Bimolecular Coupling in Olefin Metathesis: Correlating Structure and Decomposition for Leading and Emerging Ruthenium−Carbene Catalysts

Bimolecular catalyst decomposition is a fundamental, long-standing challenge in olefin metathesis. Emerging ruthenium–cyclic(alkyl)(amino)carbene (CAAC) catalysts, which enable breakthrough advances in productivity and general robustness, are now known to be extraordinarily susceptible to this pathway. The details of the process, however, have hitherto been obscure. The present study provides the first detailed mechanistic insights into the steric and electronic factors that govern bimolecular decomposition. Described is a combined experimental and theoretical study that probes decomposition of the key active species, RuCl2(L)(py)(=CH2) 1 (in which L is the N-heterocyclic carbene (NHC) H2IMes, or a CAAC ligand: the latter vary in the NAr group (NMes, N-2,6-Et2C6H3, or N-2-Me,6-iPrC6H3) and the substituents on the quaternary site flanking the carbene carbon (i.e., CMe2 or CMePh)). The transiently stabilized pyridine adducts 1 were isolated by cryogenic synthesis of the metallacyclobutanes, addition of pyridine, and precipitation. All are shown to decompose via second-order kinetics at −10 °C. The most vulnerable CAAC species, however, decompose more than 1000-fold faster than the H2IMes analogue. Computational studies reveal that the key factor underlying accelerated decomposition of the CAAC derivatives is their stronger trans influence, which weakens the Ru−py bond and increases the transient concentration of the 14-electron methylidene species, RuCl2(L)(=CH2) 2. Fast catalyst initiation, a major design goal in olefin metathesis, thus has the negative consequence of accelerating decomposition. Inhibiting bimolecular decomposition offers major opportunities to transform catalyst productivity and utility, and to realize the outstanding promise of olefin metathesis.


Scheme S3. Synthesis of Pyridine Adducts.
Representative Procedure for Synthesis of RuCl2(C1 Ph )(py)(=CH2), 1-C1 Ph . In a 10 mL Schlenk flask, a dark-green solution of the PC1 Ph (100 mg, 0.117 mmol) in 2 mL CH2Cl2 was frozen in N2(l). The sample was freeze-pump-thaw degassed 3x, and thawed under 1 atm ethylene at -45 °C (MeCN-dry ice bath). The resulting dark red solution was stirred for 15 min, briefly exposed to vacuum to remove ethylene, then stirred under N2. A solution of pyridine (18.7 μL, 0.231 mmol, 2 equiv) in 500 μL nhexane, chilled in an EtOH-N2(l) cold bath (-110 to -80 °C), was then added via syringe as a slow dribble down the flask wall (ca. 10 sec). The solution rapidly turned dark green, then brown-yellow. The mixture was stirred for a further 10 min. Cold n-hexane (4 mL; -110 to -80 °C) was then added using a cannula chilled with dry ice. The mixture was stirred for 10 min to precipitate the brown phosphonium salt [H2C=CHP i Pr3]OTf, filtered cold, and the orange filtrate was immediately stripped to dryness at -45 °C to afford yellow 1-C1 Ph . The flask containing solid 1-C1 Ph was transferred to a -35 °C freezer inside a glovebox until use. Product masses were not measured, given their high static charge, and the high relative error inherent in weighing small amounts of material in even a small Schlenk flask on a balance in the gloveobox. Instead, Ru concentrations for the decomposition experiments were quantified based on known concentrations of injected internal standard: see next section.

