Theoretical Investigation into Rate-Determining Factors in Electrophilic

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Theoretical Investigation into Rate-Determining Factors in Electrophilic Aromatic Halogenation Magnus Liljenberg, Joakim Halldin Stenlid, and Tore Brinck J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b10781 • Publication Date (Web): 05 Mar 2018 Downloaded from http://pubs.acs.org on March 7, 2018

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The Journal of Physical Chemistry

Theoretical Investigation into Rate-Determining Factors in Electrophilic Aromatic Halogenation Magnus Liljenberg, Joakim Halldin Stenlid and Tore Brinck* Applied Physical Chemistry, School of Chemical Science and Engineering, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden. * Corresponding author: Tore Brinck (E-mail: [email protected])

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ABSTRACT The halogenation of monosubstituted benzenes in aqueous solvent has been studied using DFT at the PCM-M06-2X/6-311G(d,p) level. The reaction with Cl2 begins with the formation of C-atom coordinated π-complex and is followed by the formation of the σ-complex, which is ratedetermining. The final part proceeds via the abstraction of the proton by a water molecule or a weak base. We evaluated the use of the σ-complex as a model for the rate-determining transition state (TS) and found that this model is more accurate the later the TS comes along the reaction coordinate. This explains the higher accuracy of the model for halogenations (late TS) compared to nitrations (early TS), i.e. the more deactivated the substrate the later the TS. The halogenation with Br2 proceeds with a similar mechanism as the corresponding chlorination, but the bromination has a very late rate-determining TS that is similar to the σ-complex in energy. The iodination with ICl follows a different mechanism than chlorination and bromination. After the formation of the π-complex, the reaction proceeds in a concerted manner without a s-complex. This reaction has a large primary hydrogen kinetic isotope effect in agreement with experimental observations.


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INTRODUCTION The putative mechanism for electrophilic aromatic substitution (SEAr) is widely believed to be in principle the same, irrespective of the electrophilic reagent (see Scheme 1). 1 It begins with the fast and reversible formation of a non-covalent complex between the active electrophile and the π-system of the aromatic ring. This species is usually referred to as the π-complex. If the reaction proceeds, the π-complex reacts to form a covalently bonded complex, the so-called σ-complex (also known as Wheland intermediate or arenium ion). The carbon that now is bonded to the active electrophile has become tetravalent and the cyclic conjugation of the aromatic system is broken. This mechanistic step requires considerable energy and the formation of the σ-complex is most often considered to be the rate-limiting step. In the last step, the proton of the tetravalent carbon is expelled and the aromaticity is regained. However, there are several experimental and computational results that indicate exceptions to this mechanism. Some authors have claimed that the σ-complex does not exist in the gas phase or in low polarity solvents and that the substitution then proceeds either via a concerted mechanism

2

or via an addition-elimination

pathway. 3 There are also open questions regarding other aspects of this reaction, for example the exact nature of the reaction intermediates and why the reaction with some electrophiles (in particular in the case of iodination) has a substantial hydrogen kinetic isotope effect.

E+

H

E+ + H π-complex

H

-H+ E

E

σ-complex

Scheme 1. Putative mechanism of the SEAr reaction.


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Unlike electrophilic aromatic nitrations there is no commonly identified active electrophile for halogenations, but a wide variety of halogenating reagents have been used.1 Most of the theoretical studies on SEAr chlorinations have focused on Cl2 or Cl+ as the active electrophiles, and on modeling the reaction in gas phase or in low-polarity solvents. Important theoretical contributions regarding aromatic halogenations have been provided by for example Ben-Daniel et al. in 2003,

4

Filimonov et al. in 2011,

5

and Sakic and Vrcek in 2012.

