Page 119 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

98 Table 1.24. Covalent Radii
from DFT
CHAPTER 1
Atom Covalent radius (au) a
Chemical Bonding
and Molecular Structure Li 1.357
B 1.091
C 0.912
N 0.814
O 0.765
F 0.671
Na 1.463
Al 1.487
Si 1.296
P 1.185
S 1.120
Cl 0.999
Se 1.209
Br 1.116
I 1.299
a. P. Politzer, R. G. Parr, and
D. R. Murphy, J. Chem. Phys., 79, 3859
(1983); M. K. Harbola, R. G. Parr, and C.
Lee, J. Chem. Phys., 94, 6055 (1991).

reactivity. The responsiveness of this electron distribution to a perturbing external
field, e.g., an approaching reagent, must be evaluated. This responsiveness is described
by the Fukui function, 158 which is a reactivity indicator is defined by

&% * r
f r = n r /N = (1.40)
& r *N
N r
where N is the change in the number of electrons in the system.
Fukui functions are defined for electrophilic f , nucleophilic f , and radical
+
−

f reactions by comparing the electron density r , with one fewer electron, one
more electron, and the average of the two 159 :
−
f r = r − N−1 r (1.41)
N
+
f r = N+1 r − r (1.42)
N
r − r
N+1 N−1
f r = (1.43)
2
The Fukui function describes interactions between two molecules in terms of the
electron transfer between them. The extent of electron transfer is related to chemical
potential (and electronegativity) and hardness (and polarizability).

% −%

N = B A (1.44)

+
B A
The responsiveness of the electron density to interaction with another field is
nonuniform over the molecule. The electron density can be further partitioned among
158 R. G. Parr and W. Yang, J. Am. Chem. Soc., 106, 4049 (1984).
159
C. Lee, W. Yang, and R. G. Parr, Theochem, 40, 305 (1988).