Driving Forces in the Sharpless Epoxidation Reaction: A Coupled

Article pubs.acs.org/IC

Driving Forces in the Sharpless Epoxidation Reaction: A Coupled AIMD/QTAIM Study Filipe Teixeira,*,† Ricardo Mosquera,‡ André Melo,† Cristina Freire,† and M. Natália D. S. Cordeiro*,† †

LAQV-REQUIMTE, Departamento de Química e Bioquímica, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre, 4169-007 Porto, Portugal ‡ Departamento de Química Física, Facultade de Química, Universidade de Vigo, 36310 Vigo, Galicia, Spain S Supporting Information *

ABSTRACT: In order to better understand the epoxide-formation step of the Sharpless epoxidation process, a set of 263 oxygen-transfer reactions reflecting the complexity of the Sharpless epoxidation process were studied using density functional theory (DFT) and Bader’s quantum theory of atoms in molecules (QTAIM). The diversity within these reactions reflects the different ligands in the coordination sphere of vanadium and also different substrates (alkene and an allylic alcohol both free and in the form of an alcoxo ligand). The transition states for 76 of these reactions were also characterized using DFT and QTAIM, allowing for an estimation of the impact of the different ligands and substrates on the activation barriers. A smaller subset of the latter was further subjected to an ab initio molecular dynamics (AIMD) simulation coupled to QTAIM analysis. The results show that the type of active catalyst plays an important role in the thermodinamic outcome of these reactions, with vanadium(V) tert-butylhydroperoxide adducts being responsible for the most exoenergetic reactions. On the other hand, the different ligands tested play only a limited role in modulating the thermodynamics and kinetics of these reactions. Moreover, no evidence was found to support a thermodynamic or kinetic preference for the epoxidation of an allylic alcohol over that of an unfunctionalized alkene. However, the results suggest that the reaction path is strongly influenced by the orientation of the substrate upon approximation to the active catalyst, confirming the well-known regioselectivity of the Sharpless epoxidation process.

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INTRODUCTION Vanadyl(IV) acetylacetonate, VO(acac)2, is a well-known catalyst precursor with known applications in a large scope of oxidation reactions.1,2 It has long been targeted as a desirable catalyst for the epoxidation of unsaturated organic compounds because it offers an environmentally safer alternative to the use of traditional stoichiometric epoxidizing agents.3 This is usually accomplished using either hydrogen peroxide, H2O2, or tertbutylhydroperoxide, TBHP, as the terminal oxidant.4 Moreover, the VO(acac)2/TBHP system is well-known for the regioselective epoxidation of allylic alcohols, such as geraniol.2,5,6 The atom economy introduced by this property, in addition to its relatively low cost and low risk of hazard in its manipulation, has raised interest in VO(acac)2 as a catalyst for the fragrance, flavoring, and pharmaceutical industries.7−9 Moreover, a number of immobilization strategies4,10−12 for VO(acac)2 have been emerging, providing novel hybrid nanostructured catalysts with additional advantages in terms of catalyst recovery. A detailed description of the catalytic cycle for the VO(acac)2/TBHP system has eluded the efforts of several authors because of the lability of the acac ligands13,14 and their tendency to irreversibly decompose into acetic acid (AcOH) and carbon dioxide (CO2).15 Recently, Vandichel et al.16 published a comprehensive theoretical study of the catalytic © XXXX American Chemical Society

cycle for the epoxidation of cyclohexene using the VO(acac)2/ TBHP system. The reaction model proposed by Vandichel et al. classifies the different vanadium species into active and inactive complexes (hereafter referred to as AC and IC, respectively). A general depiction of such complexes is given in Figure 1. As shown in Figure 1, AC complexes are characterized by a TBHP, tert-butylperoxide (TBP), or peroxide (O22−) moiety. A number of activation reactions allow the formation of AC complexes from IC ones. In turn, the AC complexes are inactivated upon the epoxidation of an olefinic substrate. The outcome of such inactivation (epoxidation) reactions depends on the possibilities offered by the set of ligands around the vanadium atom. This epoxidation step may be further classified into five categories, schematically depicted in Figure 2. In addition, a number of redox and ligand-exchange reactions are possible, allowing for the formation of vanadium(IV) and vanadium(V) complexes, as well as a multitude of configurations for the coordination sphere of the metal center.16 A deep understanding of the vanadium-catalyzed epoxidation of olefins and allylic alcohols would certainly benefit the design of novel catalysts, as well as shed some light on the structure and reactivity of the peroxo moiety in transition-metal (TM) Received: November 21, 2016

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DOI: 10.1021/acs.inorgchem.6b02770 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 1. Generic structural formulas of vanadium(IV) and vanadium(V) complexes available in the reaction medium, where Lx represents a generic mono- or bidentate ligand derived from a mononegative anion. Labels ACn and ICn denote active and inactive complexes, respectively.

