Computational study of the mechanism and selectivity of ruthenium-catalyzed hydroamidations of terminal alkynes

Density functional theory calculations were performed to elucidate the mechanism of the ruthenium-catalyzed hydroamidation of terminal alkynes, a powerful and sustainable method for the stereoselective synthesis of enamides.


A. Introduction
The enamide moiety is a key functionality in numerous natural products 1 and synthetic drugs exhibiting antibiotic, 2 antitumor, 3 cytotoxic, 4 anthelmintic 5 and antifungal 6 activities. This class of compounds also serves as intermediates in various reactions including synthesis of heterocycles, 7 [4 + 2]-cycloadditions, 8 cross-coupling reactions, 9 Heck olenations, 10 enantioselective additions 11 or asymmetric hydrogenations. 12 Established methods for syntheses of enamides all have individual drawbacks, which complicate their use in organic synthesis. Condensations of carbonyl derivatives with amides 13 require rigorous reaction conditions and lead to mixtures of Eand Z-enamides. The isomerization of N-allylamides, 14 oxidative amidation of alkenes, 15 and co-dimerization of N-vinyl amides with alkenes 16 all furnish the thermodynamically favorable Eisomer as the major product. Only few synthetic methods, such as the Curtius rearrangement of a,b-unsaturated acyl azides, 17 Peterson elimination, 18 transition metal-catalyzed crosscoupling reactions of vinyl halides, 19 vinyl triates, 20 or vinyl ethers, 21 are applicable for the synthesis of the thermodynamically less favorable Z-isomer, but here, the starting materials are poorly available and expensive. In 1983, Shvo et al. 22 reported the synthesis of enol esters using a ruthenium-catalyzed nucleophilic addition of carboxylic acids to non-activated alkynes. Thereaer, additions of other nucleophiles such as water, 23 amines, 24 alcohols, 25 thiols, 26 etc. have been investigated by several groups. In 1995, the groups of Heider 27 and Watanabe 28 observed that E-enamides can be prepared stereoselectively by ruthenium-catalyzed anti-Markovnikov addition of carboxamides to terminal alkynes. This was the rst report of a transition metal-catalyzed N-H bond activation and addition of amides to alkynes. Based on this pioneering work, Gooßen et al. have developed efficient ruthenium catalysts for the atom-economic addition of amides, carbamates, lactams, 29 imides 30 and thioamides 31 to terminal alkynes (Scheme 1 and 2). Recent work in this area includes, e.g. the stereoselective addition of alkynes to pyrazoles. 32 The catalyst systems are generated in situ from bis(2-methallyl)(cycloocta-1,5-diene)ruthenium(II) [(cod)Ru(met) 2 ], phosphine ligands, and bases or Lewis acids. In all cases, the reaction proceeds highly regioselectively in favor of the anti-Markovnikov products. 33 The stereoselectivity is controlled by the choice of ligands: with a combination of tri-n-butylphosphine (P(Bu) 3 ) and 4dimethylaminopyridine (DMAP), the E-enamides are obtained in high yield and selectivity. With bis(dicyclohexylphosphino) methane (dcypm), the stereoselectivity is inverted, and the Zenamides are preferentially formed (Scheme 2). 34 The dependence of the stereoselectivity on the catalyst system and the reaction conditions is a key advantage of this synthetic approach, as it allows accessing both stereoisomers from the same precursors. However, all efforts to pinpoint the origin of this effect have failed so far.
Various catalytic pathways have been considered for ruthenium-catalyzed hydroamidation and related additions of nucleophiles such as carboxylic acids, alcohols and water to C-C triple bonds. Watanabe initially proposed a mechanism that involves oxidative addition of the amide, insertion of the alkyne into the Ru-H or Ru-N bond and reductive elimination. 28 A similar pathway was sketched out by Uchimaru for the ruthenium-catalyzed addition of aromatic amines to alkynes, which, however, proceeds with Markovnikov selectivity. 24a In both pathways, the alkyne insertion step was believed to control the regioselectivity of the addition process.
