COMMENT pubs.acs.org/JPCA
Reply to “Comment on ’Ruling Out Any Electrophilicity Equalization Principle’” Laszlo von Szentpaly* Institut f€ur Theoretische Chemie, Universit€at Stuttgart, Pfaffenwaldring 55, D 70569 Stuttgart, Germany he recent controversial discussion on a “principle of electrophilicity equalization” in molecules and its qualification as a new structural principle prompts another look at the claims and their criticism. This reply provides further analysis of equalized hardness and electrophilicity and supports the conclusion to rule out any principle of equalization of atomic hardness and electrophilicity indices. The widely differing experimental electrophilicities of singlet and triplet dioxygen, O2, are highlighted in this context, and the question of isomers having different electrophilicities is addressed. Cationic electrophiles, E+, form the most important class of strong electrophiles, but there is no general prescription for mixing and equalizing atomic and cationic electrophilicities. For heteronuclear E+, basic problems arise, when trying to point out a particular atom carrying the unit positive charge. For the homonuclear fullerene-ion C60+, the global electrophilicity indices, ω1 = (I + A)2/8(I A) and ω2 = IA/(I A), are each about a factor 5 larger than for the neutral C60, but the corresponding geometric averages of atomic and cationic indices increase by a few percent only. It is maintained that any generalization based on a narrow set of data and limited evidence can be misleading instead of useful and therefore should not be proposed as a new principle. Three conflicting publications13 under scrutiny investigate and discuss the proposal to equate the ParrSzentpalyLiu electrophilicity indices,47 ω, of arbitrary chemical species to the geometric mean of the indices of their atoms
encyclopaedic meaning of the word “principle” will be addressed. Should “principle” be reserved for basic and solid rules with important consequences? The authors13 certainly agree that it is “needless to mention” that a newly proposed principle becomes invalid if some of its preconditions are found invalid. If, however, the newly proposed rule or principle basically relies on the validity of several previously proposed rules, the latter rules have to be carefully re-examined. The problem here is that the “hardness equalization principle” lacks empirical support. This is also evidenced by the hardness data, η = I A, shown in Figure 1 and Tables 1 and 2 of ref 1. For 46 molecules in the range 5.6 eV < η < 14.6 eV, the standard deviation of the linear plot GM vs η amounts to SD = 1.378 eV (15% of the value range), and the correlation coefficient is R2 = 0.595 only. Chattaraj et al.3 argue in favor of their principle by reducing the set of 46 molecules to a subset of 21 halo compounds, which raises the correlation coefficient for GM to R2 = 0.641 and that for plotting GM vs ω1 from R2 = 0.430 to R2 = 0.723.1 However, it is nearly always possible to find some suitably reduced subset to replace a larger data set and “improve” a poor correlation. Nevertheless, none of the correlations is convincing because coefficients R2 < 0.800 traditionally indicate poor quality correlations. Especially the hardness equalization seems to be more the exception than the rule. The “geometric mean principle for hardness equalization” has been proposed on the argument that electron affinity was negligible, i.e., A , I.10,11 This assumption does not even work for atoms12,13 and is much less correct for large molecules.2,14 Politzer et al. have very recently listed some striking inconsistencies due to neglecting electron affinity and oversimplifying Mulliken-type electronegativity (EN) scales, χ = 1/2(I + A).13 Nevertheless, there are attempts to eliminate the difference between hardness, EN, and even electrophilicity altogether by neglecting A and equating 1/2η = χ = 2χ2/η.11 It appears to be a terrible simplification to propagate that “the effort of quantification of the hardness and the electronegativity in terms of density functional theory degenerate to give an equation declaring the equality of χ, η, and I”.11 Any reference made to such papers in ref 3 seems counterproductive. It does not serve any purpose to insist on a principle based on an “ansatz” of very limited validity. Regarding the critical and contested point whether “hardness also gets equalized like electronegativity”,1 I have listed several large sets of compounds, namely, metal clusters and [n]fullerenes, whose hardness values cannot be obtained by averaging atomic hardness data.2 This has led to conclusions like “the electrophilicity of fullerenes increases with cluster size”.2 In the
