Kinetics and Mechanistic Insight from D - American Chemical Society

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Complete Reaction Pathway of Ruthenium-Catalyzed Olefin Metathesis of Ethyl Vinyl Ether: Kinetics and Mechanistic Insight from DFT Yury Minenkov, Giovanni Occhipinti, and Vidar R. Jensen* Department of Chemistry, University of Bergen, Allégaten 41, N-5007 Bergen, Norway S Supporting Information *

ABSTRACT: Density functional theory calculations accounting for dispersion, thermochemical, and continuum solvent effects have been applied to study the metathesis of ethyl vinyl ether (EVE) as mediated by ruthenium catalysts L(PCy3)(X)2RuCHPh (L = PCy3, IMes (1,3-dimesitylimidazol-2-ylidene), H2IMes (1,3-dimesityl-4,5-dihydroimidazol-2-ylidene); X = Cl, Br, I) in toluene. The computational approach has been validated against experimental data for ruthenium-based olefin metathesis catalysts and is found to give acceptable accuracy even for weakly bound transition states of phosphine and olefin dissociation and association. All relevant stationary points of the EVE metathesis reaction have been included in the study, allowing comparison with experimental kinetic data (Sanford, M. S.; Love, J. A; Grubbs, R. H. J. Am. Chem. Soc. 2001, 123, 6543). From the active 14-electron complex, the barriers to both phosphine association (at a rate proportional to k−1) and olefin binding (k2) involve contributions from entropy and solute−solvent interactions. The overall barrier to EVE cycloaddition (k2*) is higher than that to binding only (k2). The thus obtained ratios k−1/k2* compare nicely with those originally measured and interpreted as k−1/k2 by Sanford et al., suggesting that the experimental obtained ratios are better understood as k−1/k2*. Complementing the theoretical rate constants with concentrations, the thus obtained “computational kinetics” reproduces known trends among the various catalysts and also offers mechanistic insight.

1. INTRODUCTION Olefin metathesis has evolved to become one of the most versatile chemical reactions for formation of carbon−carbon bonds,1,2 with important applications in advanced organic synthesis and in the production of fine chemicals, polymers, and pharmaceuticals.3,4 The well-defined Grubbs ruthenium catalysts, which combine excellent activities with functional group tolerance and a certain degree of stability in air, have in particular spurred this development.5,6 The Grubbs catalysts, which are the focus of the current contribution, are known to operate via the general Hérisson− Chauvin mechanism,7 which involve a metallacyclobutane intermediate (see Scheme 1). Many of the fundamental aspects particular to the way in which this class of catalysts mediates olefin metathesis were established early on by Sanford et al. in their seminal work,8,9 which has been used actively as a standard against which to compare in many of the subsequent experimental (for example, see refs 10−31) and computational (for example, see refs 13, 29, and 32−64) mechanistic contributions. Using NMR and UV−vis spectroscopic techniques, Sanford et al. examined the kinetics of phosphine exchange and early parts of the olefin metathesis reaction for a series of catalysts, including those of general formula L(PCy3)(X)2Ru CHPh (L = PCy3, IMes, H2IMes; X = Cl, Br, I), thus singling out the effects of ligand variation on the mechanism and activity of ruthenium-based olefin metathesis catalysts. For example, they found that, for all the catalysts investigated, initiation proceeds by dissociative substitution of a phosphine ligand PCy3 by the © XXXX American Chemical Society

Scheme 1. Hérisson−Chauvin Mechanism for Olefin Metathesis Adapted for the Grubbs Ruthenium Catalystsa

a Enumeration of rate constants k1−k3 as given in ref 9 and labeling of intermediates (in boldface) as used in the present study.

olefinic substrate. This conclusion is in agreement with evidence from gas-phase mass spectrometry experiments,65−67 and a dissociative initiation pathway was also early on shown to be favorable in molecular-level computational st udies.13,32−34,39,42,68−70 In contrast, the relative rate with which Sanford et al. observed phosphine dissociation to occur in first (L Received: December 10, 2012

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dx.doi.org/10.1021/om301192a | Organometallics XXXX, XXX, XXX−XXX

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computational study of the transition region of olefin binding as part of this mechanism involved only relatively small model catalysts.32 In fact, the weakly bound transition states of phosphine and olefin dissociation and association are difficult to obtain in computational studies, and the lack thereof for reaction of Grubbs catalysts with EVE has so far hampered quantitative comparison with the experimental k−1/k2 data of Sanford et al.8,9 However, during the last couple of years, reports of transition states for coordination/dissociation of ethylene54,73 and other olefins64 started to appear. The fact that it has become possible to address the energetics of dissociation and binding of phosphine and olefin ligands, including the barriers arising from transition states involving weakly interacting fragments, is largely due to the development of cost-efficient DFT methods capable of handling dispersion interactions.45,74−76 Moreover, the success with respect to description of phosphine and olefin dissociation and association suggests that it should also be possible to address the corresponding transition states and barriers of EVE coordination and association for these catalysts and thus to obtain complete reaction pathways of EVE metathesis. The availability of calculated relative free energies in solution for each stationary point along the reaction pathway, in turn, would allow the first broad and quantitative comparison with the experimental reference kinetic data of Sanford et al. By comparison of calculated k−1/k2 ratios with the experimental counterparts it should, for example, be possible to identify catalysts for which assumptions 1 and 2 above do not hold and, more generally, to single out which elementary steps and rate constants, in addition to k−1 and k2, that should be included to characterize the activity of these catalysts. In other words, quantitative comparison of the calculated and experimental kinetic data is likely to give additional insight into the mechanism of ruthenium-catalyzed olefin metathesis. To achieve a comparison with the data of Sanford et al. described above, we have performed density functional calculations and located all stationary points of metathesis of ethyl vinyl ether (EVE) for catalysts 1−7 in Chart 1. Solvent effects have been accounted for using an implicit solvent model, and thermochemical corrections, obtained from harmonic

= PCy3)- and second-generation (L = N-heterocyclic carbene (NHC)) catalysts proved hard to reproduce computationally.42,46,62,71 In spite of the higher catalytic activities and the larger expected trans effect of the NHC ligands, Sanford et al. found the initial phosphine dissociation to be slower for the second-generation catalysts.8,9 Faster subsequent steps are therefore the explanation for the higher activity observed for the second-generation catalysts, and the more favorable partitioning to products has been termed “commitment”,12 in analogy to similar phenomena in enzyme catalysis. Only with the advent of density functional theory (DFT) methods accounting for dispersion and keen attention to conformational issues for realistic model catalysts could the difference in the initiation rates of the first- and secondgeneration catalysts be reflected in the corresponding calculated bond dissociation energies.46,72 Moreover, using similar costefficient computational methods, it has been possible to obtain accurate absolute ruthenium−phosphine bond dissociation energies and enthalpies, in the gas phase14,72 as well as in solution.62 Recently, good (MUE/MSE = 6.0/6.0 kcal/mol)64 to very good (MUE/MSE = 2.5/1.4 kcal/mol)63 agreement with the experimental solution free energy barriers of phosphine dissociation8,9 from Grubbs catalysts for olefin metathesis was also obtained using DFT accounting for dispersion interactions. In their comparison of the catalytic performance of systematically varied catalyst structures, Sanford et al.8,9 focused in particular on two crucial elementary reactions which the active 14-electron complex can undergo (see Scheme 1): (i) it can regenerate the 16-electron precursor complex via rebinding of a phosphine (k−1) or (ii) it can bind an olefinic substrate (k2) and proceed with the rest of the catalytic cycle. Thus, to a large extent these authors based their comparison on the k−1/k2 ratios, which were obtained from the observed reaction rates with the following assumptions: 1. Olefin binding (k2) essentially is irreversible. 2. All steps subsequent to olefin binding are fast. Even if the authors themselves warned that in particular the first assumption could be “somewhat unrealistic”,9 their k−1/k2 ratios discriminate nicely between the different catalysts and offer valuable insight by giving an easy-to-grasp measure of the extent to which the active center (AC1) engages in actual catalysis (k2) or is inactivated via phosphine recoordination (k−1), i.e., the degree of “commitment”. We note that, if both assumptions hold, olefin binding (AC1 → PC1 in Scheme 1) is left as the only candidate rate-limiting step for the fast initiating but less “committed” first-generation catalysts. Moreover, for catalysts for which assumptions 1 and 2 are less appropriate, k−1/k2 is likely to be overestimated since additional terms, in particular k3 and k−2, are not included. Results from computational32,42 and mass spectrometry12 studies have later suggested that the steps subsequent to olefin binding are not necessarily faster than the preceding steps. For example, in the latter investigation12 experimental evidence for a barrier significantly higher than that of phosphine dissociation, attributed to formation of the metallacyclobutane ring (PC1 → MCB), was obtained for the first-generation catalyst 1. Due to the excess quantities of olefin normally applied in olefin metathesis reactions, olefin binding (AC1 → PC1) was furthermore ruled out as a candidate rate-limiting step,12 thus contrasting assumptions 1 and 2 above. In spite of being a prominent, possibly even rate-limiting, step in the dissociative mechanism of olefin metathesis, until recently the only