are usually more extreme than those derived from other partitioning schemes,20 they provide a “high-contrast” image of the charge distribution in TM complexes, thus facilitating the rationalization of their properties and reactivity.21 Under the formalism of QTAIM, a molecule is decomposed into atomic domains (commonly referred to as basins). These atomic basins are defined as zero-flux surfaces in the gradient vector field of the electron density, ∇ρ(r). Such partitioning warrants that the quantum definition of each atom in the system coincides with that of a proper open quantum system.22 This allows calculation of the physical observables that are derivable from the one-electron density matrix, such as the kinetic energy, charge, and dipole and multipole moments. Moreover, it is well-known that the topological features of both ρ(r) and its Laplacian, ∇2ρ(r), can be translated into traditional chemical concepts, such as bond strength and the presence of nonbonding pairs and/or lone electrons.22 The application of QTAIM to TM complexes by Bader, Gillespie, and co-workers23−26 has yielded some interesting insights. For example, the penultimate shell of a TM atom contains a number of local charge concentrations [minima of ∇2ρ(r)] named inner-valence-shell charge concentrations (iVSCCs), which, according to Gillespie, are always in opposition to the bonds between the metal center and its ligands.23,24 These observations allowed Gillespie and coworkers to provide new perspectives on the extended valenceshell electron-pair-repulsion model and better describe the geometry of TM complexes. More recently, Teixeira et al.27 have applied QTAIM to the vanadium acetate linkage isomerism, revealing that the arrangement of the iVSCC around vanadium is sometimes nonconformant with Gillespie’s observations (nongillespiean). Such situations carry an energetic penalty to the metal center, which might be compensated for by stabilization of the acetate ligand.27 Furthermore, similar nongillespiean arrangements are also observed in bidentate peroxo- and alkylperoxo complexes. However, the implications of these observations on the reactivity of the AC species in the Sharpless epoxidation remain unexplored. In this work, we endeavor to explore the oxygen-transfer step of the Sharpless epoxidation using an assortment of densitybased theoretical techniques, including Born−Oppenheimer ab initio molecular dynamics (AIMD) coupled to a QTAIM analysis of samples taken from the AIMD trajectories. The main goal of this work is to gather relevant data to allow

Figure 2. Generic representation of the different reaction types considered for the oxygen-transfer step in the Sharpless epoxidation process, using ethene as an example substrate. For simplicity, ligands not involved in the reaction are omitted, and the AC complex for which each reaction available (as well as the resulting respective IC complex) is given.

complexes. For example, it is not known whether the reported regioselectivity toward epoxidation of the allylic CC bond in geraniol is driven by thermodynamic or kinetic processes or if it is best explained by stereochemical hindrances. Also, the current trend of immobilizing VO(acac)2 and other vanadium catalyst precursors onto functionalized supporting materials11,17−19 raises some interesting questions regarding the manner in which these ligands (such as acac-derived Schiff bases and carboxyl groups) influence the efficiency and regioselectivity of the catalyst. Well-established theoretical frameworks are available to conduct such a study, such as density functional theory (DFT) and Bader’s quantum theory of atoms in molecules (QTAIM). Indeed, Vandichel’s work presents experimental validation of the DFT calculations that support their model.16 Further rationalization of the epoxidation process may be achieved by resorting to QTAIM. Although QTAIM charges B


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Inorganic Chemistry

Thermodynamical Survey. The scope of this work is limited to the study of the oxygen-transfer reaction involving the AC complex, which complies with the following rules: compounds have a maximum of one ligand 2 (see Figure 3a); the total number of ligands 1 and 2 must be equal or less than two; at most one ligand 6 may be present, and no ligand 7 is present in the coordination sphere of the metal center (ligand 7 is only considered for a IC complex resulting from the substrate scenario S3, shown in Figure 3b). Geometry optimizations were carried out for all relevant species using redundant internal coordinates. When different isomers were conceivable, these were optimized, and the most stable one was selected for further consideration. Vibrational analysis was carried out at the same level of theory as the optimizations. Information about the thermochemistry of each compound was gathered, including groundstate energetics, zero-point energy corrections, and thermal contributions for the enthalpy and Gibbs energy at 298.15 K and 1.0 atm. A permutation script was written in Python, allowing the computation of the thermodynamic properties for all possible oxygen-transfer reactions from the output of ORCA. Statistical analysis was performed using the R language and environment, version 3.3.1,33 encompassing the computation of distribution parameters such as mean values, kernel density estimation, and visualization of the distribution plots of the collected data. Further analysis of the calculated thermodynamic data included the use of regression tree models to determine the most important parameters determining the thermodynamic outcome of each reaction. Such models were elaborated using the Party package34,35 for R. Study of TS Structures. Starting from the optimized geometries of the AC complexes, relaxed scans of the potential energy surface (PES) were performed in which either Ca or Cb from the substrate (see Figure 3b) approached either the proximal (Oprox) or distal (Odist) oxygen atoms of the TBHP or TBP moiety or either of the oxygen atoms in the peroxo group of AC8 complexes (OOO; see Figure 1). The constrained maxima of each relaxed scan were used as initial guesses for the saddle-point optimization calculations. A vibrational analysis was performed for the resulting TS structures, which were signaled for further consideration if they presented only one negative (imaginary) vibrational frequency and if the atomic displacements over its corresponding vibrational mode (reaction coordinate, ξ) were compatible with the oxygen-transfer step. Finally, the accepted TS structures were infinitesimally displaced in each direction along ξ and allowed to relax, in order to ascertain the geometries of the molecular complexes related to the reactants (MC1) and products (MC2). Vibrational analysis on MC1 and MC2 allowed their identification as minima of the PES upon the absence of any negative vibrational frequency. This procedure was performed for a set of 76 randomly chosen oxygen-tranfer reactions. Thermochemistry data for the MC1, MC2, and TS structures of each reaction were also gathered from the vibrational analysis. AIMD Simulations. The geometry of each of the selected TSs was used as the starting point for the AIMD simulations, which were carried out under the Born−Oppenheimer approximation. The initial velocity vector for each atom was taken from the reaction coordinate ξ, which was scaled in order to ensure that the initial kinetic energy of the system was 1.0 kJ·mol−1 and multiplied by either 1 or −1 to simulate the displacement toward MC2 or MC1, respectively (forward and reverse directions). The simulations ran using the velocity Verlet thermostat36 for approximately 24 ps (1000 steps) in each direction, with a time per step of 24.19 fs (10.0 aut). The first five steps of each simulation, as well as every step corresponding to a 10 kJ·mol−1 drop in energy, were sampled from the MD trajectory for further analysis using QTAIM. Finally, QTAIM analysis of all relevant species and samples from the AIMD trajectories was carried out using AIMAll,37 version 14.10.27.