T
ω≈ < ω>GM
ð1Þ
The indices quantify the propensity of chemical species to lower their energy by acquiring additional electronic charge from the environment.47 In terms of the first ionization energy, I, and the first electron affinity, A, the pertinent electrophilicity indices ω are48 ω1 ¼ ðI þ AÞ2 =8ðI AÞ
ð2Þ
and ω2 ¼ IA=ðI AÞ
ð3Þ
The claim that “the electrophilicity gets equalized during molecule formation” has been called the “electrophilicity equalization principle”.1,3 Its proponents have already heralded in a related paper that “an electrophilicity equalization principle is proved”.9 Doubts about the adequacy of such a proof and about the correct use of the word “principle” in this context have been raised by the present author.2 A comment by Chattaraj et al. has been submitted and published.3 This reply is organized as follows: the criticism by Chattaraj et al.3 is discussed, followed by additional experimental and theoretical evidence opposing the “electrophilicity equalization principle”, and finally the dictionary and r 2011 American Chemical Society
Received: November 1, 2011 Published: December 07, 2011 792
dx.doi.org/10.1021/jp210486g | J. Phys. Chem. A 2012, 116, 792–795
The Journal of Physical Chemistry A
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Table 1. Comparison of Electrophilicity Indices, ω1 and ω2, with Their Geometric Mean Values, GM and GMa ω1
I
ω2
species
A
O
1.4611
13.6182
2.3380
-
1.6367
-
O2 (X3Σg)
0.440, ad
12.060, ad
1.681
2.3380
0.457
1.6367
2.3380
1.631
1.6367
GM
GM
O2 (a1Δg)
1.422, ad
11.078, ad
2.023
CNO
3.20, adb
11.29, adb
3.24
OCN
3.61, adb
11.34, adb
3.61
5.30
CON
b
1.71, ad
8.98, adb
1.965
2.11
C
1.2621
11.2603
1.9605
-
1.4214
-
C+ C60
11.2603 2.666(1)
24.3833 7.57(1), vc
12.1015 2.671
1.9605
20.9223 4.115
1.4214
C60+
7.57(1), vc
11.46(5), vc
11.64(15)
2.0209
22.3(3)
1.4866
4.47
≈ 4.4 ω1(C60)
≈ 5.4 ω2(C60)
The first electron affinity and ionization energy are denoted A and I, respectively. Values A and I taken from ref 14 unless noted otherwise. All values in eV; v refers to vertical and ad to adiabatic data. b Ref 22. c Ref 26.
a
Comment, Chattaraj et al. feel that it “is very crucial” for such conclusions to use constrained linear regressions, I vs n1/2 and A vs n1/2, with equal intercepts at n1/2 = 0. Let me show that constrained regressions are no crucial conditions. First, the intercepts do not represent deliberate constraints but the work function of the corresponding infinite systems, thus valid physical values to be incorporated into meaningful regressions. Second and to end an unnecessary controversy, I run unconstrained linear regressions for the [n]fullerenes, n g 78, on the experimental data of Seifert and Boltanina et al.15 without forced intercept at the work function. The established value for an infinitely large fullerene, 5.13 eV, is taken as a single point in the set of 17 experimental data points, and all data carry the same statistical weight. The results IðCn Þ=eV ¼ 5:105 þ 18:709n1=2
R 2 ¼ 0:9883
ð4Þ
AðCn Þ=eV ¼ 5:128 17:978n1=2
R 2 ¼ 0:9940
ð5Þ