Chart 1. First (1−3)- and Second-Generation (4−7) Grubbs Catalysts for Olefin Metathesis Studied in the Present Work

B


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geometry optimizations above. All PRIRODA defaults were adopted except for the gradient optimization threshold, which was tightened to 1 × 10−5 (au). IRC step lengths in the range 0.5−2.0 Å amu0.5 were used, depending on the flatness and degree of curving in each region of the individual reaction pathways. Single-Point (SP) Energy Evaluations. In all cases, the energy was reevaluated, using the Gaussian 09 suite of programs,88 at the optimized geometries using the standard generalized gradient approximation (GGA) functionals BP86,89,90 PBE,77,78 and BLYP,89,91,92 the hybridGGA functionals B3LYP93 and PBEh,77,78,94 and the hybrid meta-GGA functional ωB97XD.95−98 All but the last of these functionals (which already contains empirical and long-range corrections) were also used in combination with an empirical dispersion correction (termed D3(BJ)) proposed by Grimme,99 to arrive at DFT-D3(BJ) estimates. In addition, the BLYP energies were also combined with a previously proposed dispersion correction (termed D2),95 forming the estimates here termed DFT-D2, due to the excellent performance observed for the latter approach in describing free energy profiles of phosphine dissociation from ruthenium catalysts.63 Finally, the last two functionals included, the Minnesota meta-GGA (M06L) and the hybrid counterpart thereof (M06),45,75 account for noncovalent interactions and dispersion via extensive parametrization and were used without additional dispersion terms. It is well-known100−102 that modern meta-GGA functionals, and in particular the Minnesota (M0*) family, are very sensitive to the choice of grid for numerical integrations. Thus, the “ultrafine” (pruned, 99 radial shells and 590 angular points per shell) grid of Gaussian 09 was employed in all SP calculations. Furthermore, the SP energy evaluations were corrected for basis set superposition errors (BSSE) using the counterpoise method in combination with the following fragments.103 In the precatalyst (P) and the first transition state (TS1), two fragments corresponding to the active complex (AC1) and PCy3, respectively, were used. In the second (TS2) and third (TS3) transition states as well as in the π complex (PC1), the fragments were the active complex (AC1) and ethyl vinyl ether (EVE), respectively. In the fourth (TS4) and fifth (TS5) transition states as well as in the second π complex (PC2), the second active complex (AC2) and benzylidene were defined as fragments. In the metallacyclobutane (MCB) intermediate, two sets of fragments, AC1 and EVE and AC2 and styrene, respectively, were tested. Counterpoise estimates based on these two sets of fragments agreed to within 0.5 kcal/mol, and it was thus decided to take the average of these two approaches as our BSSE estimate for MCB. Stuttgart type effective core potentials (ECPs) accounting for the inner electrons of C (2-electron ECP), N (2), O (2), P (10), Cl (10), Br (28), I (46),104 and Ru (28)105 were used in the SP calculations. Their accompanying [2s2p] (C, N, P) and [2s3p] (O, Cl, Br, I)104 and [6s5p3d] (Ru)105 contracted valence basis sets were improved as follows. First, for ruthenium, two f functions106 were added to the (8s7p6d) primitive basis set.107,108 The resulting (8s7p6d2f) primitive basis set was contracted to [7s6p4d2f]. The valence basis sets of all nonmetal and non-hydrogen elements104 were supplemented by single sets of diffuse s and p functions, obtained even-temperedly (C (αs = 0.059143, αp = 0.040337), N (αs = 0.031820, αp = 0.057319), O (αs = 0.042628, αp = 0.018294), P (αs = 0.026847, αp = 0.035571), Cl (αs = 0.0346338, αp = 0.0048339), Br (αs = 0.0422669, αp = 0.0144112), I (αs = 0.0476431, αp = 0.0108044)). Finally, single sets of polarization d functions, obtained from the EMSL basis set exchange Web site,109,110 were added to the basis sets of C (exponent αd = 0.720), N (αd = 0.980), O (αd = 1.280), P (αd = 0.465), Cl (αd = 0.619), Br (αd = 0.389), and I (αd = 0.266). The resulting (5s5p1d) (C, N, P) and (5s6p1d) (O, Cl, Br, I) primitive basis sets were contracted to [4s4p1d] (C, N, P) and [4s5p1d] (O, Cl, Br, I), respectively. Hydrogen atoms were described by a Dunning triple-ζ basis set111 augmented by a diffuse s function (αs = 0.043152), obtained even-temperedly (i.e., estimating the exponent of the diffuse function from the ratio of the exponents of the outer valence basis functions),112,113 and a polarization p function (αp = 1.00). We have used the basis sets described above for SP calculations in previous studies on which the present study partially builds,62,63 and part of the reason for using these basis sets in the present study thus is one of maintaining a reasonable internal consistency. It should be mentioned

frequencies, have been included to give estimates of the relative free energies in solution.

