Rinaldo Poli

Michael P Shaver

ATRP and OMRP of Styrene Mediated by Diaminobis(phenolato)iron(II) Complexes: A DFT Study

This study has addressed the radical polymerization of styrene mediated by the diaminobis(phenolate) complexes [Fe(O-2,4-Y2C6H2-5-CH2)2NCH2CH2NMe2], abbreviated as [Fe II ].

The system is known to be well controlled when Y = Cl but not when Y = alkyl. The control was proposed to occur by a dual ATRP+OMRP mechanism. We have used DFT calculations to address the Y = Cl and Y = CH3 systems. The growing radical chain, ATRP dormant chain and OMRP dormant chain were simplified to PhCH(CH3) • , PhCH(CH3)-Cl and [PhCH(CH3)-Fe III ]. The idealized ATRP activation/deactivation equilibrium involves [Fe III -Cl] (I Y ) and PhCH(CH3) • on the active side and [Fe II ] (II Y ) and PhCH(CH3)-Cl on the dormant side, whereas the OMRP activation/deactivation relates [Fe II ] and PhCH(CH3) • with [PhCH(CH3)-Fe III ] (III Y ). A benchmarking of various functionals against the known spin properties of alkylporphyriniron(III)

shows B3PW91* to be a suitable functional. For the purpose of bond dissociation energy calculations, a dispersion correction was made (B3PW91*-D3). For both Y systems, the ground state is a spin sextet for I, a spin quintet for II and a spin quartet for III. The calculations show a greater energy cost for the ATRP activation process involving Cl atom addition to II Cl to yield I Cl (7.2 kcal/mol) relative to the process transforming II Me to I Me (2.1 kcal/mol). On the other hand, the alkyl addition transforming II to III provides slightly greater stabilization for II Cl (27.1 kcal/mol) than for II Me (26.1 kcal/mol). As a result, both ATRP and OMRP trapping processes provide greater stabilization for the Y = Cl system, in agreement with the observed better control. The charge analysis attributes these minor but determining energy differences to the inductive electron withdrawing effect of the phenolato Cl substituents. The ATRP and OMRP activation/deactivation pathways have been analyzed in relation to the spin state change; they show in each case the absence of an activation barrier, both processes corresponding to spin allowed single-state pathways occurring on the quartet (OMRP) and quintet (ATRP) potential energy surfaces. Molecular volume calculations suggest that the balance between ATRP and OMRP may shift in favor of the latter at higher pressures.

Introduction

Reversible deactivation radical polymerization (RDRP) is now a well established technique for the assembly of complex, precision-controlled, macromolecular architectures. [START_REF] Matyjaszewski | Macromolecular Engineering: Precise Synthesis, Materials Properties, Applications[END_REF] Numerous strategies exist for retarding the termination of growing macromolecular radicals, thereby prolonging the chain life and allowing the generation of materials with characteristics that approach those of ideal living polymers. Among these, atom transfer radical polymerization (ATRP) has emerged as one of the most general and robust methods. Inspired by the initial discovery of active Cu I /Cu II -X [START_REF] Wang | [END_REF]3 and Ru II /Ru III -X 4,5 redox couples (X = halogen, typically Cl or Br), complexes of many other metals have been used to control an expansive monomer scope. 6,7 One of the challenges of this synthetic method is contamination of the isolated polymer by the metal complex. Although the metal complex exerts a catalytic function, namely it is not incorporated in the halogen chain-end functionalized polymer (Scheme 1), significant quantities of the potentially toxic or colored metal remain entrapped in the polymer, limiting its possible applications, particularly in the biomedical sector. Even though solutions exists for limiting the amount of catalyst down to the ppm level, 8 there has been interest in developing ATRP catalysts based on iron, which is an abundant, inexpensive and especially biocompatible element. 9 generic metal, x for its formal oxidation state and L/ for its coordination sphere), starting from a R0X initiator (X = halogen). ATRP catalyzed by iron complexes was first introduced in 1997 10 and has since become a very active area of research. The vast majority of the investigated systems are based on a reversible activation/deactivation equilibrium involving the Fe II /Fe III couple (i.e. Mt x = Fe II in Scheme 1), supported by many different types of neutral ligands, L, including phosphines, imines, amines and combinations thereof, with halides, alkoxides, phenolates and others as anionic ligands. 11 One remarkable system is [FeCl2(α-diimine)] where α-diimine = R 1 N=C(R 2 )C(R 2 )=NR [START_REF] Matyjaszewski | Macromolecular Engineering: Precise Synthesis, Materials Properties, Applications[END_REF] , introduced by Gibson and co-workers and applied to the polymerisation of styrene and acrylate monomers. [12][13][14] This system acts as a catalyst for controlled chain growth when R2 = H, whereas complexes with R2 = aryl lead, in general, to polymers with low-molecular weights that do not increase with conversion, indicating a catalyzed chain transfer (CCT) process. [12][13][14] This phenomenon was interpreted as resulting from a competing trapping of the growing radical chain by the excess Fe II catalyst, leading to an organometallic Fe III dormant chain that has the possibility to eliminate the chain by β-H elimination and start a new chain by insertion of monomer into the resulting Fe III -H bond. 15 This phenomenon is an example of a more general scheme, first demonstrated with Mo compounds, 16 where the three basic processes of controlled chain grown by ATRP, controlled chain growth by OMRP (organometallic mediated radical polymerization), [17][18][START_REF] Poli | Polymer Science: A Comprehensive Reference[END_REF][START_REF] Allan | [END_REF] and CCT can interplay, because the same [L/Mt x ] species can act as ATRP catalyst, OMRP chain trap and CCT catalyst, respectively. 21 More recently, new Fe catalysts based on a functionalized bis(phenolate) ligand has been developed that show no apparent interference of CCT. 22 The Fe III complexes used to mediate the polymerizations (Scheme 2) do not have the appropriate oxidation state for direct application as an ATRP catalyst, but can be used under reverse ATRP conditions (R-ATRP): A conventional radical initiator is used to abstract the halogen atom, generating the ATRP Fe II activator and the halide initiator in situ. The convenience of this method is that the Fe III complex is air stable, whereas the corresponding Fe II complex is extremely air sensitive. A few of these systems, particularly those with dimethylaminoethyl functionality and chlorinated phenolates, led to rapid, extremely efficient and well controlled polymerizations of substituted styrenes and methyl methacrylates. For instance, the system with the CH2CH2NMe2 donor, R 1 =R 2 =Cl and X = Br yielded a PMMA with Mn = 10500 (vs. a theoretical Mn of 8378) and Mw/Mn = 1.21 at ca. 99% monomer conversion, whereas related complexes with R 1 and R 2 = alkyl gave polymers with a greater discrepancy between observed and theoretical Mn and Mw/Mn > 1.5. 22 Scheme 2. Functionalized bis(phenolate) Fe III complexes used in the reverse ATRP of styrenes and MMA.

Two points are of interest for this system. The first point concerns the proposed mechanism of control. Experimental mechanistic investigations, carried out on the dimethylaminoethyl derivative with the 2,4-dichloro-substituted phenolates for the polymerization of styrene, suggest that the Fe complex may exert a dual (ATRP+OMRP) controlling mechanism, the radicals being trapped by both the Fe III -X and the Fe II complexes to yield X-terminated and Fe III -terminated dormant chains, respectively (see Scheme 3, R = Cl). 23 In this case, due to the challenges of isolating and characterizing the parent Fe II (II R ) and Fe III -alkyl (III R ) species, this evidence is largely circumstantial or indirect. The second point of interest is the dramatic effect of the arene substituents R 1 and R 2 on the controlling ability of this system. Whereas the nature of the halogen X and donor function D did not significantly affect the mediator performance, only when using R 1 = R 2 = Cl was it possible to obtain polymers with molecular weights in agreement with theory and with narrow molecular weight distributions. Scheme 3. Proposed dual controlling mechanism for the polymerization of styrene.

Dual (ATRP+OMRP) controlling mechanisms for radical polymerization have also been previously described for complexes of molybdenum, 16,24,25 chromium 26 and osmium. 27 In the latter case, DFT calculations gave support for the simultaneous action of both trapping equilibria, 28 whereas for a chromium system it was concluded that control is solely imparted by OMRP trapping, even under ATRP conditions. 26 In this contribution, we present the results of a computational investigation aimed at investigating the dual controlling mechanism for the Fe complex in Scheme 3 and at understanding the peculiar effect of the arene substitution.

