Quantifying Reactivity for Electrophilic Aromatic Substitution Reactions

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Quantifying Reactivity for Electrophilic Aromatic Substitution Reactions with Hirshfeld Charge Shubin Liu J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b00443 • Publication Date (Web): 27 Feb 2015 Downloaded from http://pubs.acs.org on March 1, 2015

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The Journal of Physical Chemistry

Quantifying Reactivity for Electrophilic Aromatic Substitution Reactions with Hirshfeld Charge Shubin Liu* Research Computing Center, University of North Carolina, Chapel Hill NC 27599-3420, USA

Abstract An electrophilic aromatic substitution is a process where one atom or group on an aromatic ring is replaced by an incoming electrophile. The reactivity and regioselectivity of this category of reactions is significantly impacted by the group that is already attached to the aromatic ring. Groups promoting substitution at the ortho/para and meta position are called ortho/para and meta directing groups, respectively. Earlier, we have shown that regioselectivity of the electrophilic aromatic substitution is dictated by the nucleophilicity of the substituted aromatic ring, which is proportional to the Hirshfeld charge on the regioselective site. Ortho/para directing groups have largest negative charge values at the ortho/para positions, whereas meta directing groups often have the largest negative charge value at the meta position. The electron donation or acceptance feature of a substitution group is irrelevant to the regioselectivity. In this contribution, we extend our previous study by quantifying the reactivity for this kind of reactions. To that end, we examine the transition state structure and activation energy of an identity reaction for a series of mono-substituted-benzene molecules reacting with hydrogen fluoride using BF3 as the catalyst in the gas phase. A total of 18 substitution groups will be considered, nine of which are ortho/para directing and the other nine groups meta-directing. From this study, we found that the barrier height of these reactions strongly correlates with the Hirshfeld charge on the regioselective site for both ortho/para and meta-directing groups, with the correlation coefficient R2 both better than 0.96. We also discovered a less accurate correlation between the barrier height and HOMO energy. These results reconfirm the validity and effectiveness of employing the Hirshfeld charge as a reliable descriptor of both reactivity and regioselectivity for this vastly important category of chemical transformations.

* E-mail address: [email protected]. Tel: (919)962-4032 1 ACS Paragon Plus Environment


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I. INTRODUCTION As one of the most fundamental organic transformation processes, an electrophilic aromatic substitution replaces an atom or a group, usually hydrogen, which is attached to an aromatic system, by an incoming electrophile.1-4 Prominent examples of such reactions include nitration, halogenation, sulfonation, and acylation and alkylating Friedel–Crafts reactions. The dominant determinant of the reactivity for this category of reactions should be the nucleophilicity of the carbon atoms on the aromatic ring, i.e., the capability for the carbon atom on the aromatic ring to donate electrons to the attacking electrophile. If the six carbon atoms on the benzene ring have different nucleophilicity (electron-donating) properties, then the electrophile will preferably attack the one or ones with the largest nucleophilicity. The outcome of this selective attack is the origin of regioselectivity. Relevant to the reactivity and regioselectivity of these reactions is the so-called substituent effect. It has long been known5 that both reactivity and regioselectivity of an electrophilic aromatic substitution are affected by the substituents that are already attached to the aromatic ring. The group that promotes substitution at the ortho/para and meta position is, respectively, called ortho/para and meta directing group. Typical ortho/para directing groups are alkyl, amino, amide, aryl, ether, halogen, hydroxyl, and ether, and common meta-directing groups are aldehyde, cyano, carboxylic acid, ester, ketone, nitro, nitroso, quaternary amine, sulfonate, and trihalide. Resonance and inductive effects are often employed to explain and justify these phenomena in textbooks and in the literature,1-4 yet a satisfactory quantitative explanation is still lacking. Very recently, a novel explanation has been proposed by us,6 based on a recent quantification of nucleophilicity,7-9 which should be the root cause of the above substituent effect, using the Hirshfeld charge10 in the framework of density functional reactivity theory (DFRT).11-14 This work was based on our recent efforts in understanding information-theoretic quantities`15-23 in DFRT. We found that regioselectivity of the electrophilic aromatic substitution is determined by the nucleophilicity of the