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COMPUTATIONAL DETAILS

Conformational Issues. For all catalysts 1−7 the conformations of the precursors (P) and the active complexes (AC1) were taken to be those of catalysts 1 and 4 as determined by Tsipis et al.42 For the π complex PC1, the metallacyclobutane MCB, and the product styrene π complex PC2, the conformations were assumed to be similar to those determined by Adlhart and Chen.13 Additional EVE-related conformations were tested by geometry optimization using DFT (see below for details), but these always turned out to be higher in energy than those taken from ref 13. For catalysts 1−3 the 180° rotation of the PCy3 group around the Ru−P bond needed to regenerate the starting conformation (required to reflect the symmetry of degenerate ethylene metathesis) has been shown to take place late in the reaction13 and is here assumed to occur after TS5. The transition states located in the present work are those that connect the respective reactant and product minima, which means that conformational searches have not been performed for transition state structures. Geometry Optimization and Calculation of Thermochemical Corrections. All geometry optimizations were performed using the generalized gradient approximation (GGA) functional PBE77,78 as implemented in the PRIRODA 08 DFT code.79 This GGA functional was chosen for geometry optimization due to its computational efficiency (faster than meta-GGA and hybrid functionals) and because of its performance in a recent validation study of functionals for geometry optimization of ruthenium-based alkylidene complexes and other homogeneous transition-metal catalysts.80 For metal−ligand bond distances and ligand−metal−ligand angles, PBE was found to be among the best functionals tested and to match functionals (B97D and ωB97XD) including dispersion. Similar small effects of including dispersion in the geometry optimization of transition-metal complexes have been noted by other workers (see, e.g., refs 81 and 82). It is gratifying, however, that, if dispersion should turn out to be important for the present geometries, the functional used (PBE) has been shown to be less “repulsive”, for example, than B3LYP and to account, to some extent, for dispersion interactions.83,84 Numerical integrations required for the exchange-correlation (XC) term were performed using the default, adaptively generated PRIRODA grid, corresponding to an accuracy of the exchange-correlation energy per atom equal to 1 × 10−8 hartree. Default values were also used for the SCF convergence (1 × 10−6 au) and the maximum displacement geometry convergence criterion (0.01 au), whereas the corresponding maximum gradient for geometry optimization convergence was decreased by a factor of 10 (in comparison with the default 1 × 10−4 au). All stationary geometries were characterized by the eigenvalues of the analytically computed energy second derivative matrix. All stationary points of catalysts 2 and 5 were connected by intrinsic reaction coordinate (IRC) calculations,85 and selected minima and transition states of other catalysts were also connected. Translational, rotational, and vibrational partition functions for thermal corrections to give total enthalpies and Gibbs free energies were computed within the ideal-gas, rigid-rotor, and harmonic oscillator approximations following standard procedures. The temperature used in the calculation of thermochemical corrections was set to 298.15 K in all cases. All-electron basis sets essentially comparable in quality to the correlation consistent valence double-ζ plus polarization (cc-pVDZ) basis sets of Dunning were used,86 with the following element-specific contractions: Ru, (26s23p16d5f)/[7s6p4d1f]; C, (10s7p3d)/[3s2p1d]; O, (10s7p3d)/[3s2p1d]; Cl, (15s11p3d)/[4s3p1d]; N, (10s7p3d)/ [3s2p1d]; P, (15s11p3d)/[4s3p1d]; H, (6s2p)/[2s1p]; Br, (21s17p11d)/[5s4p2d]; I, (26s23p16d)/[6s5p3d]. Scalar relativistic effects were accounted for by the Dyall Hamiltonian.87 Intrinsic Reaction Coordinate (IRC) Calculations. All reactionpath calculations were performed using the efficient (i.e., time-saving) implementations of the PBE functional and the IRC-following routine85 in the PRIRODA program79 using the basis sets described for the C


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that this strategy ensures inclusion of scalar relativistic effects important for the heavier elements, and we have also found that such “ECP-rich” basis sets are computationally efficient.62 In order to test that these “workhorse” basis sets also offer sufficient accuracy for the current task, a few additional SP calculations were performed, as reported in the validation subsection at the start of the Results and Discussion section below, using well-known and high-quality all-electron, correlationconsistent basis sets (termed “cc-pvtz”). All results which in the following have been labeled “cc-pvtz” have thus been obtained using the following basis sets: H (5s2p1d)/[3s2p1d],114 C (10s5p2d1f)/ [4s3p2d1f], 114 N (10s5p2d1f)/[4s3p2d1f],114 P (15s9p2d1f)/ [5s4p2d1f],115 Cl (15s9p2d1f)/[5s4p2d1f].115 The 28 core electrons of ruthenium were described by a relativistic ECP,116 which was accompanied by a (10s9p8d2f1g)/[5s5p4d2f1g] contracted valence basis set (the latter often termed “cc-pvtz-pp”).116 Solvent Effects. Electrostatic and nonelectrostatic solvent effects were estimated by means of the polarizable continuum model (PCM)117−119 as implemented in Gaussian 09.88 The solute cavity was constructed using the united atom topological model with atomic radii optimized for Hartree−Fock (termed “UAHF”) (see refs 117 and 120 as well as the useful discussions in refs 121 and 122). The internal program values for toluene (dielectric constant, number density, etc.) were adopted. The temperature used in the calculation of solvation Gibbs free energies was set to 298.15 K in all cases. Finally, a standard state corresponding to 1 M infinitely diluted solution has been adopted in the calculation of thermodynamic functions; see the Supporting Information for more information. Calculation of Rate Constants. Rate constants were calculated from activation Gibbs free energies following the simple transition state theory (TST) relation (eq 1), where k(T) is the rate constant at

k(T ) = κ

kBT ΔG⧧(T )/ kBT e h

Scheme 2. Gas-Phase Phosphine Binding Energies for Grubbs Olefin Metathesis Catalysts 1 and 4

Scheme 3. Gas-Phase Norbornene Binding and Cycloaddition Energies for Grubbs Catalyst 4

(1)

reproducing these four energies (in calculations on 1 and 4, i.e., without the phosphonium label used in the ESI-MS experiments),14 are presented in Table 1. In general, functionals accounting for dispersion perform better than those that do not. Whereas the best functionals (lowest MUEs) occupying the top rows of Table 1 are all either DFT-D methods (containing D2 or D3 corrections) or Minnesota functionals (M06*) that have been designed to account for dispersion (see Computational Details for explanations of the corrections and functionals used), the bottom rows of the table (largest MUEs) are occupied by plain GGA or hybrid-GGA functionals not including dispersion corrections. A similar trend, albeit not as pronounced, can be observed for the counterpoise corrections, as illustrated by the fact that the top four rows of Table 1 are held by CP-corrected functionals. Of course, this result may seem unremarkable, since improvements of the basis sets should in general lead to better results. It is still gratifying to note that this is also the case here for the CP-corrected functionals, because the superior accuracy is obtained in conjunction with treatment of dispersion and can thus be taken as a sign of the soundness of the approach. To illustrate, if, hypothetically, a dispersion-including functional without CP correction would have given the lowest MUE, it would have indicated a degree of arbitrariness and would certainly not be an indication of the “right result for the right reason”. In fact, density functionals accounting for dispersion should, in general, be used in conjunction with large basis sets or be corrected for basis set incompleteness. Incomplete basis sets give rise to BSSE, which manifests itself as additional attractive interactions. In combination with the latter nonphysical attractive forces, an otherwise well-designed, dispersionincluding functional will of course appear to overshoot dispersion and to predict artificially high stability for assemblies

temperature T, kB is the Boltzmann constant, h is the Plank constant, and κ is the transmission coefficient (taken equal to unity). Standard state conditions (1 M infinitely diluted solution) were assumed in the calculations of ΔG⧧. Calculation of thermodynamic functions at temperatures different from 298.15 K is hampered by the fact that continuum models poorly describe the temperature dependence of the Gibbs free energy of solvation. Fortunately, the temperatures for which Gibbs free energies are calculated in the current work are relatively close to 298.15 K, and it is reasonable to assume that the reaction temperature dependence of the final Gibbs free energies in solution can be described by the TS term only. The linear Eyring plots obtained over the experimental temperature range in ref 9 suggest that this assumption holds.