Computational details

The computational work was carried out using the Gaussian09.D01 suite of programs. [START_REF] Frisch | Revision C.01[END_REF] The geometry optimizations were performed without any symmetry constraint using the BPW91, B3PW91*, B3PW91, M06 and M06L functionals. The B3PW91* is a modified version of the B3PW91 functional, in which the c3 coefficient in Becke's original three-parameter fit [START_REF] Becke | [END_REF] to thermochemical data was changed to 0.15. The 6-31G basis functions were used for all atoms except Fe and Cl. The Cl atom was described with the 6-31G(d) basis set, whereas the SDD basis set and ECP were used for the Fe atom, augmented by an f polarization function (α = 2.462). 31 The unrestricted formulation was used for all open-shell molecules, yielding only minor spin contamination. Maximum deviations for <S 2 > at convergence were 0.855 (vs. the theoretical value of 0.75) for spin doublets, 4.158 (vs. 3.75) for quartets, 6.022 (vs. 6) for quintets and 8.767 (vs. 8.75) for sextets. Corrections for dispersion on selected results were carried out at the fixed B3PW91* optimized geometries using Grimme's D3 empirical method (B3PW91*-D3), using SR6 and S8 parameters identical to those optimized for B3PW91. 32

Results

(a) General considerations.

Two systems were chosen for our computational investigation, one being a system that leads to a well controlled polymerization and one for which the control is poor. Both systems contain the Me2NCH2CH2 arm on the amine-bis(phenolate) ligand (refer to Scheme 2), the first one having R 1 = R 2 = Cl, the second one with R 1 = R 2 = CH3. Both systems are exact replicas of catalysts studied, with the Cl derivative extensively investigated and the CH3 system serving as a computationally inexpensive but electronically similar group to the tBu functionality, as confirmed by recent experimental polymerizations. 23 Referring to the compound numbering in Scheme 3, the complexes that have been investigated will be referred to as I Cl , II Cl , III Cl for system one and as I Me , II Me , III Me for system two. For the organometallic dormant species III, the polymer chain was modeled by a 1-phenylethyl group (namely, the entire chain prior to the last monomer unit was replaced by an H atom).

Iron complexes are a particularly challenging task for computational chemistry, because of their variability of spin state that can be fine-tuned by the ligand environment. 33 Coordination compounds with low-field ligands tend to yield the highest possible spin state, namely sextet (five unpaired electrons, S = 5/2) for Fe III and quintet (four unpaired electrons, S = 2) for Fe II . However, alkyl ligands establish more covalent bonds with the metal center, strengthening the ligand field and leading to electron pairing phenomena in organometallic derivatives. 34 This can lead to Fe III ground states with an intermediate spin (quartet, S = 3/2) or even a low spin (doublet, S = 1/2). Thus, whereas the Fe III -X complex of interest in this investigation (Scheme 2) and the Fe II complex that results from X atom abstraction certainly adopt a high spin state, a question arises about the possible spin state of the organometallic dormant species.

A further challenge concerns the quality of the computational method. When the interest is focused on systems that can adopt more than one possible spin state, low-level monoelectronic Hartree-Fock methods are not reliable and only more sophisticated and computationally expensive strategies that take electron correlation into account can lead to satisfactory results. On the other hand, the effects that we are probing rely on modifications in a remote area of the molecule, far from the metal. Ligand simplification is therefore not prudent. Given the size of the molecules of interest, the general method offering the best compromise in terms of accuracy and computational time is density functional theory. However, no clear guideline in terms of the best functional to use exists; benchmarking is necessary, using experimentally known systems that are as close as possible to those of interest. Previous work on Fe systems with variable spin states has shown that functionals based on the local approximation and on the generalized gradient approximation tend to overestimate the stability of the lower spin state. 35 On the other hand, hybrid functionals such as the popular B3LYP and B3PW91 show the opposite trend, generally overestimating the stability of the higher spin state. 35 The use of modified hybrid functionals, where the percent of exact Fock exchange was decreased to some extent from that of standard hybrid functionals, has often provided an optimum choice for computational accuracy. [35][36][37][38][39] However, no such benchmarking of this functional has been conducted for organometallic Fe III systems.

(b) Benchmarking functionals on organometallic Fe III complexes.

The putative organometallic dormant species III (Scheme 3) could not be properly characterized in terms of its spin state properties and model compounds with simple alkyl ligands

are not yet available for this system. Indeed, alkyliron(III) complexes appear as rather fragile species when supported by low-field ligands, which is indeed a reason why they are of interest in OMRP. For benchmarking purposes, we sought organometallic compounds reported in the literature that were isolable, stable and magnetically characterized. 34 Among these, we were particularly attracted by the family of (porphyrin)Fe III R compounds, since the spin state was shown to depend on the nature of the alkyl group. 40 The systems were reported to adopt a high spin state (sextet) or a low spin state (doublet) depending mostly on the nature of the axial ligand (high spin for perfluoroaryl derivatives such as C6F5, low spin for alkyl and non-fluorinated groups). The spin state does not seem to depend on the porphyrin substituents, but we did not wish to simplify the porphyrin system for our calculations (e.g. by replacing the various substituents on the porphyrin periphery with H atoms), nor to treat these groups at the molecular mechanics level. The smallest experimentally investigated porphyrin system was tetraphenylporphyrin (TPP). Hence, we carried out calculations in the low and high spin states for (TPP)Fe(CH3) and (TPP)Fe(C6F5). To reduce computational costs the spin state difference was evaluated with all functional at the fixed geometries optimized at the B3PW91* level rather than systematically reoptimizing the geometry with each functional (geometries are reported and discussed in SI). The essential energy results are shown in Table 1. However, specific reoptimizations were carried out for the high spin systems, at the BPW91 level for R = C6F5 and at both the BPW91 and B3PW91 levels for R = CH3. The geometries changed insignificantly and the energy decreased only by ca. 3 kcal/mol for the BPW91 calculations and by only 0.1 kcal/mol for the B3PW91 calculation. [35][36][37][38][39] we have elected to continue our investigations with this modified hybrid functional.

(c) The ATRP equilibrium.

For system I, an X-ray structure is available in the literature for I Me , 41 providing the opportunity to test the suitability of the functional to reproduce experimental geometries. The complex was also shown to adopt a high spin ground state from magnetic susceptibility measurements. However, we have also carried out the geometry optimization of the quartet ground state, for later comparison with the quartet alkyl species III. The selected bond distances and angles reported in Table 2 demonstrate good agreement between the experimental and optimized geometry. The greatest discrepancy concerns the bond distances to the neutral N donor atoms, Fe-NMe2 (eq) and Fe-N (ax), which are overestimated by ca. 0.08 Å. Representations of the optimized structures are shown in Figure 1. On going from the sextet to the quartet state for each compound, structural changes are largely as expected: a general shortening of the bond lengths is observed, in particular the Fe-N (ax) bond (ca. 0.2 Å), with a concomitant widening of the O-Fe-O angle. Thus, while the sextet structure is closer to an ideal trigonal bipyramid, the quartet structure can better be described as a distorted square pyramid, with the NMe2 donor group occupying the apical position. This geometrical change can be conveniently monitored by the well known τ parameter, 42 the values of which for the different structures are also reported in Table 2. The large bond shortening is accentuated by the fact that the high spin configuration contains one electron in a metal-ligand antibonding orbital, which is removed upon electron pairing when switching to the intermediate spin configuration. On going from I Me to I Cl , there is a slight shortening of the Fe III -Cl distance (by 0.03 Å in the sextet state and 0.04 Å in the quartet state). This may be attributed to an increase of the effective positive charge on the Fe atom, as a result of the inductive effect of the phenolate ring Cl substituents. Indeed, the calculated Mulliken charge on Fe increases on going from I Me to I Cl (Δq(Fe) = +0.032). This inductive effect causes a greater transfer of charge from the Cl ligand to Fe, a greater covalence and a stronger bond, correlating with the decreased negative charge of the Cl -ligand (Δq(Cl) = +0.052). Note that this effective charge is reduced more significantly when moving from the sextet to the quartet state and the Fe positive charge is consequently reduced. This is associated with the removal of one electron from an antibonding orbital and with the Fe-Cl bond shortening and agrees with the expected greater Fe-Cl bond covalence in the lower spin state. The calculations yield greater stability for the sextet state, in agreement with the experimental evidence, with a sextet-quartet gap that is only slightly greater for I Cl . The optimizations of the I Me sextet and quartet systems were also carried out at the M06 level, yielding a much greater sextet-quartet gap and a less accurate geometry for the sextet (further details provided in the SI).

This confirms that M06 is a less suitable functional for this system.

System II has not been structurally characterized. This extremely air sensitive compound could be isolated in the case of II Cl , but only with co-crystallized LiCl to yield a Fe2Li2Cl2-core dinuclear species. 23 A possible reason for the instability of this complex is the tension imposed by the tetradentate ligand, not allowing relaxation to the preferred tetrahedral geometry for 4coordinate Fe II . The geometry optimization of II was carried out only in the quintet state, the undoubtedly preferred spin state for this complex given the low coordination number and the weak ligand field, as experimentally verified for other similar compounds (i.e. FeCl2(αdiimine). 43 The selected bonding parameters are collected in Table 3 and optimized geometries are shown in Figure 2. The effective charge increase for the Fe atom on going from II Me to II Cl (Δq = +0.065) is greater than for system I (Δq = +0.032). The OMRP equilibrium involves species II (vide supra) as a spin trap and III as dormant species (Equation 2). The latter was modeled by shortening the polymer chain to the CH(Ph)CH3

group.