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aromatic ring, which is inversely proportional to the Hirshfeld charge on the regioselective site. Ortho/para directing groups have largest negative charges on the ortho/para positions, whereas meta directing groups often have the largest negative charge on the meta position. We also showed that the feature of electron donation or acceptance of a substitution group is irrelevant to the phenomenon of ortho/para and meta directing. It is the electron redistribution of the aromatic ring after a group is introduced that matters. In addition, strong linear correlations between the Hirshfeld charge on the regioselective site and the HOMO energy have been disclosed, providing the first link between the frontier molecular orbital theory and DFRT. We also predicted ortho/para and meta group directing behaviors for a list of groups whose regioselectivity is previously unknown.6 Our previous work unambiguously determined the root of regioselectivity, which should be the nucleophilicity of carbon atoms on the aromatic benzene ring. However, it is limited by the fact that, from the reactivity perspective, it is still of qualitative nature. This is because chemical reactivity should ultimately be determined by the activation energy or barrier height of the transition state. To overcome this limitation, in this work, we provide a quantitative account of this new explanation. To that end, we at first choose nine systems with ortho/para directing groups and another nine systems with metadirecting groups, and then investigate their kinetic behaviors for an identity reaction. The transition state structure of this system has been well studied in the literature,24,25 which was found to be a onestep reaction in gas phase. The barrier height represented by the total energy difference between the reactant and transition state is compared with the Hirshfeld charge and HOMO energy of the monosubstituted benzene derivatives. What we are interested in observing in this work is to see whether or not there exist strong linear correlations between the barrier height and the Hirshfeld charge in systems with different directing groups.



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II. COMPUTATIONAL DETAILS The electrophilic aromatic reaction to be considered in this work is the following identity reaction of mono-substituted-benzene molecules reacting with hydrogen fluoride using BF3 as the catalyst in the gas phase (Scheme 1).

Scheme 1. Electrophilic aromatic substitution reaction studied in this work.

The nine ortho/para groups chosen are X= -F, -Cl, -CH3, -C2H5, -C3H7, -tBu, -NH2, -NMe2, and -OH. The nine meta-directing groups picked are X= -CCl3, -CF3, -CHO, -CN, -COF, -NH3+, -NO2, -NO, and -SO3H. Following the literature,24,25 we represent the catalyst by one BF3 molecule. The reactant complex consisting of one mono-substituted benzene ring with one hydrogen fluoride (HF) and one BF3 was fully optimized at the M062X/aug-cc-pVDZ level of theory.26,27 For each system studied, no matter if it contains either an ortho/para or a meta directing group, we examined its electrophilic substitution at both meta and para positions. The QST2 technique was employed to obtain the optimized transition state structure of the reaction. After a transition-state search is accomplished, a single-point frequency calculation was performed to ensure that the final structure obtained (i) has only one imaginary frequency and (ii) the vibration mode of the negative frequency corresponds to the anticipated bond formation and breaking. In addition, intrinsic reaction coordinates (IRCs) were calculated to verify the relevance of transition-state structures. All calculations were performed with the Gaussian 09 DO1 package28 with tight SCF convergence and ultra-fine integration grids. The Hirshfeld charge was obtained by the population analysis. We also calculated other charges such as Mulliken, NPA (Natural Population Analysis), and CHELPG (CHarges from Electrostatic Potentials using a Grid based method) charges from 4 ACS Paragon Plus Environment

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the population analysis and compared them with the results from the Hirshfeld charge. We employed ab initio Hartree-Fock and Møller–Plesset perturbation theory (MP2) methods as well as density functional theory (DFT) methods with Pople’s standard triple-zeta split-valence basis set and Dunning’s augmented correlation consistent basis set.27,29 B3LYP30,31 and M062X functionals were used in DFT calculations. No qualitatively different result among these methods was observed. We will only show the results from the M062X/aug-cc-pVDZ level of theory below.

III. RESULTS AND DISCUSSION Table 1 displays the results for the systems with an ortho/para directing group, where the HOMO energy, Hirshfeld charges of mono-substituted benzene derivatives at both meta and para positions, and barrier heights of the identity reaction at both meta and para positions are tabulated for the nine systems. As can be seen from the Table, (i) the Hirshfeld charge at the para position is always more negative than that at the meta position, indicating that for the systems with para-directing groups, the para position is invariably more nucleophilic, and (ii) the barrier height at the para position is always smaller than that at the meta position, suggesting that the preferred, i.e., regioselective, site of the electrophilic substitution of these systems should be at the para-position. These results agree well with the fact that these groups are indeed ortho/para directing groups. These results are also consistent with what we have observed in our previous work.6 That is, benzene derivatives with ortho/para-directing groups possess the most negative Hirshfeld charges, and thus the strongest nucleophilicity, at the ortho/para positions, and their regioselective reaction sites of electrophilic substitution should therefore be at the ortho/para positions. Shown in Fig. 1 are the two strong correlations about the barrier height for the systems with ortho/para directing groups in Table 1. Figure 1a is a reasonably strong, inversely linear relationship between the barrier height of the substitution occurring at the para position and the HOMO energy. This



