Theoretical Investigation of the Mechanism of the Hock Rearrangement with InCl3 as Catalyst **

The Hock rearrangement is an acid catalyzed reaction involving organic hydroperoxides and resulting in an oxidative cleavage of adjacent C−C bonds. It has significant industrial applications, like the production of phenol (cumene process), but it remains scarcely used in organic synthesis. In addition, its detailed mechanism has never been studied. Thus, we report herein a theoretical study of the Hock rearrangement, using InCl3 as a Lewis acid catalyst. The aim of this work was to fully understand the mechanism of this fundamental reaction, and to rationalize the influence of the substrate electronic properties on the reaction outcome. Furthermore, the structure of the active indium(III) catalyst interacting with the peroxide substrate was investigated, revealing the co‐existence of several energetically close reaction pathways. The coordinated monomeric form of the Lewis acid emerges as the most active catalyst compared to dimeric species. However, we show that In2Cl6 species coordinated to the substrate are central in this catalytic cycle, primarily serving as a reservoir of active monomeric species.


Introduction
The Hock rearrangement is an acid-catalyzed reaction of an organic hydroperoxide that leads to the oxidative cleavage of a CÀ C bond. [1] This cleavage involves the migration of one of the adjacent carbons onto the closest oxygen atom of the hydroperoxide, concomitantly with the heterolytic cleavage of the OÀ O bond. The resulting oxocarbenium species usually reacts with water, leading to hydrolysis and the straightforward formation of oxygenated products (Scheme 1a).
Since the discovery of the cumene (1) process by Hock and Lang, [1] this reaction has played a crucial role in the production of millions of tons of phenol (3) and acetone (4) from cumene hydroperoxide (2) each year (Scheme 1b). [2] Moreover, this rearrangement has recently been used to produce artemisinin, an antimalarial drug. [3] However, harnessing its potential to develop new synthetic transformations remains a real challenge for organic chemists. Indeed, there have only been limited systematic studies on the selectivity of the Hock cleavage, [4][5][6] the effect of substituents, [7][8][9] the catalyst scope [10,11] or synthetic applications. [12][13][14][15][16][17][18][19][20] In a recent study, we demonstrated the potential of this reaction in synthesizing benzoxacycles (e. g. chromane 6) through tandem processes under InCl 3 catalysis (Scheme 1c). [21] By utilizing the electrophilic oxocarbenium intermediate generated during the Hock cleavage of indane (e. g. 5 a) or tetralin hydroperoxides, the usual hydrolytic process of the reaction could be bypassed by adding nucleophilic species. This work also established InCl 3 as a mild and versatile catalyst for promoting the Hock cleavage step.
In spite of this potential, unlike the Baeyer-Villiger rearrangement involving Criegee perester intermediates, [22][23][24][25][26][27][28] to the best of our knowledge the Hock reaction has never been theoretically studied. Furthermore, the aforementioned synthetic work raises fundamental issues. The relationship between the structure of the hydroperoxide substrate and the efficiency of the reaction remains underinvestigated. Another point of interest is the active form of the Lewis acid catalyst InCl 3 , which can potentially act as a monomer or dimer, [29][30][31][32] or as a cationic InCl 2 + species, [33] thereby questioning its superelectrophilicity. [34] In this study, we aim to address these gaps by reporting the first computational investigation of the Hock rearrangement at the DFT level. Our goal is to comprehensively assess the reaction mechanism and provide a clear understanding of the observed reactivity. This study also sheds light on the role and structure of the Lewis acid catalyst InCl 3 , which has already found numerous applications in organic synthesis. [29][30][31]35]

Results and Discussion
In accordance with our recent synthetic work, [21] this theoretical study focuses on the InCl 3 -catalyzed Hock rearrangement of indane (5 a and 5 b) and tetralin (5 c and 5 d) hydroperoxides, leading to chromane and benzoxepane products. Experimental observations [4,21] allow to anticipate several possible reactions from these reactants in the presence of a Lewis acid, depending on the coordination site of the catalyst or the migratory group (Scheme 2). Firstly, during the expected Hock rearrangement from Ia-d, two oxocarbenium species could be formed depending on the migration of the sp 2 (giving IIa-d, Pathway A) or the sp 3 carbons (giving IIIa-d, Pathway B). This would result in isomeric benzoxacycle derivatives 7 a-d or 8 a-d, respectively. Yet, the latter has never been observed in our experiments. Secondly, the elimination of the peroxide group could occur (Pathway C through IVa-d), leading to a benzylic carbocation Va-d and resulting in alkene 9 a-d upon proton elimination. All these reaction paths have been considered and computationally studied hereafter.