The geometry optimization of III was the most challenging part of this study, because stable model compounds do not exist and the spin state is unknown. Given the large size of the molecule, a preliminary investigation was carried out on a system containing a simple CH3 as the alkyl group and H atoms on the 2 and 4 positions of the phenolate benzene rings. This system, abbreviated as III H , was optimized in all possible spin states (sextet, quartet and doublet). The details of the optimized structures are given in the SI. The energetic results are in favor of an intermediate spin state for this system, slightly more stable than the high spin state (at +4.6 kcal/mol relative to the quartet) and much more stable than the low spin state (at +18.9 kcal/mol). Calculations on a related system, a Fe(CH2Ph)Cl2(α-diimine) complex, also yielded a quartet state lower than the sextet, whereas the double state was not calculated. 44 Using the fixed B3PW91* geometries for single point calculations and restricting the analysis to the quartet-sextet gap, the other functionals also yielded a quartet ground state (Esext-Equart = 8.5 for BPW91, 3.1 for B3PW91, and 0.9 kcal/mol for M06L) except for the M06 functional, for which the sextet state was found more stable than the quartet by 3.2 kcal/mol. The subsequent calculations on the full system were therefore carried out only in the quartet state.

It is interesting to observe that, upon increasing the ligand field strength from halide to alkyl, the preferred high spin state of the former switches to the low spin state for the alkylporphyrin systems (vide supra) while the intermediate spin state is favored for the diaminobis(phenolato)alkyl system. This is certainly related to the different constrained geometries of the two systems: the porphyrin derivatives force the strong alkyl ligand to occupy the apical position of a square pyramidal geometry, therefore inducing strong destabilization of the dx2-y2 orbital and dz2 orbitals, whereas system III can accommodate the alkyl group in a pseudo-basal position.

Indeed, the geometry of III, shown in Figure 3, is closer to a square pyramid than to a trigonal bipyramid, with quite similar angular parameters to those of the quartet chloride analogue (cf.

Table 4 with Table 2), and with the 1-phenylethyl group occupying a pseudo-basal position.

However, all the bonds between the Fe atom and the diaminobis(phenolate) ligand are significantly longer in III relative to I with the same ligand. The Fe-NMe2 and Fe-O distances in III are even longer than those in the corresponding complex I in the higher (sextet) spin state, whereas the Fe-N distances in III are shorter than the same distances in sextet I, but still > 0.1 Å longer than in quartet I. This peculiar effect may be related to the greater steric encumbrance of the alkyl group in III relative to Cl in I. The most stable optimized geometry has the methyl group of the 1-phenyethyl ligand facing the "empty" coordination site, underneath the square base, opposite to the apical NMe2 ligand. An alternative rotamer where the phenyl group faces the same site (shown in SI) is slightly higher in energy (+4.6 kcal/mol). A possible reason for this energy difference is a weak interaction between the α-H atom and one of the phenolate O atoms. This is also supported by the small Fe-C-H angle, approaching 90° (Table 4). In the higher energy isomer, the steric preference of the Ph ring forces the α-H atom to be further away comparable to that reported recently for the BDE of methylcobalamin on going from B3LYP to B3LYP-D (ca. 15 kcal/mol). 45 The underestimation of BDE's by hybrid functionals and the effect of the dispersion correction on these calculations is well established. 46,47 The reason for the small effect of the dispersion correction on the ATRP equilibrium is the cancellation of error given the compensation of one bond breaking with one bond making.

(e) Comparison of the two equilibria and dual control

The energetic results of the ATRP and OMRP activation/deactivation equilibria for the two investigated systems are summarized in Figure 4. They indicate that the system with the 2,4dichloro-substituted phenolate ligands affords more stable dormant species for both ATRP and OMRP deactivation modes. The relative stabilization trends can be understood on the basis of the electron withdrawing effect of the 2,4-Cl substituents on the phenolato benzene rings. These electron-withdrawing Cl atoms disfavor the ATRP activation because they remove electron density from Fe II , making it more difficult for the system to be further oxidized to Fe III -Cl by the ATRP activation process. The calculated Mulliken charges support this view, with the charge of +0.610 in II Me becoming +0.669 in I Me (Δq = +0.059) for the dimethyl-substituted system, whereas the same process for the dichloro system involves a metal charge increase from +0.675 in II Cl to +0.701 in I Cl (Δq = +0.026). In the formation of the organometallic dormant species, on the other hand, the newly formed Fe III -CH(Ph)CH3 bond is less polar, given the lower electronegativity of carbon. The metal charge changes very little during the OMRP trapping process for the dimethyl system (from +0.610 in II Me to +0.613 in III Me ; Δq = +0.003) and actually decreases for the dichloro system from +0.675 in II Cl to +0.644 in III Cl (Δq = -0.031).

We can therefore assume that the Fe-C bond formation in the OMRP trapping process provides better stabilization for the dichloro derivative. Good control in RDRP occurs when the active radical species equilibrates with at least one thermodynamically favored dormant species. Greater relative stability of the dormant species leads to better control by promoting lower radical concentrations. Thus, the results in Figure 4 agree with the experimental evidence of better control imparted by the I Cl /II Cl /III Cl system. More specifically, the polymerization is well controlled when carried out under ATRP conditions, although a significant fraction of the polymer chain-ends were not halogen end-capped. The dynamics of the controlled polymerization process in the presence of an ATRP/OMRP interplay is well understood 21 generates the propagating radicals in equilibrium with the halogen-terminated dormant chain plus the catalyst II. However, since the ATRP equilibrium is displaced toward complex II, this complex is also available to trap the active chains leading to the OMRP dormant chain III. The OMRP trapping synergistically interplays with the ATRP trapping to further decrease the steadystate radical concentration in solution and to increase the system controllability. When initiated under ATRP conditions, concurrent OMRP trapping cannot be avoided. However, when initiated under OMRP conditions, the polymerization can be regulated by just this mechanism, without participation of ATRP trapping. A styrene polymerization experiment carried out under OMRP initiation conditions with system II Cl , which was generated by in situ reduction of I Cl with ascorbic acid, and AIBN as radical source gave again a controlled polymerization, although not as well controlled as in the presence of the two synergistically interplaying equilibria. 23 However, as the in situ reduction by ascorbic acid is likely not complete in the timescale of the initiation to establish the dynamic equilibria it is difficult to eliminate a mixed, or indeed an ATRP-only mechanism from operating.

(f) Interpretation of computational results when predicting experiment

Several notes of caution should be made regarding the veracity of conclusions drawn. The first is the suggestion from the computational data that the OMRP equilibrium would be the dominant control mechanism in this system. It is dangerous to draw quantitative significance from the calculated energy differences. As pointed out at the beginning of the Results section, the choice of functional highly affects the absolute energy values and also the relative ones since there is a change of spin state during the activation/deactivation process. Although benchmarking has guided us toward the B3PW91* functional, which gives qualitatively correct results for the ground state of known alkyl-Fe III complexes, the absolute ΔE values obtained for the present system should not be considered as reliable, especially since they also heavily depend on the correction applied for dispersion effects. What are more reliable are the observed trends within each equilibrium (ΔEATRP and ΔEOMRP), where errors effectively cancel, on going from the dimethyl to the dichloro system. Even comparing the absolute ΔEATRP and ΔEOMRP values for the same system as an indication of trapping efficiency is not quantitatively reliable: Equilibria depend on ΔG, not ΔE. Whereas the ATRP trapping process involves one metal complex and one small organic molecule on each side, hence ΔG ~ ΔE (the TΔS term is small), the OMRP trapping process leads to disappearance of one small molecule (ΔS < 0), thus the ΔG stabilization is smaller than the computed ΔE. Calculating these ΔG values by DFT with the standard gas phase approximation would not provide reliable numbers as these reactions occur in a condensed phase, where translational and rotational modes are significantly quenched. Even calculating the thermochemical parameters in solution by a polarizable continuum method does not provide an ideal solution, as pointed out in various theoretical contributions. [48][49][50][51] Therefore, we purposely avoided making additional corrections of uncertain value (except for the recommended correction for dispersion 52 ) and prefer to directly present the original gas phase electronic energy data. From a strictly qualitative point of view, the ATRP equilibrium stabilization is probably not significantly affected by thermal, entropy, and solvent corrections, especially in non-polar media such as the styrene monomer itself, used in the bulk polymerization experiments. The OMRP equilibrium stabilization, on the other hand, is likely to be less important on the G scale than the calculated ΔE value. This consideration is also in agreement with the experimental observations. Firstly, styrene polymerization mediated by I Cl is controlled more poorly by an ascorbic acid reduction facilitating an OMRP-initiation than by ATRP+OMRP. If the relative stabilization of the dormant species was as indicated in Figure 4 on a Gibbs energy scale, OMRP should provide the major controlling mechanism and perhaps lead to good control even in the absence of ATRP. Secondly, styrene was less efficiently controlled by I Me under the ATRP+OMRP regime than by I Cl under the OMRP only regime, supporting our doubt of quantitative relevance. Finally, it is important to note that this is an idealized system. In an experimental operation, protic impurities would surely react vigorously with the organometallic trapping intermediates, decomposing catalysts and minimizing observed OMRP trapping. Thus, this computational work suggests that the OMRP trapping mechanism is accessible and helps to improve the control alongside a dominant ATRP controlling mechanism.