S1.1.4. Bimolecular Coupling of Methylidene Complex 1
The procedure for the coupling reaction is summarized in Scheme S4. In our original study, the objective was quantitation of ethylene evolved from 1-C1 Ph , and considerations of purity were minor. 7 The solid methylidene complex 1-C1 Ph was thus not purified to remove the phosphonium salt [H2C=CHP i Pr3]OTf. In the present kinetics study, removal of phosphonium salt as described above yielded a powder with a high static charge, which could not be weighed: moreover, the CAAC Representative Procedure for Bimolecular Coupling of 1-C1 Ph : The Schlenk flask containing solid 1-C1 Ph was removed from the glovebox freezer and bedded in a cold sand-bath (chilled to −35 °C by storing in the freezer overnight). To a J-Young NMR tube also bedded in the sand-bath was added cold DMT (20.0 μL of a stock solution of 10 mg DMT in 1 mL CDCl3; 1.03 μmol); NMR integration standard (IS). Solid 1-C1 Ph was dissolved in cold CDCl3 (0.6 mL) and transferred to the NMR tube via a chilled pipette. The NMR tube was sealed, transported to the NMR facility in a dry ice-MeCN bath (−45 °C), then quickly shaken and inserted into an NMR probe precooled to −40 °C. The initial integration ratio of 1-C1 Ph vs IS was measured, after which the NMR probe was warmed to -10 °C to effect liberation of four-coordinate 2-C1 Ph . After an initial 15 min period for thermal equilibration, loss of the [Ru]=CH2 NMR signal was measured over time: see Figure 1 in the main text.
The same procedure was carried out for 1-C1 Me , 1-C3 Ph and 1-C1 Ph (I2). For H2IMes complex 1-H2IMes, a higher volume of 1.2 mL CDCl3 was used to reduce the headspace, to ensure that any propenes formed via -H elimination could be detected (none were observed).
Sample calculation: initial Ru concentration of 2-C1 Ph , based on known concentration of DMT. For a volume of 20 L injected into the NMR tube:            The downfield signal in the alkylidene region is assigned to a rotamer, as seen for other CAAC complexes. 10 The instability of the complex over 7 h at -40 °C hindered acquisition of a 13 C{ 1 H} NMR spectrum.