rationalization of the Sharpless epoxidation of olefins and allylic alcohols and thus contribute to the design of enhanced catalytic solutions for the fragrance, flavoring, and pharmaceutical industries. For this purpose, the ligands present in the complexes under study (Figure 3a) not only reflect possible

Figure 3. Ligand (a) and substrate scenarios (b) considered in this study. Ligands 1 and 2 are always considered as bidentate, whereas ligand 5 may be present as a mono- or bidentate ligand. The different scenarios considered for the olefinic substrate include alkene (S1), allylic alcohol (S2), and its alkyloxo derivative coordinated to vanadium in an AC (S3) complex.

ligands in the homogeneous Sharpless epoxidation but also include the Schiff base derivative of acac (2) and a carboxylate ligand (5), which are surrogates for ligands commonly found in recent immobilization strategies.4,11,12,17,28 This work also intends to shed some light on the forces driving the regioselective epoxidation of geraniol by the VO(acac)2/ TBHP system. In order to achieve this, three different scenarios are considered for the substrate (Figure 3b): free alkene, free allylic alcohol, and the alkyloxo derivative of the latter coordinated to vanadium in an AC complex.

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COMPUTATIONAL METHODS

Throughout this work, the following nomenclature is used: each active complex is written in the form ACn-aX-bY-cZ, where n is the group number (as depicted in Figure 1) and X, Y, and Z are the numbers corresponding to the different ligands given in Figure 3a, with unnecessary suffixes being omitted. A similar notation is used for the inactive complexes, which follows the template ICn-Aw-Bx-Cy-Dz. This work is divided into three parts: (1) a thermodynamic assessment of a large number of possible oxygen-transfer reactions; (2) an analysis of the stationary points [reactants, products, transition states (TSs), and molecular complexes] along the reaction path of a subset of these oxygen-transfer reactions; (3) an AIMD survey of a selected number of oxygen-transfer reactions representative of the different reaction types depicted in Figure 2. All DFT calculations were performed using the ORCA version 2.8 electronic structure software,29 except for the AIMD studies, which were performed using software version 3.0.2 because of its improved capabilities on this matter. The X3LYP functional30 was chosen because previous studies suggested its adequacy for studying first-row TM complexes at an affordable computational effort.20 A mixed basis set was used in this work, which was available in the software under the keyword DefBas-4 and corresponded to a polarized triple-ζ-valence basis set with contraction patterns {311/1} for hydrogen, {62111/411/11} for other atoms in the main group, and {842111/63111/411/1} for vanadium.31,32

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RESULTS AND DISCUSSION The systematic survey of all possible vanadium complexes in the VO(acac)2/TBHP system (or some of its variants) yielded C


Article

Inorganic Chemistry Table 1. Average QTAIM Charges for Each Ligand of the 261 IC and AC Species under Study and Their Corresponding Standard Deviationsa ligand oxo TBHP OOtBu OO 1 2 3 4 5 6 7 a

average charge (au) −0.77 −0.04 −0.51 −0.93 −0.61 −0.49 −0.51 −0.46 −0.61 −0.47 −0.51

± ± ± ± ± ± ± ± ± ± ±

0.06 0.04 0.05 0.04 0.04 0.09 0.09 0.06 0.13 0.08 0.04

All values are given in atomic units of charge.

a large number of Ac and IC species with diverse properties. For the sake of conciseness, the following discussion mimics the exploration path taken on the course of this work: First, the different vanadium complexes are presented and analyzed. The thermodynamic balances of 263 epoxidation reactions, reflecting all possible reactions for each compound under consideration (cf. Figure 2) are analyzed and rationalized in terms of the properties of their reactants and products. From these, a set of 76 reactions are further analyzed in terms of the structure and relative energy of their TSs. Finally, seven reactions representative of this latter set are subjected to a coupled AIMD/QTAIM study, the results of which are analyzed and discussed. Characterization of the AC and IC Species. Following the restrictions mentioned in the Computationl Methods section, geometry optimization of 303 vanadium complexes was attempted. Preliminary results showed that AC7 are highly unstable and that their formation (from water and an AC6 complex) is strongly endoenergetic. Indeed, obtaining optimized structures for AC7 complexes containing ligand 5 was a difficult process because the acetate moiety would spontaneously abstract a proton from the hydroxyl group and form an