The same proverbial grain of salt should be taken with the analysis, to follow in the subsequent sections, of the effect of electronic structure on trapping barriers and the role pressure plays in controlling these equilibria.

(g) Effect of the electronic structure on the trapping barriers

Considering the spin state variability for Fe II and Fe III complexes and the ground state dependence on the coordination geometry, it is of interest to examine the effect of the spin state on the reaction coordinate. Reactions with a change of spin state between reagents and products, termed two-state reactions, 53 or spin crossover reactions, 34,[START_REF] Poli | Comprehensive Inorganic Chemistry II[END_REF] may be characterized by greater activation barriers relative to analogous single state reactions for enthalpic and/or entropic reasons, the former related to the possible need to reach a crossover point between the two potential energy surfaces, the latter related to a "forbidness" factor. [START_REF] Harvey | [END_REF]56 For the OMRP trapping process, while the trapping species is most definitely a spin quintet (S = 2) Fe II complex, the resulting R-Fe III dormant species has a quartet (S = 3/2) ground state for this particular system, but the sextet state (S = 5/2) is also close in energy and may become the ground state for other systems. The spin doublet (S = 1/2) state is much higher in energy for this system, but it could also become the ground state for other coordination geometries and ligand sets (e.g. see section (b)). The combination of trapping Fe II complex and organic radical (S = 1/2) yields two degenerate states with S = 2±1/2 (5/2, 3/2) depending on whether the radical spin is parallel or antiparallel to the metal spin. Hence, a pathway without spin crossover can be envisaged for the trapping processes leading to both the sextet and the quartet R-Fe III species, whereas there should be at least one spin crossover point for the reaction coordinate leading to a spin doublet R-Fe III species.

We have explored the reaction coordinate for the OMRP trapping leading to both the quartet and the sextet state alkyl product, limited however to the better performing II Cl /III Cl system, by performing partial optimizations at various fixed Fe-C distances. The association process (from right to left in Figure 5) proceeds smoothly, without any apparent barrier, for both spin states.

The profile for the quartet state is that of a typical Morse-type dissociation curve. Interestingly, for a Fe-C distance as short as 3.9 Å, the energy of the sextet is still essentially degenerate with the quartet state, even though the system is already energetically stabilized by ca. 3 kcal/mol relative to the dissociation asymptote. Thus, the orbital interaction is already sufficiently developed to provide a significant energetic stabilization that is independent of the relative orientation of the two spins. At shorter distances, however, while the quartet drops significantly in energy, the sextet remains essentially at the same energy, converging to a stable minimum with a long Fe-C distance of 3.236 Å and an energy 5.0 kcal/mol higher than the quartet. The geometry of the optimized sextet is given in the SI. Hence, this analysis suggests that OMRP trapping should be a fast process whenever a spin quintet Fe II complex leads to a dormant species in either a quartet or a sextet ground state. Concerning the ATRP trapping process, the Cl-Fe III trapping species is characterized by a high spin state (sextet, S = 5/2). This is likely the case for all Fe II -based ATRP catalysts reported so far. The combination of Cl-Fe III and the radical yields two degenerate states with spin 5/2±1/2 (3,

2), of which the second one correlates with the spin state of the Fe II product. Therefore, the ATRP trapping process is also a single state reaction. As shown in Scheme 5, this reaction coordinate is also expected to involve an electronic redistribution because the new metal-based orbital generated in the Fe II complex from the Cl-Fe III bond/antibond combination contains one unpaired electron formally deriving from the Cl-Fe III antibond, thus one of the two electrons originating from the Cl-Fe III bond (shown in green in Scheme 5) must shift to another metal-shell orbitals (see Scheme 5) to establish new bonds. Hence, the ClFe donor-acceptor interaction must push one metal electron up in energy in an antibonding molecular orbital. For comparison, the Fe-Cl distance in the I Cl product, where there is also one antibonding electron, is shorter at 2.254 Å (Table 2), which is related to its covalent rather than dative nature. R-XMt interactions have previously been calculated for other models of ATRP catalyst/initiator combinations. In case of the CH3CH(Cl)COOCH3-RuCl2(PH3)2 combination, model for the initiating system of Sawamoto's RuCl2(PPh3)3 catalyst, 57 a stabilization of 5.8 kcal/mol was calculated with a slightly different level of theory (B3LYP functional) for the interaction that involves an empty metal orbital, 58 whereas other molecules that can only provide singly occupied metal orbitals (CpMoCl2(PH3)2 or MoCl3(PH3)3, models of other efficient catalysts 16,59 ) were found to yield repulsive interactions. 58 The positive interaction in the present case may be attributed to the greater tolerance of the harder, first row transition metal to the presence of antibonding electrons and to the lower steric encumbrance relative to the 2 nd row systems investigated in the previous study. This contrasts the computational analysis of CH3CH(Cl)OOCCH3-CpCr(ArN=CH-CH=NAr) where Ar = C6H3R2-2,6 and R = H, Me, iPr; 26 this system can also only offer half-filled metal orbitals to establish new bonds, but the steric encumbrance is greater and the interaction was found repulsive. results suggest the presence of a significant interaction between the radical and the Cl atom of compound I Cl , making the atom transfer process not only energetically favorable but also barrierless. This positive interaction may be associated to the significant spin density on the Cl atom (0.229 according to the Mulliken analysis, vs. 4.060 on the Fe center), due to the electron located in the antibonding orbital with significant Fe-Cl character (see Scheme 5). Hence, the positive interaction between this electron and the antiparallel spin on the alkyl radical is an efficient entry into the atom transfer pathway. This situation differs substantially from the atom transfer pathway calculated for the aforementioned CH3CH(Cl)OOCCH3-CpCr(ArN=CH-CH=NAr) system, where the interaction between the S = 3/2 Cl-Cr III moiety and the alkyl radical is repulsive leading to a significant barrier to the atom transfer process. In this case, the spin density for the Cr III complex is nearly fully localized on the metal atom (the unpaired electrons are on pure metal based d orbitals: for the C6H3R2-2,6 derivatives with R = H, Me, iPr Ph, the calculated spin densities are respectively 3.072, 3.071 and 3.086 on the Cr atom and 0.022, 0.017 and 0.019 on the Cl atom) and the interaction occurs with parallel spins, leading through a single-state pathway from the S = 3/2+1/2 combination to the S = 2 ground state of the Cr II ATRP catalyst.

In conclusion, ATRP processes with Fe II catalysts are likely to be associated with single-state pathways with either a relatively low activation barrier or no barrier at all, because Fe II and X-Fe III (X = Cl, Br) species are always likely to adopt a high spin configuration (quintet and sextet, respectively), providing evidence for the efficacy of iron in these controlled radical polymerizations. The OMRP trapping process, however, is likely to be most efficient (low or zero activation barrier) when leading to a R-Fe III dormant species with either a quartet or a sextet ground state, as in the diamine-bis(phenolato) system under specific scrutiny in this contribution.

(h) Effect of pressure

A final point for consideration in this contribution is the effect of pressure on the rate of styrene polymerization mediated by systems I. Under the steady-state approximation for the radical concentration, the rate law for a polymerization process that takes place in the ATRP or OMRP regime is as shown in equations 3 and 4, respectively, where KATRP and KOMRP are the thermodynamic equilibrium constants for the corresponding activation/deactivation equilibria (K = ka/kda) of equations 1 and 2, and kp is the propagation rate constant. The pressure dependence of a reaction rate is reflected by the activation volume, which corresponds to the sum of the reaction volume for the activation/deactivation pre-equilibrium of interest (VATRP or VOMRP) and the activation volume of the free radical propagation step (V ‡ p).

diaminobis(phenolato) ligand (cf. Table 3 and Table 4). Consequently, and perhaps counterintuitively, VOMRP is negative and is predicted to have a positive effect on the polymerization rate at high pressures.

Table 5. Calculated molecular volumes (cm 3 /mol) for the species involved in the ATRP and OMRP equilibria. It is important to point out that the calculated molar volume changes for the two controlling equilibria do not take into account solvation effects. Solvation may have a dramatic effect on the volume change in RDRP activation equilibria, as was pointed out in the recent experimental study of the ATRP equilibrium for the FeBr2/FeBr3 couple. 62 In principle, the tetradentate diaminobis(phenolato) ligand is unlikely to be displaced by coordinating solvents. However, the coordination sphere may be expanded by additional coordination of a donor molecule for the 5coordinate I and III systems and especially for the 4-coordinate II system, hence the values reported in Table 5 should be considered of no great significance when the polymerization is conducted in coordinating solvents. In a non-coordinating solvent, or in bulk monomer, the values may be closer to the reality. Monomer coordination through the π electrons should not take place given the high spin configuration and no olefin complexes of Fe II or Fe III are known in the presence of unpaired electrons. If solvation may indeed occur, this should in principle affect the less saturated Fe II species to a greater extent. In that case, the transformation of the Fe II system to the Fe III system in ATRP activation and in OMRP deactivation might be associated to an even greater volume increase, further increasing the values shown in the table (more positive VATRP, more negative VOMRP). The same effect is expected if species II dimerizes.

