Page 116 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

T.1.5.1. DFT Formulation of Chemical Potential, Electronegativity, Hardness 95
and Softness, and Covalent and van der Waal Radii
TOPIC 1.5
DFT suggests quantitative expressions and interrelation of certain properties such Application of Density
as electronegativity and polarizability, and the related concepts of hardness and softness Functional Theory
to Chemical Properties
introduced in Sections 1.1.3 through 1.1.6. 144 DFT calls the escaping tendency of an and Reactivity
electron from a particular field its chemical potential, 145 %, defined by

$ = *E/*N (1.31)
v
which is the slope of a curve for the energy of the system as a function of the change
in the number or electrons.
A stable system, such as a molecule, attains a common chemical potential among
its components. That is, there is no net force to transfer electron density from one
point to another. The idea that chemical potential is equivalent throughout a molecule,
and specifically between bonded atoms, accords with the concept of electronegativity
equalization (see Section 1.1.4). 146 Chemical potential is related to electrophilicity and
nucleophilicity. A system with an attraction toward electrons is electrophilic, whereas
a system that can donate electrons is nucleophilic. Chemical potential is considered to
be the opposite of absolute (Mulliken) electronegativity and can be approximated by
IP +EA
$ =− (1.32)
2
which is negative of the Mulliken absolute electronegativity:

IP +EA
= (1.33)
2
Since % is the slope of electronic energy as a function of the change in the number
of electrons, the Mulliken equation gives the energy for the +1 (IP) and −1 (EA)
ionization states. This is illustrated in Figure 1.43, which shows that IP+EA /2 is the
average slope over the three points and should approximate the slope at the midpoint,
where N = 0. 147
The Luo-Benson expression for electronegativity 148

V = n/r (1.34)

which relates electronegativity to the number of valence shell electrons n and the atomic
radius r is both theoretically related 149 and empirically correlated 150 with the Mulliken

144 P. W. Chattaraj and R. G. Parr, Structure and Bonding, 80, 11 (1993); G.-H. Liu and R. G. Parr, J. Am.
Chem. Soc., 117, 3179 (1995).
145
R. G. Parr, R. A. Donnelly, M. Levy, and W. E. Palke, J. Chem. Phys., 68, 3801 (1978).
146 R. T. Sanderson, J. Am. Chem. Soc., 105, 2259 (1983); R. T. Sanderson, Polar Covalence, Academic
Press, New York, 1983.
147
R. G. Pearson, Chemical Hardness, Wiley-VCH, Weinheim, 1977, p. 33; see also R. P. Iczkowski and
J. L. Margrave, J. Am. Chem. Soc., 83, 3547 (1961).
148
Y. R. Luo and S. W. Benson, J. Phys. Chem., 92, 5255 (1988); Y.-R. Luo and S. W. Benson, J. Am.
Chem. Soc., 111, 2480 (1989); Y. R. Luo and S. W. Benson, J. Phys. Chem., 94, 914 (1990); Y. R. Luo
and S. W. Benson, Acc. Chem. Res., 25, 375 (1992).
149 P. Politzer, R. G. Parr, and D. R. Murphy, J. Chem. Phys., 79, 3859 (1983).
150
Y. R. Luo and P. D. Pacey, J. Am. Chem. Soc., 113, 1465 (1991).