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correlation shows that the higher the HOMO level of a system, the easier it donates the electron pair from HOMO to the incoming electrophile, and thus the faster the electrophilic substitution process. This relationship agrees well the frontier orbital theory.32,33 However, since the HOMO distribution is delocalized over the entire molecule, this correlation does not contain the information of regioselectivity. That is, it does not tell us which carbon atom will be the preferred reaction site. Plus, for post-Hartree-Fock methods, where more than one Slater determinants are employed, the picture of frontier orbitals makes no more physiochemical sense. Figure 1b shows a stronger linear relationship between the same barrier height and the Hirshfeld charge at the para position with the correlation coefficient R2 equal to 0.966. This latter relationship not only illustrates that the more negative Hirshfeld charge on the para position, the smaller the barrier height for the reaction to take place, but also distinguishes the preferred reaction site from other possible spots. This strong linear correlation between the barrier height and Hirshfeld charge on the para position unambiguously demonstrates that the Hirshfeld charge is an accurate descriptor of both reactivity and regioselectivity for the electrophilic aromatic substitution of systems with ortho/para directing groups. A similar good correlation between the reaction barrier height and the Hirshfeld charge on the ortho position has also been obtained (not shown). In addition, we tried to correlate the barrier height with other charges, but much worse results were obtained (not shown). Table 2 exhibits the results for the systems with a meta directing group, from which we can see that (i) the Hirshfeld charge at the meta position is always more negative than that at the para position, suggesting that the meta carbon is able to donate more electrons, and (ii) the barrier height of the reaction happening at the meta position is always smaller than that at the para position, indicating that the reaction prefers to take place at the meta carbon. These results suggest that for the monosubstituted benzene systems with meta-directing groups, the meta position is most nucleophilic and most reactive. Figure 2 shows the two strong linear correlations for the barrier height of the reaction


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occurring at the meta position, similar to Fig. 1, one with the HOMO energy (Fig. 2a) and the other with the Hirshfeld charge at the meta position (Fig. 2b). Again, these results confirm that for systems with meta-directing groups, it is the meta position that possesses the most negative Hirshfeld charge, the strongest nucleophilicity, and thus the smallest barrier height for the electrophilic aromatic substitution. It clearly demonstrates that the Hirshfeld charge is a quantitatively accurate descriptor of both reactivity and regioselectivity for electrophilic aromatic substitution of systems with meta directing groups. We notice in passing that the results obtained from this work should also be applicable to traditional aromatic electrophilic substitutions, where a cyclohexadienyl cation (arenium ion) is formed as the reactive intermediate, which is often called the Wheland intermediate34 (sigma complex or σcomplex). In this case, besides the impact from the substitution group, the delocalization of the positive charge in this intermediate is also important. We anticipate that the kinetic of the first step, i.e., the formation of the arenium ion, is dictated by the nucleophilicity of the substituted benzene, but the subsequent step is governed both by the nucleophilicity of the benzene ring and by the nature of the incoming electrophile. Since the formation of the sigma complex is an endothermic and energetically unfavorable process, the first step should therefore be the rate determining step of this process.

IV. CONCLUSIONS Put together, the statement that reactivity and regioselectivity properties of electrophilic aromatic substitution reactions are governed by the nucleophilicity of carbon atoms in the aromatic ring has been rigorously examined and thoroughly verified. With the new quantification approach of nucleophilicity (and electrophilicity) we recently proposed using the Hirshfeld charge, we are able to determine these properties simultaneously. Above numerical results from the transition state perspective for a list of mono-substituted benzene + HF + BF3 reaction systems with both ortho/para and meta-directing groups have clearly demonstrated that point. The strong linear correlations of the



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reaction barrier height with both the HOMO energy and Hirshfeld charge establish a novel and reliable approach to quantify reactivity and predict regioselectivity for this vastly important category of chemical transformations. This new view of reactivity and regioselectivity provides us with an improved understanding about these reactions and should therefore be incorporated in future textbooks.

