COMMENT pubs.acs.org/JPCA
Comment on “Ruling Out Any Electrophilicity Equalization Principle” Pratim Kumar Chattaraj,* Santanab Giri, and Soma Duley Department of Chemistry and Center for Theoretical Studies, Indian Institute of Technology, Kharagpur 721302, India o put the 00 Electrophilicity Equalization Principle00 in proper perspective vis-a-vis a recent criticism, a careful scrutiny is presented in this Comment. Applicability of that principle and the flaws associated with the said criticism are thoroughly analyzed with the help of the existing literature. It has been shown that although these popular qualitative electronic structure principles within a conceptual density functional theory framework are empirical in nature they do serve their purpose by unifying experimental data and identifying trends in a wide variety of systems and processes. An “Electrophilicity Equalization Principle” was proposed1 which is recently criticized by Szentpaly.2 A clarification is in order. In the proposition of an electrophilicity equalization principle, it was explicitly mentioned:1 1. It is known in the literature that there exist two electronic structure principles, viz., electronegativity (χ) equalization principle35 and hardness (η) equalization principle.68 2. Simultaneous validity of the above two principles implies an electrophilicity (ω) equalization principle. Needless to mention, in the case item no. 1 is not valid, then item no. 2 is also not valid. 3. Numerical values presented there1 highlighted the inherent empiricism in all three related principles. In the second set (presented in the inset), χ (R2 = 0.746) and ω (R2 = 0.723) performed similarly, albeit not very good, contrary to the claim of Szentpaly.2 According to the Oxford Dictionary, principle means “a truth or general law that is used as a basis for a theory or system of belief”. Unlike the principles such as variational principle, Heisenberg’s uncertainty principle, or Pauli’s exclusion principle, the principles like Sanderson’s electronegativity equalization principle,35 arithmetic mean principle of softness,9 hardsoft acids and bases (HSAB) principle,10 maximum hardness principle12 (MHP), etc. are empirical as they depend on some ansatz, e.g., the exponential ansatz of energy.5 Additionally, there is no first-principle approach through which definitions of various quantities, e.g., χ, η, and ω, can be obtained. Moreover, their method of calculation including the level of sophistication as well as the quality of the basis sets used and also the choice of the molecules can give qualitatively different results. There are systems for which μ is positive as is the case with many anions/dianions, and the proposed definition12 of ω = (μ2/2η) provides qualitatively wrong trends because of the quadratic appearance of μ. Several definitions of ω, as in ref 13, are needed depending on what one would like to show. An electrophilicity equalization principle is obtained from a different angle.7c It may be noted that an assumption of the validity of any two of these principles will imply that of the third and the use of an adjustable parameter7c will make the ω values in other papers comparable. Let us examine the counterexample provided by Szentpaly.2 In his reference 11 (henceforth 11/2 and likewise), it is mentioned
that I (ionization potential) and A (electron affinity) when fitted as a function of n1/3, the intercepts are equal (which is very crucial in Szentpaly’s counter example so that the denominator in ω tends to zero) only in the case of constrained regression, and this is not true for the unconstrained regression. Moreover, in 11/2 and 13/2, it was explicitly shown that the correct stability trends (magic clusters11/2 as well as fullerene13/2) are provided by the so-called disproportionation energy (second difference in cluster energy), Δ2En = En+1 2En + En1, and the HOMOLUMO gap. As these quantities14,15 represent hardness without and with Koopmans’ approximation, respectively, it is a clear-cut vindication of the MHP. In support of his claim, he cited references 20(a)/2, 22/2, and 23/2. A three-level GyftopoulosHatsopoulos model does provide20(b)/2 a formal proof16 of the MHP in the case one uses the correct definition14,15 of the equilibrium chemical potential (μ = (I + A/2)) as opposed to zero (ref 20/2). He also relied on ref 22/2, where the more stable isomer was claimed to have higher energy apparently violating the variational principle again indirectly refuting the claim of Szentpaly. The minimum electrophilicity principle provided in ref 23/2 has several counter examples, and the conditions under which it may be valid