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RESULTS AND DISCUSSION Validation of Density Functional for SP Energy Evaluation. We have recently validated functionals and computational models for the description of ruthenium− phosphine association/dissociation.62,63 The current investigation also includes the olefin metathesis reaction, and additional validation of the computational model is thus warranted. In the current work the functional and computational models were selected on the basis of the performance as measured against four relative energies from the gas-phase mass-spectrometry measurements of Torker et al.14 Two of these energies, ΔE0,1 and ΔE0,2, are phosphine binding energies obtained for the active 14electron species of Grubbs catalysts 1 and 4 (see Scheme 2). The other two, ΔE0,3 and ΔE0,4, are olefin (norbornene) and cycloaddition binding energies for the active species to form π complexes (see Scheme 3). The resulting mean signed and mean absolute errors for the currently included functionals, with and without dispersion (D2 and D3(BJ); see Computational Details for explanation) and counterpoise (CP) corrections, in D


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“workhorse” basis sets by including also calculations using highquality all-electron, correlation-consistent basis sets, labeled “ccpvtz” (see Computational Details for the definition) in Table 1. First, as expected when turning to better basis sets, the relative energies not corrected for BSSE are improved markedly, with a lowering of the MUE in the range 0.7−0.9 kcal/mol, upon switching to cc-pvtz. Gratifyingly, however, the improvement turns out to be much smaller for the CP-corrected relative energies, the MUEs of cc-pvtz being within 0.5 kcal/mol of those of our workhorse basis sets. Further support for our standard computational procedure is lent by the fact that the CP-corrected BLYP-D2 energies are the most accurate (MUE and MSE equal to 1.9 and −1.8 kcal/mol, respectively) among those calculated with the cc-pvtz basis sets. Overview of the Mechanism of Ethyl Vinyl Ether (EVE) Metathesis. A number of experimental8,9,65−67,124 studies testify to the predominance of the dissociative mechanism (P → AC1 in Scheme 1) in olefin metathesis using ruthenium precatalysts of the kind shown in Chart 1. Moreover, molecularlevel computational studies13,32,125 have shown that the subsequent steps most likely involve a Ru−olefin π complex (PC1) with the olefin positioned trans to the remaining donor ligand, and only this route is followed in the current work. This is also the mechanism followed by Adlhart and Chen13 in an earlier computational study of EVE metathesis by first- and secondgeneration ruthenium methylidenes. In the present study, a number of factors which could not be included at the time13 will be accounted for in order to obtain a more complete description of the reaction path and to allow for comparison with the kinetics reported by Sanford et al.8,9 First, the currently studied precatalysts 1−7 are all benzylidenes, which means that the EVE metathesis reactions followed here are identical with those that were utilized by Sanford et al. to obtain clean kinetics via regioselective, irreversible, and quantitative formation of Fischer carbene FC (see Chart 2).8,9,126

Table 1. Mean Unsigned (MUE) and Mean Signed Errors (MSE) (kcal/mol) with Respect to the Experimental GasPhase Energies ΔE0,1−ΔE0,4a methodb c, d

PBE-D3(BJ)-CP BLYP-D2-CPd,e M06L-CPd M06-CPd M06L BLYP-D3(BJ)-CPc,d BLYP-D2e PBE-D3(BJ)c BLYP-D3(BJ)c M06 B3LYP-D3(BJ)-CPc,d PBEh-D3(BJ)-CPc,d B3LYP-D3(BJ)c ωB97XD-CPd PBEh BP86-D3(BJ)-CPc,d PBEh-D3(BJ)c PBEh-CPd ωB97XD BP86-D3(BJ)c PBE PBE-CPd BP86 B3LYP BP86-CPd B3LYP-CPd BLYP BLYP-CPd

MUE

MSE

2.3 2.4 (1.9)f 2.6 (2.8)f 3.1 (2.9)f 3.2 (2.5)f 4.0 4.2 (3.3)f 4.5 4.6 4.9 (4.0)f 5.3 6.5 7.4 7.6 7.6 8.8 9.2 9.7 10.0 11.0 11.6 14.0 16.4 17.4 18.7 19.6 24.7 26.7

−2.2 −2.2 (−1.8)f −0.2 (0.1)f −2.5 (−1.9)f −2.7 (−2.0)f −2.6 −4.2 (−3.3)f −4.5 −4.6 −4.9 (−4.0)f −5.3 −6.5 −7.4 −7.6 7.0 −8.8 −9.2 9.7 −10.0 −11.0 11.6 14.0 16.4 17.4 18.7 19.6 24.7 26.7

a

See Schemes 2 and 3 for definitions of reaction energies. bSee Computational Details for an explanation. cThe functional includes the D3(BJ) empirical dispersion correction.99 dThe energies are corrected for basis set superposition error (BSSE) using the counterpoise method. eThe functional includes the D2 empirical dispersion correction.95 fAs computed using the “cc-pvtz” basis sets. See Computational Details for more information.

Chart 2. Fischer Carbene Product of EVE Metathesis

of atoms or fragments.123 The lower part of Table 1 nicely illustrates the opposite effect, namely that functionals not including dispersion (such as plain BLYP), which are already too repulsive, are made even more repulsive when they are combined with CP corrections. Looking at Table 1 with an eye to select a functional for the current SP energy evaluations, it can be noted that the smallest MUE is obtained for PBE complemented by the recent Grimmetype dispersion corrections (D3) with Becke−Johnson (BJ) damping as well as by counterpoise corrections (CP): i.e., to give the overall functional here termed PBE-D3(BJ)-CP. However, the improvement over BLYP with an earlier version (D2) of the Grimme dispersion and with counterpoise corrections, i.e., BLYP-D2-CP, is tiny (0.1 kcal/mol in MUE). The latter functional was found to perform excellently and was used in our recent study of phosphine dissociation/association.63 We thus chose to remain compatible with our earlier work62 and to adopt the same functional also for the current work. Unless otherwise noted, all relative energies reported in the following are those obtained using BLYP-D2-CP in SP energy evaluations. Three functionals accounting for dispersion, BLYP-D2, M06L, and M06, used with and without counterpoise corrections (CP), have been selected for additional tests of the quality of our

The use of a substituted alkylidene (as opposed to methylidene), in turn, means that EVE may coordinate and react with the ethoxy substituent either cis or trans with respect to the phenyl ring of the benzylidene (see below). As will become evident in the following, both coordination modes contribute and should be accounted for to obtain a reasonably complete picture of the mechanism. Next, the present contribution also includes the weakly bound transition states of phosphine dissociation and olefin coordination/dissociation. Importantly, inclusion of these transition states allows comparison with the k−1/k2 ratios of Sanford et al. Third, as described in Computational Details, the current computational approach is designed to include all major contributions, such as solvation effects, dispersion interactions, and thermochemical corrections, in order to allow for comparison with experiment. The reaction starts with dissociation of phosphine from precatalysts (P) 1−7 at a rate proportional to k1 (see Scheme 1). The corresponding transition state (TS1) is not very pronounced on the potential energy surface (PES; see IRC E


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Figure 1. Gibbs free energies, given relative to the precatalyst P, for the reaction of catalysts 1 and 4 with ethyl vinyl ether (EVE). As shown in Figures 5 and 6, EVE may coordinate in a cis or trans mode relative to the benzylidene fragment. The energies of both of these pathways are shown. Gibbs free energies are given relative to infinitely separated precatalyst and EVE.

Figure 2. Gibbs free energies, given relative to the precatalyst P, for the reaction of catalysts 2 and 5 with EVE. As shown in Figures 5 and 6, EVE may coordinate in a cis or trans mode relative to the benzylidene fragment. The energies of both of these pathways are shown. Gibbs free energies are given relative to infinitely separated precatalyst and EVE.

Figure 3. Gibbs free energies, given relative to the precatalyst P, for the reaction of catalysts 3 and 6 with EVE. As shown in Figures 5 and 6, EVE may coordinate in a cis or trans mode relative to the benzylidene fragment. The energies of both these pathways are shown. Gibbs free energies are given relative to infinitely separated precatalyst and EVE.

curves in the Supporting Information), but could nevertheless be located for the catalysts 1−7. In contrast, there is a marked free energy barrier for this reaction, in the range 16.7−24.2 kcal/mol (see Figures 1−4 and Table S1 (Supporting Information)). This

barrier is dominated by effects from entropy, dispersion, and solvation and can be addressed using computational approaches of the present kind.63,64 In particular, it can be noted that the calculations nicely reproduce the observation9 that firstF


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Figure 4. Gibbs free energies, given relative to the precatalyst P, for the reaction of catalysts 4 and 7 with EVE. As shown in Figures 5 and 6, EVE may coordinate in a cis or trans mode relative to the benzylidene fragment. The energies of both of these pathways are shown. Gibbs free energies are given relative to infinitely separated precatalyst and EVE.