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In the two former

studies, the stationary points on the potential energy surface of the reaction were only characterized in the gas phase, and solvent calculations using a continuum model were applied on the gas phase structures. Sakic and Vrcek used a stochastic search methodology to search for prereactive complexes between Cl2 and benzene using a polarizable continuum model (PCM) to simulate a low polarity solvent (carbon tetrachloride). They could not find a σ-complex without having counter ions in close contact with the modeled system. The reaction rate of aromatic halogenations is generally enhanced in highly polar solvents as they stabilize the intermediate σ-complex, and thus make such conditions the most important from a preparative or industrial view. Aqueous acetic acid is for example a common solvent mixture for the reaction with the Cl2 and Br2 electrophiles, as well as in iodinations. The active chlorinating agent in aqueous solutions varies depending the on the conditions. Cl2 in water partly dissociates to HOCl and HCl, and HOCl in turn form an equilibrium with Cl2O. Cl2 and Cl2O are the more reactive chlorinating species, but under many circumstances HOCl is the most abundant. All three species have been suggested to be the active electrophile in aromatic chlorination.

1

In two recent papers, Roberts and coworkers performed a series of kinetic

experiments in order to assess the importance of the different electrophiles in aromatic chlorination in aqueous solution.

7, 8

HOCl was found to be most important electrophile only in


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the case of the very activated aromatic 1,3,5-trimethoxybenzene. However, for the less activated 3-methylanisole, the kinetic data investigated as a function of pH and [Cl-] indicates that Cl2O is the dominating electrophile at pH > 7.5 while it is Cl2 at pH < 6.5. 7 Furthermore, it was found at low pH that the chlorination rate increases when Cl- is present; this was attributed to the reaction of HOCl and Cl- to form Cl2. 8 Considering that most reference data for aromatic halogenation is in aqueous acetic acid and thus under acidic conditions, we have chosen Cl2 as the electrophile in our computational study. The reaction with Cl2 has been shown to follow second-order kinetics.9 In non-polar solvents, the reaction is catalyzed by Brønsted/Lewis acids with an overall third order reaction kinetics. 10 This work is a continuation of our work on SEAr nitration and halogenations and focuses on mechanistic and reactivity aspects of the uncatalyzed halogenations of monosubstituted benzenes in aqueous solution.

11, 12

Moreover, we have evaluated the validity and accuracy of using the

transition state for the alleged rate determining formation of the σ-complex, both for global (substrate) and local (positional) reactivity. This approach is compared to the use of the relative energy of the σ-complex as an approximate reactivity indicator. The comparison is carried out for Cl2 chlorination of a series of congeneric arenes and related to experimental regioisomeric distributions. In addition, the reactivities of Cl2 and Br2 are compared, and the nature of the stationary points on the free energy surfaces (i.e. TS and σ-complex) is studied with consideration of the much lower reactivity and higher selectivity for Br2. The mechanism behind the common hydrogen kinetic isotope effect in iodinations is investigated, and this reveals a dissimilar mechanism for iodination compared to chlorination and bromination.


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COMPUTATIONAL DETAILS Quantum chemical structure optimizations were performed using the Gaussian09 program suite.

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All structures were fully optimized with Kohn-Sham density functional theory (DFT),

employing the meta hybrid functional M06-2X

14

and the integral equation formalism of the

PCM solvent model (IEF-PCM) 15, 16 with water as model for polar, protic solvents. The M06-2X functional has been shown to perform strikingly better than other common functionals, including the popular B3LYP, regarding for example π-systems, kinetics (barrier heights) and noncovalent interactions.14 In addition, we have previously found this computational set-up appropriate for studies of the closely related aromatic nitration reaction type. 12 The 6-311G(d,p) basis set was used for all geometry optimizations with exception for the structures containing iodine, where the LACV3P 17 basis set with Los Alamos type Effective Core Potentials 18 on the 46 innermost electrons were used for the iodine atom(s), and 6-311G(d,p)

19

for the remaining

atoms. This basis set is optimized for the Cl- anion and thus, despite lack of diffuse functions, is appropriate for reactions that generate Cl-, such as the chlorination and iodination reaction of this study. 19 All structures have been characterized by frequency calculations as either minimum (no imaginary vibrational mode) or transition state (one imaginary vibrational mode). The transition state structures were further characterized by means of IRC calculations, to assure that a given transition state structure indeed connects to the correct energy minima. In order to investigate the sensitivity of the mechanistic and structural predictions for this type of reactions to the theoretical method, the stationary points on the potential energy surface for the chlorination of benzene were optimized also at the following levels of theory, M06-2X/6-311+G(d,p) wB97-XD/6-311G(d,p), PBE0/6-311G(d,p), B3LYP/6-311G(d,p) MP2/6-311G(d,p) and MP2/6311G(3df,2p), in all cases together with IEF-PCM solvation. With the exception of B3LYP/6-