Conclusion

The present computational investigation supports the proposition of a dual controlling mechanism via ATRP and OMRP for the polymerization of styrene by complex I Cl . 22,23 The energy change associated with the radical trapping process increases for both the ATRP (I Me to I Cl ) and OMRP (II Me to II Cl ) trapping equilibria. The Cl substituents' electronic inductive effects make it more difficult for the Fe II in II to be oxidized to Fe III -Cl, rendering the reverse trapping process in ATRP more favorable. By our calculations, the greater electron withdrawing power of the bis(phenolato) ligand does not negatively affect the formation of the Fe III -alkyl bond in the OMRP dormant species; indeed the latter is slightly more stabilized for the chloro-substituted system III Cl . Geometry and spin state analyses are insensitive to modification of the phenolate substituents, but the small energetic changes are sufficient to affect the delicate activation/deactivation equilibria in a relevant way for polymerization control. The system was further explored by examining the effect of electronic structure on the trapping barriers, suggesting that Fe II systems, in particular, should provide essentially barrier-free ATRP whilst spin-state factors would be important in the organometallic reaction pathway. This particular system has no trapping barrier because it leads to an intermediate spin organoiron(III) dormant species but a barrier may be expected for the two-state reaction when the dormant species has a low spin ground state. Finally, pressure as a tool for shaping and understanding controlled radical polymerization reactivity was studied with preliminary results suggesting model OMRP reactions should be favored at high pressures in non-coordinating solvents. These studies point to the qualitative, not quantitative, mechanistic lessons these computational studies may provide in support of understanding metal-mediated RDRP.

ASSOCIATED CONTENT Supporting Information. Additional tables of structural parameters and views of optimized structures as described in the text. List of Cartesian coordinates for all optimized structures. This material is available free of charge via the Internet at http://pubs.acs.org.

Figure 1 .

 1 Figure 1. Views of the optimized geometries of I Me and I Cl in the sextet and quartet states.

Figure 2 .

 2 Figure 2. Views of the optimized geometries of spin quintet II Me (left) and II Cl (right).

  from the O atom (2.539 Å) with an expanded Fe-C-H angle of 97.8°.The effect of the 2,4-dichloro substitution on the phenolate benzene rings is opposite relative to I and II: on going from III Me to III Cl , the distance to the alkyl ligand significantly lengthens.The effective positive charge on the Fe atom increases as expected on going from III Me to III Cl , but this time it does not result in a bond strengthening, perhaps because the Fe-C bond has a greater covalent nature relative to the Fe-Cl bond. Taking into account the energy of the PhCHCH3 • radical, the energy change for the OMRP equilibrium of equation 2 is calculated as 8.0 kcal/mol for the II Me /III Me system and 9.4 kcal/mol for the II Cl /III Cl system. These calculations were more strongly affected by the dispersion correction than those of the ATRP equilibrium. The B3PW91*-D3 calculations yielded 26.1 and 27.1 kcal/mol, respectively. The large increase of BDE by ca. 18 kcal/mol on going from B3PW91* to B3PW91*-D3 is

Figure 4 .

 4 Figure 4. Energy diagram summarizing the ATRP and OMRP activation/deactivation equilibria

Figure 5 .

 5 Figure 5. Reaction coordinates for the OMRP equilibrium process through partial optimizations

Scheme 4 .

 4 Scheme 4. Qualitative orbital interaction diagram and reaction coordinate for the R-Fe III bond formation (OMRP trapping process) from the spin quintet Fe II trapping species for the two cases

Figure 6 .

 6 Figure 6. Reaction coordinates for the ATRP equilibrium process through partial optimizations

Table 1 .

 1 Relative energy (E5/2-E1/2 in kcal/mol) of high and low spin (TPP)FeR systems (R = Since the C6F5 compound is known to have a high spin ground state, the results show the expected overestimation of the low spin state stability for the BPW91 functional. Conversely the M06 functional, which performs satisfactorily when applied to problems of long-range weak

	CH3, C6F5) with different functionals.

interactions, incorrectly predicts a high spin ground state for the CH3 derivative. Thus, these two functionals are unsuitable for transition metal spin state predictions. The B3PW91, B3PW91* and M06L functionals correctly predict the ground state for both compounds. Unfortunately no quantitative indications of the doublet-sextet gap are available for these compounds from the experimental studies. On the basis of the established suitability of B3PW91* to other Fe chemistry,

Table 2 .

 2 Selected parameters for compounds I Me and I Cl .

			I Me			I Cl
	Parameters a	X-ray b	DFT (sextet)	DFT (quartet)	DFT (sextet)	DFT (quartet)
	Fe-Cl	2.29(1)	2.284	2.262	2.254	2.225
	Fe-NMe2	2.152(2) 2.226	2.214	2.211	2.200
	Fe-N	2.288(2) 2.363	2.138	2.377	2.118
	Fe-O	1.855(2), 1.868(2)	1.857, 1.862	1.837, 1.851	1.866, 1.872	1.853, 1.864
	Cl-Fe-N	170.1(1) 170.1	177.3	171.2	178.5
	Cl-Fe-NMe2	92.2(1)	91.6	98.7	92.6	96.9

a Distances in Å, angles in °, effective charges in electrons, ΔE in kcal/mol. b From ref.

Table 3 .

 3 Selected parameters for compounds II Me and II Cl .

	Parameters a	II Me	II Cl
	Fe-NMe2	2.193	2.174
	Fe-N	2.166	2.170
	Fe-O	1.891, 1.903 1.895, 1.908
	N-Fe-NMe2	84.4	85.0
	O-Fe-N	95.7, 95.5	94.7, 94.3
	O-Fe-O	144.5	144.5
	q(Fe)	0.610	0.675

a Distances in Å, angles in °, effective charges in electrons.

Table 4 .

 4 Selected parameters for compounds III Me and III Cl .Figure 3. Views of the optimized geometries of spin quartet III Me (left) and III Cl (right). For clarity purposes, the H atoms are not shown except for the α-H of the alkyl ligand (additional representations available in the SI).

	Parameter a	III Me	III Cl

a Distances in Å, angles in °, effective charges in electrons.

  Mt x and R0-X, see Scheme 1, or from L/Mt x+1 -X and R0 • as in the present case)

	(from either L/
	(ATRP trapping)		(OMRP trapping)
	+ I	PhCHCH 3 •	+ II
	2.1 kcal/mol
	(+ II Me )
	7.2 kcal/mol
	(+II Cl )
	PhCH(CH 3 )-Cl		26.1 kcal/mol
			27.1 kcal/mol
			(III Me ) (III Cl )
			PhCH(CH 3 )-[Fe III ]

and will briefly be summarized here: activation under ATRP conditions

This work was granted access to the HPC resources of CINES under the allocation 2014-086343 made by GENCI (Grand Equipement National de Calcul Intensif) and to the resources of the CICT (Centre Interuniversitaire de Calcul de Toulouse, project CALMIP). RP gratefully acknowledge the Centre National de la Recherche Scientifique (CNRS) and the Institut Universitaire de France (IUF) for additional support. We are grateful to Prof. A. Lledós for helpful discussion. ABBREVIATIONS RDRP, reversible deactivation radical polymerization; ATRP, atom transfer radical polymerization; OMRP, organometallic mediated radical polymerization; CCT, catalytic chain transfer.

based orbital to generate a metal based lone pair, whereas the other Cl-Fe III bonding electron couples with the radical electron to generate the R-Cl bond. Scheme 5. Qualitative orbital interaction diagram and reaction coordinate for the ATRP trapping process involving Cl atom transfer from the spin sextet Cl-Fe III complex to the organic radical R, with formation of a spin quintet Fe II complex.

