philicity” shown above and dual philicity to give a “multiphilic descriptor” which
reflects simultaneously the nucleophilicity and the electrophilicity of a given site in
a molecule [ 163 ]; AIM calculations (in Section 5.54) were said to give the best
results with condensed Fukui functions (Eqs.7.41and7.42)[ 164 ]; and the appro-
priateness of the Fukui function for describing hard-hard, as distinct from soft-soft,
interactions has been questioned [ 165 ].
7.3.6 Visualization......................................................
The only cases for which one might anticipate differences between DFT and
wavefunction theory as regards visualization (Sections 5.5.6 and 6.3.6) are those
involving orbitals: as explained in Section7.2.3.2,The Kohn–Sham equations, the
orbitals of currently popular DFT methods were introduced to make the calculation
of the electron density tractable, but in “pure” DFT theory orbitals would not exist.
Thus electron density, spin density, and electrostatic potential can be visualized in
Kohn–Sham DFT calculations just as in ab initio or semiempirical work. However,
visualization of orbitals, so important in wavefunction work (especially the HOMO
and LUMO, which in frontier orbital theory [ 154 ] strongly influence reactivity)
does not seem possible in apureDFT approach, one in which wavefunctions are not
invoked. In currently popular DFT calculations one can visualize the Kohn–Sham
orbitals, which are qualitatively much like wavefunction orbitals [ 130 ] (Section7.3.5,
Ionization energies and electron affinities).
7.4 Strengths and Weaknesses of DFT......................................
7.4.1 Strengths..........................................................
DFT includes electron correlation in its theoretical basis, in contrast to wavefunc-
tion methods, which must take correlation into account by add-ons (Møller-Plesset
perturbation, configuration interaction, coupled-cluster) to ab initio Hartree–Fock
theory, or by parameterization in semiempirical methods. Because it has correlation
fundamentally built in, DFT can calculate geometries and relative energies with
an accuracy comparable to MP2 calculations, in roughly the same time as needed
for Hartree–Fock calculations. Aiding this, DFT calculations tend to be basis-set-
saturated more easily than are ab initio: limiting results are (sometimes) approached
with smaller basis sets than for ab initio calculations. Calculations of post-Hartree–
Fock accuracy can thus be done on bigger molecules than ab initio methods
make possible. DFT appears to be the method of choice for geometry and energy
calculations on transition metal compounds, for which conventional ab initio
calculations often give poor results [ 76 , 166 ] (see too chapter 8, Section 8.3).
7.4 Strengths and Weaknesses of DFT 509