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311G(d,p), and to a smaller extent PBE0/6-311G(d,p), all investigated levels of theory give highly similar geometries for the stationary points. In particular, there is good agreement between the M06-2X/6-311G(d,p) and MP2/6-311G(3df,2p) geometries; as an example, the structures of rate-determining transition state (TS1) at the two levels are presented in the S.I. Furthermore, the geometries are relatively insensitive to the solvation model, the TS1 geometry is only marginally altered by reducing the dielectric constant from 80 (water) to 10 (e.g. propanal) as shown in the S.I. On the other hand, gas phase structure optimization is not applicable since the stationary points corresponding to TS1 and sigma-complex in the solution reaction do not exist on the gas phase potential energy surface. Whereas the geometries of the stationary points for the chlorination reaction are rather insensitive to basis set and solvation model, this is not the case for the activation energy and the energy for forming the sigma-complex. Rather surprisingly, we found that these two energies increased significantly when the 6-311G(d,p) basis set was augmented by diffuse functions and additional polarization functions. Two reasons for this behavior were identified. The first is associated with the implementation of IEF-PCM in Gaussian 09, which does not seem to fully compensate for the electronic charge lying outside the cavity. This has the effect that the solvation energy of a negative ion, e.g. Cl- increases (becomes less negative) when the basis set is increased, e.g. the solvation energy of Cl- has the values -75.4, -71.1 and -70.2 for the STO3G, 6-311G(d,p), and 6-311+G(d,p) basis sets, respectively. As the experimental solvation energy of Cl- is -81 kcal/mol, it is clear that the solvation correction of IEF-PCM, in particularly with larger basis sets, will overestimate the activation energy and the sigma-complex formation energy because the reaction generates a Cl-. The other reason for the increase in activation energy and sigma-complex energy with increasing basis set is that a very large basis set is


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needed to describe the electron structure of the Cl2 molecule; the gas phase bond dissociation energy of Cl2 increases from 48.0 to 58.7 when going from the 6-311G(d,p) basis set to the large and diffuse ma-def2-TVZPP basis set with the M06-2X functional. The latter value is in good agreement with the experimental BDE of 57.2 kcal/mol at 0 K. 20 As the chlorination reaction has Cl2 as a reactant and the Cl-Cl bond is broken during the reaction, it is clear that a large basis set is needed to obtain proper energetics, and thus to use a smaller basis set to reduce the error in the IEF-PCM solvation energy is not a viable alternative. We therefore decided to calculate single point energies using M06-2X with the ma-def2-TVZPP basis set 21, 22 and the C-PCM 16 solvation model of the orca 4.01 software.

23

This basis set is similar in size and functionality to 6-

311++G(2df,2p), but use an ECP representation of the inner electrons of iodine. The C-PCM method in the orca implementation has an explicit correction for the excluded charge effect, and with this correction the dielectric solvation energy of Cl- is -75.6 kcal/mol at the M06-2X/madef2-TVZPP level, in better agreement with experiment than the IEF-PCM model. The gas phase BDE of Cl2 and the electron affinity (EA) of Cl-, which are crucial to obtain accurate reaction energetics for chlorination, are also in good agreement with experiment at this level. The experimental

20

and computed EAs are 3.62 and 3.65 eV, respectively. In order to further

benchmark the accuracy of the computational procedure for halogenation reactions, we computed the activation energy for the chlorination of benzene by CCSD(T) extrapolated to infinite basis using MP2 with atomic natural orbital basis set of size up to ano-pVTZ and CPCM.

24

The activation energy (Born-Oppenheimer energy difference) is 16.4 kcal/mol at the

M06-2X/ma-def2-TVZPP level and 16.9 kcal/mol by the CCSD(T) approach, and thus the agreement is very good.