Dixneuf proposed that the key mechanistic step is the formation of a vinylidene intermediate via 1,2 or 1,3-proton transfer at the alkyne moiety. 35 The electrophilic nature of the acarbon in vinylidenes would explain the exclusive formation of the anti-Markovnikov products, and the required rearrangement the limitation of this reaction to terminal alkynes. Caulton and co-workers performed computational studies to investigate pathways of ruthenium-vinylidene complex formation. 36 Their key message is that the formation of vinylidenes via 1,2 or 1,3-proton transfer is energetically difficult. In contrast, ruthenium-vinylidene complexes easily form via rearrangement of the corresponding vinyl complexes, which themselves are easily generated by the insertion of p-coordinated alkynes into Ru-H bonds. A related vinyl-vinylidene rearrangement pathway was also proposed by Wakatsuki for the hydration of alkynes. 23b The complete array of potential mechanistic pathways was evaluated by Gooßen et al. with regards to their applicability to the hydroamidation of terminal alkynes with secondary amides. 37 Extensive experimental and computational data including mass spectrometry, DFT optimizations of intermediates, deuterium labeling studies and NMR spectra were used to narrow down the possible mechanistic pathways to the route delineated in Scheme 3. The cycle starts with the Ru 0 species [Ru 0 (DMAP) 2 (PBu 3 ) 2 ], which was conrmed by strong signals in the in situ ESI-MS experiments. It is followed by the oxidative addition of amide giving rise to an octahedral Ru II -hydride complex [Ru II (DMAP) 2 (PBu 3 ) 2 (H)(pyr)] (pyr ¼ 2-pyrrolidinyl anion). The NMR signals of the reaction mixture correspond to those observed for a mixture of the Ru II -hydride complex with amide, but not to those for a mixture of the Ru II -hydride complex with alkyne. 35  This mechanism serves well to explain the regioselectivity of the reaction. However, these extensive spectroscopic investigations do not provide any explanation for the strong dependence of the stereoselectivity on the phosphine employed since they suggest that the same intermediates are present both for P(Bu) 3 and dcypm as phosphine ligands although they led to products with the opposite stereochemistry. 37 In-depth theoretical studies were clearly required to gain an understanding why the stereoselectivity of this reaction can so efficiently be controlled by the ligand. Only if the origin of this effect can be understood, a rational development of highly efficient catalyst systems for both E-and Z-selective addition reactions of amides and related nucleophiles to alkynes will become possible.
In the theoretical studies disclosed herein, the entire catalytic cycle of the hydroamidation of amides to terminal alkynes has been computed using realistic model systems of high complexity. The calculations conrm that the catalytic cycle that has been proposed based on the spectroscopic studies is viable and has a realistic energy prole. They also reveal that the stereochemistry of the reaction is determined by the preferred geometry of the vinylidene intermediate that undergoes the intramolecular nucleophilic transfer step: in presence of P(Bu) 3 , the butyl chain is in anti-orientation to the incoming 2-pyrolidinyl unit, while the steric interaction between the cyclohexyl groups in the dcypm ligands and the butyl chain forces it into the opposite orientation. Consequently, E-products are predicted to form in the presence of P(Bu) 3 , whereas Z-products should predominate when using dcypm. This is in excellent agreement with the experimental ndings.

B. Computational details
All the calculations were performed using Gaussian03 (ref. 38) and Gaussian09 (ref. 39) program packages. The geometries of stationary points and transition states were optimized with the generalized gradient approximation (GGA) by means of the Becke exchange functional 40 in addition with the Perdew correlation functional 41 (BP86). We employed Double-z basis set with the relativistic effective core potential of Hay and Wadt (LANL2DZ) 42 for the ruthenium atom and 6-31G(d) 43 basis sets for other elements (H, C, N, O, and P). To reduce computational cost, all calculations were performed using a two-layer ONIOM(MO:MO) 44 method for reaction pathways emanating from the cyclic phosphine-containing catalyst system 1 c . The ONIOM high level was designated to the whole molecules except the cyclohexyl ring (-Cy) in dcypm (V in Fig. 1) and treated at a BP86/LANL2DZ(Ru)/6-31G*(H, C, N, O and P) level. The ONIOM low level (-Cy) has been described at the HF/STO-3G method. For all our DFT calculations, the resolution-of-the-identity (RI) approximation (also called "density tting") was employed for the two-electron integrals. 