The reaction coordinate was explored by carrying out partial optimizations at intermediate positions along the reaction coordinate (Cl atom transfer), as measured in this case by the Fe-Cl distance. The results are shown in Figure 6. A first point of interest is the presence of a local minimum for a Lewis acid-base adduct between the ATRP catalyst II Cl and PhCH(CH3)-Cl, energetically stabilized by 6.4 kcal/mol relative to the sum of the two separate molecules. The Fe•••Cl distance (2.679 Å) is already rather short and indicative of a significant donor-acceptor interaction, even though the S = 2 state of the Fe II complex can only offer half-filled valence The effect of pressure was shown to be positive on both the free radical propagation step (negative V ‡ p) and on the activation/deactivation equilibrium for the Cu-catalyzed ATRP of styrene (negative VATRP). 60,61 The ATRP equilibrium for the FeBr2/FeBr3 couple in polar solvents S (N-methylpyrrolidin-2-one and acetonitrile), however, was shown to be disfavored by pressure (positive VATRP), supposedly because of the pressure-induced formation of [Fe(S)6] 2+ species. 62 Preliminary high-pressure studies of the styrene polymerization mediated by I Cl have demonstrated faster polymerizations at high pressures and raise their own questions about the mechanism of action in these system, in apparent contradiction with the ATRP+OMRP model. [START_REF] Buback | personal communication to MPS[END_REF] In order to learn more about this phenomenon and to see whether either the ATRP mechanism or the OMRP mechanism or both could have a positive influence of pressure on the polymerization rate, we have carried out volume calculations on the optimized structures of the species involved in the two equilibria. The results are reported in Table 5. For the ATRP activation process, there is an expected volume increase on going from II to I (40.7 cm 3 /mol for the CH3 system, 30.8 cm 3 /mol for the Cl system), which is greater that the volume decrease associated to the transformation of the dormant species to the active radical (-11.5 cm 3 /mol). Consequently, VATRP is positive and is predicted to have a negative effect on the polymerization rate at high pressure.

Conversely, the molar volume decrease associated to the transformation of III to II (-158.0 cm 3 /mol for the CH3 system, -109.3 cm 3 /mol for the Cl system) is greater than the volume loss associated to the generation of the free radical (89.5 cm 3 /mol). This trend can be attributed to the shortening of all the bonds between the Fe atom and the donor atoms of the

AUTHOR INFORMATION

Corresponding Author

* Rinaldo Poli. Fax: +33-651553003. Email: rinaldo.poli@lcc-toulouse.fr.

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

ACKNOWLEDGMENT

SYNOPSIS

The action of a diaminobis(phenolato) iron system as a controlling agent for the polymerization of styrene has been addressed by a DFT study, supporting the view that the system operates by combined ATRP and OMRP moderating equilibria. The study also addresses the electronic effect of ligand substituents on the controlling ability, the effect of pressure on rates through volume calculations, and the effect of the spin state change on the activation barriers for the trapping processes.


Mohammed Loubidi

Dominique Agustin
email: dominique.agustin@iut-tlse3.fr

Ahmed Benharref
email: benharref@uca.ma

Rinaldo Poli

TBHP using [MoO2(SAP)]2 as catalyst. Epoxydation des himachalènes et de leurs dérivés par TBHP en procédé sans solvant catalysé par [MoO2(SAP

Keywords: Homogeneous catalysis, Tridentate ligands, molybdenum, Natural Products, Epoxidation, Green chemistry, Terpenoids

Solvent-free epoxidation of himachalenes and their derivatives by TBHP using [MoO2(SAP)]2 as a catalyst

INTRODUCTION

Plants are important natural sources of organic molecules used in different sectors, such as the perfume industry as fragrances, the food industry as additives, or the cosmetics and the pharmaceutical industries. 1 Essential oils from plants are complex mixtures of several organic molecules, containing terpenes as notable components. These molecules bear several biological properties (biocides, pesticides) making them interesting biosourced compounds for many applications. 2 However, chemical transformation is crucial to generate derivatives with novel properties and uses. 3 In order to valorize these natural compounds, some of us have long been involved in the study of the sesquiterpenes called "himachalenes" (see Scheme 1Erreur ! Source du renvoi introuvable.), extracted from the essential oil of Cedrus Atlantica, an endemic tree in Morocco. 4 Himachalenes have been a topic of investigation for several years.

While research has been devoted to their total synthesis, 5 other studies have revealed the versatility of natural himachalenes to different types of transformations (especially exploiting the selective reactivity of the double bonds) through reactions in organic solvents, such as Rucatalyzed aerobic epoxidation 6 , diol formation using KMnO4, 7 or epoxidation through m-CPBA 8 as well as formal dihalocarbene addition or halogen addition,7 these transformations leading to monoolefinic compounds. From the formed epoxides, Lewis acid catalyzed rearrangements have recently been described. 9

Scheme 1 -Different himachalene isomers.

Himachalenes and their halogenated derivatives were epoxidized using the classical organic peroxide m-CPBA as epoxidating agent in organic solvents, often chlorinated ones. With the increasing demand of cleaner and safer processes, the epoxidation of himachalenes and their derivatives should be revisited and hopefully lead to efficient and "greener" transformations.

We are currently interested in solvent-free epoxidations and have reported efficient protocols for the epoxidation of cyclooctene using molybdenum- 10,11 and vanadium-12 based catalysts, as well as polyoxometalates 13 . We present herein the results of the epoxidation reaction of the himachalenes using the solvent-free catalyzed method using aqueous TBHP as oxidant and [MoO2(SAP)]2 (SAP= salicylideneaminophenolato) (Scheme 2) as catalyst.

Scheme 2 -[MoO2(SAP)]2 catalyst

Results and discussion

Himachalenes and chlorinated derivatives.

The "raw" essential oil studied herein was extracted from the grinded wood of Atlantic Cedar (see experimental part for details). This essential oil contains a high quantity (around 70% wt of the total oil) of the three himachalene isomers, called α-cis (1)-, β-(2) and γ-cishimachalene, the isomerism depending on the position of the olefinic function of the 7membered cycle (Scheme 1Erreur ! Source du renvoi introuvable.). The β himachalene is the most abundant isomer in the mixture followed by the α-cis and a minor quantity of the γ-cis.

The present work is focused on the study of the two main compounds 1 and 2.

Two methods were employed to obtain halogenated monoolefinic compounds from himachalenes. The first halogenated compound, 3-chlorohimachal-7,13-ene, (3, Scheme 3) is the product of formal hydrochlorination of α-cis-himachalene. Action of gaseous HCl on a himachalene mixture followed by recrystallization in hot methanol leads to 3 as a unique species containing an exocyclic double bond. 14 The advantage of this compound in comparison to the himachalenes 1 and 2 is the presence of a unique double bond available for functionalization. The structure of this compound was elucidated by X-ray crystallography and 13 C NMR 15 .

Scheme 3 -Synthetic pathway for the formation of 3-chlorohimachal-7,13-ene (3) from the himachalene mixture

The second investigated halogenated himachalene derivative, (1S,3R,8R)-2,2-dichloro-3,7,7,10-tetramethyltricyclo [6,4,0,0 1,3 ]-dodec-9-ene (4, Scheme 4), corresponds to the formal addition of a dichlorocarbene to the tetrasubstituted double bond of the β-himachalene (2), using in situ dichlorocarbene generation from chloroform and NaOH in the presence of an ammonium salt. 16 This compound was characterized by different methods, including single crystal X-ray diffraction 17 and 13 C NMR. 16 Scheme 4 -Synthetic pathway for the formation of the (1S,3R,8R)-2,2-dichloro-3,7,7,10tetramethyltricyclo[6,4,0,0 1,3 ]-dodec-9-ene (4) from β-himachalene (2)

Epoxidations.

It has to be noticed that a few himachalene epoxides have already been identified as minor components of the essential oils. 18 However, the low natural quantity has stimulated investigations to find efficient synthetic epoxidation methods from the more abundant himachalenes using simple organic reactions (m-CPBA in chloroform or dichloromethane).

According to the accepted mechanism of the epoxidation reaction, 19,20 the reactivity is related to the electron density of the olefin double bond, leading to the reactivity trend shown in Scheme 5. The reactivity is also related to the electrophilic character of the oxygen atom transferred from the oxidant, hence meta-chloroperbenzoic acid (m-CPBA) is typically chosen as oxidizing agent. [START_REF] Plesnicar | Oxidation in Organic Chemistry, Part C[END_REF] All reactions using m-CPBA need the use of organic solvents. In the quest of greener reaction conditions, the recently introduced solvent-free method using [MoO2(SAP)]2 as catalyst was tested herein. 12 The advantages of this catalytic method are the use of a small quantity of catalyst (1% Mo vs. substrate), a smoother oxidant (TBHP in water), and no added organic solvent.

Epoxidation of himachalenes by the m-CPBA method

Epoxides were obtained using an improved method relative to that already reported in the literature,8 from the α-, β-, himachalene mixture. The reaction occurs in dichloromethane at room temperature with one equivalent of m-CPBA, giving the corresponding (2S, 3R)-2 ,3epoxy-cis-himachal-7,13-ene 5 and (1R,6S,7R) -6,7-epoxy-3,7,11,11-tetramethylbicyclo-[5,4,0]undec-2-ene 6 in a 28/72 ratio (Scheme 6). Both products could be separated by column chromatography (see experimental part for details) and additional IR and NMR characterisation of both epoxides is presented herein. The C-O-C vibration corresponding to the oxirane ring was observed around 890 cm -1 and 1034 cm -1 for 5 and 6 respectively.

Scheme 6 -General scheme of epoxidation of (1) and (2) into the corresponding epoxides ( 5) and ( 6).