AUTHOR INFORMATION Corresponding Author * E-mail: [email protected]. Telephone: (919)962-4032

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS The author is grateful to an anonymous referee of Ref. [6], who correctly pointed out the importance to work on the transition state structure reported in this work. For that, the author acknowledges and appreciates. The author is also grateful to Research Computing Center, University of North Carolina at Chapel Hill, for accessing needed computing facilities for the present study.

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5. Crum Brown, A; Gibson, J. A rule for determining whether a given benzene mono-derivative shall give a meta-di-derivative or a mixture of ortho- and para-di-derivatives, J. Chem. Soc. Trans. 1892, 61, 367 - 369. 6. Liu, S.B. Where does the electron go? The nature of ortho/para and meta group directing in electrophilic aromatic substitution, J. Chem. Phys. 2014, 140, 194109. 7. Liu, S.B. ; Rong, C.Y.; Lu, T. Information conservation principle determines electrophilicity, nucleophilicity, and regioselectivity, J. Phys. Chem. A 2014, 118, 3698 - 3704. 8. Zhou, X.Y.; Rong, C.Y.; Lu, T.; Liu, S.B. Hirshfeld charge as a quantitative measure of electrophilicity and nucleophilicity: Nitrogen-containing systems, Acta Phys.-Chim. Sin. 2014, 30, 2055 - 2062. 9. Rong, C.Y. ; Lu, T.; Liu, S.B. Dissecting molecular descriptors into atomic contributions in density functional reactivity theory, J. Chem. Phys. 2014, 140, 024109. 10. Hirshfeld, F.L. Bonded-atom fragments for describing molecular charge densities, Theor. Chim. Acc. 1977, 44, 129 - 138. 11. Parr, R.G.; Yang, W.T. Density Functional Theory for Atoms and Molecules; Oxford University: London, 1989. 12. Geerlings, P.; De Proft, F.; Langenaeker, W. Conceptual density functional theory, Chem. Rev. 2003, 103, 1793 - 1873. 13. Chattaraj, P.K.; Sarkar, U.; Roy, D.R. Electrophilicity index, Chem. Rev. 2006, 106, 2065 - 2091. 14. Liu, S.B. Conceptual density functional theory and some recent developments, Acta Phys.-Chim. Sin. 2009, 25, 590 - 600. 15. Nalewajski, R.F.; Parr, R.G. Information theory, atoms in molecules, and molecular similarity, Proc. Natl. Acad. Sci. USA 2000, 97, 8879 - 8882. 16. Nalewajski, R.F.; Parr, R.G. Information theory thermodynamics of molecules and their Hirshfeld fragments, J. Phys. Chem. A 2001, 105, 7391 - 7400. 17. Parr, R.G.; Ayers, P. W.; Nalewajski, R. F. What is an atom in a molecule? J. Phys. Chem. A 2005, 109, 3957 - 3959. 18. Ayers, P. W. Information theory, the shape function, and the Hirshfeld atom, Theor. Chem. Acc. 2006, 115, 370 - 378. 19. Kullback, S. Information Theory and Statistics; Dover: Mineola, N.Y., 1997. 20. Nalewajski, R.F. Information Theory of Molecular Systems; Elsevier: Amsterdam, The Netherlands, 2006. 21. Nalewajski, R. F. Information origins of the chemical bond; Nova Science: Hauppauge, N.Y., 2010. 9 ACS Paragon Plus Environment