S3.1. Mechanism of Bimolecular Coupling of Ru Methylidene
In our prior communication, 9 we briefly outlined key inferences from a computational analysis of the mechanism for bimolecular coupling: that is, interaction of two Ru-methylidene species to form a bond between the methylidene carbons, ultimately releasing ethylene. Here we present fuller details of this pathway ( Figure S19, Figure S21, and Figure S22). In the discussion of the computational results, the py-stabilized methylidene species 1-H2IMes is represented by model structure M1. The latter is the reference point against which relative free energies are calculated at 263 K (the temperature at which bimolecular decomposition was explored experimentally). M1 is presumed to release pyridine to form methylidene species M2. These 14-electron species may increase their electronic saturation by reacting with each other to form chloride-bridged ruthenium dimers, 11,12 the nature of which is discussed below. Whereas the methylidene unit is largely coplanar with RuCl2 in M1, it is essentially orthogonal to this plane in the most stable conformer of 14-electron M2. Assuming a mechanism that is dissociative in py, 9 this conformer may dimerize with minimal conformational and geometrical changes to form M3. We refer to dimers with this M2-like methylidene conformation as dimer1 (see Scheme 3 in the main text). Although numerous possible mechanisms exist for dimerization, including pathways with involvement of solvent, the minimal geometrical adaption required to form dimer1 suggests that this reaction requires negligible enthalpic activation, if any. Rather than screening a vast number of dimerization mechanisms, we estimated a lower bound for the dimerization barrier by assuming that the reaction rate is limited solely by diffusion of the monomers in solution. The free energy of the variational transition state (TSVAR, at ca. 19 kcal/mol vs M1) for dimerization of M2 is thus obtained by adding an estimate of the barrier to diffusion (4.4 kcal/mol, see Computational Methods) to the sum of the energies of the isolated monomers M2 (a value of 14.8 kcal/mol vs M1). Whereas M3 exhibits the syn-methylidene disposition of the H2C=Ru-Ru=CH2 moieties required for C-C coupling, bond formation also requires rotation of both methylidene units by ca. 90°, to become essentially coplanar with their respective RuCl2 planes, as in M1. 9 We refer to this structure as dimer2 below and in the main text. Within the H2IMes system, M7 is a model for dimer2 and already has a C-C bond distance (3.39 Å) more than 1 Å shorter than that of M3 (4.54 Å). M7 is readily accessed from M3 via transition state M6. The imaginary mode of M6 is dominated by rotation of a single Ru=CH2 bond, whereas the second Ru=CH2 bond twists later along the minimum-energy pathway connecting M6 and M7. On the latter pathway, the potential energy surface surrounding the geometry in which only a single Ru=CH2 twist has occurred is quite flat. All attempts to locate a minimum in this flat region instead converged to M7. Similarly, rotating the Ru=CH2 bond in M7 to move backwards toward M6 led to M8, the transition state for rotation of one Ru=CH2 unit. Following the intrinsic reaction coordinate of M8 along either direction led to the same basin of M7. In conclusion, all these explorations of the potential energy surface between M6 and M7 suggest that no minimum exists that corresponds to a structure with a single methylidene twisted relative to its geometry in M3.
In addition to M3 and M7, we considered the singly-Cl bridged intermediate M4. This intermediate could in principle enable formation of a doubly-bridged dimer. However, its high energy excludes its involvement in the dimerization. Similarly, although known M5 is the most stable methylidene dimer, the methylidene carbon atoms are too far apart to engage in C-C bond formation. Moreover, its Ru=C bond conformations correspond to those in M1, and are thus incompatible with a dimerization pathway that requires minimal geometric adaptation by monomeric M2. M7, although more stable than M3, would also require considerable conformational adaption to form directly from M2. All these computational results, and the experimentally-observed evolution of ethylene (which implies an M3-M5 equilibrium if M5 is the primarily formed dimer), suggest that M3, formed by dimerization of M2, rearranges to M7, which undergoes C-C bond formation as described below.
From dimer M7, C-C bond formation commences with geometric distortion (via transition state M9) to bring the π orbital of one methylidene into the metal coordination sphere of the other Ru=CH2 entity. In the resulting shallow minimum M10, one methylidene serves as an unusual dative ligand for the other Ru center. Close in energy is transition state M11, in which the bonding interaction between the two methylidene carbons first emerges. We previously described the orbital interaction involved. 9 Here we point out that the barrier to C-C bond formation from M7 via M11 is lower than that for sequential rotation of the Ru=CH2 bonds to transform M7 into M3 (ca. 9 vs 12 kcal/mol, respectively), and considerably lower than the 19 kcal/mol overall barrier from pyridine adduct M1 to M7 via M3 (that is, the variational transition state for dimerization of M2). We conclude that the rate-determining step in this pathway is dimerization, rather than formation of the C-C bond between the two methylidene units.
The first intermediate following C-C bond formation is M12, in which the carbon atoms are singlybonded, as judged from the 1.55 Å C-C distance and the C-C-H bond angles (107°, 112°, 113°, 113°). The geometry suggests interaction of one CH2 moiety with both Ru centers, while the other CH2 moiety is bonded to only one Ru atom. The Ru atoms are only 2.5 Å apart, suggesting a metal-metal bond. Whereas electronic rearrangements leading to a spin-triplet pathway are treated below, the spin-singlet reaction pathway involves facile sliding of the C2 Me H4 fragment to form M14 via transition state M13. M14 is best interpreted as containing an ethylene ligand (C-C 1.42 Å)  2 -coordinated to one Ru center and with a C-H agostic interaction to the second Ru atom. Breaking this agostic interaction is unexpectedly demanding, with a barrier of ca. 10 kcal/mol from M14 via M15, but is facilitated by  2coordination of a H2IMes mesityl ring trans to the agostic site. Mesityl binding, although transient, contributes to a rather substantial change in configuration at one Ru center, accounting for the significant energy barrier associated with M15. In the resulting structure M16, a conventional  2 -bound ethylene ligand (C-C 1.40 Å) is coordinated to a single Ru atom. Alternative structures bearing an ethylene ligand bound to a single Ru center (see M18, and M19) are higher in energy than M16, although not prohibitively so.
Finally, we modelled hypothetical spin-singlet species resulting from dissociation of ethylene. The pair of electron-deficient Ru(II) centers is likely to coordinate any electron-donating ligand, in particular the pyridine released earlier from the starting material. Moreover, especially when pyridine is not present in sufficient amounts, the Ru(II) species are expected to engage in aggregation to form Ru nanoparticles. 13 Figure S21. Reaction pathway for formation of ethylene from methylidenes along the spin-singlet surface. Free energy (kcal/mol, at 1 mM standard-state concentration) relative to M1.
As indicated above, M12 may undergo electronic rearrangement to reach its spin-triplet counterpart 3 M23 (the superscript indicates spin multiplicity) via the minimum energy crossing point (MECP) M22.   Finally, as with the spin-singlet surface, we considered the relative energy of ethylene-free intermediates of high spin. However, the energies of both the triplet 3 M34 and quintet 5 M35 are significantly higher than M20, their simplest counterpart on the spin-singlet surface. Ethylene dissociation may thus occur either completely on the singlet surface, or may terminate on the spin-singlet surface after undergoing spin inversion during ethylene dissociation.
The most significant barrier along the spin-triplet path is associated with rupture of the Ru-CH2CH2-Ru bridge in 3 M23 via 3 M27 (16 kcal/mol). The ensuing release of ethylene may occur from the resulting 3 M28 or by rearrangement via 3 M29 to give isomer 3 M33 (barrier ca. 17 kcal/mol from 3 M23). Either barrier is lower than the variational estimate for dimerization of M2 (19 kcal/mol vs M1). Similarly, the most demanding step after formation of the C-C bond on the spin-singlet surface is rearrangement of M14 to yield M16 (<12 kcal/mol from M14), which could already release ethylene. Overall, the barriers along both the spin-singlet and spin-triplet pathways of C-C bond formation are lower than the barrier estimated for dimerization of M2. Thus, irrespective of whether the ethylene-generating part of the bimolecular decomposition involves spin-singlet or spin-triplet species, the initial dimerization is predicted to be rate limiting.