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For the detailed mechanistic studies of Figure 2, 3, 4 and 7, the final energies were thus evaluated at the M06-2X/ma-def2-TVZPP level with C-PCM solvation using orca. Otherwise, the energies are reported at the same level of theory as the geometry optimizations, i.e. M062X/6-311G(d,p) with IEF-PCM using Gaussian09. This level is generally appropriate for comparing relative energies among isomers and for computing substituent effects, where errors due to basis set and excluded charge are nearly cancelled. A dielectric constant of 80 and solvent parameters of water was used for C-PCM and IEF-PCM. The reported C-PCM energies also include a cavity-dispersion term that depends on surface area.

16

The reason that the solvent

parameters were taken as water is that experimental studies of halogenation typically are performed in aqueous acetic acid. The concentration of acetic acid ranges from dilute to pure, and as a consequence the dielectric constant ranges from 80 to 6. 25 However, due to the form of the dielectric response function in PCM there is a small change in solvent response when going from a dielectric constant of 80 to 20, which is a range that covers most experimental conditions. The effects of reducing the dielectric constant further will be discussed under Results and Discussion. All energies are reported as standard Gibbs free energies, if not otherwise stated. The thermal corrections to the free energies (ΔG) were obtained from frequency calculations employing the harmonic oscillator and rigid rotor approximations, and also done under the assumption of noninteracting molecules (the ideal gas approximation). We further assumed a temperature of 298.15 K and concentrations of 1.00 M for all solutes ([H2O] was set to 55 M). Since the program's default is 0.0408 M (i.e. 1 bar) we have adjusted the reported free energies in the reactions where the number of molecules changes in order to correct for the concentration differences. The free


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energy correction ΔΔGreact is e.g. -1.9 kcal/mol for complexation of a halogen electrophile with an arene, in the same manner as previously described in our work on nitrations. 12 In order to adjust for symmetry, the Gibbs free energy, ΔGsym, were corrected as ∆𝐺#$% = −𝑅𝑇ln

,,.

(1)

In eqn (1), σp and σr are the rotational symmetry numbers of the products and reactants. 26–28 The two-fold degeneracy of the ortho and meta sites with respect to the para site are accounted for by correcting the ortho and meta energies by a factor -RTln(2)=-0.41 kcal/mol.


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RESULTS & DISCUSSION Chlorination Figure 1 shows the structures of the stationary points on the potential energy surface (PES) in the chlorination of the activated structure anisole (PhOMe). The uncatalyzed halogenation with molecular chlorine as the electrophile proceeds via a C-atom coordinated p-complex before the formation of the s-complex. This mechanism is different from our previous investigation regarding aromatic nitrations,

12

insofar that the nitration begins with the formation of an

unoriented p-complex before it forms the C-atom coordinated π-complex. In solution, the scomplex has a Cl-Cl bond that is nearly dissociated, with a Cl-Cl distance of 3.3 Å and the structure can essentially be viewed as an arenium ion with a Cl- coordinated to the Cl substituent. The rate-determining transition state (TS1) is similar in structure to the s-complex. Considering the structure of the s-complex, it does not seem likely that the Cl- formed from the attacking Cl2 will tilt down and serve as base in the deprotonation of the arenium ion, and we were not able to locate an arenium ion where the Cl- is coordinated to the leaving H+. All attempts to optimize such a structure resulted in barrier-free proton abstraction and the formation of HCl that dissociated from the chloro-anisole. Deprotonation of the s-complex is easily facilitated, even by a weak base such as water. In the case of a neutral base, this process does not require the dissociation of Cl- from the s-complex. The stationary points of the proton abstraction, including the transition state (TS2w) were modeled by including an explicit water molecule that is coordinated to the acidic proton in the s-complex, with and without the Cl- coordinated, and optimized structures for the process with Cl- are provided in Figure 1. In both cases the barrier is


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low (2-3 kcal/mol). We were not successful in optimizing a transition state for the dissociation of Cl-, which is not surprising since this process can be expected to be virtually barrier-free.

