Comment on 'Hess-Schaad Group Additivity Type Model Predicts

COMMENT pubs.acs.org/JPCA

Reply to “Comment on ‘Hess-Schaad Group Additivity Type Model Predicts Superaromaticity’” Ilie Fishtik* Department of Chemical Engineering, Worcester Polytechnic Institute, Worcester, Massachusetts 01609, United States n his comments,1 Hess presents two arguments that in his opinion undermine our evaluations of the resonance energy (RE).2 The first one is concerned with the legitimacy of using the group CH3
C in addition to the eight groups comprising the original Hess
Schaad method. Namely, Hess claims that introducing the ninth group involving a sp3 hybridized methyl group alters the new reference state so that it no longer mimics the original Dewar
de Llano and Hess
Schaad ones. This argument has no merit for several reasons. Thermodynamically, the evaluation of the RE is a complex relative stability problem that involves three major postulates, namely, reference state, energetic characteristics of the species, and group additivity (GA) model. In the original Hess
Schaad approach, the first two postulates were interconnected in that the selection of the reference state was constrained by the energetic characteristics of the species, that is, HMO π energies. In other words, Hess and Schaad were forced to consider only reference species that could be handled by HMO theory. Our reference state is free of this constraint because as an energetic characteristic we use the experimental enthalpies of formation of the species. As a result, we should not care whether our reference state mimics the Dewar
de Llano and Hess
Schaad reference states or not. We still believe that calling our model a “Hess
Schaad group additivity type model” is justified in that it mimics the spirit of this outstanding model. To be completely fair, however, it should be mentioned that both our model and the Hess
Schaad model are essentially simplified versions of the Tatevskii GA model.3 In this respect, the addition of the CH3
C group is more in line with the Tatevskii rather than Hess
Schaad model. Independently on how we classify a given reference state, adding new reference species and groups while preserving the quality of the group additivity model might be the only way we can proceed in order to expand its area of application. For instance, to look at the substituent effect on the aromaticity, we simply have no choice but to introduce new reference species and groups. Indeed, there is no way to evaluate the RE of, say, toluene, employing a Hess
Schaad type reference state, without introducing at least one reference species involving a CH3
C group. According to our GA model, toluene involves two CHdCH (g2) groups, one CHdC (g4) group, two HC
HC (g6) groups, one CH
C (g7) group, and one CH3
C (g9) group. Respectively, the RE of toluene is

I

RE ¼ Δf H exp
Δf H calc ¼ 12:0
ð2H2 þ H4 þ 2H6 þ H7 þ H8 Þ ¼
22:48 kcal=mol To illustrate the stoichiometric expression of the RE and the balance of various groups, we present below an arbitrary GA r 2011 American Chemical Society

reaction for toluene.

It should be noted that similar substituent-based reference states have been abundantly considered previously in the literature, in particular, for the evaluation of RE of fluorine derivatives of benzene.4 Along the same line is a statement made by Hess to point out other “inconsistencies” in our reference state and GA, namely, “The energy of the central double bond in 1,3,5-hexatriene is certainly different from the energy of the isolated double bond in 2-butene, however, both compounds are used by Fishtik in the parameterization of the CHdCH bond.” It is obvious that the energies of the CHdCH groups in 1,3,5-hexatriene and 2-butene differ. It is also obvious that the energies of the same groups differ in any other reference state and GA model, including the original Hess
Schaad one. Moreover, the absolute values of these energy differences are impossible to evaluate. To prove or disprove such kind of statements, chemists usually assume the opposite, that is, each group has the same energy in all reference species. This assumption is then tested against experimental data. If the error is small, the assumption is considered correct. If the error is large, the assumption is considered wrong. By the way, in their original model, Hess and Schaad followed precisely the same path except that instead of enthalpies of formation the total HMO π energies were used. Under these conditions, the quality of the GA method, respectively, the reliability of the RE, is determined by the error of the GA method. We have shown that our GA model performs exceptionally well (st. dev., 0.18 kcal/mol) and, consequently, the assumption that the energies of the same groups are equal in all reference species is correct. A deeper insight into the energetic aspects of various groups may be achieved in terms of GA response reactions (RERs), that is, reactions that preserve the type and number of groups. These reactions were shown by us to be intimately related to the energetic imbalances of groups.5,6 Ideally, if the energies of the same groups were equal in all reference species, the energy changes of GA RERs would be equal to zero. In reality, these energy changes are different from zero and this difference reflects the extent to which the energies of the same groups in various species differ. For instance, if we want to know how much the energies of the group CHdCH in Received: February 1, 2011 Published: April 21, 2011 5019

dx.doi.org/10.1021/jp201089a | J. Phys. Chem. A 2011, 115, 5019–5020

The Journal of Physical Chemistry A

COMMENT

1,3,5-hexatriene and 2-butene differ, we generate a GA RER involving these species

