The Janus face of high trans-effect carbenes in olefin metathesis: gateway to both productivity and decomposition

Ruthenium–cyclic(alkyl)(amino)carbene (CAAC) catalysts, used at ppm levels, can enable dramatically higher productivities in olefin metathesis than their N-heterocyclic carbene (NHC) predecessors. A key reason is the reduced susceptibility of the metallacyclobutane (MCB) intermediate to decomposition via β-H elimination. The factors responsible for promoting or inhibiting β-H elimination are explored via density functional theory (DFT) calculations, in metathesis of ethylene or styrene (a representative 1-olefin) by Ru–CAAC and Ru–NHC catalysts. Natural bond orbital analysis of the frontier orbitals confirms the greater strength of the orbital interactions for the CAAC species, and the consequent increase in the carbene trans influence and trans effect. The higher trans effect of the CAAC ligands inhibits β-H elimination by destabilizing the transition state (TS) for decomposition, in which an agostic MCB Cβ–H bond is positioned trans to the carbene. Unproductive cycling with ethylene is also curbed, because ethylene is trans to the carbene ligand in the square pyramidal TS for ethylene metathesis. In contrast, metathesis of styrene proceeds via a ‘late’ TS with approximately trigonal bipyramidal geometry, in which carbene trans effects are reduced. Importantly, however, the positive impact of a strong trans-effect ligand in limiting β-H elimination is offset by its potent accelerating effect on bimolecular coupling, a major competing means of catalyst decomposition. These two decomposition pathways, known for decades to limit productivity in olefin metathesis, are revealed as distinct, antinomic, responses to a single underlying phenomenon. Reconciling these opposing effects emerges as a clear priority for design of robust, high-performing catalysts.


Model building
The construction of molecular structures, conformational searches, and preliminary strain relaxations of molecular models were performed with Spartan18 2 using its implementation of Merck's force field (MMFF94) 3 and of the semi-empirical method PM6. 4 These calculations were usually coupled with manually set geometrical constraints in the surrounding of the metal centers to protect special geometrical features that are not well described by empirical and semiempirical methods. All density functional theory (DFT) calculations were performed with the Gaussian 16 suite of programs, versions 09 B.01 5 and 16 C.01. 6
Electrostatic and non-electrostatic solvation effects in chloroform (the solvent used in the experiments) were taken into account by using the polarizable continuum model (PCM) in combination with the "Dis", "Rep", and "Cav" keywords and the built-in program values (dielectric constant, number density, etc.). [14][15][16][17] The solute cavity was constructed using the united atom topological model with atomic radii optimized for Hartree−Fock (termed "UAHF"). [17][18][19][20] All stationary points were characterized by the eigenvalues of the analytically calculated Hessian matrix, confirming the absence (for minima) or presence of a single negative eigenvalue (for transition states). 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 considering a temperature of 298 K, except that all frequencies below 100 cm -1 were shifted to 100 cm −1 when calculating the vibrational component of the entropy (i.e., the quasi-harmonic oscillator approximation) 21 to prevent the asymptotic behavior of the harmonic approximation with modes of very low frequencies.

Calculation of Gibbs free energies
Gibbs free energies were calculated at 298 K according to equation 1, when considering the PBE-D3M(BJ) model, or equation 2, when applying the M06L-D3 model: where E PBE-D3M(BJ)

CHCl3
are the potential energy resulting from single-point calculations with PBE-D3M(BJ) and M06L-D3, respectively, and include the contributions from the implicit solvation model; G PBE ℎ CHCl3 298K is the thermal correction to the Gibbs free energy calculated at the geometry optimization level with the quasi-harmonic approximation at 298 K; and G 1atm→1M

298K
is the standard state correction corresponding to 1 M solution (but exhibiting infinite-dilution, ideal-gas-like behavior), which is equal to 1.89 kcal mol −1 (= RT·ln(24.46)) at room temperature. ) calculated with respect to the metallacyclobutane 4 with a given carbene ligand. Namely, molecular models M20, M21, or M22 (see Table S2) are the reference points for each species bearing the H2IMes, C1 Ph , or C2 Me ligand, respectively.