2.04 2.36 2.96

∠88.1° 2.22 1.08

1.08

1.08

Reactant

∠102.7°

TS1

π-complex 3.34

3.32

∠137.4°

∠132.3° 1.80 1.11

1.81 1.10

1.95

σ-complex

σW-complex

∠160.9°

3.36

∠178.5° 3.47

1.77 1.24

1.75 2.09

1.46

0.99

TS2W

PW

Figure 1. Structures of stationary points for chlorination of the para position of anisole in aqueous solution optimized at the PCM-M06-2X/6-311G(d,p) level. Bond lengths are in Å and bond angles in degrees.

Figure 2 and Figure 3 show the free energies of the stationary points on the potential energy surface (PES) for the chlorination with Cl2 of anisole and fluorobenzene respectively (the


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corresponding energies for benzene are in Figure 4). The computed activation free energy that the chlorination of anisole is considerably faster than that of benzene and fluorobenzene. The formation of the π-complex is a weakly endergonic process by 0.5-1 kcal/mol and the different π-complex isomers are very close in energy. (The exception is the fluorobenzene para addition of Figure 3 at 3.3 kcal/mol). The subsequent formation of the s-complex is the rate-determining step. The last step in the reaction, the expulsion of the proton by a water molecule, is a fast and nearly barrierless process for anisole. We were not able to find the corresponding transition state structure for fluorobenzene and in this respect the situation mirrors our previous investigation

12

on nitrations; where we found this transition state for the activated case of phenol but not for the deactivated chlorobenzene. Neither in anisole nor in fluorbenzene where we able to find a pcomplex for the meta-isomer. In the case of anisole, the stationary points were also modeled with an explicit water molecule present during the entire reaction. However, the geometries of the pcomplex, TS1 and the complex are almost to identical to those without the explicit water; and it is only in the s-complex that water is coordinated to the leaving proton by a hydrogen bond. Furthermore, the energies of TS1 and the s-complex relative to the p-complex are very similar to the corresponding energies in the computations without explicit water. Thus, we can conclude that the modeling of the rate determining formation of the s-complex can be performed without explicit water, whereas the expulsion of the proton needs an explicit water molecule or other base. In order to investigate the dependence of solvent polarity on the mechanism, the stationary points of the rate-determining step of anisole and benzene were modeled using different dielectric constants in the solvent representation. As the dielectric constant (e) incrementally was decreased from 80, the activation energy gradually increased and the energy gap between TS1


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and the s-complex gradually decreased. The structures of the stationary points, including TS1, are only marginally changed as e is reduced. In the case of anisole, we were no longer able to find TS1 and s-complex for e < 3. This indicates that the reaction mechanism of Figure 2 is valid also in dry acetic acid (e = 6.15), 25 which is a common solvent for chlorination of anisole. 9 The activation energy increases by only 0.6 kcal/mol going from e = 80 to e = 20, but by additional 2.0 kcal/mol going down to e = 6. In the case of benzene the general behavior is similar, but the mechanism becomes invalid already below e = 10, which corresponds to circa 92 volume % acetic acid.

25

These results are consistent with that only activated aromatics are chlorinated in

dry acetic acid, 9 and that chlorination in non-polar solvents requires a catalyst, typically a Lewis base. 10 Gsol [kcal/mol]

(22.5)

Orto (Meta) [Para]

(17.3) 13.2 [13.0] TS1

0 R

[0.9] 0.8

1.6

1.4

[-1.8]

[-1.8]

2.7 [1.2] TS2W

W

[-11.1] (-11.8) -12.2 PW

(-30.1) [-31.2] -31.5 P

Figure 2. Free energies at the M06-2X/ma-def2-TVZPP level with C-PCM solvation for the stationary points on the potential energy surface in chlorination of anisole in aqueous solution. The free energy levels have been adjusted for symmetry as described in the computational details


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section. The three species to the right, indexed with “w” as in water, are calculated with one explicit water molecule coordinated to the structures. The energy level for the σw para isomer has been leveled with the corresponding para structure for the σ-complex without water, with the other structures with explicit water adjusted relative to the σw We were not able to find the πcomplex, sw or TS2w for the meta isomer. The P species refer to (Cl-Cl4H5OCH3 + Cl- ···H3O+) and its free energy is relative the separated reactants (R) ΔGsol [kcal/mol]

(26.4) 22.2 [20.9]

(21.0)

TS1 15.8 [12.4] σ [3.3] 0 R

0.2 Π

Orto (Meta) [Para]

Figure 3. Free energies at the M06-2X/ma-def2-TVZPP level with C-PCM solvation for the stationary points on the potential energy surface in the rate-determining formation of the σcomplex for chlorination of fluorobenzene.