Figure 5. Distribution of ΔG⧧ among the subset of 76 epoxidation reactions, categorized by the substrate type.

adduct of AcOH and an AC6 complex. Thus, AC7 complexes were not considered for further study. Upon removal of the AC7 entries, a total of 261 complexes remained: 99 AC complexes and 162 IC ones. The QTAIM charge of the vanadium atom, q(V), ranges from +1.92 e to +2.31 e, and presents a bimodal distribution, which is due to the formal oxidation state of the metal center. Thus, the average charge of a vanadium(IV) atom is +2.11 ± 0.07 e, while vanadium(V) atoms score an average of +2.21 ± 0.05 e. Further exploration of the distribution of q(V), using the Party package34,35 for the generation of a classification tree, shows that the presence of ligand 1 has a small positive effect on q(V), as shown in Figure S1. On the other hand, the charges of the ligands in the coordination sphere of vanadium present monomodal distributions, indicating that their mutual interference is negligible. A summary of the charge distribution of the different ligands can be seen in Table 1. Ligand 5 presents more

Figure 4. Classification tree discerning the major descriptors affecting the distribution of ΔG for the 263 epoxidation reactions considered in this study at 298.15 K (a) and the statistical distribution of ΔG for each of the groups that emerged from the classification tree analysis (b). D


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Inorganic Chemistry

Figure 6. Elementary epoxidation reactions studied using AIMD.

multimodal distribution with maxima at about −237, −184, −110, and −8 kJ·mol−1, as can be seen in Figure 4b. A classification tree was used in order to ascertain some meaning to this multimodal distributions, and the results are displayed in Figure 4a. The results shown in Figure 4a,b reveal that AC4 complexes participate in the most exoenergetic epoxidation reactions in our data, yielding IC4 complexes (reactions of type Ia, as depicted in Figure 2). At the same time, the least exothermic reactions involve the formation of IC3 complexes from either AC4 (via a type Ib reaction), AC5 (via a type IIa reaction), AC6 (via a type IIb reaction, provided there is one ligand 3 in the AC complex), or AC8 complexes. Nevertheless, most reactions gather around the modal peaks at −184 and −110 kJ· mol−1 (Figure 4a). Among these, the ones leading to the formation of IC1 complexes (from either AC1, AC2, or AC3) are slightly less exoenergetic than those yielding the IC2 ones (which are only accessible from IC1 complexes, via a type Ia reaction) and also to the formation of IC4 complexes from the AC6 ones, via a reaction of type IIa. This small preliminary study, despite its simplicity, clearly shows that reactions of types Ia and IIa are thermodynamically preferred over reactions of types Ib and IIb, respectively, in accordance with the previous accounts by Vandichel et al.16 The choice between substrate S1 or S2 does not yield substantial differences in ΔG. Indeed, for the same AC and IC complexes, varying the substrate from S1 to S2 has an average

variation in its charge, possibly because of the fact that this ligand can behave as either monodentate or bidentate,27 although in our data, the monodentate configuration is predominant. Moreover, on some complexes in which both ligands 3 and 5 are present, a hydrogen bond might form, which further increases the variability in their charge. Table 1 also shows the average charges of the THBP, TBP, and O22− moieties in the AC complexes. These charges follow an expected pattern, considering the higher electronegativity of the O22− ligand compared to that of TBP. On the other hand, the TBHP moiety in AC1 and AC4 complexes is essentially neutral, revealing that little charge is transferred from the “business end” of these epoxidizing agents to the metal center. Thus, it is reasonable to raise the hypothesis that AC1 and AC4 complexes might behave like adducts of TBHP with their corresponding IC1 and IC3 counterparts and also that the activation of TBHP might be mostly due to polarization of the Oprox−Odist bond in TBHP (or, alternatively, via the establishment of a hydrogen bond from TBHP to the one of the ligands in the complex). Thermodynamic Survey. The survey of the thermodynamic balance of all 263 epoxidation reactions available from the set of AC complexes under consideration covered 122, 166, and 25 cases involving substrate scenarios S1, S2, and S3, respectively (cf. Figure 3b). The following discussion will focus on the distribution of ΔG at 298.15 K, the analysis of which is summarized in Figure 4. Within our data, ΔG ranges from −302.4 kJ·mol−1 to about 2.22 kJ·mol−1 and presents a E