indices as shown for clusters. On the contrary, the assumption3,11 that “these quantities measure very similar properties” should reduce their established differentiation and the justification for three distinct concepts should be cut out by Ockham’s razor.20 His law of parsimony20 requires that “plurality should not be posited without necessity”. However, far from being counterintuitive, the examples listed in ref 2 support the meaningful differentiation between EN, hardness, and electrophilicity. Plurality is justified here. In addition, three kinds of new evidence are opposing the idea to equalize atomic electrophilicity indices during molecule formation. The first kind of counter-evidence is exemplified by the oxygen molecule, O2, that has already been included in ref 1. A metastable first excited singlet state, O2 (a1Δg), is found 0.982 eV above the triplet ground state, O2 (X3Σg). Note that (i) singlet oxygen is not outside the reach of DFT, as it is the lowest state of singlet symmetry, and (ii) both molecular states are formed by combining two identical ground state oxygen atoms. Thus, O2 may serve as a test molecule for the validity of electrophilicity equalization. Experimentally singlet oxygen is much stronger an electrophile than the triplet ground-state molecule. The singlet is capable of oxidizing aromatic hydrocarbons, phenols, sulfides, and amines, while the triplet is not. Singlet O2 also plays an important role in photodynamic processes and cancer therapy.21 The strongly differing experimental electrophilicities of these states need to be examined in light of the proposed new structural principle. The problem is, however, that the electrophilicity indices of singlet oxygen O2 (a1Δg) and triplet O2 (X3Σg) should be identical by equalization (Table 1). This contrasts to all experimental evidence, which therefore cannot be reproduced via electrophilicity equalization. For comparison, Table 1 includes directly calculated indices ω1 and ω2, which confirm that the triplet O2 is less electrophilic than the atom, while the singlet O2 is comparable to O. Among others, the NF, SO, and SeO systems also show low-lying metastable states and may therefore lead to similar conclusions regarding their electrophilicities. Another problem connected to an equalization of ω-indices is that the difference between the equalized indices of isomers of different bond connectivity, such as OCN, CNO, and CON, should vanish, again in contrast to established evidence. The cyanate, isocyanate, and fulminate radicals have been studied together with their cations and anions. 22 On the basis of the
confirm my earlier statements about a reasonable fulfillment of EN equalization, the lack of hardness equalization, and the failure of electrophilicity equalization from atomic indices. The hardness and electrophilicity indices of [n]fullerenes cannot be calculated from atomic increments. The other example in ref 2 is about metal clusters, Mn. For large metal clusters with n atoms the linear dependence of I, A, and (I A) as a function of n1/3 is a theoretically sound and experimentally well-documented fact.16,17 For the conclusion that the hardness and the electrophilicity cannot be calculated by averaging their atomic values, it is not necessary that the unconstrained linear regressions on experimental I(Mn) and A(Mn) converge to the work function of the metal. It is sufficient that the values of (I A) significantly decrease with increasing cluster size. Precisely, this has been found experimentally for many different metals.17 Certainly, both I and A data of clusters up to n ≈ 30 may include oddeven oscillations and shell effects.16f,18 These and similar complex behaviors upon electron detachment or attachment may be outside the scope of a detailed analysis by linear regressions and explain their reported differences.16f However, the ionic charging in larger size metal clusters and [n]fullerenes is known to induce moderate structural changes only1519 and the oddeven effects are “washed out”.17,18 Incidentally, it is not “counterintuitive”3 at all to find significantly different behaviors of EN, hardness, and electrophilicity 793