The 1 H NMR spectrum of the epoxide 5 shows a doublet at δ 4.78 corresponding to the two exocyclic methylenic protons C13-H and a doublet at δ 2.95 attributable to the proton linked to the oxirane ring C2-H, proving the selectivity of the reaction. The 13 C NMR spectrum presents relevant signals situated at δ 155 and 112, attributable to the exocyclic double bond C7=C13

and at δ 62 and 58 for the two carbon atoms of the oxirane ring.

The 1 H and 13 C NMR signals of the epoxide 6 were also completely assigned. Characteristic

Epoxidation of himachalenes by the solvent-free method

The catalyzed transformation of the himachalenes mixture (Scheme 6) was carried out at 80°C using a [Mo]/himachalenes ratio of 1/100. As already shown with m-CPBA,7 and in agreement with the reactivity trend mentioned above, -himachalene reacts faster than -himachalene in the presence of TBHP. Indeed, more than 90% of -himachalene and only 50% of -himachalene were converted after 120 minutes. However, the optimal yield for product 6 occurred after 1 hour and the subsequent decrease is certainly due to overepoxidation (four equivalents of TBHP were used) as well as to the possible subsequent formation of diols (presence of water from aqueous TBHP), which however were not identified. Several experiments with different TBHP/himachalenes ratios (0.6 to 4) were carried out using the same [Mo]/himachalenes ratio (1/100). Although the reactions were carried out on himachalene mixtures, the conversion vs. time plots of the two most abundant compounds are shown separately in Figure 2, i.e. -cis (1) (left) and -himachalenes (2) (right) as well as the influence of Mo/TBHP ratio on the conversion of both himachalenes in Figure 3. The best conversion for 1 was observed after five hours of reaction at 80°C with four equivalents of TBHP. As observed in Figure 2, quantitative conversion of the -himachalene 2 was achieved already after two hours of reaction when using 4 equivalents of TBHP in the mixture. Both products 5 and 6 could be isolated in 80% and 90% yields (in regard to each compound separately) and in pure form after chromatography from the reaction carried out under optimized conditions, i.e after 90 minutes in a 5/6 ratio of 33/67. The major difference between the m-CPBA and the solvent-free catalyzed method consists of the greener conditions of the latter. Epoxidation of (1S,3R,8R)-2,2-dichloro-3, 7,7,10-tetramethyltricyclo[6,4,0,0 1,3 ]-dodec-9-ene (4)

TBHP/himachalene ratio

As already described in the literature,8 treatment of the (1S,3R,8R)-2,2-dichloro-3,7,7,10tetramethyltricyclo[6,4,0,0 1,3 ]-dodec-9-ene 4 with a stoichiometric amount of mCPBA led to two products 7 and 7' in a 70/30 relative ratio and with a 80% total yield (Scheme 7).

Scheme 7. General scheme of epoxidation of (1S,3R,8R)-2,2-dichloro-3,7,7,10tetramethyltricyclo[6,4,0,0 1,3 ]-dodec-9-ene (4).

Epoxides 7 and 7' gave different 1 H and 13 C NMR spectra. In the 1 H NMR spectrum, the doublet corresponding to the ethylenic proton of 4 disappears and signal appears (δ 3.00 for 7 and 3.10 for 7') appears, corresponding to the oxirane formation. The 13 C NMR spectrum reveals in particular two signals at δ 55.0 and 61.9 for 7 (55.8 and 61.8 for 7') attributable to the carbon atoms of the oxirane ring. The absolute configurations of both compounds have been determined through X-ray crystallography. [START_REF] Benharref | [END_REF] The epoxidation of 4 with one equivalent of TBHP and 0.5% equivalent of [MoO2(SAP)]2 at 80°C has been monitored for seven hours (see Figure 4). An 80% conversion could be obtained after five hours. The epoxides were isolated as a mixture and analyzed by NMR, giving a 50/50 ratio for the two stereoisomers.

Epoxidation of 3-chlorohimachal-7,13-ene (3)

As previously described, 23 3 reacts in chloroform with one equivalent of m-CPBA at the exocyclic double bond and leads to two stereoisomers 8 and 8' (Scheme 8) in a 85/15 ratio with a total yield of 85% after four hours. Both compounds were separated through column chromatography.

Scheme 8 -General of epoxidation of 3-chlorohimachal-7,13-ene (3).

Both isomers 8 and 8' were characterized separately through 1 H and 13 C NMR spectrometry and gave similar spectra. 24 The two ethylenic protons of 3 disappeared and a signal corresponding to two protons appeared at δ 2.50 for 8 and 8'. In the 13 C NMR spectrum, as The solvent-free Mo-catalyzed reaction with THBP was followed under identical conditions as for the other previously described epoxidations. The substrate conversion is indicated in

Mechanistic discussion

The epoxidations of the himachalenes with peracids were studied theoretically with himachalenes 25 and -himachalenes, 26 explaining the selectivity trends on the basis of the well-known Bartlett mechanism. 27 Concerning the metal-catalyzed olefin epoxidation by TBHP, mostly realized with molybdenum or vanadium based catalysts, Mimoun and Sharpless have proposed relevant mechanisms in organic solvents that involve the addition of TBHP to the catalyst in the activation phase. 28 We have recently shown that the olefin epoxidation with the [MoO2(SAP)] fragment as catalyst and TBHP as oxidant follows a mechanism relatively similar to that operating in the presence of peracids. 11 On this basis, the slight difference in selectivity that is observed between the mCPBA epoxidation and the [MoO2(SAP)]-catalyzed epoxidation by TBHP can be attributed to the slightly different steric

Conclusion

We have shown herein for the first time that the solvent-free catalyzed epoxidation is relatively efficient for the transformation of natural substrates. The himachalenes 1 and 2 and their derivatives 3 and 4 could be efficiently transformed to epoxide products in close analogy to the classical m-CPBA method, although giving slightly different steroisomeric ratios for the epoxidation products of 3 and 4. The rational use of this method for the epoxidation of a wider range of natural compounds is an interesting perspective of this work.

Experimental part

All preparations were carried out in air. Organic solvents (ethanol, diethylether, hexane, ethylacetate), organic (acetophenone, ACROS) and inorganic (MnO2, Aldrich) chemicals were employed as received without any purification. Compounds 3 and 4 were obtained following the known procedures.8 [MoO2(SAP)]2 was freshly synthesized as described previously 11 prior to use. TBHP (70 % in water, ACROS) was used as received. The infrared spectra were recorded in KBr matrices at room temperature with a Nicolet Impact 410 spectrometer in the 4000-400 cm -1 range. Melting points were measured in capillary tubes with a Buchi 510 apparatus. 1 H NMR and 13 C NMR spectra were recorded on a Bruker Avance DPX-300 spectrometer using TMS as reference and CDCl3 as solvent. Catalytic reactions were followed by gas chromatography on an Agilent 6890 A chromatograph equipped with FID detector, a HP5-MS capillary column (0.30 m× 0.25 mm×0.25 m) and automatic sampling. The conversions were calculated relatively to an internal standard (acetophenone). The column chromatographic separations were carried out using MERCK 60 silica gel.

Extraction and separation of sesquiterpenes 29 Grinded Cedar wood (200g) was introduced in a glass flask equipped with Clevenger containing water. The system was maintained under reflux for 12 hours. The obtained oil was purified through column chromatography and a mixture of the three isomers (cisand himachalene) in (23/61/16) ratio was isolated (4.2 g).

General epoxidation procedure of himachalenes and derivatives with mCPBA

For himachalenes

In a 100 mL flask containing the himachalene mixture (2 g, 9.79 mmol) solubilized in 50 mL CH2Cl2 was added the stoechiometric amount of mCPBA (1.69 g, 9.79 mmol). The mixture was stirred for two hours at room temperature and then treated with 40 mL of a 10% aqueous solution of sodium hydrogen carbonate. The aqueous phase was extracted three times with 20 ml of diethyl ether. The combined organic phase was dried with anhydrous sodium sulfate and the volatile solvents were removed under reduced pressure. The residue was separated through column chromatography (silica gel) using hexane/ethyl acetate (97/3) as eluent. The epoxides 5 (0.44 g, 90% yield relatively to the corresponding himachalene 1) and 6 (1.24 g, 95% yield relatively to the corresponding himachalene 2) were recovered as yellow oils after removal of the volatile solvents under reduced pressure. Their identity was confirmed by comparison of the NMR properties with those reported in the literature.8

For (1S,3R,8R)-2,2-dichloro-3, 7,7,10-tetramethyltricyclo[6,4,0,0 1,3 ]-dodec-9-ene

The procedure was identical to that used for the himachalenes, using (1S,3R,8R)-2,2dichloro-3,7,7,10-tetramethyltricyclo [6,4,0,0 1,3 ]-dodec-9-ene (1.5 g, 5.4 mmol) as substrate.

Eluent: hexane/ethyl acetate (97/3). The final products are white solids. Final yield: 80 % (7/7' = 70/30).