The most direct method to compute the reactivity of a reaction is to estimate the rate constant from the free energy difference between the rate-determining transition state and the reactants. As transition state calculations are comparatively demanding and difficult to apply in e.g. automated methods (important for efficient large scale applications), one alternative approach is to use the energy for the formation of the σ-complexes to estimate the transition state energy. This approach assumes a linear relationship between the TS energies and the relative energies of the σ-complexes and has been used in several studies. 29–33


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In order to evaluate the accuracy of the σ-complex approach compared to full transition state searches, we performed an investigation on a congeneric series of monosubstituted benzenes PhX (X=OMe, Me, F, Cl, CF3 and CN). The results and the accuracy compared to the experimental results are given as mean absolute deviation (MAD)

34

and presented in Table 1.

The experimental isomer ratios have been recalculated to energy differences by us. It is quite clear that the σ-complex approach gives the most accurate results for the most deactivated substrates, that is when the rate-determining transition state comes late along the reaction coordinate. For the two most deactivated substrates (X=CF3 and CN) the accuracy of the σcomplex method is comparable to direct transition state modeling. For the intermediate cases (X=Me, F, Cl) the σ-complex approach performs moderately well and in the most activated case (X=OMe) the result is poor. Table 2 gives a summary of the structures and energies of the ratedetermining transition state and its corresponding σ-complex for our six substrates. From these results, together with our previous investigation of nitrations, 12 it is clear why the σ-complex approach is so much more successful for halogenations than for nitrations, halogenating electrophiles are generally much less reactive and have therefore later ratedetermining transition states. The halogenation σ-complex is in general a much better model for the rate-determining transition state. It is also clear that whereas the rate-determining transition state structures for nitration resemble the oriented π-complex, the corresponding chlorination structures are closer to the σ-complex. Stock and Brown

35

have provided reactivity data for the chlorination with Cl2 for four of our

investigated cases (X=OMe, Me, F, Cl) relative to the reactivity of benzene. By using this type of reaction rate ratio the selectivity of different electrophiles and the effects of substituents can be placed on a quantitative basis. In order to examine how well the chosen level of theory could


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reproduce the global (substrate) reactivity of this reaction, we compared the energy barriers from the reactants to that of the rate-determining transition state (TS1) with the corresponding value for benzene (Table 3).


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Table 1. Chlorination in aqueous solution of various monosubstituted benzenes with Cl2 in order of decreasing reactivity. Free energy differences (ΔG) between isomers in comparison to experimental data. All data in kcal/mol determined at the M06-2X/6-311G(d,p) level of theory with IEF-PCM solvation.a Substrate PhX X= OMe

Isomer

TS1

σ-complex

Exp.

Ortho Meta Para

0.1 (0.2) 9.1 (9.5) 0.0

3.1 (3.4) 19.8 (19.1) 0.0

0.8c -d 0.0c

Me

Ortho

0.6

0.6

0.0c c

MAD b TS1 0.7 (0.6)

MAD b σ-complex 2.3 (2.6)

0.5

1.5

Meta Para

3.2 0.0

4.8 0.0

2.8 0.2c

F

Ortho Meta Para

1.2 (1.3) 5.5 (5.5) 0.0

2.7 (3.9) 8.4 (8.1) 0.0

1.3e -d 0.0e

0.1 (0.0)

1.4 (2.6)

Cl

Ortho Meta Para

0.1 3.7 0.0

2.0 5.7 0.0

0.4e -d 0.0e

0.3

1.6

CF3

Ortho Meta Para

1.5 0.0 2.3

2.0 0.0 2.4

1.4f 0.0f 1.8f

0.3

0.4

CN

Ortho Meta Para

0.1 0.0 1.4

0.4 0.0 1.6

0.4f 0.0f 1.0f

0.5

0.4

a

For the OMe and F entries, corresponding energies at the M06-2X/me-def2-TVZPP level are reported in parenthesis. b In the case of two experimentally detected isomers (X=OMe, F, Cl) there is only one energy difference to consider. In those cases it would be more correct to use the expression absolute deviation. c Cl2 in acetic acid at 25 °C, ref 35. d No meta isomer detected experimentally. e Cl2 in aqueous acetic acid at 25 °C, ref 35. f Cl2 in aqueous acetic acid at 25 °C, ref 36.


