy
is relative to the energy of the nuclei and electrons infinitely separated and at rest,
i.e. it is the negative of the energy needed to dissociate the molecule into its nuclei
and electrons. AM1 and PM3 semiempirical energies (Section 6.3.2) are heats of
formation, and by parameterization zero-point energies are included. In contrast, an
ab initio or DFT molecular energy, the energy printed out at the end of any
calculation, is the energy of the molecule sitting motionless at a stationary point
(Section 2.2) on the potential energy surface; it is the purely electronic energy plus
the internuclear repulsion. In accurate work on a reaction profile (reactant, transi-
tion state, product) this “raw” energy should be corrected by adding the zero-point
vibrational energy, to obtain the total internal energy at 0 K. Analogously to the HF
equation in Section 5.2.3.6.4, Eq. (5.94) we have
Etotal0K ¼EtotalDFTþZPE *(7.29)(The Gaussian programs actually denote the DFT energy called hereEtotalDFTtotal
as HF, e.g. (in hartrees or atomic units) “HF¼"308.86101”). The main advantage
of DFT over Hartree–Fock calculations is in being able to provide, in a comparable
time, superior energy-difference results: reaction energies and activation energies.
7.3.2.2 Energies: Calculating Quantities Relevant to Thermodynamics
and Kinetics
7.3.2.2a Thermodynamics
Let’s first see how DFT handles a case where Hartree–Fock with its cavalier
treatment of electron correlation fails badly: homolytic breaking of a covalent
bond (Section 5.4.1). Consider the reaction
H 3 C"CH 3 þEdiss!H 3 C++CH 3In principle the dissociation energy can be found simply as the energy of
two methyl radicals minus the energy of ethane. Table7.3(cf. Table 5.5) shows
the results of HF, MP2, and DFT (B3LYP, M06, and TPSS) calculations, with
the 6-31G* basis. The energies shown for each species are 0 K energies
(enthalpies) and 298 K enthalpies. The HF and MP2 0 K values are corrected
for ZPE with the ZPE itself corrected, by 0.9135(HF) and 0.9670 (MP2(fc)), as
prescribed by Scott and Radom [ 77 ]. For the DFT, 0 K energies the ZPEs were
not corrected, as the factor appears to lie between 0.96 and unity [ 77 ]. The 298
7.3 Applications of Density Functional Theory 477