Levine has compared various properties from DFT with those from molecular
mechanics, ab initio, and semiempirical methods [ 66 ]. Hehre [ 67 ] and Hehre and
Lou [ 68 ] have provided extensive, very useful compilations of ab initio, semiem-
pirical, DFT, and some molecular mechanics results. More recent surveys (2007),
oriented toward the quality of molecular properties from DFT, are those by Sousa
et al. (geometries, barrier heights, atomization energies, ionization energies, elec-
tron affinities, heats of formation, isomerization energies, weak interactions) [ 44 ],
Zhao and Truhlar (geometries, barrier heights, frequencies, various thermochemi-
cal parameters – atomization energy etc., ionization energies, electron affinities,
UV, transition metal reactions, weak interactions) [ 45 ], and Riley et al. (geometries,
barrier heights frequencies, ionization energies, electron affinities, heats of forma-
tion, conformational energies, hydrogen bonds; great emphasis on comparing Pople
versus Dunning basis sets) [ 46 ].
7.3.1 Geometries.......................................................
The Figures and Tables in this section for geometries and reactions by DFT are
analogous to those that were shown for ab initio and semiempirical methods in
chapters 5 and 6, thus:
Geometries of 20 molecules, Figs. 5.23, 6.2,7.1
Analysis of errors for 20 molecules, Tables 5.7, 6.1,7.1
Dihedrals of 8 molecules, and errors, Tables 5.8, 6.2,7.2
Geometries and errors for 4 reactions: Figures 5.21, 6.3,7.2and7.3
For Fig.7.1and Tables7.1and7.2, for comparison with the presentations in
Chapters 5 and 6, values from MP2/6-31G calculations (the standard post-Hartree
Fock ab initio method; Section 5.4.2) and from experiment (Fig.7.1[ 69 ], Fig.7.2
[ 70 ]) were clearly necessary. This choice of the relatively small 6-31G basis is
discussed below. The choice of DFT functionals required some consideration.
B3LYP is retained from the first edition of this book because it continues to be
very widely used. The pBP/DN* functional/basis set (described in [ 68 ]) that was a
feature of Spartan [ 71 ] and was used in the first edition of this book showed certain
problems and is no longer available, and its replacement required some delibera-
tion. The remaining choice was now narrowed to three functionals:
- The general-purpose M06 functional. This is a hybrid meta-GGA functional
(Section7.2.3.4f) parameterized with nonmetals and metals (for a review and for
details see respectively [ 45 ] and [ 65 ]). It lies on rung six of our ladder (rung five
if LDA and LSDA are collapsed into rung one as indicated in Table 2 of [ 44 ] and
as implied in [ 65 ]). As stated in Section7.3, this belongs to a recently developed,
very promising class and M06 may eventually replace B3LYP. Persuaded by the
case made by Perdew et al. for nonempirical functionals, these two recom-
mended [ 47 ] ones were also considered:
468 7 Density Functional Calculations