For 3-chlorohimachal-7,13-ene

The procedure was identical to that used for for the himachalenes, using 3-chlorohimachal-

General catalytic epoxidation procedure with TBHP

Standard catalytic runs

In a typical experiment, one equivalent of the substrate and [MoO2(SAP)]2 (0.005 equiv) were mixed together in a round bottom flask and stirred in air. Acetophenone was added as internal standard. The reaction temperature was regulated at 80°C and then x equiv of aqueous THBP was added to the mixture under stirring, setting the zero reaction time. Samples of the organic phase were periodically withdrawn after stopping the stirring and allowing phase separation.

For each aliquot, the reaction was quenched by addition of MnO2, followed by the addition of diethylether and removal of the manganese oxide and residual water by filtration through silica before GC analysis.

Optimised procedure for the solvent-free himachalenes epoxidation

In a flask equipped with magnetic stirrer and cooler, 1 g (4.9 mmol) of the himachalene mixture and 16.6 mg of [MoO2(SAP)]2 (0.024 mmol, 0.005 equiv) were added. The mixture was warmed to 80°C and then aqueous TBHP (70%, 2.68 mL, 19.6 mmol, 4 equiv) was added. The mixture was stirred at 80°C for 90 minutes. After cooling, the organic residue was extracted with diethylther, concentrated under reduced pressure and the epoxides were then separated by column chromatography through silica gel and recovered as yellow oils (5, 0.19 g, 80 % relatively to the corresponding himachalene 1; 6, 0.62 g, 90 % relatively to the corresponding himachalene 2) as described above for the mCPBA epoxidation procedure.

Optimised procedure for the solvent-free epoxidation of (1S,3R,8R)-2,2-dichloro-3, 7,7,10tetramethyltricyclo[6,4,0,0 1,3 ]-dodec-9-ene (4).

In a flask equipped with magnetic stirrer and cooler, 1.72 g (5.98 mmol) of the dichlorocarbenehimachalene 4 and 20.3 mg of [MoO2(SAP)]2 (0.029 mmol, 0.005 equiv)

were added. The mixture was warmed to 80°C and aqueous TBHP (70%, 0.82 mL, 5.98 mmol, 1 equiv) was added. The mixture was stirred at 80°C for 6 hours. After cooling, the mixture was worked up as for the above described epoxidation of the himachalalene mixture, using hexane/ethylacetate (96/4) as eluant for the chromatographic separation. The epoxides 7 and 7' were isolated together as white crystalline powders (1.32 g, 73% yield).

Optimised procedure for solvent-free epoxidation of 3-chlorohimachal -7,13-ene (3).

In a flask equipped with magnetic stirrer and cooler, 1.15 g (4.8 mmol) of the 3chlorohimachal-7,13-ene 3 and 16.6 mg of [MoO2(SAP)]2 (0.024 mmol, 0.005 equiv) were added. The mixture was warmed to 80°C and aqueous TBHP (70%, 0.67 mL, 4.8 mmol, 1 equiv) was added. The mixture was stirred at 80°C for 4 hours. After cooling, the organic phase was worked up as described above for the himachalene mixture using hexane/ethylacetate (97/3) as eluent. The epoxides 8 and 8' were isolated in a 67/33 ratio as white solids (0.86 g, 70% yield).

13 C NMR spectrum of the 3-chlorohimachal-7,13-ene (3) 13 C NMR (δ, CDCl3): (1R,6S,7R) -6,7-epoxy-3,7,11,11-tetramethylbicyclo[5,4,0]undec-2-ene (6) Yield: 95%, 1 H NMR (δ, CDCl3): 0.88 (3H, s); 0.95 (3H, s); 1.26 (3H, s); 1.73 (3H, s); 5.38 (1H, s), 13 C NMR (δ, CDCl3: 18.6 (CH3), 20.7 (CH2), 23.8 (CH3), 24.9 (CH2), 25.4 (CH3), 27.7 (CH2), 29.9 (CH3), 36.4 (CH2), 36.5 (CH2), 44.1 (Cq sp 3 ), 48.8 (CH), 65.0 (Cq sp 3 ) ,65.1 (Cq sp 3 ) 112.4 (CH sp 2 ), 134.3 (C sp 2 )

From dichlorocarbenehimachal-2-ene 2,2-dichloro-9, 10-epoxy-3,7,7,10-tetramethyltricyclo[6,4,0,0 1.3 Ecol., 14 (1988)1145.

  1 H NMR signals are the doublet at δ 5.38 corresponding to the olefinic C2-H proton coupled to the signal at δ 2.00, which corresponds to C1-H. The relevant 13 C NMR signals appear at δ 134 and 112 for the carbon of the endocyclic double bond C3=C2-H and two signals around δ 65.0 and 65.1 ppm for the carbon atoms of the oxirane function.

  The reaction was followed by GC during four hours with samples from the mixture withdrawn periodically and analyzed. No extra solvent was added to the reaction mixture. The conversion vs. time of the himachalenes and the formation of the corresponding epoxides are shown in Figure 1with a TBHP/himachalenes ratio of 4.

Figure 1 -

 1 Figure 1-Conversion of himachalenes (left) and relative formation of epoxides (right) of -cis (◊), () and -cis () himachalenes vs. time. The left graph considers the formation of each epoxide separately, the 100 value being the maximal formation for each epoxide. Experimental conditions: Mo/TBHP/himachalenes = 1/400/100. T= 80°C.

Figure 2 -

 2 Figure 2-Conversion of -cis-himachalene (1, left) and -himachalene (2, right) vs. time (in hours) with different THBP ratio. Experimental conditions: [Mo]/TBHP/himachalenes = 1/x/100. T = 80°C. x = 60 () 150 () 250 ().400 ().

Figure 3 -

 3 Figure 3-Relative conversion of -cis-himachalene 1 (◊) and -himachalene 2 () at 5h vs. TBHP/himachalenes ratio. Experimental conditions: [Mo]/himachalenes = 1/100. T = 80°C.

Figure 4 -

 4 Figure 4 -Conversion of (1S,3R,8R)-2,2-dichloro-3,7,7,10-tetramethyltricyclo[6,4,0,0 1,3 ]-dodec-9-ene (4) vs. time (in hours). Experimental conditions: Mo/TBHP/substrate = 1/100/100. T = 80°C.

  previous reaction, the signals corresponding to the ethylenic carbon atoms of 3 disappeared and two signals in agreement with formation of the oxirane ring appeared at δ 45.3 and 57.0.

Figure 5 .

 5 Figure 5. The conversion was very high even after one hour and a 70% selectivity was observed at the end of the reaction, yielding the two diastereoisomers 8 and 8' in a 67/33 ratio.

Figure 5

 5 Figure 5 -Conversion of 3-chlorohimachal-7,13-ene (3) vs. time. Experimental conditions: [Mo]/TBHP/substrate = 1/100/100. T = 80°C.

  Scheme 9 -Transitions states of epoxidation of olefin with m-CPBA (A) and with [MoO2(SAP)]/TBHP (B)

From

  1 H NMR (δ, CDCl3): 0.80 and 0.90 (CH3, 6H, 2s), 1.60 (CH3, 3H, s), 2.50 (CH2,s), F. Balandrin, J. A. Klocke, E. S. Wurtele, W. H. Bollinger Science 228 (1985) 1154. 2 a)M. Daoubi, R. Hernandez-Galan, A. Benharref, I. G.Collado, J. Agr. Food Chem. 53 (2005) 6673. (b) D.Singh and S.K. Agarwal, J. Chem.

  ]dodecane 7 and 7'M.p.=134-136°, IR ν (cm -1 ): 615, 1050, 1230, 1410. 7 : NMR 1 H (δ, CDCl3): 1.04 -1.09 (6H, 2s), 1.15 (3H, s), 1.30 (3H, s), 3.00 (1H, d, J = 1 Hz), NMR 13 C (δ, CDCl3): 15.0 (CH3), 19.8 (CH2), 20.8 (CH2), 23.9 (CH3), 25.8 (CH2), 27.8 (CH3), 28.9 (CH3), 29.1 (CH2), 31.1 (Cq), 31.5 (Cq), 35.5 (Cq), 37.0 (Cq), 43.4 (CH), 55.0 (Cq), 61.9 (CH), 77.3 (Cq).7': NMR 1 H (δ, CDCl3): 1.12 -1.17 (6H, 2s), 1.25 (3H, s), 1.32 (3H, s), 3.10 (1H, d, J = 2.44 Hz), NMR 13 C (δ, CDCl3): 17.8 (CH3), 21.8 (CH2), 22.1 (CH2), 22.9 (CH3), 24.5 (CH3), 28.8 (CH2), 30.5 (CH3), 32.1 (Cq), 35.6 (CH2), 35.9 (Cq), 39.6 (Cq), 43.6 (CH), 49.9 (Cq), 55.8 (Cq), 61.8 (CH), 77.8 (Cq).

Acknowledgements

We acknowledge the Centre National de la Recherche Scientifique (CNRS) and the Institut Universitaire de France (IUF) for financial support, the Université Paul Sabatier and its Institut Universitaire Technologique for the facilities, and the International Associated Laboratory (LIA) "French-Moroccan Laboratory of Molecular Chemistry" (LCMMF).