are laid down.17 In eqs 8 and 9 of Szentpaly,2 the hardness goes to zero as n f ∞. It is expected as the softness increases with the size. In the original definition12 of ω = μ2/2η (GS and VS), the electrophilicity cannot be calculated in such cases. However, as shown,2 χ can be calculated implying completely different behavior of ω and χ which is counterintuitive as both of these quantities measure very similar properties. It may be noted that these problems are inherent in this definition of electrophilicity,12 and it does not matter whether one brings in any geometric mean and hence equalization principle or not. It may also be noted that in the case one uses the unconstrained regression formulas of 11/2 the problems highlighted by Szentpaly will vanish, and both χ and ω can be calculated at that limit provided the finite difference analogues used in eqs 6, 7, 10, and 11 are valid there. Interestingly, some of the inequalities obeyed2 by ω are also obeyed by χ, both calculated using his data. One needs to compare the validity of the two related geometric mean (ωGM; χGM) principles in all such counterexamples especially that involving isomers, cationic electrophiles or molecules in different electronic states. It may be noted that a factor of 1/2 is missing in his eq 4, and the condition ωL,GM e max(ωL,K) is valid in all cases as opposed to what is claimed by him.2 Although the popular qualitative electronic structure principles involving different conceptual density functional theory based reactivity descriptors like electronegativity, hardness,
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r 2011 American Chemical Society
Received: September 5, 2011 Published: December 22, 2011 790
dx.doi.org/10.1021/jp208541x | J. Phys. Chem. A 2012, 116, 790–791
The Journal of Physical Chemistry A
COMMENT
softness, electrophilicity, etc. are known to be empirical as all of them possess several counter examples, they have been shown to be extremely useful in understanding the experimental trends in a wide variety of systems/processes in a unified way as is quite explicit in the literature.14,15
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ REFERENCES (1) Chattaraj, P. K.; Giri, S.; Duley, S. J. Phys. Chem. Lett. 2010, 1, 1064. (2) von Szentpaly, L. J. Phys. Chem. A 2011, 115, 8528. (3) (a) Sanderson, R. T. Science 1951, 114, 670. (b) Sanderson, R. T. J. Chem. Educ. 1954, 31, 238. (c) Sanderson, R. T. Science 1955, 121, 207. (4) Parr, R. G.; Donnelly, R. A.; Levy, M.; Palke, W. E. J. Chem. Phys. 1978, 68, 3801. (5) Parr, R. G.; Bartolotti, L. J. J. Am. Chem. Soc. 1982, 104, 3801. See also Wilson, M. S.; Ichikawa, S. J. Phys. Chem. 1989, 93, 3087 and Komorowski, L. Chem. Phys. 1987, 55, 114 for problems associated with the geometrical mean principle of electronegativity. In the former it is also shown that the constancy of η/χ is implicit in Sanderson’s electronegativities,9 implying the validity of the hardness equalization principle. (6) Datta, D. J. Phys. Chem. 1986, 90, 4216. (7) (a) Ghosh, D. C.; Islam, N. Int. J. Quantum Chem. 2011, 111, 1961. (b) Islam, N.; Ghosh, D. C. Eur. Phys. J. D 2011, 61, 341. (c) Islam, N.; Ghosh, D. C. Int. J. Mol. Sci. 2011, 12, DOI: 10.3390/ ijms120x000x. (8) Ayers, P. W.; Parr, R. G. J. Chem. Phys. 2008, 128, 184108. (9) Yang, W.; Lee, C.; Ghosh, S. K. J. Phys. Chem. 1985, 89, 5412. (10) (a) Pearson, R. G. Hard and Soft Acids and Bases; Dowden, Hutchinson & Ross: Stroudsberg, PA, 1973. (b) Pearson, R. G. Coord. Chem. Rev. 1990, 100, 403. (c) Pearson, R. G. Chemical Hardness: Applications from Molecules to Solids; Wiley-VCH: Weinheim, 1997. (d) Ayers, P. W.; Parr, R. G.; Pearson, R. G. J. Chem. Phys. 2006, 124, 194101/1. (11) (a) Pearson, R. G. J. Chem. Educ. 1987, 64, 561. (b) Parr, R. G.; Chattaraj, P. K. J. Am. Chem. Soc. 1991, 113, 1854. (c) Pearson, R. G. Acc. Chem. Res. 1993, 26, 250. (d) Ayers, P. W.; Parr, R. G. J. Am. Chem. Soc. 2000, 122, 2010. (12) Parr, R. G.; von Szentpaly, L.; Liu, S. J. Am. Chem. Soc. 1999, 121, 1922. (13) (a) von Szentpaly, L. Int. J. Quantum Chem. 2000, 76, 222. (b) von Szentpaly, L. J. Phys. Chem. A 2010, 114, 10891. (14) Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and Molecules; Oxford University Press: Oxford, U.K., 1989. (15) Geerlings, P.; De Proft, F.; Langenaeker, W. Chem. Rev. 2003, 103, 1793. (16) Chattaraj, P. K.; Cedillo, A.; Parr, R. G. Chem. Phys. 1996, 204, 429. (17) (a) Chamorro, E.; Chattaraj, P. K.; Fuentealba, P. J. Phys. Chem. A 2003, 107, 7068. (b) Parthasarathi, R.; Elango, M.; Subramanian, V.; Chattaraj, P. K. Theor. Chem. Acc. 2005, 113, 257.
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