S3.2. H2IMes vs C3 Ph
To limit the computational demand arising from the asymmetry of C3 Ph , which also involves a chiral center, we assumed that the general mechanistic features established for the H2IMes catalyst would remain valid also for C3 Ph . Therefore, only the stationary points and elementary steps found to influence the decomposition rate of the H2IMes-coordinated catalyst were investigated for the C3 Ph -coordinated catalyst ( Figure S23 and Table S1).
First, the calculations predicted that the two rotamers of the catalyst precursor (M36 and M37, in which the CAAC N-Ar moiety is syn or anti relative to the methylidene ligand, respectively) have similar solution stability. M36 is marginally more stable, by 0.4 kcal/mol. Each rotamer exists as a racemic mixture.
Dissociation of pyridine from M36 and M37 leads to the 14-electron methylidene complexes (M39 and M38, respectively). These are 6.2 kcal/mol and 5.7 kcal/mol less stable than M36, the most stable precursor rotamer. Loss of py is thus less costly with C3 Ph as ligand (6.2 or 5.7 kcal/mol) than with H2IMes (7.4 kcal/mol). Opposite orders of stability are found for the rotamers of the 14-electron methylidene complex with respect to the catalyst precursor: The most stable rotamer for the precursor, M36, leads to the least stable 14-electron rotamer M39. The rotational barrier (via M40) between M38 and M39 is 15.9 kcal/mol vs M36, uphill from M39 by only 9.7 kcal/mol. Given the very low concentration of the 14-electron species, equilibration of the rotamers M38 and M39 is likely to precede dimerization. The less stable C3 Ph rotamer in the precursor is thus probably the most abundant in the dimer, meaning that both rotamers are important for bimolecular decomposition.
For the H2IMes complex, pyridine dissociation is accompanied by methylidene rotation. Whereas the methylidene unit is largely coplanar with RuCl2 in M36 and M37, it is essentially orthogonal to the RuCl2 plane in the four 14-electron species M38 (R' and S') and M39 (R and S); see Figure S23 for labelling). As seen above for the H2IMes catalyst ( Figure S19), coupling of 14-electron methylidene S24 species may lead to a number of different dimers. For C3 Ph , we investigated only those dimers, labeled M3 (dimer1) and M7 (dimer2) for the H2IMes catalyst, that are located along the C-C coupling pathway ( Figure S23). The methylidene orientation of the 14-electron monomer is retained in dimer1, and dimerization is associated with minimal geometrical adaption. Assuming (as for the H2IMes catalyst) that formation of this dimer is limited only by monomer diffusion in the solvent (see Section S4.4.1 The Barrier of Diffusion-Controlled Reactions), the barrier to dimerization is estimated to be 2-3 kcal/mol lower for the C3 Ph species than its H2IMes analogue.