Natural bond orbital (NBO) analyses
The natural bond orbital analyses were performed with the NBO7 software, 30 using the electron density of the single-point energy calculations as input.
The ligand-metal -donation of the carbene ligands (H2IMes, C1 Ph , and C2 Me ) in metallacyclobutane complex 4 was determined as the difference between the electron population of the carbene lone pair (LP) in 4 and that of the corresponding carbene ligand 'frozen' in the geometry of 4. Similarly, the -back-donation to each of the carbene ligands in 4 was determined as the difference between the electron population of the carbene lone vacancy (LV) in 4 and that of the corresponding carbene ligand 'frozen' in the geometry of 4. To ensure a comparable set of orbitals between the complexes and the 'frozen' ligand fragments, the Lewis structures were explicitly required (via the $CHOOSE input section) to have a lone pair (LP) at the carbene carbon atom as well as on the adjacent N-atom.
Bond orders in the transition states for ethylene and styrene metathesis were estimated using the Wiberg bond index (WBI). 31 The steric exchange repulsion energy between the carbene, the methylidene, and the chloride ligands in methylidene complexes 2 and 2' was calculated using natural steric analysis. 32 This was accomplished by summing all pairwise steric energies contributions ≥ 0.1 kcal/mol. The methylidene moiety employed in the calculations included the ruthenium-carbon -and -bonds and the C-H bonds, whereas the lone pairs and the rutheniumchloride -bonds were included for the chloride ligands.
To ensure a comparable set of orbitals, the second-order perturbation theory analysis of transition state TS4-5 (Table S1) was performed with the Lewis structures were explicitly required (via the $CHOOSE input section) to S12 have a lone pair (LP) at the carbene carbon atom as well as on the adjacent N-atom as shown in Table S1, and a single covalent bond at the braking -C-H interaction.

Calculated steric volumes
Buried volumes (the percentage of a sphere that is occupied, %Vbur) and steric maps for the carbene ligand H2IMes, C1 Ph , and C2 Me in the DFT-optimized metallacyclobutane 4 were obtained using the SambVca 2.1 web application developed by Cavallo and co-workers. 33 A sphere of radius 3.5 Å centered on ruthenium was used, and the van der Waals radii were those of Bondi, 34 scaled by 1.17. The mesh spacing for numerical integration was 0.10 Å. Hydrogen atoms were excluded.

Natural bond orbital (NBO) analyses
Calculated Wiberg bond indices (WBIs) of the transition states for ethylene and styrene metathesis are shown in Fig. S8. As discussed in the main part of the paper, these indices, or bond orders, suggest that the transition states for ethylene metathesis (TS3'-4/TS4-3, deemed 'early' transition states) resemble -complexes more than metallacyclobutane intermediates. Conversely, the 'late' transition states for self-metathesis of styrene (a model 1alkene) are more like metallacyclobutane intermediates than -complexes. The NBO-based second-order perturbation analysis of donor-acceptor interactions in TS4-5 (Table S1) confirms that the carbene lone pair and the -C-H bond compete for -donation to the same ruthenium acceptor orbital. Simultaneously, the corresponding carbene -acceptor orbital and the antibonding -C-H and Ru-C orbitals compete for the same Ru lone pair.

Calculated steric volumes
Steric maps and %Vbur describe the steric effects of the carbene ligands at the Ru center and give an idea of the steric potential of the ligand, but do not quantify the steric interaction with other ligands.
The steric properties of the H2IMes, C1 Ph , and C2 Me complexes were expected to differ based on the nature of the substituents flanking the carbene carbon, and the shorter bonds to Ru for the CAAC complexes vs H2IMes. However, the calculated percent buried volumes 35 (%Vbur; Fig. 9) of 4 bearing these three carbenes differ by only 2.6 percentage points. The steric distinction between the three carbenes thus appears to be small, albeit C1 Ph is predicted to be slightly more sterically demanding.    -a The relative Gibbs free energy of each species bearing the H2IMes, C1 Ph , or C2 Me ligand is calculated with respect to the corresponding energy model of metallacyclobutane 4, namely, M20, M21, or M22 respectively.