’ ASSOCIATED CONTENT

Clearly, the enthalpy change of this reaction represents the overall difference in energies of all groups. In principle, it may occur that the small enthalpy change in this reaction is a result of cancelation of large differences between the energies of the same groups in different reference species. This conjecture may be checked by generating a complete list of GA RERs. If the difference in energies of the same groups in various reference species is large, then at least one GA RER will possess a large enthalpy change. A complete set of GA RERs involving our reference species is presented in the Supporting Information. It may be seen that the enthalpy changes of all GA RERs are small, thus, confirming our initial assumption that energies of the same groups in all reference species are close. The second issue raised by Hess is that of planarity of reference species. Hess claims that, because three of our reference species, namely, B6, B8, and B9, are nonplanar and have lower energies, the RE may be strongly overestimated. The effect of planarity on RE is more complex and cannot be judged in such simplistic and qualitative terms. That is, a higher energy of the planar reference species does not necessarily result in a lower absolute value of the RE. To illustrate the effect of planarity on the RE, let us employ the Hess estimations of the “forced” planar energies of the reference species B6, B8, and B9. According to Hess, these energies are higher than the energies of nonplanar species B6, B8, and B9 by 5.6, 3.0, and 4.8 kcal/mol, respectively. Next, let us assume that these energy differences represent the differences between the enthalpies of formation of planar and nonplanar species. Given the experimental enthalpies of formation of B6 (61.8 kcal/mol), B8 (38.0 kcal/mol), and B9 (30.9 kcal/mol), the enthalpies of formation of the respective planar species are 61.8 þ 5.6 = 67.4, 38.0 þ 3.0 = 41.0, and 30.9 þ 4.8 = 35.7 kcal/mol. We repeated the entire calculation procedure, substituting the nonplanar reference species B6, B8, and B9 with the planar ones. As expected, the error of the GA is slightly worse. Thus, the standard deviation of the error increases to 0.34 kcal/mol. The new group values are H1 = 5.032, H2 =
2.84047, H3 =
4.72341, H4 =
10.0983, H5 =
16.1883, H6 = 16.2698, H7 = 20.6063, H8 = 25.7869, and H9 =
2.88841 (units in kcal/mol). Amazingly, the effect of planarity on RE is just opposite to that predicted by Hess! In other words, planar reference species significantly increase the extent of superaromaticity! For instance, the average RE of coronene becomes
215.14 kcal mol and REPE =
8.96 kcal/mol. This should be compared with REPE =
7.32 kcal/mol for nonplanar B6, B8, and B9. Much more pronounced is the effect of planarity of reference species B6, B8, and B9 on the RE of buckminsterfullerene C60. Thus, based on planar B6, B8, and B9, REPE =
7.70 kcal/mol, while based on nonplanar B6, B8, and B9, REPE =
4.34 kcal/mol. To complete the comparison, we finally mention that the RE of benzene changes insignificantly, namely, from
20.75 kcal/mol for nonplanar to
20.49 kcal/mol for planar reference state. Notice that the absolute value of the RE of benzene based on the planar reference state is smaller than the RE based on the nonplanar reference state by 0.26 kcal/mol, and consequently, the direction of change is that predicted by Hess. In summary, the reference state and GA model proposed by us are firmly grounded and so are our evaluations of the RE.

’ AUTHOR INFORMATION

bS

Supporting Information. Additional data. This material is available free of charge via the Internet at http://pubs.acs.org.

Corresponding Author

*E-mail: ifi[email protected].

’ ACKNOWLEDGMENT The author greatly appreciates ample and fruitful discussions with Dr. Robert J. Meier. ’ REFERENCES (1) Hess, B. A. J. Phys. Chem. A, DOI: 10.1021/jp200469v. (2) Fishtik, I.; Datta, R. J. Phys. Chem. A 2010, 114, 11017. (3) Tatevskii, V. M. The Structure of Molecules; Khimiya: Leningrad, 1977. (4) Baric, D.; Kovaevic, B.; Zvonimir, B.; Maksic, Z. B.; Muller, T. J. Phys. Chem. A 2005, 109, 10594. (5) Fishtik, I.; Datta, R.; Liebman, J. F. J. Phys. Chem. A 2003, 107, 2334. (6) Fishtik, I. J. Phys. Chem. A 2006, 110, 13264.

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dx.doi.org/10.1021/jp201089a |J. Phys. Chem. A 2011, 115, 5019–5020