To complement the previous work, [21] an experimental study was performed with substrates 5 a-d to assess their reactivity in the presence of InCl 3 (Scheme 3). Pathway A shown in Scheme 2, corresponding to the migration of the aryl sp 2 carbon, appeared to be predominant for all substrates. Indane peroxides gave lactols 7 a/7 b, and dimeric derivatives such as 2,2'-oxydichromane 10 a (anti isomer, providing suitable crystals for crystallography, Scheme 3) or 2,2'-peroxydichromanes 11 a/ 11 b (two diastereoisomers; structure confirmed by HRMS). These two peroxyacetals indicated the release of hydrogen peroxide during the reaction (Scheme 2, Pathway C). However, indene 9 a, an apolar volatile product, was not identified during the isolation process. Conversely, tetralin peroxides afforded acyclic phenolic derivatives 12 c and 12 d (resulting from transient benzoxepane lactols 7 c and 7 d). Neither the regioisomeric isochromanes or 2-benzoxepanes (8 a-d) resulting from Pathway B nor the elimination products (9 a-d) from Pathway C were observed during this experiment. In the absence of an additional nucleophile, the reaction mixture, however, was more complex than that of our previous study, [21] probably due to numerous side-reactions occuring on such electrophilic products.
Our DFT study began with 1-indanyl hydroperoxide 5 a interacting with a single InCl 3 molecule (Figure 1). At first, the coordination of InCl 3 to the peroxide group provides two potential intermediates, Ia and IVa, depending on the oxygen involved. Both coordinations are exergonic, with respective energies of 4.6 and 4.5 kcal/mol. Transition state TS Ia-IVa , with an energy barrier of~3 kcal/mol, enables easy interconversion between the two intermediates. We first considered the elimination reaction originating from the coordination of the internal oxygen through intermediate IVa (see also Scheme 2, Pathway C). The formation of carbocation Va along with InCl 3 (OOH) À is endergonic by 17.3 kcal/mol. Since the dissociation of InCl 3 (OOH) À is more challenging than that of InCl 3 , this reaction pathway (C) is therefore disfavoured from 5 a, in agreement with the experimental results.
Alternatively, the coordination of InCl 3 to the external oxygen of 5 a (Ia) can lead to two possible intermediates, VIa through TS Ia-VIa (migration of the adjacent aryl sp 2 carbon) or VIIa through TS Ia-VIIa (migration of the adjacent alkyl sp 3 carbon). Both transition states involve a Hock rearrangement. However, the energy barrier of TS Ia-VIa (referred to as ΔG Hock in Figure 1, blue path) is favored by 9.5 kcal/mol compared to TS Ia-VIIa , and by 8.5 kcal/mol compared to the formation of Va. This strongly suggests that only the Hock rearrangement involving the sp 2 carbon can occur, as observed experimentally since the products stemming from TS Ia-VIa (7 a, 10 a, 11 a) were the only ones identified (total yield of 69 % for the Hock cleavage, Scheme 3).