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Table 2. Chlorination in order of decreasing reactivity. Distances [Å] between Cl and C4 (X= OMe, Me, F, Cl) or C3 (X= CF3, CN), energies and MAD for the σ-complex and TS1 for PhXCl2. Energies in kcal/mol determined at the M06-2X/6-311G(d,p) level of theory with IEF-PCM.a PhX;

distance

distance

X=

(TS1)

(σ-complex)

Δdistance

ΔG

(TS1- MAD

σ-complex)

OMe Me F Cl CF3 CN

2.221 1.807 0.414 14.5 (14.8) 2.097 1.797 0.300 7.7 2.057 1.796 0.261 6.8 (8.0) 2.038 1.798 0.240 5.9 1.963 1.785 0.178 3.0 1.940 1.785 0.155 2.6 a For the OMe and F entries, corresponding energies at level with C-PCM solvation are reported in parentheses.

Table 3. Experimental

35

TS1

MAD σ-complex

0.7 (0.6) 2.3 (2.6) 0.5 1.2 0.1 (0.0) 1.4 (2.6) 0.3 1.6 0.3 0.4 0.5 0.4 the M06-2X/me-def2-TVZPP

and calculated free energies of activation for the chlorination with Cl2

at the para-position of PhX (X= OMe, Me, F, Cl) or the meta-position (X= CF3, CN) in relation to that of the corresponding single position chlorination of benzene. Free energies in kcal/mol determined at the M06-2X/6-311G(d,p) level of theory with IEF-PCM solvation. PhX;

rp-X/ rHa

(ΔGTSH-ΔGTSp-X)exp

(ΔGTSH-ΔGTSp/m-X)compb

deviation

X= OMe Me F Cl CF3 CN

Absolute

4.6x107 820 3.93 0.406 -c -c

10.4 4.0 0.8 -0.5 -

8.9 4.9 0.9 -1.4 -6.7 -8.1

1.5 0.9 0.1 0.9 (0.2)d (0.2)d

a

The partial rate factor (rp-X/ rH) defined as kpara-PhX/ksingle-benzene. The degeneracy for benzene have been accounted for in the calculated ratios such that ksingle-benzene= kbenzene/6. b Calculated based on the identified TS1 structures. c No experimental data available. d There is no data from Baciocchi


19


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et al 36 regarding the relative reaction rate towards benzene, but the relative reaction rates for the meta positions kCl2PhCF3/ kCl2PhCN is 118.0/16.3 (the chlorination of the para position in PhNO2 being set to unity), corresponding to an energy difference between these two substrates of 1.2 kcal/mol, giving an absolute deviation of 0.2 kcal/mol for this comparison.

Bromination Both the reaction rate and positional selectivity of bromination is strongly substituent dependent, and this has been seen as an indication of a late transition state with a close energetic and structural resemblance to the σ-complex. 1 In order to compare chlorination and bromination regarding this question we performed calculations of the halogenation of anisole (PhOMe) with Cl2 and Br2 respectively. Kinetic experiments have been carried out under similar conditions for these two reactions (acetic acid at 25 °C) and the para position is the preferential site of attack in both cases (79% for Cl2 and 98.4% for Br2). 35 For anisole the reaction rate ratio with benzene is 4.6x107 for Cl2 and 1.1x1010 for Br2.