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The Journal of Physical Chemistry A available data, their calculated electrophilicity indices clearly differ in contrast to their postulated equality (Table 1). We now turn to a third and largest class of counter-examples, that of cationic electrophiles, E+. They play a central role in the experimental research on electrophilicity23,24 and have also become a focus of theoretical work.9,25 In averaging the atomic indices of a singly charged molecular cation, one of the atoms must be counted as a cation. It is not clear, however, which atom should be attributed the cationic electrophilicity index. This sets a severe limit to the applicability of the proposed rule. Except for the simple cases of homonuclear cluster ions, Mn+, and highly polar systems, e.g., NaCl +, there is no unique prescription to determine which of the constituent atoms should carry the integer positive charge. To test the usefulness of geometric averaging, we need larger homonuclear ions with well-determined vertical ionization energies and electron affinities. This is the case for the cluster cation C60+.26 The comparison of its electrophilicity with that of neutral C60 serves as evidence that ω 6¼ GM (Table 1). The geometric average is only slightly shifted to higher values by 35%, whereas ω1 (C60+) ≈ 4.4ω1 (C60) and ω2 (C60+) ≈ 5.4ω2 (C60) increase by large factors. Having extended the list of exceptions to the proposed electrophilicity equalization rule by three new classes, (i) electrophiles acting in metastable excited states, (ii) the isomers, and (iii) the cationic electrophiles, a clarification of the correct meaning of “principle” is in order. Chattaraj et al.3 quote the Oxford Dictionary, only to go on arguing with its definition of a principle as “a truth or general law that is used as a basis for a theory or system of belief”. For Chattaraj et al. a difference has to be made between first principles and “empirical principles”, which depend on some “ansatz”.3 Empirical or not, however, is no relevant differentiation between principles. Empiric or heuristic principles also follow the high general standards formulated, e.g., in the Oxford Dictionary and Chambers Science and Technology Dictionary, where representative examples are listed. Thermodynamics is altogether empirical; it is based on a few empiric principles.27 Initially Pauli’s exclusion principle has been formulated in terms of the BohrSommerfeld model; in fact, Pauli’s historic formulation has been heuristic and empirical. “Theories are not verifiable, but they can be corroborated,”28 and so are principles. Thus, the genesis and corroboration of a new principle is a long and often tedious process.27 Once sufficiently corroborated, principles are basic (empirical) truths from which one can begin to reason and which serve as a basis for other laws and rules. It becomes obvious from the present data and those supplied in refs 13 that the propositions of hardness equalization and electrophilicity equalization are not corroborated from their very start. On the other hand, I would be the last to disagree on the success of Sanderson’s concept of EN equalization. In fact, much of my research since 1991 is based on it.5,29,30 I gladly agree that the “maximum hardness principle”, MHP, belongs to a different category of rules than the propositions of electrophilicity equalization and hardness equalization. However, sometimes proponents of new rules tend to forget the facts that do not corroborate with them. Therefore, a few examples of clear-cut failures and suggested remedies of some principles/concepts may be added. In a very recent review of ambident reactivity31 the HSAB concept has been found to yield approximately as many hits as failures. Thus, Mayr et al. suggest abandoning the HSAB concept as a guide for predicting ambident reactivity.31 Parr and Chattaraj showed a serious restriction to the MHP, which is strictly valid in
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processes of constant electronegativity and external potential only.32,33 As a remedy for reactions with significant EN changes, Ghanty and Ghosh proposed to scale the hardness with χ1/3 to obtain a reaction hardness profile with its minimum at the transition structure.33 I just find it unfortunate and confusing to use the same term “principle” for statements of very different stringency and significance. For the sake of scientific methods and progress, it would be helpful to keep the terminology and semantics clean and avoid any dilution and bagatellization of the meaning of principles. If scientific terms are used in an imprecise way, it needlessly confuses students and sets a poor example for the next generation.