In fact, this transition state (TS Ia-VIa ) first leads to Wheland intermediate VIa (benzenium), which connects to VIIIa without an activation barrier through TS VIa-VIIIa . A Similar intermediate does not exist in the case of sp 3 carbon migration. The stabilization of VIa through conjugation explains the lower energy of TS Ia-VIa compared to TS Ia-VIIa . To shed light on the electronic structure changes along this preferred reaction path, the intrinsic bond orbitals (IBO) [36][37][38] and the atomic charges in the framework of the natural bond orbital [39] (NBO) analyses were computed ( Figure 2). IBO enables visual tracking of the orbital relocalization during a molecular transformation. It shows that the cleavage occurs with an asynchronous movement of two pairs of electrons. From Ia to VIa, part of the aryl π cloud is transferred to the closest oxygen of the hydroperoxide (Figure 2a), enabling the formation of the CÀ O bond and the cleavage of the hydroperoxide OÀ O bond. From VIa to VIIIa, the cleavage of the CÀ C bond is associated with an electronic transfer from this σ-bond back to the aryl group ( Figure 2b). Furthermore, NBO analysis underlines the same phenomenon. The charges carried by the benzenium cycle in ortho and para positions of the reactive center are less negative in TS Ia-VIa and VIa than in the coordinated compound Ia. For example, the charge carried by the para carbon changes from À 0.23 to À 0.06 e, which corresponds to a loss of 0.17 e (Figure 2c). Following TS VIa-VIIIa, the formation of VIIIa enables the carbon atoms of the aromatic cycle to retrieve their original charge. Notably, the charges carried by the carbon atoms in the meta position remain the same along the reaction path, which is consistent with the classical mesomeric forms drawing of the pentadienyl cation moiety of VIa. [40] This electron transfer also suggests that the Hock rearrangement is favored by electronrich aryl rings.
The calculation for para-substituted substrates confirmed that π-withdrawing (5 e, 5 f) and π-donating (5 g, 5 h) substituents respectively increase and decrease the energy barrier of the Hock rearrangement (ΔG Hock ), in good agreement with the electronic density flow analysis during the course of the reaction ( Figure 3). Compound 5 i, with a π-donating methoxy group in the ortho position, shows a similar effect as 5 h. In addition, 5 j highlights that the meta position has no influence on the barrier of the rearrangement, in good agreement with the above analysis. These results are confirmed by experimental observations regarding the reactivity of substituted substrates: [21] for example, the presence of a strongly πdonating group such as a OMe in the para position induces an enhanced reactivity of the hydroperoxide substrate, which no longer allows its isolation, whereas the reactivity is not modified when the same substituent is in the meta position.
Stemming from VIIIa, the release of InCl 3 (OH) À to form the oxocarbenium species IIa is endergonic by 20.2 kcal/mol. The release of the catalyst alone from VIIIa to generate 7 a is a much less energetically costly process, as it is only endergonic by 5.0 kcal/mol. With regards to this weak coordination affinity of the catalyst for both the starting material and the product compared to the important exergonicity of the Hock rearrangement, it appears that the turnover of the catalyst is supported. Yet, this fact does not address the catalyst's active structure (vide infra).
To complete this work, the Hock rearrangement of tertiary hydroperoxide 5 b and that of tetralin hydroperoxides 5 c and 5 d was computationally studied, allowing comparison with the previous case (Table 1). Regarding tertiary hydroperoxide 5 b, a better stabilization of benzylic carbocation intermediates Vb is expected, favoring a competing elimination of the hydroperoxide over the Hock rearrangement. The formation of the tertiary carbocation Vb from Ib is easier than that of the secondary one (step Ia!Va), being endergonic by only 10.7 kcal/mol (17.3 kcal/mol for Va). However, the Hock rearrangement remains consistently favored (TS Ib-VIb ), in agreement with experimental results in which no carbocation-derived compound was observed. [21] Furthermore, the Hock reaction is favored by~2 kcal/mol (ΔG Hock ) when involving a tertiary hydroperoxide rather than a secondary one (Table 1, entry 4). As for 5 a, substrate 5 b led to the direct formation of 7 b without going through the higher energy oxocarbenium intermediate IIb (Table 1, entries 6-7). Similar observations were made for 5 c and 5 d, while these rearrangements did not stop at the lactol products but proceeded to the thermodynamically favored open forms 12 c and 12 d, unlike substrate 5 a, which led to the more stable lactol 7 a.   A final question arose concerning the exact nature of the catalyst. Recent studies showed that the catalytically active species of Lewis acids of type AX 3 (A = Al, Ga, Fe, In and X = H, Cl) are in the dimeric form A 2 X 6 , or in the form of a superelectrophile like X 2 AÀ XÀ AX 3 . [32][33][34]41,42] The Hock rearrangement of 5 a was thus investigated in the presence of dimeric InCl 3 (Figure 4, not all intermediates are presented, see Supporting information for details).