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Inorganic Chemistry

AC3 or AC6 reactants, respectively. This shortcoming is minor because type IIb reactions usually have higher activation barriers and smaller thermodynamic yields compared to type IIa reaction paths connecting the same reactants and products.16 Contrary to the multimodal distribution of ΔG (shown in Figure 4), the activation Gibbs energy (ΔG⧧ = GTS − GMC1) presents a monomodal distribution, ranging from +17 to +141 kJ·mol−1, with an average value of +78 ± 24 kJ·mol−1. The values for individual reactions are in good agreement with the ones calculated in previous works.16 The lower ΔG⧧ was observed for the epoxidation of S1 by AC4-a3 in a reaction of type Ia, whereas the oxidation of the same substrate by AC6-a2b4 (type IIa) attained the highest activation barrier. As shown in Figure 5, there is a tendency for reactions involving substrate S1 toward lower ΔG⧧. In turn, the distribution of ΔG⧧ for the epoxidation of S2 shares the same overall shape (albeit broader) as that of S3. Such results indicate that the epoxidation of an alkene is not only thermodynamically but also kinetically favored in comparison to that of an allylic alcohol. Nevertheless, upon coordination to vanadium (S3), there is a shift toward smaller activation barriers. This is well illustrated by comparing the epoxidation of ligand 6 in AC6-a1b6 (ΔG = −191 kJ·mol−1 and ΔG⧧ = +80.0 kJ·mol−1) with the epoxidation of S2 using some similar AC complexes, via a reaction of type IIa. Indeed, the epoxidation of S2 by either AC6-a1-b3 or AC6-a1-b4 is less exoenergetic (ΔG = −170 and −164 kJ·mol−1, respectively) and bears a higher activation barrier (ΔG = +125 and +113 kJ·mol−1, respectively) than such a reference. AIMD Studies. In order to better understand how the epoxidation step develops, a series of AIMD simulations were performed. Considering the cost and complexity of the calculations involved (and also the relative homogeneity of the different reactions examined), this part of the study was restricted to seven case studies. These were chosen in order to reflect the most prominent variables at hand (AC, substrate, and reaction types) and will be henceforward referred to by their reaction number (Rn), as depicted in Figure 6. Our analysis starts with the epoxidation of S1 by AC8-a3 [reaction (R1)], due to the structural simplicity of the vanadium species involved. Figure 7 displays a number of relevant characteristics of the systems varying over the time of the AIMD simulations. The results show that the most interesting changes in the system take place within 10 ps of the TS (for the amount of initial kinetic energy used in this study). These involve the surpass of a activation barrier of about 40 kJ·mol−1 and the release of about 330 kJ·mol−1, for a total ΔE = −250 kJ·mol−1, as depicted in Figure 7a. More interestingly, the bond-breaking process for the Oa−Ob bond starts about 5 ps before the TS, at a time were the substrate is about 2.7 Å away from Oa. Analysis of the molecular graph for the system at t = −5.1 ps shows the presence of a bond critical point (BCP) along a bond path connecting Oa to Ca. This BCP is in a low-density region (ρBCP = 0.016 au) and corresponds to a weak, noncovalent interaction [positive Hamiltonian energy density,42 H(ρBCP) = +0.002 au]. The region immediately preceding the TS is characterized by the divergence of the V−Oa and V−Ob interatomic distances. At the TS (t = 0 ps), the BCP connecting Oa to Ca remains at a sparsely populated region, with ρBCP = 0.040 au. On the other hand, a bond path connecting Oa to Cb is not observed at the TS. Indeed, while the BCP for the Oa−Ca bond is present at the

Figure 7. Stacked plots of the relative energy (a), interatomic distances (b), QTAIM charges (c), and relative electronic energies for the atomic basins of V, Ooxo, OH, Oa, and Ob (d) varying with time for the AIMD simulation of reaction (R1). Energies are given in kilojoules per mole, taking the first point of the graph (close to MC1) as the reference, distances are given in angstroms, and QTAIM charges are given in atomic units. The TS is located at t = 0 ps, and the time axis is oriented in the direction from reactants to products.

impact on ΔG of only 3.31 ± 0.13 kJ·mol−1, favoring the S1 substrate. The results thus far suggest that the AC4 and AC6 complexes are the strongest epoxidizing agents. Concomitantly, AC6 complexes are also the most common AC species in the Sharpless epoxidation process.13,14,16,38,39 Moreover, the results do not support the hypothesis that the regioselectivity of the Sharpless epoxidation toward allylic alcohols is thermodynamically driven, as previously proposed.40,41 TSs and Activation Barriers. Starting from the equilibrium geometries of the reactants in each reaction, a relaxed PES scan was performed in order to have an educated guess for the geometry of their respective TSs. This guess was then subjected to a saddle-point optimization and subsequent inspection of the vibrational modes of the optimized geometry. This procedure successfully yielded 76 TS structures. These structures belong to the epoxidation step of all reaction types, with the exception of type IIb. Despite best efforts, none of the candidate structures was able to perform the proton transfer and epoxidation in a single-step reaction of type IIb. On the other hand, it was found that the proton-transfer step would take place before the oxygen-transfer step, yielding an intermediary AC1 or AC4 complex related to the original F