TS CC
Labeling rule for dimeric species: L left L right L Ru-left L Ru-right where L left is the label defining the left-hand side monomer, L right is the label defining the right-hand side monomer, L Ru-left is the configuration of the Ru atom on the left-hand side, and L Ru-right is the configuration of the Ru atom on the right-hand side. L Ru-left and L Ru-right are defined in Figure  S24. (e.g., RS'AA is the dimer resulting from having monomer R on the left-hand side, S' on the right-hand side, and both Ru atoms with configuration corresponding to chiral symbol A) these combinations (involving AC and CA), the Ru=CH2 moieties are mutually anti, as in M5, and these structures are not suitable for direct C-C bond formation. The remaining 32 consist of 16 pairs of enantiomers, six of which are redundant due to the symmetry of the dimer, leaving 10 diastereoisomeric dimers to model (see Table S1). Whereas two of these combinations (S'S'AA and RSAA, each with its degenerate stereoisomers (see Table S1) converge directly to dimer2, two (SS'AA and R'SAA) lead to a dimer with features intermediate between dimer1 and dimer2 (see Table S1 for details). The free energies of the six minima clearly corresponding to dimer1 span over 5.8 kcal/mol (from 7.1 to 12.7 kcal/mol vs M36), with four being more stable than dimer1 of the H2IMes catalyst (M3, at 12.2 kcal/mol vs M1). Thus, with C3 Ph as ligand, some of the dimer1 isomers form more rapidly, and are thermodynamically more stable, than those of H2IMes. Nevertheless, dimer1 is not the most stable dimer and, as for the H2IMes catalyst, relaxation of dimer1 leads to the more stable dimer2 in which both methylidene ligands are essentially coplanar with RuCl2. Except for the high-energy, symmetric combinations of R and S monomers (RR and SS), relaxation to dimer2 leads to significant shortening of the distance between the two methylidene units. The energies of the dimer2 complexes span 6.3 kcal/mol (from -1.9 to 4.4 kcal/mol, Table S1). With the exception of M49 (enantiomers RRAA and SSCC), all are higher in energy relative to M36 than the corresponding H2IMes dimer M7, relative to M1 (0.2 kcal/mol). Still, in all cases dimer2 is more stable than dimer1 and has the appropriate methylidene conformation for C-C coupling via transition state TSCC.
In TSCC the two methylidene ligands have very different chemical environments, with one methylidene being weakly coordinated to the second ruthenium center ( Figure S23). Therefore, whereas some stereochemical combinations were symmetrically redundant for dimer1 and dimer2 (e.g., RR'AA = R'RAA and RSAA = SRAA), these combinations become independent stereoisomers in TSCC (e.g., RR'AA ≠ R'RAA and RSAA ≠ SRAA). In total, 16 diastereoisomeric alternatives exist for TSCC (Table  S1), spanning 8.6 kcal/mol in free energy (from 7.5 to 16.1 kcal/mol vs M36). For most of these isomers, C-C coupling is thus more costly than for the H2IMes catalyst (with M11 at 9.4 kcal/mol vs M1). However, by grouping all the alternatives for each symmetrically equivalent pair of monomers we identify six groups (I-VI in Table S1).
To illustrate, we consider the equivalence between the combination of two monomers R and that of two monomers S. Model M59 represents TSCC with stereochemistry RRAA and its mirror image SSCC. Instead, M63 represents TSCC with stereochemistry SSAA and its mirror image RRCC. Group I includes M59 and M63 because these identify two alternative pathways for a pair of either R or S monomers. Within this group, M59 identifies the lowest-energy pathway. Therefore, the coupling of a pair of either R or S monomers occurs via M59 and not via M63. Table S1) span the range 7.5-9.8 kcal/mol vs M36. Thus, in all cases the barrier to C-C bond formation is lower than that of the initial dimerization (TSVAR at 16-17 kcal/mol vs M36). The dimerization step is thus rate-determining for C3 Ph , as it is for H2IMes. Moreover, with TSVAR at 16-17 kcal/mol vs M36, the dimerization step is clearly easier with C3 Ph than with H2IMes as ligand (TSVAR at 19 kcal/mol vs M1), accounting for the more rapid bimolecular decomposition observed for the C3 Ph catalyst.