The dimerization of InCl 3 gives rise to a stable homodimer (In 2 Cl 6 ) favored by 9.6 kcal/mol. This dimer is bridged by two chlorin atoms and can coordinate to the peroxide, leading to complex IXa. As expected, this coordination is less stabilizing than that of monomeric InCl 3 (+ 1.7 vs À 4.6 kcal/mol) and is slightly endergonic due to entropic terms. Multiple processes are possible from this intermediate and have been studied in detail. Firstly, In 2 Cl 6 can dissociate, leading to a free InCl 3 monomer and complex Ia from which the transition state of the Hock rearrangement (TS Ia-VIa ) is located at + 13.9 kcal/mol relative to the reference (5 a + In 2 Cl 6 ) (Figure 4, red pathway).
Interestingly, IXa can also reorganize to structure Xa bridged by a single chlorin atom between the two indium atoms, thus adopting the Cl 2 InÀ ClÀ InCl 3 scaffold. Unexpectedly, unlike Ga 2 Cl 6 catalysis displaying gallium superelectrophilic species during the reorganization of 1,6 enynes [32] or the methylation of benzene, [42] the dimeric species Cl 2 InÀ ClÀ InCl 3 is not a superelectrophile able to promote the Hock rearrangement. Indeed, not only Xa is not significantly more stable than IXa (À 0.5 kcal/mol), but more importantly the activating barrier for the Hock rearrangement is in this case higher (+ 11.2 kcal/ mol from Xa to TS Xa-XIa ) than with monomeric InCl 3 (+ 8.9 kcal/ mol from Ia to TS Ia-VIa ). NBO analysis underlines the fact that the In atom coordinated to the hydroperoxide group in Xa has a greater positive charge (+ 1.74 e) than the other In atom (+ 1.61 e). However, the InÀ ClÀ In bonds show that the Cl atom is closer by 12 pm to the In atom coordinated to the peroxide ( Figure 5).
These structural and electronic differences in the two In atoms of Xa do not seem sufficient to allow a representation as [InCl 2 + -InCl 4 À ]. Finally, further calculations demonstrated that InCl 2 + can be a superelectrophilic catalyst for the Hock rearrangement, with an energy barrier reduced to + 2.2 kcal/ mol from the complex 5 a-InCl 2 + (XIIa) to TS XIIa-XIIIa . However, the high endergonicity of the formation of this complex (+ 21.4 kcal/mol from Xa) precludes any possibility for InCl 2 + to be the catalyst of this reaction.  Finally, we investigated the possible coordination of In 2 Cl 6 to two molecules of peroxide substrate (5 a), leading to symmetrical, dimeric intermediate XIVa (5 a · In 2 Cl 6 · 5 a). Even though this process is weakly endothermic, this double coordination is consistent with the presence of an excess of substrate 5 a during the reaction.