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Inorganic Chemistry

Figure 8. Stacked plots of the relative energies (a and b), interatomic distances (c and d), QTAIM charges (e and f), and relative electronic kinetic energies for the atomic basins of V, Ooxo, OH, Oprox, and Odist (g and h) varying with time for the AIMD simulation of reactions (R2) (a, c, e, and g) and (R3) (b, d, f, and h). Energies are given in kilojoules per mole, taking the first point of the graph (close to MC1) as the reference, distances are given in angstroms, and QTAIM charges are given in atomic units. The TS is located at t = 0 ps, and the time axis is oriented in the direction from reactants to products.

early stages of the reaction and gradually increases ρBCP, the one corresponding to the Oa−Cb bond appears only at t = +8.37 ps, but already with the characteristics of a well-defined covalent bond [ρBCP = 0.155 au and H(ρBCP)=−0.071 au]. Such a BCP is undetected in the previous sample (taken at t = +8.06 ps). Thus, the data strongly suggest the Oa−Ca bond to be formed first, despite the relative coincident graphs for the Oa−Ca and Oa−Cb interatomic distances presented in Figure 7b. Analysis of the QTAIM charges for the most relevant parts of the system shows that most of the charge-transfer phenomena associated with the epoxidation of S1 happens during the fist 10 ps after the TS, as shown in Figure 7c. Throughout the course of the reaction, the QTAIM charge of vanadium remains nearly constant [q(V) = +2.15 ± 0.02 e]. The same may also be observed for the oxo ligand and also for the spectator ligand 3 (Figure 7c). Indeed, this pattern of relative charge stability for the vanadyl group is observed in all reactions in this study. Moreover, the intraatomic dipole momentum on both the metal center and oxo ligand remained approximately constant in the course of the AIMD simulations, allowing us to postulate that the intraatomic polarization terms concerning the vanadyl group are also negligible. Considering the fact that QTAIM charges and intraatomic polarizations are highly sensitive to the chemical environment,20,21,43,44 these results point toward a very stable electronic population at the vanadyl moiety along the course of the epoxidation process. This is in contrast with the two oxygen atoms in the peroxo group (Oa and Ob) and the two carbon atoms in the substrate (Ca and Cb) directly involved

in the oxygen-transfer step. For these atoms, the time evolution of the intraatomic polarizations follows that of the charge transfer, with the increase of the intraatomic polarizations of both Ca and Cb reflecting their linkage to the more electronegative oxygen atom. The evolution of the relative atomic electronic energies (ΔEΩ, taking the atomic electronic energies, EΩ, at MC1 as the reference) with time in AC8-a3 is given in Figure 7d. These energies are calculated from the electronic kinetic energy (kΩ) on each atomic basin (following Bader’s partition scheme) and assume the validity of the virial approximation for the total electronic energy on each basin. Similar to what was observed for the QTAIM charges, Ooxo and the ligand 3 retain about the same value along the reaction course. The variation on ΔEΩ for V, Oa, and Ob allows us to have some insight on the changes taking place during the oxygen-transfer step. As shown in Figure 7d, there is a small destabilization of Ob and V in the early stages of the reaction (t ≈ −5.0 ps), as the substrate approaches the former, and the Oa−Ob bond starts to elongate. Nevertheless, the most prominent feature in Figure 7d is the sharp decline in ΔEΩ for the metal center and Ob, taking place after the TS. This suggests a progressive stabilization of the latter as its chemical environment changes from being part of the peroxo moiety to being an oxo ligand of the vanadium atom. In turn, ΔEΩ for vanadium shows a definitive increase for t > +6.7 ps. This decrease in the stability of the metal center coincides with a noticeable stabilization of Oa as it leaves the coordination sphere of vanadium and forms the epoxide ring G