The lowest energy values for TSCC of each group (values underlined in
The above results are obtained for a standard-state concentration for all the species equal to 1 mM. However, in the kinetic experiments, the initial concentration of 1 varies: it is 1.4 mM for 1-H2IMes and 0.027 mM for 1-C3 Ph . The concentration affects the relative energies. Table S2 displays the values for the lowest energy TSCC calculated for a standard-state concentration corresponding to the initial experimental concentration of 1. (See Section S5, Computational Data, for the complete list of concentration-corrected energies). For H2IMes, the change is small, and the barrier to dimerization (∆ 2 ‡ = 19.5 kcal/mol, see Table 1 of main text) remains clearly higher than that to CC coupling (M11, ∆ [1.4 ] = 9.1 kcal/mol vs M7). For C3 Ph , the change is greater, due to the larger numerical difference between 1 mM and the experimental value of 0.027 mM. Thus, nearly all the dimer2 species become more stable than the precursor M36 (Table S2). Nevertheless, the energy demands of C-C coupling remain substantially lower than the barrier to dimerization (∆ 2 ‡ = 12.1 kcal/mol; see Table 1 in the main text). The latter therefore remains the rate determining step when a standard-state concentration of 0.027 mM is used for all species in the decomposition of 1-C3 Ph . Labeling rules defined in Figure S23. b Energies calculated relative to M36. The most favorable pathways within each group are rendered in bold face. c Attempts to optimize the geometry of dimer1 gave a dimer with features intermediate between dimer1 and dimer2, in which the monomer S' or R' retains the methylidene conformation present in dimer1, but the methylidene ligand in monomer S is rotated by ca. 90° as in dimer2. d Attempts to optimize the geometry of dimer1 resulted in dimer2.

S28
Labeling rules defined in Figure S23. b Energies calculated relative to M36. c Attempts to optimize the geometry of dimer1 gave a dimer with features intermediate between dimer1 and dimer2, in which the monomer S' or R' retains the methylidene conformation present in dimer1, but the methylidene ligand in monomer S is rotated by ca. 90° as in dimer2. d Attempts to optimize the geometry of dimer1 resulted in dimer2.
e Despite several attempts, this stationary point could not be located.

S3.3. Computational Models for Catalysts Bearing Carbenes C1 Ph , C2 Me , and C1 Me
The data above for 1-H2IMes and 1-C3 Ph suggests that dissociation of pyridine from 1 and the ensuing dimerization of 2 are the key factors governing the rate of bimolecular decomposition. We therefore extended our computational investigation to include the pyridine-bound catalysts 1 and the 14-electron complexes 2 for the other CAAC catalysts, i.e., 1-C1 Ph (Figure S26

S4. Computational Methods
Construction, analysis, and visualization of molecular structures were carried out using the following software packages: ChemAxon's Marvin (version 6.2.1), 15 UCSF Chimera (version 1.14), 16 and Molden (version 5.0). 17 Conformational searches and preliminary strain relaxations of molecular models were performed in Spartan18 using the Merck force field (MMFF94) 18 and the semi-empirical PM6 methods 19 . As such empirical and semi-empirical methods are generally less accurate for transitionmetal chemistry than for organic chemistry, internal coordinates, such as metal-ligand bond distances and angles, describing the immediate metal coordination environment, were frozen in these preliminary calculations. All density functional theory (DFT) calculations were performed with the Gaussian suite of programs, versions 09 D.01 20 and 16 C.01. 21

