Page 122 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

which influence interactions with approaching reagents and thus affect reactivity. We 101
also discussed the concept of polarizability, which refers to the ease of distortion of the
electron density distribution of an atom or an ion and can be described as hardness or TOPIC 1.5
softness. Since chemical reactions involve the reorganization of electrons by breaking Application of Density
Functional Theory
and forming bonds, polarizability also has a major influence on reactivity. to Chemical Properties
There have been a number of efforts to assign numerical values to electronegativity and Reactivity
of substituent groups, analogous to the numbers assigned to atoms (see Section 1.1.3).
These have been based on structural parameters, charge distribution, thermodynamic
relationships and or MO computations. 164 More recently, as DFT descriptions of
electron density have developed and these, too, have been applied to organic functional
groups. DFT suggests quantitative expressions of some of the qualitative concepts such
as electronegativity, polarizability, hardness, and softness. 165 DFT describes a molecule
as an electron density distribution, in which the nuclei are embedded, that is subject
to interaction with external electrical fields, such as that of an approaching reagent.
Several approaches are currently being explored to find correlations and predictions
based on DFT concepts that were introduced in Section 1.3.
De Proft, Langenaeker, and Geerlings applied the DFT definitions of electronega-
tivity, hardness, and softness to calculate group values, which are shown in Table 1.25.
These values reveal some interesting comparisons. The electronegativity values calcu-
lated for C H ,CH =CH, and HC≡C are in accord with the relationship with
2 5 2
hybridization discussed in Section 1.1.5. The methyl group is significantly more
electronegative and harder than the ethyl group. This is consistent with the difference
noted between methyl and ethyl diazonium ions in Section 1.4.3. Typical EWGs such
as CH=O, C≡N, and NO show high electronegativity. Hardness values are more
2
difficult to relate to familiar substituent effects. The acetyl, carboxamide, and nitro
groups, for example, are among the softer substituents. This presumably reflects the
electron density of the unshared electron pairs on oxygen in these groups.
AIM results from methyl compounds were also used to develop a group
electronegativity scale. Boyd and Edgecombe defined a quantity F in terms of r , the
A
H
location of the bond critical point to hydrogen, N the number of valence electrons of
A
the atom A, and , the electron density at the bond critical point 166 :
c
F = r /N r r AH (1.48)
A
c
n
H
These were than scaled to give numerical comparability with the Pauling electroneg-
ativity scale. 167 In another approach, the charge on the methyl group was taken as the
indicator of the electronegativity of the group X and the results were scaled to the
Pauling atomic electronegativity scale. 168 It was also noted that the electronegativity
value correlated with the position of the bond critical point relative to the bond length:
r /R = 0 785−0 042 0 (1.49)
c x
As the group becomes more electronegative, the critical point shifts toward the
substituent. Table 1.26 compares two of the traditional empirical electronegativity

164
A. R. Cherkasov, V. I. Galkin, E. M. Zueva, and R. A. Cherkasov, Russian Chem. Rev. (Engl. Transl.),
67, 375 (1998).
165
P. W. Chattaraj and R. G. Parr, Struct. Bonding, 80 11 (1993); G.-H. Liu and R. G. Parr, J. Am. Chem.
Soc., 117, 3179 (1995).
166 R. J. Boyd and K. E. Edgecombe, J. Am. Chem. Soc., 110, 4182 (1988).
167 R. J. Boyd and S. L. Boyd, J. Am. Chem. Soc., 114, 1652 (1992).
168
S. Hati and D. Datta, J. Comput. Chem., 13, 912 (1992).