35

Thus, halogenation with Br2 is associated with higher

positional selectivity and a larger substituent effect on the reactivity compared to the corresponding reactions with Cl2. Our results are presented both as a free energy surface in Figure 4 as well as a comparison of the stationary points in Table 4. For both the chlorination and the bromination, the formation of the π-complex is a weakly endergonic process by less than 1 kcal/mol. Our result confirm that the formation of the σ-complex is the rate-determining step in both cases. In addition, we show that the rate-determining transition state comes much later along the reaction coordinate for Br2, and thus is much closer to the σ-complex in both energy and structure than for Cl2. This is evidenced by the result that the bonding between Br and the para carbon is closer to completion in the Br transition state compared to Cl, and that there is a more substantial positive charge present (as determined by Mulliken and NBO37 charges) on the ring than in the corresponding Cl


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case. Figure 5 shows the structure of the stationary points in the bromination of anisole, which can be compared with the corresponding Cl2 structures in Figure 1.

20.7

ΔGsol [kcal/mol] Benzene + Cl2 (Anisole + Cl2) [Anisole + Br2]

(13.0) [10.8] TS1

0 R

13.4

[7.9]

(0.9) [0.4] -0.4 Π

(-1.8) σ

Figure 4. Free energies at the M06-2X/ma-def2-TVZPP level with C-PCM solvation for the stationary points on the potential energy surface in the halogenation of the para position of anisole with Cl2 and Br2 in aqueous solution. The results are compared to the chlorination of benzene.


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Table 4. A comparison between the para isomer of chlorination and bromination of anisole (PhOMe). Distances [Å] between Cl/Br and the para carbon atom and free energy differences between TS1 and the corresponding σ-complex for PhOMe-X2. Energies in kcal/mol. distance

distance

(TS1)

(σ-complex)

Cl2

2.221

1.807

Br2

2.130

2.014

a

ΔG (TS1-σ-

kXanisol/

ring charge b

complex)

kXbenzene a

(TS1)

0.414

14.8

4.6x107

+0.49 (+0.48)

0.116

2.9

1.1x1010

+0.63 (+0.77)

Δ distance

Experimental reaction rate ratio. 35 b Mulliken charge, NBO charge in parentheses.

2.32

3.04

2.86

∠90.6°

3.32 ∠111.2°

2.13 1.09

∠113.3° 2.02 1.10

1.08

π-complex

TS1

σ-complex

Figure 5. Structures of stationary points for bromination of the para position of anisole in aqueous solution optimized at the M06-2X/6-311G(d,p) level with IEF-PCM solvation. Bond lengths are in Ångstroms and bond angles in degrees. The structure of the Br2 and benzene complex (π-complex) in the solid state has been determined experimentally by X-ray crystal structural analysis at -150 ˚C. 38 As can be seen from Figure 6, the crystal structure is very similar to our computed solution structure. The agreement is remarkable considering that the experimental data are from the solid phase and the calculations correspond to aqueous solution and have been performed with the IEF-PCM model.


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2.31 (2.30) 3.33 (3.36) 3.10 (3.18)

∠86.9° (81.4°)

π-complex Figure 6. Structure of the Br2 and benzene π-complex in aqueous solution optimized at the M062X/6-311G(d,p) level with IEF-PCM solvation. Bond lengths are in Å and bond angles in degrees. Values in parentheses and italics refer to a X-ray crystallographic study of a cocrystal of Br2 and benzene.38 Iodination An interesting feature about iodination of aromatic systems is that the reaction often possesses a significant hydrogen kinetic isotope effect (KIE), and the measured deuterium isotope effect (kH/kD) is typically found in the range 1.5 -4.5, 39–42 indicating that the effect is primary. This is in sharp contrast to most other SEAr reactions including chlorinations, brominations and nitrations, where such an effect is virtually nonexistent. 43 A KIE of this magnitude will arise if the second step in the reaction, the expulsion of the proton, is at least partially rate-determining (k2 ≤ k1), and the origin of this effect has most often been interpreted along this line. 40, 41 It is, however, also possible that the KIE originates from the so called partitioning effect, arising from the reversibility of the first step. 1 The provisions for this scenario are that the hydrogenated σ-complex goes to product faster than its deuterated analogue, that their rate of reversion back to starting material are about equal and finally that k2 is not much faster than k-1 (k2D < k2H, k-1D≈ k-1H and k2≈k-1/k2

Theoretical Investigation into Rate-Determining Factors in Electrophilic

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