Electrophilicity Index Robert G. Parr,* ,² La ´ szlo ´ v. Szentpa ´ ly, ‡ and Shubin Liu ²,§ Contribution from the Department of Chemistry, UniVersity of North Carolina, Chapel Hill, North Carolina, 27599-3290, Chemistry Department, UniVersity of the West Indies, Mona Campus, Kingston 7, Jamaica, and Department of Biochemistry and Biophysics, School of Medicine, UniVersity of North Carolina, Chapel Hill, North Carolina, 27599-7260 ReceiVed October 5, 1998. ReVised Manuscript ReceiVed December 15, 1998 Abstract: Prompted by a recent paper by Maynard and co-workers (Maynard, A. T.; Huang, M.; Rice, W. G.; Covel, D. G. Proc. Natl. Acad. Sci. U.S.A. 1998, 95, 11578), we propose that a specific property of a chemical species, the square of its electronegativity divided by its chemical hardness, be taken as defining its electrophilicity index. We tabulate this quantity for a number of atomic and molecular species, for two different models of the energy-electron number relationships, and we show that it measures the second-order energy change of an electrophile as it is saturated with electrons. Ligand-binding phenomena are of general interest in catalysis, drug design, and protein and DNA functioning. Although many kinds of interactions are involved in the process, in many cases partial charge transfer through covalent bonding, dative bonding, or hydrogen bonding takes place. The capability of a ligand to accept precisely one electron from a donor is measured by its electron affinity (EA). However, the question we here address is to what extent partial electron transfer contributes to the lowering of the total binding energy by maximal flow of electrons. As yet there has been no direct answer to this question. We here provide validation for the recent qualitative suggestion by Maynard et al. 1 that electronegativity squared divided by hardness measures the electrophilic power of a ligand, its propensity to “soak up” electrons, so to speak. Consider an electrophilic ligand immersed in an idealized zero-temperature free electron sea of zero chemical potential, which could be an approximation to its binding environment in a protein, a DNA coil, or a surface. It will become saturated with electrons, to the point that its chemical potential increases to zero, becoming equal to the chemical potential of the sea. To second order, the energy change ΔE due to the electron transfer ΔN satisfies the formula 2 where μ and η are the chemical potential (negative of the electronegativity) 3 and chemical hardness 4 of the ligand, defined by μ ) (∂E/∂N) ν and η ) (∂ 2 E/∂N 2 ) ν . If the sea provides enough electrons, the ligand becomes saturated with electrons when ΔE/ ΔN ) 0. That is, Notice that since η > 0, ΔE < 0, i.e., the charge transfer process is energetically favorable. We propose as the measure of electrophilicity of the ligand. In view of the analogy between eq 2 and the equation, power ≡ W ) V 2 /R in classical electricity, one may think of ω as a sort of “electrophilic power”. Various other theoretical and experimental discussions of electrophilicity are available in the literature, 5-11 without there being a consensus as to how it should best be determined or defined. Even if third-order and higher terms are important to add to eq 1, we suggest retaining eq 3 as the definition of electrophilicity index of a species. To obtain approximate expressions for ω, we consider two models of the total energy E as a function of the electron number N, E(N). The first is the ground-state parabola model, where 2 where I and A denote the ionization potential (IP) and EA, respectively. For this model, one has ² Department of Chemistry, University of North Carolina. ‡ University of the West Indies. § Department of Biochemistry and Biophysics, University of North Carolina. (1) Maynard, A. T.; Huang M.; Rice, W. G.; Covel, D. G. Proc. Natl. Acad. Sci. U.S.A. 1998, 95, 11578. (2) Parr, R. G.; Yang, W. Density Functional Theory of Atoms and Molecules; Oxford University Press: Oxford, 1989. (3) Parr, R. G.; Donnelly, R. A.; Levy, M.; Palke, W. E. J. Chem. Phys. 1978, 68, 3801. (4) Parr, R. G.; Pearson, R. G. J. Am. Chem. Soc. 1983, 105, 7512. (5) Bader, R. F. W.; Chang, C. J. Phys. Chem. 1989, 93, 5095. (6) Morris, S. J.; Thurston, D. E.; Nevel, T. G. J. Antibiot. 1990, 43, 1286. (7) Droskowki, R.; Hoffmann, R. AdV. Mater. 1992, 4, 514. (8) Benigni, R.; Cotta-Ramusino, M.; Andreoli, C.; Giuliani, A. Car- cinogenesis 1992, 13, 547. (9) Mekenyan, O. G.; Veith, G. D. SAR QSAR EnViron. Res. 1993, 1, 335. (10) Mayr, H.; Patz, M. Angew. Chem. 1994, 106, 990; Angew. Chem., Int. Ed. Engl. 1994, 33, 938. Mayr, H.; Kuhn, M.; Gotta, F.; Patz, M. J. Phys. Org. Chem. 1998, 11, 642. (11) Roy, R. K.; Krishnamurti, S.; Geerlings, P.; Pal, S. J. Phys. Chem. A 1998, 102, 3746. ΔE ) μΔN + 1/ 2 ηΔN 2 (1) ΔE )- μ 2 2η and ΔN max )- μ η (2) ω ≡ μ 2 /2η (3) E(N) ) E(N 0 ) - I + A 2 (N - N 0 ) + I - A 2 (N - N 0 ) 2 + ... (4) ΔN max ) N max - N 0 ) I + A 2(I - A) (5) 1922 J. Am. Chem. Soc. 1999, 121, 1922-1924 10.1021/ja983494x CCC: $18.00 © 1999 American Chemical Society Published on Web 02/18/1999