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Inorganic Chemistry

is in contrast with reaction (R3), where this process apparently starts before the Cb−Odist bond reaches its equilibrium length. Regarding the relative stabilization of the individual atoms in the system, Figure 8g reveals a considerable destabilization of the vanadium atom during the course of reaction (R3) coinciding with the proton-transfer process. On the other hand, Figure 8h shows that the electronic energies for the metal center and its oxo ligand do not vary as much in reaction (R1) as in reaction (R1). Figure 8h further shows a destabilization of Odist at the TS associated with reaction (R3). Such a feature is not observed in the case of reaction (R2) and might be associated with the higher activation barrier of reaction (R3) compared to that of reaction (R2) (ΔGR2⧧ = +17.0 kJ·mol−1, versus ΔGR3⧧ = +53.1 kJ·mol−1). A similar analysis of reaction (R4) (the results of which are shown in the Supporting Information) gave results similar to those observed for reaction (R3), thus suggesting that the behavior highlighted for reaction (R3) is representative of other reactions of type Ib and also that the oxidation state of the metal center bears little influence on the course of this class of reactions. Further insight on these competing reaction paths may be gathered by taking a look at the molecular graphs of their respective TSs. As can be seen in Figure 9a, reaction (R2) is characterized by a roughly perpendicular orientation of the substrate relative to the V−Oprox−Odist plane. Figure 9a also shows that the electronic density at the CC bond is noticeably distorted toward Odist (denoting the beginning of the formation of the epoxide) and that a five-atom ring is formed between V, Oprox, Odist, HTBHP, and Ooxo. As Odist moves toward the CC bond, the V−Oprox and Ooxo−HTBHP bonds become shorter. This is in contrast to the in-plane approach observed for the TS associated with reaction (R3) (Figure 9b), which favors the asynchronous formation of the two C−O bonds. At the TS, all of the BCPs B1−B7 show a significant amount of electronic density, the lowest of which is observed for point B6 in the TS of reaction (R2) [ρ(B6,R2) = 0.046 au]. Moreover, H(r) is negative at all BCPs, showing the covalent character of these seven bonds in both reaction paths. A more detailed characterization of such points is given in Table S1. In summary, Figure 9 highlights the fact that the relative orientation between the substrate and AC complex plays an important role and might be the most important aspect driving a substrate/AC system toward a specific reaction path. The last three cases shown in Figure 6 [reactions (R5)− (R7)] are representative of type IIa reactions using different substrates. According to Vandichel et al.,16 these are the most common reactions during the Sharpless epoxidation process, particularly those involving AC6 complexes. Figure 10 shows an overview of the changes in energies, interatomic distances, QTAIM charges, and atomic electronic energies for selected atoms during the course of each reaction. The results show that the three reactions share the same energetic profile (Figure 10a−c), with reaction (R6) being the most exothermic of the three (ΔGR6 = −212 kJ·mol−1). Figure 10c further shows a softer decay of the energy in the case of reaction (R7) during the last phase of the reaction (t > 8 ps). This is trivially explained by the adjustment in the conformation of ligand 7 after oxygen transfer took place. Figure 10e shows that formation of the epoxide ring is slightly more asynchronous in the case of reaction (R6), whereas the epoxidation of either the alkene S1 (Figure 10d) or the “internal” substrate S3 (Figure 10f) takes place in a more synchronized fashion. On the other hand, the point at which Oprox becomes closer to

Figure 9. Molecular graphs and contour plot of ∇2ρ(r) at the V− Oprox−Odist plane of the TS for reactions (R2) (a) and (R3) (b). In both graphs, vanadium, oxygen, carbon, and hydrogen atoms are represented by blue, red, gray, and white spheres, whereas the BCPs are represented by small red spheres. Hydrogen and carbon atoms in the methyl groups of the substrate and TBP do not take part in the epoxidation process and were cloaked to improve readability.

with the substrate. Furthermore, analysis of the molecular graph and the minima of ∇2ρ(r) in AC8-a3 reveals five iVSCCs in a nongillespiean configuration in the atomic basin of the vanadium atom.27 Such a configuration is also present in the initial stages of the reaction course. As the reaction progresses, the Oa−Ob distance increases, and the inner valence shell of the metal center rearranges into four iVSCCs under a gillespiean configuration, thus granting greater stability to vanadium. In order to better ascertain the differences between two competing reaction paths (i.e., Ia and Ib), reactions (R2) and (R3) were taken into consideration for a coupled AIMD/ QTAIM study, the results of which are summarized in Figure 8. The data clearly show a “shoulder” in the energetic profile of both reactions (Figure 8a,b), suggesting that oxygen transfer and the proton-transfer processes take place at different times; such a hypothesis is also suggested by the evolution of the interatomic distances over time. The early stages of both reactions (R2) and (R3) are marked by elongation of the Odist− Oprox bond as the substrate approaches the AC (Figures 8c,d). Figure 8f further reveals an asymmetric approximation of the substrate toward the AC in the case of reaction (R3), suggesting that the two C−O bonds of the epoxide are formed in an asynchronous fashion, while the same process happens in a more synchronized manner in the case of reaction (R2) (Figure 8e). Moreover, the proton-transfer step in reaction (R2) takes place at about t ≈ +11 ps, which is after both C−O bonds reach their equilibrium lengths (at about t ≈ 9 ps). This H


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Inorganic Chemistry

Figure 10. Stacked plots of the relative energies (a−c), interatomic distances (d−f), QTAIM charges (g−i), and relative electronic kinetic energies for the atomic basins of V, Oprox, Odist, Ca, and Cb (j−l) varying with time for the AIMD simulations of reactions (R5) (a, d, g, and j), (R6) (b, e, h, and k), and (R7) (c, f, i, and l). Energies are given in kilojoules per mole, taking the first point of the graph (close to MC1) as the reference, distances are given in angstroms, and QTAIM charges are given in atomic units. The TS is located at t = 0 ps, and the time axis is oriented in the direction from reactants to products.

when the substrate is S1 [as shown for reaction (R6) in Figure 10h] but presents a logarithmic profile when the substrate is S2 [illustrated by reaction (R5) in Figure 10g]. The use of substrate S3 in reaction (R7) (Figure 10i) yields a profile closer to that found for substrate S1 rather than S2. The similarities between the three reactions extend to the relative stabilization/destabilization of the individual atoms. As previously observed (cf. Figures 7d and 8g,h), parts j−l of Figure 10 show that ΔEΩ for vanadium has a small increase at about t = 5 ps prior to reaching the TS. It then decreases substantially and has a second high at about t = 9 ps, stabilizing toward the end of the reaction. This rather erratic behavior of the metal center is also observed in the case of reactions (R2)− (R4) (cf. Figures 8g,h and S3). Indeed, among the different cases studied, only reaction (R1) stands out for having a slightly different behavior. A recent study27 on the structures of the V− OO and V−TBP bonds shows that nongillespiean arrange-