Next, similar to relevant phosphine63,64 and olefin54,64,73,127 coordination reactions studied thus far, coordination of EVE to AC1 via TS2 to give the π complex PC1 involves a free energy barrier, of which loss of entropy and solute−solvent interactions are important components. However, the barrier to coordination of EVE is both smaller and less discriminating between the individual catalysts than the barrier to phosphine dissociation (see Figures 1−4), which has also been observed in calculations on the reaction of N,N-diallylmethanesulfonamide with 1 and 4.64 As also seen for phosphine dissociation (vide supra), following the IRC path backward (i.e., dissociation of EVE) from TS2 leads to a weakly bound complex that vanishes on the free energy surface and plays no role in the kinetics (see IRC curves in the Supporting Information). As shown in Figures 5 and 6, both cis and trans coordination of EVE relative to the benzylidene fragment is possible and the pathways resulting from both coordination faces of EVE have been explored. Whereas most of

generation catalysts (1−3) are associated with somewhat lower barriers (by 2.1−4.3 kcal/mol (2.9−4.1 kcal/mol) according to the present calculations (experiment)) to dissociation in comparison with the second-generation catalysts (4−7). In contrast, the corresponding free energies of dissociation discriminate much less between first- and second-generation catalysts. For example, for catalyst 4 the dissociation free energy calculated here (6.9 kcal/mol) is only 0.1 kcal/mol higher than that of 1, the corresponding differences for the other two pairs of first- and second-generation catalysts (2 and 5, and 3 and 6, respectively) being 0.2 and 1.3 kcal/mol, respectively. These differences are considerably smaller than the observed and calculated differences in dissociation barriers noted above and also smaller than the corresponding differences in dissociation enthalpies (see Table S2 (Supporting Information)) as well as some differences in calculated dissociation free energies reported earlier.13,43,64 Whereas the neglect of vibrational and rotational contributions to the free energies may have contributed to overestimation of the difference in calculated dissociation free energies in one of these studies,13 the contrast between our (small) dissociation free energy differences and the larger differences of refs 43 and 64 could, potentially, be rooted in the use of two different functionals for geometry optimization and calculation of frequencies (the latter entering into the thermochemical corrections). The current functional for this purpose (PBE) has been chosen on the basis of its performance in a recent validation study with emphasis on the structures of ruthenium-based olefin metathesis catalysts.80 Our calculated free energies thus suggest that the difference in activation free energies between the two generations of catalysts vanishes at the dissociation limit, which is consistent with the suggestion9 that this difference is “not a ground-state effect”. In contrast, an enthalpy difference of 3−4 kcal/mol between the two generations of catalysts appears to remain at the dissociation limit (see Table S2), consistent with previously calculated differences in bond dissociation energies.14,45,46,62,63,72 On the PES, the dissociation reaction proceeds over TS1 to give a weakly bound complex of the 14-electron ruthenium fragment and PCy3 (see IRC curves in the Supporting Information). However, this complex plays no role in the free energy surface, and phosphine dissociation thus results in free phosphine (PCy3) and 14-electron active catalyst (AC1).63

Figure 5. Optimized geometries of TS2 and TS3 for complex 1. Color coding: C, gray; O, red; P, yellow; Cl, green; Ru, dark green. Hydrogen atoms have been omitted for clarity. Both cis and trans coordination of EVE relative to the benzylidene fragment is possible, and the pathways resulting from both coordination faces of EVE have been explored. G


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dissociation via TS1 and 21.9−27.0 kcal/mol for olefin addition via TS3, respectively. A tendency to lowering of the latter barrier in comparison with the former when going from first- to secondgeneration catalysts can be seen, consistent with earlier computational studies of olefin metathesis reactions.13,32,40,42,43 Thus, already at this stage we can note that the free energy profiles (Figures 1−4) indicate that some catalysts (4 and 7, Figure 4) will have their olefin metathesis rates controlled by phosphine dissociation while others, such as 3, appear to be limited by cycloaddition. A more quantitative assessment of this transition in the rate-determining step will have to include also the concentrations of catalyst and substrate to obtain estimates of actual rates, and we will return to this issue below. For now we limit ourselves to noting that it is gratifying that the calculations reflect, in a qualitative sense, a difference in commitment12 between the first- and second-generation catalysts. The PC1 → MCB step is endergonic for all catalysts 1−7 and even more so if we consider the effective cycloaddition step AC1 → MCB. We can, again, note a sterically induced difference in comparison with the corresponding methylidene complexes, for which the PC1 → MCB step was found to be exergonic for 1 and 4.13 Given the higher stability consistently seen for the MCB intermediate for the second-generation catalysts, its more facile formation via TS3 is to be expected from Hammond’s postulate.128 Next, the discrimination between first- and second-generation catalysts is surprisingly pronounced in the MCB intermediate. For example, if it is defined as the difference in MCB stability relative to AC1 for a given catalyst pair (e.g., 1 and 4), this discrimination is in the range 1.4−9.7 kcal/mol for catalysts 1−7, much larger than that seen in TS3 itself, which probably is part of the reason why the stability of this intermediate has proved to be a very useful measure for the relative catalytic activity for Grubbs-type ruthenium-based catalysts.60 The next step, the rupture of the MCB ring to form the styrene π complex PC2, a step that is endergonic for some substrates,64 is highly exergonic for EVE metathesis, with a low or even vanishing barrier MCB → TS4. In fact, the insignificance of the barrier to MCB rupture is illustrated by the fact that, in a previous detailed computational study of EVE metathesis,13 neither MCB nor TS4 could be located for catalyst 1, and in the present study this barrier vanishes on the free energy surface for all but catalysts 3 and 6. The fact that G(TS4) falls below G(MCB) for most of the catalysts can be understood from the fact that the PES near TS4 is very flat, for some catalysts the energy difference E(TS4) − E(MCB) being a tiny 0.04 kcal/mol at the geometry optimization level, and only small modifications in the computational protocol and inclusion of thermochemical corrections etc. may contribute to the energy of TS4 falling below that of MCB. We have found that the main contribution to stabilization of TS4 relative to MCB stems from the switch of functional and basis sets upon going from geometry optimization to SP energy evaluation (see Computational Details for more information). Inclusion of thermochemical, solvent, and CP corrections plays a lesser role in this stabilization. Also the final step, decoordination of styrene from PC2 to give the new active complex AC2, is markedly exergonic. Although the barrier PC2 → TS5 is, as expected, comparable to that of the corresponding decoordination of EVE from PC1 and is not vanishing, it is small in comparison to the dominating effective barriers (to phosphine dissociation and formation of the MCB, respectively) leading up to formation of the MCB. The role of the styrene decoordination barrier in the overall kinetics of

Figure 6. Optimized geometries of TS2 and TS3 for complex 4. Color coding: C, gray; N, blue; O, red; Cl, green; Ru, dark green. Hydrogen atoms have been omitted for clarity. Both cis and trans coordination of EVE relative to the benzylidene fragment is possible, and the pathways resulting from both coordination faces of EVE have been explored.