From XIVa, three possible pathways can be envisaged: (i) the reversible formation of IXa by releasing a molecule of hydroperoxide (exergonic by 1.7 kcal/mol), finally resulting in monobridged Xa and the In 2 Cl 6 -catalyzed Hock cleavage with an energy barrier of + 12.4 kcal/mol compared to the reference; (ii) the direct rearrangement of a peroxide molecule bound by In 2 Cl 6 · 5 a through transition state TS XIVa-XVIa located at + 15.8 kcal/mol relative to the reference. This indicates that the coordination of a second reactant molecule 5 a to In 2 Cl 6 decreases its electrophilicity, as the activation barrier of the Hock rearrangement step increases from + 11.2 kcal/mol (from Xa to TS Xa-XIa ) to + 12.4 kcal/mol (from XIVa to TS XIVa-XVIa ). Surprisingly, this decrease in electrophilicity is not observed when In 2 Cl 6 is bound by a lactol, as the activation barrier goes from + 11.2 kcal/mol (from Xa to TS Xa-XIa ) to + 10.5 kcal/mol (from XVIa to TS XVIa-XVIIa ), meaning that this path would favor In 2 Cl 6 · 7 a as the catalyst of the Hock reaction; (iii) Lastly the dissociation of dimeric XIVa releasing two molecules of monomeric complex Ia, is associated to a gain of 3.0 kcal/mol. The latter should thus be the privileged pathway as it leads through TS Ia-VIa to the InCl 3 -catalyzed rearrangement endergonic by only 9.3 kcal/mol compared to the reference.
Starting from two complexes Ia, the rearrangement to VIIIa can occur twice in a row, with the driving force each time being the significant energy gain associated with the formation of two new CO bonds. The most favorable pathway for dissociating product 7 a from the catalyst firstly involves the dimerization of VIIIa to XVIIa (7 a · In 2 Cl 6 · 7 a) associated to a cost of 1.3 kcal/mol. Then, the consecutive dissociation of two molecules of 7 a to regenerate In 2 Cl 6 occurs with a global release of 0.9 kcal/mol (see Figure S1 for the complete profile). It should be noted that this dissociation can also occur after the first transformation, going first through the formation of the heterodimer 7 a · In 2 Cl 6 · 5 a (XVIa). In contrast to the rearrangement step, which has an activation barrier of roughly 9 kcal/mol and corresponds therefore to the rate-determining step of the catalytic cycle, these dissociation processes require very little energy (< 3 kcal/mol) and are practically thermoneutral.
This study thus points out to monomeric InCl 3 as the active catalyst of the rearrangement. It is important to note however that this monomeric catalyst is generated from XIVa and only exists in a coordinated form. While InCl 3 has a similar affinity for the substrate (5 a) and the product (7 a), its dimerization is a more favorable process. Consequently, free monomeric InCl 3 does not exist in solution, while the dimer In 2 Cl 6 can be regenerated at the end of the reaction, finally explaining the turnover of this catalyst (Scheme 4).
One last point needs to be addressed. It is well known that evaluating entropic terms in static DFT calculations is approximate, and this can have consequences when the number of molecules changes during the reaction path, as is the case in this study. [43] To verify the influence of this point, several approaches have been attempted to calculate these corrective terms for the energy profiles in Figures 1 and 4 (Figures S3 and  S4, respectively). Regardless of the method used to estimate the entropic terms, the mechanism presented in Figure 1 remains unchanged. However, the relative Gibbs free energies of the transition states in Figures 4 can be altered. Indeed, when a scaling factor of 0.5 is applied to the entropic terms, the lowest energy pathway goes through the transition state TS XIVa-XVIa , with TS Ia-VIa slightly higher in energy (+ 1.8 kcal/mol). Therefore, it is likely that, depending on the experimental conditions of temperature and concentration, the reaction pathway involving direct Hock rearrangement within the 5 a · In 2 Cl 6 · 5 a dimer coexists with the pathway involving the dissociation of this dimer (Scheme 4).