vanadium than Odist happens at the TS for reactions (R6) and (R7), while it precedes the TS by about 4 ps in the case of reaction (R5), given the initial conditions on which the AIMD simulations took place. Following the evolution of the QTAIM charges of Ca and Cb across parts g−i of Figure 10, one finds that the charge of these carbon atoms is approximately zero at the beginning of the reaction, regardless of the substrate used. Indeed, only the reaction using substrate S2 stands out because the charge of Ca increases at a greater rate than that of Cb. This, however, can be traced back to the asynchronous formation of the two C−O bonds. In turn, and considering our analysis of reactions (R2) and (R3), such an asynchronous process is likely to be dictated by the relative orientation of the substrate upon approach in the early stages of the reaction. More interestingly, as Odist starts to form the epoxide moiety, its charge decreases from about −0.5 e to about −0.9 e in all cases. Such a decay follows a linear path I


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Inorganic Chemistry

drive the documented regioselectivity of the Sharpless epoxidation process.

ments of the iVSCCs are present in the symmetrical bond to OO but are usually absent in the asymmetrical bond to TBP. Such a difference may be at the origin of the differentiated behavior of AC8-a3 in the course of reaction (R1). What is more, one may safely consider that the distinctive behavior of ΔEΩ (V) during the oxygen-transfer step is due to the changes in the O22− moiety, considering the effect of nongillespiean configurations of the iVSCCs on the ΔEΩ of vanadium27 and the data collected in this work. In all cases, ΔEΩ for the oxygen atom involved in formation of the epoxide ring reaches a maximum at the TS, whereas for the oxygen atoms that remain attached to vanadium [Ob in reaction (R1) and Oprox in the other reactions], ΔEΩ tends to decrease gradually during the course of the reaction. Finally, parts j−l of Figure 10 also show how the destabilization of Ca and Cb during formation of the threemembered ring is compensated for by the huge stabilization of Odist during the course of the reaction. Because this is observed in all reactions covered in this study, it is sensible to hypothesize that the oxygen atom(s) involved in vanadium peroxide and vanadium alkylperoxide linkages is (are) the energy reservoirs driving formation of the epoxide rings.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.6b02770. Raw results from the classification tree models for q(V) and ΔG298 K, summary of coupled AIMD/QTAIM analysis for reaction (R4), and atoms-in-molecules characterization of the BCPs displayed in Figure 9 (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: fi[email protected]. *E-mail: [email protected]. ORCID

Filipe Teixeira: 0000-0001-8786-0086

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Notes

CONCLUSIONS In this work, a large number of possible oxygen-transfer elementary reactions portraying part of the Sharpless epoxidation process of an alkene and an allylic alcohol (both free and coordinated to vanadium as an alkyloxo ligand) were studied. The vanadium(V) tert-butylhydroperoxide complexes are the reactants for the most exothermic reactions. On the other hand, the formation of vanadium(V) complexes with two oxo groups is thermodynamically unfavored. All other reactions tend to gather around the modal peak at about −184 kJ·mol−1. The overlap between these groups of reactions suggests that the ligands surrounding the vanadium atom play a small role in determining the thermochemistry of these reactions. QTAIM analysis of the different AC catalysts revealed that the charge of the metal center, and also of the O22− (or alkylperoxide) moieties, remains stable and independent of the composition of the coordination sphere of vanadium. Given these results, the most likely way in which the ligands may influence the outcome of these reactions would be via steric conditioning of the conformation of both reactants and products. Further analysis of a subset of these reactions showed that the activation barriers gather around a modal value of +78 kJ· mol−1. A direct correlation between ΔG⧧ and either the type of oxygen-transfer reaction, AC catalyst, substrate, or composition of the coordination sphere of vanadium (or any combination of these effects) eluded our best efforts. What is more, the absence of a lowering in the activation barriers when using allylic alcohol as the substrate provides some grounds against a hypothetical lowering of the activation barriers due to the more electrophilic carbon atoms in this type of substrate. A closer look at the course of some of these reactions using AIMD coupled with QTAIM analysis of samples taken from the AIMD trajectories confirmed the relative homogeneity regarding the overall behavior of the different AC catalysts and substrates. The major exception to this is the behavior of the peroxovanadium(V) complexes, for which some peculiarities were observed. This analysis also revealed that the choice between the two available reaction paths is mostly dictated by the orientation of the substrate as it approaches the AC catalyst. Thus, a steric, rather than electronic, effect is more likely to

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by Fundaçaõ para a Ciência e a Tecnologia (FCT/MEC) through national funds and cofinanced by FEDER, under the Partnership Agreement PT2020 (Projects UID/QUI/50006/2013 and POCI/01/ 0145/FEDER/007265). F.T. further acknowledges FCT/ MEC for a Doctoral Grant (SFRH/BD/64314/2009). M.N.D.S.C. also acknowledges FCT/MEC for Grant SFRH/ BSAB/127789/2016.

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REFERENCES

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Driving Forces in the Sharpless Epoxidation Reaction: A Coupled

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