S4.1. Location of Stationary Points and Minimum Energy Crossing Points (MECPs)
Molecular geometries were optimized using Head-Gordon's long-range-and dispersion-corrected hybrid density functional ωB97XD functional. 22 This functional produces geometries in good agreement with those from X-ray diffraction for ruthenium catalysts for olefin metathesis and other homogeneous catalysts. 23 All elements except ruthenium were described with Dunning's correlation-consistent valence double-ζ plus polarization basis sets (cc-pVDZ) 24,25 as obtained from the EMSL basis set exchange database. 26,27 Ruthenium atoms were described by combining the Stuttgart 28-electron relativistic effective core potential (termed ECP28MDF 28 at the Stuttgart/Cologne Group website) 29 with the correlation-consistent valence double-ζ plus polarization basis set (cc-pVDZ-PP) 28 obtained from the EMSL basis set exchange database. 26,27 Numerical integration was performed using Gaussian's "ultrafine" grid. Wavefunctions were converged using the default convergence criteria for selfconsistent field (SCF) procedures (RMS change in density matrix < 1.0·10 −8 , max. change in density matrix = 1.0·10 −6 ), which correspond to the SCF option conver=8. All SCF solutions were checked for internal instability before optimizing geometry. Unstable solutions were re-optimized to a real, spinrestricted or unrestricted solution for spin-singlet or higher multiplets, respectively.
Next, geometries were optimized without symmetry constraints using tight convergence criteria (i.e., opt=tight, corresponding to max. force 1.5·10 −5 , RMS force 1.0·10 −5 , max. displacement 6.0·10 −5 , RMS displacement 4.0·10 −5 ). In a few cases, the SCF convergence criteria were tightened tenfold compared to the above-described default (i.e., conver=9 was used instead of conver=8) to speed up geometry optimization. In all these cases, the resulting geometry was re-optimized with the default SCF convergence criteria. All reported geometries have thus been obtained with the default SCF convergence criteria (conver=8).
Minimum energy crossing points (MECPs) between spin-singlet and spin-triplet surfaces were located using Gaussian 09.d01 in conjunction with via the seam-of-crossing optimizer developed by Harvey (version: November-2009). 30 The DFT model, basis sets, and options of these calculations were identical to those of the regular geometry optimizations described above. To convergence criteria for the seam-ofcrossing optimizations were as follows: The maximum allowed electronic energy gradient was 1.0·10 -4 a.u., and the maximum allowed energy difference between the two spin-states was 0.00050 a.u. The curvature along the seam was confirmed by the eigenvalues of state-averaged Hessian matrix obtained using the Glowfreq program (version November-2015). 31 The input files of the geometry optimizations and Hessian calculations are available in the ioChem-BD repository. 32

S4.2. Hessian Calculations and Thermochemical Corrections
All located stationary points were subjected to analytical calculation of the second derivatives, i.e., the Hessian matrix. Except for the integration grid being reduced from "ultrafine" to "finegrid" in these coupled perturbed Hartree-Fock (CPHF) calculations, the basis sets and options of these Hessian calculations were identical to those of the geometry optimizations. The eigenvalues of the analytically calculated Hessian matrices were used to characterize each stationary point as either a minimum (positive eigenvalues only) or a transition state (a single negative eigenvalue) on the potential energy surface. The translational, rotational, and vibrational components of the thermal corrections to enthalpies and Gibbs free energies were calculated within the ideal-gas, rigid-rotor, and harmonic oscillator approximations (temperature = 263 K), except that all frequencies below 100 cm −1 were shifted to 100 cm −1 when calculating the vibrational component of entropy (i.e., quasi-harmonic oscillator approximation). 34,35

S4.3. Single-Point Energy Calculations
The energy of all stationary points and MECPs was calculated with the PBE functional developed by Perdew, Burke and Ernzerhof 36,37 in combination with Grimme's D3 empirical dispersion term with Becke-Johnson damping (GD3BJ). 38 When corrected for basis set superposition errors (BSSE), this combination of functional and empirical dispersion was found to be the most accurate in a validation study of density functionals for ruthenium-catalyzed olefin metathesis, reproducing mass-spectrometrydetermined relative energies of olefin metathesis reaction steps in the gas phase with absolute errors close to 2 kcal/mol. 39 The PBE-D3BJ combination is expected to perform well also in the present study of ruthenium-mediated reactions related to olefin metathesis, and the large single-point (SP) basis sets (see below) should eliminate the need for BSSE corrections and contribute to accurate relative energies, with errors expected to remain within 2-5 kcal/mol. The BJ damping parameters used were those of Smith and co-workers, which were shown to increase the accuracy substantially compared to the original parameters. 40 Electrostatic and non-electrostatic solvation effects in CHCl3 were accounted for using the polarizable continuum model (PCM) in combination with the "Dis", "Rep", and "Cav" keywords. [41][42][43] The solvent (CHCl3) was characterized by the built-in value for the dielectric constant, and the solute cavity was constructed using the united atom topological model with atomic radii optimized for Hartree-Fock (keyword "UAHF"). Ruthenium was described by the ECP28MDF relativistic effective core potential 28 accompanied by a correlation-consistent valence quadruple-ζ plus polarization basis set (ECP28MDF_VQZ), 28 both obtained from the Stuttgart/Cologne Group website. 29 Carbon and hydrogen atoms were described by valence quadruple-ζ plus polarization (cc-pVQZ) 24,25 as obtained from the EMSL basis set exchange database. 26,27 For all other atoms, augmented valence quadruple-ζ plus polarization (aug-cc-pVQZ) 24,25,44 basis sets were taken from the EMSL repository. 26,27 Finally, numerical integrations were performed with the "ultrafine" grid of Gaussian 16. The densitybased SCF convergence criteria were 1.0·10 −5 (RMS change) and 1.0·10 −3 (maximum change), respectively, corresponding to the SCF option conver=5.
Input files are available in the ioChem-BD repository. 32 where 3 is the energy resulting from single-point calculation, including solvent effects (from the implicit solvation model) and the dispersion correction,