Conclusions
In conclusion, this study of the InCl 3 -catalyzed Hock rearrangement elucidates for the first time the details of the electronic mechanism of this reaction. In particular, the demonstration that a key benzenium intermediate is involved in the reaction gives clues for better stabilization of this intermediate through the choice of appropriate substituents. This benzenium intermediate is a consequence of the migration of the aryl sp 2 ipsocarbon onto the internal peroxide oxygen, with concommittant cleavage of the OÀ O bond. The cleavage of the CÀ C bond appears to be consecutive to the benzenium formation, highlighting an asynchronous mechanism.
Furthermore, we propose that the catalysis of this reaction (Scheme 4) involves a monomeric complex of InCl 3 coordinated to one molecule of hydroperoxide substrate (InCl 3 · ROOH), originating from the cleavage of the symmetrical homodimer In 2 Cl 6 · (ROOH) 2 , although direct rearrangement from this homodimer could also be a competing pathway due to entropic effects. By decreasing the activation barrier of the Hock rearrangement, this coordinated InCl 3 monomer behaves as a better electrophile compared to the dimer that is significantly less activating (e. g. 8.9 kcal/mol vs. 11.2 kcal/mol for substrate 5 a). Therefore, unlike previous studies highlighting superelectrophilic dimeric species such as A 2 X 6 or AX 2 + AX 4 À among the group 13 elements, [32,34,42] our study shows the absence of superelectrophilicity for the dimeric In 2 Cl 6 species during this Hock rearrangement. These species are however central in our catalytic cycle, serving as a reservoir of active monomeric catalytic species. Overall, while monomeric species are mostly considered in In(III)-based methodologies, we can reasonably suggest that homodimeric and other coordinated species should be given better attention as part of the catalytic cycle.

Computational Details
The calculations were performed using Gaussian 09 software. Geometry optimizations and transition states (TS) were obtained employing the 6-31G(d,p) basis set [44,45] on all atoms except for indium which was modeled using LANL2DZ effective core potential and associated double-zeta valence basis, [46] in combination with B3LYP-D3 functional. [47,48] This level of theory previously proved reliable to study the Baeyer-Villiger mechanism. [49] Both TS and geometry optimization were confirmed using frequency calculations at the same level of theory. Solvent effects were included in the calculations thanks to IEFPCM continuum solvation model [50] using dichloromethane as solvent. For every TS found, intrinsic reaction coordinates (IRC) [51,52] were calculated to ensure that the corresponding TS is connected to the proper reactant(s) and product(s). The energy obtained were improved thanks to single point calculation with the same method and aug-cc-pVTZ basis set [53] for all atoms except Indium. Indium was modeled using the multi electron fit fully relativistic effective core potential ECP28MDF [54] in combination with basis set aug-cc-pVTZ-PP. The three-dimensional optimized stuctures were prepared using CYLview20. [55] Intrinsic bond orbitals (IBO) analyses were performed using Iboview software [36][37][38] on the optimized geometries with default method (PBE/def2-TZVP) to generate Kohn-Sham wave functions. IBO analyses enable to visually follow the movement of electrons during a molecular transformation thanks to the representation of localized molecular orbitals. NBO charges were computed using NBO6 software at the IEFPCM(CH 2 Cl 2 )-B3LYP-D3/6-31G(d,p) -LanL2DZ level. The Gibbs free energies presented in this article are IEFPCM(CH 2 Cl 2 )-B3LYP-D3/aug-cc-pVTZ(À PP)// IEFPCM(CH 2 Cl 2 )-B3LYP-D3/6-31G(d,p) -LanL2DZ electronic energies modified with thermal corrections from IEFPCM(CH 2 Cl 2 )-B3LYP-D3/ 6-31G(d,p) -LanL2DZ calculations. Thermal corrections to Gibbs free energies were calculated using Grimme's quasi-rigid rotorharmonic oscillator approximation at 298 K [56] using the Goodvibes program. [57] The influence of the computational level used on the studied reaction profiles is described in the SI.

Author Contributions
The manuscript was written through contributions of all authors.