the path derived from trans coordination is lower in energy than that of cis coordination, including the rate-determining parts (see below), for the AC1 → PC1 step itself, cis coordination is faster for catalysts 2, 5, and 6, i.e., G(TS2)(cis) − G(AC1) < G(TS2)(trans) − G(AC1) for these catalysts, whereas the opposite is true for the other catalysts. Similarly to the trend seen for phosphine dissociation (discussed above) and coordination of N,N-diallylmethanesulfonamide to AC1 formed from catalysts 1 and 4,64 coordination of EVE is generally more facile (by 0.1− 2.2 kcal/mol according to the calculations) for first-generation than for second-generation catalysts (the only exception being cis coordination of EVE to catalyst 6, which turned out to be more facile by 4.0 kcal/mol than the corresponding cis coordination to catalyst 3, and cis coordination of EVE to catalyst 7, which turned out to be more facile by 0.1 kcal/mol than corresponding cis coordination to catalyst 1). However, as noted above, the spread in barriers among the various catalysts is relatively small for this step. The π complex PC1, in turn, may undergo [2 + 2] cycloaddition to give the metallacyclobutane (MCB) via TS3. Relative to PC1 the barriers to cycloaddition are modest (in the range 9.8−14.8 kcal/mol; see Figures 1−4), with 12.5 and 9.8 kcal/mol being obtained for trans-coordinated EVE for catalyst 1 and 4, respectively. These barriers are, as expected, slightly higher than those calculated for the corresponding methylene complexes,13 7.2 and 4.6 kcal/mol, respectively, for which less steric congestion can be expected upon formation of the MCB. These PC1 → TS3 barriers are, regardless of whether the precursor is a methylidene or benzylidene complex, clearly smaller than the above barriers for phosphine dissociation. However, in order to understand the olefin metathesis kinetics in a qualitative sense, it is more useful to view the addition reaction as taking place from the active complex AC1. This picture results in an effective olefin addition barrier for AC1 → TS3 in the range 14.7−21.9 kcal/mol. It is also instructive to note that that the two candidate kinetic bottlenecks, represented by TS1 and TS3, respectively, give overlapping ranges of barriers relative to the resting state P, with 16.7−24.2 kcal/mol for phosphine H


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Table 2. Selected Computed and Experimental Rate Constants and Their Ratiosa compdb

k−1c (L mol−1 s−1)

1 2 3 4 5 6 7

2.9 × 10 9.3 × 102 5.7 × 102 1.3 3.5 × 101 3.5 1.2 2

k2,trans*c (L mol−1 s−1) −1

1.2 × 10 8.4 × 10−3 2.9 × 10−4 6.4 6.6 × 10−1 1.8 × 10−1 1.2 × 101

k2,cis*c (L mol−1 s−1) −3

k2*c,d (L mol−1 s−1) −1

3.6 × 10 7.3 × 10−4 8.6 × 10−5 6.0 × 10−2 1.6 × 10−1 5.4 × 10−3 2.7 × 10−1

1.2 × 10 9.1 × 10−3 3.8 × 10−4 6.5 8.3 × 10−1 1.8 × 10−1 1.3 × 101

k−1/k2*c

k−1/k2 (exptl)e

2.3 × 10 1.0 × 105 1.5 × 106 2.0 × 10−1 4.2 × 101 1.9 × 101 9.3 × 10−2

1.3 × 104 8.2 × 104 2.6 × 106 1.3 n/af 3.3 × 102 n/af

3

a

See Scheme 1 for definition of rate constants. The ethoxy substituent of EVE may either be cis or trans relative to the benzylidene phenyl ring (see Figures 5 and 6). bSee Chart 1 for catalyst labeling. cAs computed for 323.15 K. dk2* = k2,cis* + k2,trans*. eDerived from kinetic NMR measurements in toluene at 325.15 K.9 fNot available.

cycloaddition (rate proportional to k2*), which means that the ratios extracted from the observed rates as k−1/k2 actually are better characterized as k−1/k2*. The agreement also lends support to the computational results more generally, implying that the present results may be used to gain additional and more detailed insight, for example from comparisons involving elementary reaction steps of individual catalysts. Regarding some of the details of the current approach, it should be noted that the overall agreement with the experimental ratios basically would remain even if only the path derived from trans coordination of EVE were considered. The dominance of the trans path can be realized by comparing the total effective rate constant for cycloaddtion, k2*, with those of the cis (k2,cis*) and trans routes (k2,trans*). Still, for some of the catalysts, notably 2, 3, and 5, the cis path is competing, with rate constants k2,cis* roughly within an order of magnitude of those of the trans path, which is why the cis-derived route has been included here to give a more complete picture of the mechanism. The current resolution of the individual rate constants also makes it possible to obtain rough estimates and comparisons of the rates of the key elementary steps by including the phosphine and olefin concentrations for the AC1 → P and AC1 → MCB steps, respectively (see Table 3). Whereas the EVE concentration

catalysts 1−7 is thus insignificant for the strongly exergonic metathesis of EVE as mediated by catalysts 1−7. However, for metathesis of other substrates, the barrier to dissociation of styrene may turn out to play an important role.64 Comparison with the Observed Solution Kinetics. We recall that the k−1/k2 ratios of Sanford et al.8,9 have been obtained from the observed reaction rate, assuming that olefin binding (k2) essentially is irreversible and that the steps subsequent to olefin binding are fast. These assumptions appear to be inconsistent with the calculated free energies of EVE metathesis discussed above, which indicate that the olefin coordination step is neither a candidate rate-determining step nor irreversible. Still, our free energy profiles do support the idea that the essentials of the mechanism and kinetics may be expressed in a simple ratio of rate constants of reaction steps involving the active center (AC1). However, instead of basing this ratio on the olefin coordination elementary step, a pivotal role is suggested for what may be termed an effective olefin cycloaddition step, AC1 → MCB. For EVE metathesis, the subsequent elementary steps are indeed fast and should be exergonic enough to ensure effective irreversibility (see above). In other words, if the free energy profiles of olefin metathesis presented here are realistic, a certain degree of agreement between the data of Sanford et al. and those obtained here using a revised definition of k2 (here termed k2*) should be expected. Indeed, with k−1 derived straightforwardly from the barrier to recoordination of phosphine (G(TS1) − G(AC1)), k2* derived from the effective barrier to cycloaddition, G(TS3) − G(AC1), counting the contributions from both trans and cis coordination of EVE with respect to the phenyl ring of the benzylidene ligand of the active catalyst AC1 (i.e., k2* = k2,cis* + k2,trans*), the present k−1/k2* ratios agree with the k−1/k2 ratios of Sanford et al. basically to within 1 order of magnitude (only for catalyst 6 is the calculated ratio off by (slightly) more than a factor of 10) (see Table 2). Moreover, just as the experimental k−1/k2 ratios, the calculated k−1/k2* ratios are able to distinguish clearly between the first (1−3)- and second-generation catalysts (4−7), with values for the former catalysts about 4 orders of magnitude higher than those of the latter. Not only does the agreement mean that the calculations provide useful estimates of the ratios for the catalysts for which experimental values are not available, which is the case for instance for catalysts 5 and 7, but also it means that the calculations may be used to gain reliable additional insight not available from the experiments alone. First and foremost, the agreement strongly suggests that the assumptions made here to arrive at an explanation for the experimentally observed ratios are basically sound. This means that the reactivity of the active center can be approximated as a competition between inactivation via phosphine recoordination (rate proportional to k−1) and olefin

Table 3. Selected Rate Constants and Their Productsa compdb

k1c (s−1)

[PCy3]c,d (mol L−1)

k−1[PCy3]c,d (s−1)

k2*[EVE]c,e,f (s−1)