, ℎ =263
is the thermal correction to the Gibbs free energy calculated at the geometry optimization level using the quasi-harmonic approximation, and is the standard-state correction corresponding to a solution (but exhibiting infinite-dilution, ideal-gas-like behavior) with a given concentration ([M]). The concentration is set to either 1 mM for general-purpose data that need to be comparable across different species, or to the experimental concentration used in the kinetic experiments, namely, 1.4 mM for computational data referring to experiments with 1-H2IMes, 61 M for 1-C1 Ph , 586 M for 1-C1 Ph (I2), 10 M for 1-C2 Me , 10 M for 1-C1 Me , and 27 M for 1-C3 Ph . Free energy values calculated with one or the other concentration are clearly identified by table/figure captions and footnotes.
All values are collected in Table S4, Table S6, Table S7, Table S8, Table S9, and Table S10 of the Computational Data section.

S4.4.1. The Barrier of Diffusion-Controlled Reactions
Dissociative elementary reaction steps that require small or no geometrical strain sometimes do not involve enthalpic barriers on the potential energy surface. In such cases, attempts to explore the dissociation of the two fragments typically lead to minimum energy pathways with monotonically increasing potential energy, with the barrier corresponding to complete separation of the two fragments. However, even without a maximum on the potential energy surface, the corresponding free energy surface in solution may still be associated with a maximum corresponding to a variational transition state. The free energy of the latter can be estimated by reversing the Eyring equation using a typical rate constant (410 9 s -1 in common organic solvents) for diffusion-controlled reactions in usual conditions. 45 The associated free-energy barrier (4.4 kcal/mol) is calculated by reversing the Eyring equation (using 298 K to account for the fact that the above typical value of the reaction rate refers to usual conditions, thus room temperature rather than -10°C). 46 Finally, the estimated free energy for the variational transition state (labeled TSVAR) of dimerization is obtained by adding the above correction to the energy of the two isolated monomers.

S4.4.2. The Barrier Associated with Spin Inversion
The free energy of MECPs was calculated as follows: i) The single-point energy was taken to be the average of the single-point energies obtained for the two spin multiplicities at the MECP geometry, ii) the thermochemical corrections were taken to be the average obtained for the minima on either side of the MECP on the seam of crossing, and, iii) an additional penalty ( ), suggested by Schneider and co-workers to be in the range 1-5 kcal/mol, 47  are the thermal corrections to the Gibbs free energy calculated at the geometry-optimization level with the quasi-harmonic approximation for the neighboring minima on the spin-singlet and spin-triplet surface, respectively. The resulting values are collected in Table S5.

S4.5. Natural Bond Order and Partial Charge Analysis
The natural bond orbital analyses were performed with the NBO7 software, 49 using the electron density of the single-point energy calculations as input. To obtain a comparable set of orbitals among the complexes, Lewis structures were explicitly given via the $CHOOSE input section.

S4.6. Calculations of Buried Volume
Buried volumes (the percentage of a sphere that is occupied, %Vbur) for the DFT-optimized pyridinefree, 14-electron active complexes 2, including hydrogen atoms, were obtained using the SambVca 2.1 web application developed by Cavallo and co-workers. 50 A sphere of radius 3.5 Å centered on ruthenium was used, and the van der Waals radii were those of Bondi, 51 scaled by 1.17. The mesh spacing for numerical integration was 0.10 Å.