’ 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) Chattaraj, P. K.; Giri, S.; Duley, S. J. Phys. Chem. A 2011, DOI: 10.1021/jp208541x. (4) Parr, R. G.; von Szentpaly, L.; Liu, S. J. Am. Chem. Soc. 1999, 121, 1922. Due to typos in its Figure 1, the index ω2 was incorrectly printed as W2 and ω1 as W1. (5) von Szentpaly, L. Int. J. Quantum Chem. 2000, 76, 222. (6) (a) Chattaraj, P. K.; Sarkar, U.; Roy, D. R. Chem. Rev. 2006, 106, 2065. (b) Chattaraj, P. K.; Giri, S.; Duley, S. Chem. Rev. 2011, 111, PR43. (7) Chattaraj, P. K.; Giri, S. Annu. Rep. Prog. Chem., Sect C 2009, 105, 13. (8) It has been noted3 that eq 4 in ref 2 is missing a factor 1/2. In fact ω2 = IA/(I A) is correct,4,5 but the index of the groundstate-exponential model has to be ω GSE = 1/2ω2. (9) Chattaraj, P. K.; Duley, S. J. Chem. Eng. Data 2010, 55, 1882. (10) Datta, D. J. Phys. Chem. 1986, 90, 4216. (11) Ghosh, D. C.; Islam, N. Int. J. Quantum Chem. 2011, 111, 40. (12) Nazewajski., R. J. Phys. Chem. 1985, 89, 2831. (13) Politzer, P.; Shields, Z. P.-I.; Bulat, F. A.; Murray, J. S. J. Chem. Theory Comput. 2011, 7, 377. (14) von Szentpaly, L. J. Phys. Chem. A 2010, 114, 10891. (15) (a) Seifert, G.; Vietze, K.; Schmidt, R. J. Phys. B 1996, 29, 5183. (b) Boltanina, O. V.; Dashkova, E. K.; Sidorov, L. N. Chem. Phys. Lett. 1996, 256, 253. (c) Boltanina, O. V.; Ioffe, I. N.; Sidorov, L. N.; Seifert, G.; Vietze, K. J. Am. Chem. Soc. 2000, 122, 9745. (16) (a) de Heer, W. A. Rev. Mod. Phys. 1993, 65, 611. (b) Brack, M. Rev. Mod. Phys. 1993, 65, 677.(c) Alonso, J. A., Balbas, L. C. In Struct. Bonding (Berlin); Sen, K., Ed.; Springer: Berlin, 1983; Vol. 80, pp 230257; (d) H€aberlen, O. D.; Chung, S.-C.; Stener, M.; R€osch, N. J. Chem. Phys. 1997, 106, 5189. (e) Jaque, P.; Toro-Labbe, A. J. Phys. Chem. B 2004, 108, 2568. (f) Assadollahzadeh, B.; Thierfelder, C.; Schwerdtfeger, P. Phys. Rev. B 2008, 78, 245423. (17) (a) Roduner, E. Nanoscopic Materials: Size-Dependent Phenomena; RSC Publishing: London, 2006. (b) Kostko, O. Photoelectron Spectroscopy of Mass-selected Sodium, Coinage Metal and Divalent Metal Cluster Anions; Doctoral Thesis, Universit€at Freiburg, 2007, www. freidok.uni-freiburg.de. (c) Svanquist, M.; Hansen, K. Eur. Phys. J. D 2010, 56, 199–203. (18) Taylor, K. L.; Pettiette-Hall, C. L.; Chesnovsky, O.; Smalley, R. E. J. Chem. Phys. 1992, 96, 3319. (19) (a) Walters, T.; Wang, X. B.; Wang, L.-S. Coord. Chem. Rev. 2007, 251, 474.(b) Wang, X. B. Wang, L.-S. Annu. Rev. Phys. Chem.; Annual Reviews Inc., Palo Alto, CA, USA, 2009; Vol. 60, p 105. 794
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(20) Encyclopædia Britannica. www.britannica.com (accessed 2011). (21) DeRosa, M.; Crutchley, R. J. Coord. Chem. Rev. 2002, 233, 351. (22) Dua, S.; Bowie, J. H. J. Phys. Chem. A 2003, 107, 76. (23) Mayr, H.; et al. J. Am. Chem. Soc. 2001, 123, 9500. (24) Denekamp, C.; Sandlers, Y. Angew. Chem., Int. Ed. 2006, 45, 2093. (25) Perez, P.; Toro-Labbe, A.; Aizman, A.; Contreras, R. J. Org. Chem. 2002, 67, 4747. (26) Steger, H.; de Vries, J.; Kamke, B.; Kamke, W.; Drewello, T. Chem. Phys. Lett. 1992, 194, 452. (27) Julius R. Mayer had extreme difficulties to publish his pioneering work on the Principle of Conservation of Energy, the First Law of Thermodynamics. Mayer had been fiercely attacked for years until his health collapsed. Physicists including von Helmholtz and Joule viewed his ideas with hostility and rejected the energy conservation principle. (28) (a) Popper, R. K. Logik der Forschung; Springer: Vienna, 1935. (b) Primas, H. Chemistry, Quantum Mechanics and Reductionism; Springer: Berlin, 1981; p 26. (29) von Szentpaly, L. J. Mol. Struct.: THEOCHEM 1991, 233, 71. (30) Glasser, L.; von Szentpaly, L. J. Am. Chem. Soc. 2006, 128, 12314 with earlier refs quoted therein. (31) Mayr, H.; Breugst, M.; Ofial, A. R. Angew. Chem., Int. Ed. 2011, 50, 6470. (32) Chattaraj, P. K.; Liu, G. H.; Parr, R. G. Chem. Phys. Lett. 1995, 237, 171. (33) Ghanty, T. K.; Ghosh, S. K. J. Phys. Chem. A 2002, 106, 4200.
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