Page 120 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

the atoms of a molecule by condensed Fukui functions. These calculations must use 99
a scheme, such as Mulliken population analysis (see Section 1.4.1) for dividing the
electron density among the atoms. The condensed Fukui functions identify regions of TOPIC 1.5
space that are electron-rich f and electron-poor f . 160 Reactivity at individual Application of Density
+
−
Functional Theory
atoms can also be expressed as local softness, which is the product of the Fukui to Chemical Properties
function and global softness S. 161 As with the Fukui function, these are defined for and Reactivity
electrophilic, nucleophilic, and radical reactants.
−
s = N − N−1 S (1.45)
+
s = N+1 − S (1.46)
N
and

s = ½ N+1 − N−1 S (1.47)
The idea that frontier orbitals control reactivity introduced in the context of MO
theory has an equivalent in DFT. The electron density distribution should have regions
of differing susceptibility to approach by nucleophiles and electrophiles. Reactivity
should correspond to the ease of distortion of electron density by approaching reagents.
This response to changes in electron distribution is expressed in terms of the Fukui
function, which describes the ease of displacement of electron density in response to
a shift in the external field. Since the electron distribution should respond differently
to interaction with electron acceptors (electrophiles) or electron donors (nucleophiles),
there should be separate f + and f − functions. Reaction is most likely to occur at
+
locations where there is the best match (overlap) of the f function of the electrophile
and the f − function of the nucleophile. 162 For example, the f + and f − functions
for formaldehyde have been calculated and are shown in Figure 1.45. 163 The f +
function, describing interaction with a nucleophile, has a shape similar to the MO.
∗
It has a higher concentration on carbon than on oxygen and the maximum value is
perpendicular to the molecular plane. The f function is similar in distribution to the
−
nonbonding n electron pairs of oxygen. This treatment, then, leads to predictions
about the reactivity toward nucleophiles and electrophiles that are parallel to those
developed from MO theory (see p. 45). A distinction to be made is that in the MO
formulation the result arises on the basis of a particular orbital combination—the
HOMO and LUMO. The DFT formulation, in contrast, comes from the total electron
density. Methods are now being developed to compute Fukui functions and other
descriptors of reactivity derived from total electron density.
DFT can evaluate properties and mutual reactivity from the electron distribution.
These relationships between qualitative concepts in chemistry, such as electronega-
tivity and polarizability, suggest that DFT does incorporate fundamental relationships
between molecular properties and structure. At this point, we want to emphasize
the conceptual relationships between the electron density and electronegativity and
polarizability. We can expect electrophiles to attack positions with relatively high
electron density and polarizability. Nucleophiles should attack positions of relatively

160
Y. Li and J. N. S. Evans, J. Am. Chem. Soc., 117, 7756 (1995).
161 W. Yang and W. J. Mortier, J. Am. Chem. Soc., 108, 5708 (1986).
162 R. F. Nalewajski, Top. Catal., 11/12, 469 (2000).
163
A. Michalak, F. De Proft, P. Geerlings, and R. F. Nalewajski, J. Phys. Chem. A, 103, 762 (1999); F.
Gilardoni, J. Weber, H. Chermette, and T. R. Ward, J. Phys. Chem. A, 102, 3607 (1998).