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22. Rong, C.Y.; Lu, T.; Chattaraj, P.K.; Liu, S.B. On the relationship among Ghosh-Berkowitz-Parr entropy, Shannon entropy and Fisher information, Indian J. Chem. A 2014, 53, 970 - 977. 23. Rong, C.Y.; Lu, T.; Ayers, P.W.; Chattaraj, P.K.; Liu, S.B. Scaling properties of information-theoretic quantities in density functional reactivity theory, Phys. Chem. Chem. Phys. 2015, 17, 4977 - 4988. 24. Alagona, G.; Scrocco, E.; Silla, E.; Tomasi, J. The catalytic effect of BF3 on the electrophilic hydrogen exchange reaction in benzene, Theoret. Chim. Acta, 1977, 45, 127 - 136. 25. Heidrich, D. The transition state of electrophilic aromatic substitution in the gas phase, Phys. Chem. Chem. Phys. 1999, 1, 2209 - 2211. 26. Zhao, Y.; Truhlar, D.G. The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals, Theor. Chem. Acc. 2008, 120, 215 - 241. 27. Dunning Jr., T. H. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen, J. Chem. Phys., 1989, 90, 1007 - 1023. 28. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, Revision D.01, Gaussian, Inc., Wallingford CT, 2009. 29. Ditchfield, R.; Hehre, W.J.; Pople, J.A. Self-consistent molecular-orbital methods. IX. An extended gaussian-type basis for molecular-orbital studies of organic molecules, J. Chem. Phys. 1971, 54, 724 728. 30. Becke, A. D. A new mixing of Hartree–Fock and local density-functional theories , J. Chem. Phys., 1993, 98, 1372 - 1377. 31. Lee, C.; Yang, W.; Parr, R.G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B, 1988, 37, 785 - 789. 32. Fukui, K.; Yonezawa, T.; Shingu, H. A molecular orbital theory of reactivity in aromatic hydrocarbons, J. Chem. Phys. 1952, 20, 722 - 725. 33. Fukui, K. Recognition of stereochemical paths by orbital interaction, Acc. Chem. Res. 1971, 4, 57 - 64. 34. Wheland, G.W. A Quantum Mechanical Investigation of the Orientation of Substituents in Aromatic Molecules, J. Am. Chem. Soc. 1942, 64, 900 – 908.


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Table 1. Results for nine mono-substituted benzene derivatives, Ar-R, with para-directing groups, R. Shown here are their HOMO energy, Hirshfeld charges at meta- and para-positions, and barrier heights of electrophilic aromatic substitution, Eq. (1), for these species at both meta- and para-positions. Units of HOMO and Hirshfeld charges are in atomic unit, and barrier heights in kcal/mol.

Hirshfeld Charge

Barrier Height

-R

HOMO

Meta

Para

Meta

Para

-H

-0.3080

-0.0498

-0.0498

28.41

28.41

-Cl

-0.3039

-0.0414

-0.0488

31.57

27.35

-Et

-0.2947

-0.0506

-0.0554

27.79

25.23

-F

-0.3069

-0.0419

-0.0560

31.64

25.38

-Me

-0.2947

-0.0506

-0.0558

28.45

24.59

-NH2

-0.2595

-0.0501

-0.0717

30.29

11.09

-NMe2

-0.2430

-0.0525

-0.0748

29.83

12.18

-OH

-0.2818

-0.0474

-0.0658

29.56

16.69

-Pr

-0.2939

-0.0508

-0.0554

28.49

24.69

-tBu

-0.2945

-0.0514

-0.0554

27.63

25.34



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Table 2. Results for nine mono-substituted benzene derivatives, Ar-R, with meta-directing groups, R. Shown here are their HOMO energy, Hirshfeld charges at meta- and para-positions, and barrier heights of electrophilic aromatic substitution, Eq. (1), for these species at both meta- and para-positions. Units of HOMO and Hirshfeld charges are in atomic unit, and barrier heights in kcal/mol.

Hirshfeld Charge

Barrier Height

-R

HOMO

Meta

Para

Meta

Para

-H

-0.3080

-0.0498

-0.0498

28.41

28.41

-CCl3

-0.3206

-0.0417

-0.0387

31.10

31.89

-CF3

-0.3293

-0.0399

-0.0368

32.23

33.16

-CHO

-0.3234

-0.0449

-0.0337

31.16

32.96

-CN

-0.3273

-0.0380

-0.0326

33.47

33.94

-COF

-0.3329

-0.0408

-0.0292

33.00

34.90

-NH3+

-0.4752

-0.0082

-0.0048

53.02

54.92

-NO2

-0.3392

-0.0365

-0.0296

34.29

35.37

-NO

-0.3032

-0.0420

-0.0298

31.85

34.08

-SO3H

-0.3394

-0.0356

-0.0296

33.68

35.33


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Figure 1. Strong correlations of the electrophilic substitution barrier height for mono-substituted benzene derivatives with para-directing groups with (a) HOMO energy and (b) Hirshfeld charge at the para-position.



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Figure 2. Strong correlations of the electrophilic substitution barrier height for mono-substituted benzene derivatives with meta-directing groups with (a) HOMO energy and (b) Hirshfeld charge at the meta-position.


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Quantifying Reactivity for Electrophilic Aromatic Substitution Reactions

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