1 2 3 4 5 6 7

1.2 × 10−2 1.1 × 10−1 3.7 7.3 × 10−5 3.3 × 10−3 2.6 × 10−3 1.1 × 10−5

4.1 × 10−4 6.4 × 10−4 4.0 × 10−3 3.9 × 10−4 5.3 × 10−4 1.4 × 10−3 1.7 × 10−4

4.7 × 10−1 2.9 1.2 × 101 3.1 × 10−3 1.0 × 10−1 2.9 × 10−2 1.2 × 10−3

3.7 × 10−1 2.8 × 10−2 1.1 × 10−3 2.9 × 101 3.5 6.5 × 10−1 5.4 × 101

a

See Scheme 1 for definition of rate constants. The ethoxy substituent of EVE may either be cis or trans relative to the benzylidene phenyl ring (see Figures 5 and 6). bSee Chart 1 for catalyst labeling. cAs computed for 298.15 K. d[PCy3] is estimated from the equilibrium (X)2Ru(PCy3)(L)CHR ⇌ (X)2Ru(L)CHR + PCy3 at 298.15 K with [Ru] = 0.017 mol L−1 (X = Cl, Br, I; L = PCy3, H2IMes, IMes). e k2* = k2,cis* + k2,trans* f[EVE] = 0.5 mol L−1.

(0.5 mol L−1)9 is much higher than that of the catalyst and can be considered constant, the phosphine concentration has been approximated by considering the initial dissociation equilibrium P → AC1 only. For the second-generation catalysts 4−7, the k2*[EVE] products are between 2 and 6 orders of magnitude higher than the corresponding constants k1, clearly illustrating that the rate of EVE metathesis with these catalysts is limited by I


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frequencies of carbonyl ligands in NHC complexes of nickel and iridium.138,139 Turning to the steric effects, the metal−C(NHC) bond distance appears to be shorter and the N−C−N bond angle is larger for H2IMes than for IMes complexes (see, e.g., ref 140). Also, whereas the NHC ring is planar for IMes, this is not so for the saturated counterpart. These geometric differences explain much of the slightly higher steric pressure for the H2IMes ligand, which, together with the degree of σ donation, has been noted to have a positive influence on catalytic activity.60 The very low rate constants for phosphine dissociation, k1, compared to those for the products, k2*[EVE] (see the above discussion on the rate-limiting step), underscores that, at least for metathesis of EVE, the aforementioned differences between the two ligands manifest themselves mainly in the phosphine dissociation step. Indeed, the most noticeable difference in calculated kinetic parameters for the two catalysts is the close to 7-fold higher k1 of 4 in comparison with that of 7. For a rate constant derived from a quantum chemical calculation, this is not a large difference, and its significance should not be exaggerated. As is evident from eq 1, an error of only 1.4 kcal/mol in the calculated barrier (which is not much) has a 1 order of magnitude impact on the corresponding rate constant. Nevertheless, the molecular structures of these two catalysts are very similar, suggesting that error cancellation should be particularly helpful to the accuracy of this difference. It should, however, be kept in mind that, for OM transformations more challenging than the current unproductive reaction, the rate may well be limited by subsequent reaction steps rather than by the initial dissociation. For example, DFT calculations have shown that the rate of cyclohexene metathesis using catalyst 4 is limited by cycloreversion of the metallacylobutane intermediate:49 that is, to use the present labeling scheme, by TS4. In fact, also this transition state discriminates between the two catalysts, in favor of that (4) based on the saturated ligand, as measured by barriers relative to both the catalyst precursor (P → TS4) and the active complex (AC1 → TS4).

the initial phosphine dissociation, as suggested by both solution8,9 and gas-phase12 experiments. In contrast, for 3, k1 is 4 orders of magnitude higher than k2*[EVE], which shows, as expected for a first-generation catalyst,12 that cycloaddition is rate determining. For 1 and 2, the olefin cycloaddition and phosphine dissociation rates are predicted to be much more similar (within 1 order of magnitude), with the qualitative order reflecting the observed rate-determining step only for 2. Thus, the results indicate that, at least for 1, the calculated phosphine dissociation barrier could be slightly underestimated relative to that of cycloaddition. Finally, it should be kept in mind that many olefin substrates can be expected to react more slowly than EVE. Thus, even if the rate of EVE metathesis is limited by phosphine dissociation for all the second-generation catalysts, it cannot be excluded that, for other possibly sterically demanding substrates, cycloaddition may turn out to be rate limiting even for these catalysts.49 Detailed Comparison of Individual Catalysts. Sanford et al.9 explained the difference between PCy3 and NHC complexes by the better electron-donating properties of the carbene ligands. The latter have been reported to promote metal-to-olefin backbonding to a greater extent than phosphines,129 which should stabilize both PC1 and TS2 relative to P and AC1. However, as noted above, the olefin coordination step appears to discriminate relatively little between the different catalysts, much less than the subsequent cycloaddition step. In addition, the order among the catalysts with respect to barrier height AC1 → TS2 is not the same as that of AC1 → TS3. We conclude that the metal-toolefin back-bonding properties of a complex do not seem to be important for the effective olefin cycloaddition step: i.e., for k2*. Rather, as noted above, the larger rate constant k2* for the second-generation catalysts has its origin in the superior stability for the MCB intermediate for the NHC complexes, which carries over in a difference also in the AC1 → TS3 barrier. However, the different catalytic properties of first- and secondgeneration catalysts are not only due to the olefin cycloaddition step. Our calculated rate constants for AC1 → P (k−1; see Table 2) are between 1 and 2 orders of magnitude larger for the firstgeneration catalysts and show that active catalysts of the first generation are considerably more prone to being inactivated via phosphine recoordination than their second-generation counterparts, thus contributing considerably to their much higher observed k−1/k2 and calculated k−1/k2* ratios. Sanford et al.9 noticed a 100-fold increase in k−1/k2 upon substitution of chloride with iodide. The current access to individual estimates of k−1 and k2* makes it possible to resolve this difference in catalytic behavior. It turns out that the rate constant for recoordination of phosphine, k−1, does not change much within a single series Cl−Br−I and that most of the variation in k−1/k2 is controlled by a reduction in the effective rate constant for olefin cycloaddition, k2*, upon going from catalyst 1 to 3 and 4 to 6, respectively. The second-generation catalyst 4 based on the saturated H2IMes ligand is known to display higher phenomenological activity than the corresponding catalyst 7 based on the unsaturated IMes ligand.16,130−136 The observed higher activity of 4 has been explained by a variety of steric and electronic factors36,60,137 thought to facilitate either phosphine dissociation36 or the olefin cycloaddition step.137 Whereas both the ligand-to-metal σ donation and the π back-donation are somewhat stronger for H2IMes than for IMes,60 the two carbene ligands appear to be approximately equally good overall electron donors, as suggested, for example, by the similar stretching

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CONCLUSIONS Thoroughly validated density functional theory calculations accounting for dispersion, thermochemical, and continuum solvent effects have made it possible to address weakly bound transition states of phosphine and olefin dissociation and association. Thus, a complete set of intermediates and transition states of the EVE metathesis reaction has been obtained, allowing comparison with the experimental reference kinetic data of Sanford et al.8,9 The calculations show that, from the active 14electron complex, olefin coordination proceeds (at a rate proportional to k2) over a barrier involving contributions from entropy and solute−solvent interactions. The components of this barrier are thus similar to those of the barrier to phosphine association from the active complex, leading to deactivation of the catalyst (at a rate proportional to k−1). The barrier to olefin coordination is still clearly smaller than that of the coordination and cycloaddition step taken together to form an overall effective barrier to EVE addition (at a rate proportional to k2*). The thus obtained ratios k−1/k2* compare nicely with those originally measured and interpreted as k−1/k2,8,9 suggesting that the experimentally obtained ratios, which have proved to discriminate efficiently between various catalysts and to offer easy-tograsp mechanistic insights, are better understood as k−1/k2*. Complementing the theoretical rate constants with concentrations, the thus obtained “computational kinetics” reproduces J


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(15) Ritter, T.; Day, M. W.; Grubbs, R. H. J. Am. Chem. Soc. 2006, 128, 11768. (16) Clavier, H.; Nolan, S. P. Chem. Eur. J. 2007, 13, 8029. (17) Hejl, A.; Day, M. W.; Grubbs, R. H. Organometallics 2006, 25, 6149. (18) da Costa, R. C.; Gladysz, J. A. Adv. Synth. Catal. 2007, 349, 243. (19) Hong, S. H.; Wenzel, A. G.; Salguero, T. T.; Day, M. W.; Grubbs, R. H. J. Am. Chem. Soc. 2007, 129, 7961. (20) Bieniek, M.; Michrowska, A.; Usanov, D. L.; Grela, K. Chem. Eur. J. 2008, 14, 806. (21) Monsaert, S.; De Canck, E.; Drozdzak, R.; Van Der Voort, P.; Verpoort, F.; Martins, J. C.; Hendrickx, P. M. S. Eur. J. Org. Chem. 2009, 655. (22) Clavier, H.; Urbina-Blanco, C. A.; Nolan, S. P. Organometallics 2009, 28, 2848. (23) Jarzembska, K.; Seal, S.; Woźniak, K.; Szadkowska, A.; Bieniek, M.; Grela, K. ChemCatChem 2009, 1, 144. (24) Broggi, J.; Urbina-Blanco, C. A.; Clavier, H.; Leitgeb, A.; Slugovc, C.; Slawin, A. M. Z.; Nolan, S. P. Chem. Eur. J. 2010, 16, 9215. (25) Leitao, E. M.; van der Eide, E. F.; Romero, P. E.; Piers, W. E.; McDonald, R. J. Am. Chem. Soc. 2010, 132, 2784. (26) Keitz, B. K.; Grubbs, R. H. J. Am. Chem. Soc. 2011, 133, 16277. (27) Samojłowicz, C.; Bieniek, M.; Pazio, A.; Makal, A.; Woźniak, K.; Poater, A.; Cavallo, L.; Wójcik, J.; Zdanowski, K.; Grela, K. Chem. Eur. J. 2011, 17, 12981. (28) Xi, Z.; Bazzi, H. S.; Gladysz, J. A. Org. Lett. 2011, 13, 6188. (29) Thiel, V.; Hendann, M.; Wannowius, K.-J.; Plenio, H. J. Am. Chem. Soc. 2012, 134, 1104. (30) Beach, N. J.; Lummiss, J. A. M.; Bates, J. M.; Fogg, D. E. Organometallics 2012, 31, 2349. (31) Ashworth, I. W.; Nelson, D. J.; Percy, J. M. Dalton Trans. 2013, 42, 4110. (32) Vyboishchikov, S. F.; Bühl, M.; Thiel, W. Chem. Eur. J. 2002, 8, 3962. (33) Adlhart, C.; Chen, P. Angew. Chem., Int. Ed. 2002, 41, 4484. (34) Fomine, S.; Vargas, S. M.; Tlenkopatchev, M. A. Organometallics 2003, 22, 93. (35) Bernardi, F.; Bottoni, A.; Miscione, G. P. Organometallics 2003, 22, 940. (36) Cavallo, L. J. Am. Chem. Soc. 2002, 124, 8965. (37) Costabile, C.; Cavallo, L. J. Am. Chem. Soc. 2004, 126, 9592. (38) Vyboishchikov, S. F.; Thiel, W. Chem. Eur. J. 2005, 11, 3921. (39) Fomine, S.; Ortega, J. V.; Tlenkopatchev, M. A. J. Mol. Catal. A: Chem. 2005, 236, 156. (40) Straub, B. F. Angew. Chem., Int. Ed. 2005, 44, 5974. (41) Lippstreu, J. J.; Straub, B. F. J. Am. Chem. Soc. 2005, 127, 7444. (42) Tsipis, A. C.; Orpen, A. G.; Harvey, J. N. Dalton Trans. 2005, 2849. (43) Naumov, S.; Buchmeiser, M. R. J. Phys. Org. Chem. 2008, 21, 963. (44) Cramer, C. J.; Truhlar, D. G. Phys. Chem. Chem. Phys. 2009, 11, 10757. (45) Zhao, Y.; Truhlar, D. G. Acc. Chem. Res. 2008, 41, 157. (46) Zhao, Y.; Truhlar, D. G. Org. Lett. 2007, 9, 1967. (47) Straub, B. F. Adv. Synth. Catal. 2007, 349, 204. (48) Diesendruck, C. E.; Tzur, E.; Ben-Asuly, A.; Goldberg, I.; Straub, B. F.; Lemcoff, N. G. Inorg. Chem. 2009, 48, 10819. (49) Fomine, S.; Tlenkopatchev, M. A. Organometallics 2007, 26, 4491. (50) Fomine, S.; Ortega, J. V.; Tlenkopatchev, M. A. J. Mol. Catal. A: Chem. 2007, 263, 121. (51) Fomine, S.; Tlenkopatchev, M. A. J. Organomet. Chem. 2006, 691, 5189. (52) Fomine, S.; Gutiérrez, S.; Tlenkopatchev, M. A. J. Organomet. Chem. 2009, 694, 3287. (53) Tonner, R.; Frenking, G. Chem. Commun. 2008, 1584. (54) Poater, A.; Ragone, F.; Correa, A.; Szadkowska, A.; Barbasiewicz, M.; Grela, K.; Cavallo, L. Chem. Eur. J. 2010, 16, 14354. (55) Fomine, S.; Tlenkopatchev, M. A. Organometallics 2010, 29, 1580. (56) Credendino, R.; Poater, A.; Ragone, F.; Cavallo, L. Catal. Sci. Technol. 2011, 1, 1287.

known trends, such as the slower phosphine dissociation but greater “commitment” toward olefin metathesis of the secondgeneration catalysts. The agreement with the experimentally obtained kinetics and the completeness with respect to intermediates and transition states allow extraction of new mechanistic insights, both with respect to the role of individual elementary steps and with respect to comparison between catalysts. An example of the latter is offered by the catalysts based on the saturated (H2IMes, catalyst 4) and unsaturated NHC ligands (IMes, catalyst 7). For olefins easily undergoing metathesis, such as EVE, the calculations show that the higher activity of 4 is due solely to its faster phosphine dissociation. In contrast, for the currently studied catalysts, the barrier to cycloreversion will limit the rate of productive metathesis of comparably unreactive olefins, and also this barrier is lower with 4 than with 7.

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ASSOCIATED CONTENT

S Supporting Information *

Total energies, thermochemical corrections, dispersion corrections, solvent corrections, and Cartesian coordinates calculated for the individual compounds, relative Gibbs free energies (Table S1) and enthalpies (Table S2) of intermediates and transition states, intrinsic reaction coordinate (IRC) curves for catalysts 2 and 5, and information on the treatment of standard states. This material is available free of charge via the Internet at http://pubs. acs.org.

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AUTHOR INFORMATION

Corresponding Author

*V.R.J.: e-mail, [email protected]; tel, (+47) 555 83489; fax, (+47) 555 89490. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The Norwegian Research Council (NFR) is acknowledged for financial support via the KOSK programme (Grant No. 177322) as well as for CPU resources granted via the NOTUR supercomputing programme.

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REFERENCES

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