45 The geometries were optimized without any symmetry constraints. Harmonic force constants were computed at the optimized geometries to characterize the stationary points as minima or saddle points. Zero-point vibrational corrections were determined from the harmonic vibrational frequencies to convert the total energies E e to ground state energies E 0 . The rigid-rotor harmonic-oscillator approximation was applied for evaluating the thermal and entropic contributions that are needed to derive the enthalpies H 298 and Gibbs free energies, G 298 at 298 K. All transition states were located using the linear synchronous transit (LST) 46 method in which the reaction coordinate was kept xed at different distances while all other degrees of freedom were relaxed. Aer the linear transit search the transition states were optimized using the default Berny algorithm implemented in the Gaussian09 code. 39 All transition states were conrmed by IRC (Intrinsic Reaction Coordinate) calculations. For further validation, single-point BP86 calculations (E L ) were performed on the BP86/LANL2DZ(Ru)/6-31G*(H, C, N, O and P) optimized geometries employing a valence triple-z-type of basis set (TZVP) 47 for light atoms (H, C, N, O, and P) and LANL2TZ(f) 42 basis set for ruthenium incorporated in the Gaussian program suites. 39 It has been shown that the current DFT method (with BP86 functional) provides reliable geometries, energies and vibrational frequencies in related mechanistic studies. 48 Using this functional, validation studies of transition metal compounds, particularly ruthenium(II) complexes, are reported in the literature. Additionally, Tonner and Frenking studied the effect of carbodiphosphorane ligands in olen metathesis using Grubbs catalyst at BP86/SVP level of theory. 49 To account for dispersion effects, single-point calculations were performed using the empirical dispersion-corrected BP86-D 50 functional using the larger basis set employed for calculating E L energies. For further validation in computing dispersion effects, we also obtained single-point energies with functionals B97D 50 and M06-2X 51 using the same larger basis sets described above (refer to ESI, Fig. S1 and S2 †). We have tested several dispersion corrected functionals, e.g. BP86-D, B97D and M06-2X. The empirical correction for dispersion interactions results in a signicant reduction of the energies. These attractive forces are not considered in pure DFT methods. The variations between the methods compared result from the different way these treat exchange-correlation in the functionals. However, potential mistakes will similarly affect related catalytic pathways, so that the overall effect of systematic errors in this context is low. Solvation energies (E S L ) were evaluated by a self-consistent reaction eld (SCRF) approach for all the intermediates and transitions states, using the SMD continuum solvation model 52 implemented in Gaussian09. Toluene was chosen as a solvent (dielectric constant 3 ¼ 2.374) with SMD-intrinsic Coulomb radii for the respective atoms. In the Gaussian program, the concentration can be specied by adjusting the pressure value based on the ideal gas law p i ¼ RTn i /V, where p i is the pressure, R the gas constant, T the absolute temperature, n i the molar quantity, and V the reaction volume. The experimental concentrations of catalyst and reactants at the reaction temperature are approximated by setting the partial pressures of the substrates as follows: alkyne (I): 2.0 Â 10 À3 mol a 20 atm; amide (II): 1.0 Â 10 À3 mol a 10 atm, of DMAP (iv) as 1.4 Â 10 À4 mol a 1.386 atm, and of the intermediates of the catalytic cycles as follows: catalyst (1): 6.8 Â 10 À5 a 0.693 atm; catalyst (1 c ): 6.6 Â 10 À5 a 0.673 atm. 53 In the present study, we have considered only four energy terms: H L , G L G S L and G SD L . H L and G L represents the gas-phase enthalpy and Gibbs free energy at the higher basis set mentioned before. These values were obtained by augmenting the E L energy terms with the respective enthalpy and free energy corrections at the BP86/LANL2DZ(Ru)/6-31G*(H, C, N, O and P) level. The Gibbs free energy in the solution phase (G S L ) was calculated as: Here, H S L represents the solventphase enthalpy calculated from E S L and the enthalpy corrections at the lower basis set, whereas the solvation entropy (S S L ) was estimated as two/third of the gas-phase value. 54 G SD L additionally contains the dispersion-corrected energies to the G S L values. All single-point calculations were performed with tight wavefunction convergence criteria and an "ultrane" (99 950) grid was used in numerical integration. The charge distribution was analyzed using Weinhold's NPA (Natural Population Analysis) approach. 55 Additionally, we have performed AIMALL calculations 56 to characterize the electron distribution around some selected bonds (Ru-ligand, C a -C b ) applying Bader's AIM (atoms-inmolecule) theory. 57 The bond critical point (BCP) is a point on this line where the gradient of the density is equal to zero. The magnitude of the electron density (r(r b )) and its Laplacian (V 2 r(r b )) at the BCP provide information about the strength and type of bond. The Laplacian indicates whether the density is locally concentrated (V 2 r(r b ) < 0) or depleted (V 2 r(r b ) > 0). Figures were generated using the Chemcra visualization program. 58

C. Results and discussion
In the current computational study, we have selected 2-pyrrolidone (I) and 1-hexyne (II) as the reactants, in analogy to those used in the experimental setup. 37 Three possible products are likely to be generated in the nucleophilic addition of I to II, namely the Markovnikov gem-enamide (VI) and anti- Markovnikov Z-(VII) and E-enamides (VIII) (Fig. 1a). Two different catalyst systems generated in situ from the pre-catalyst [Ru II (methallyl) 2 (cod)] in the presence of different sets of ligands and additives are [Ru 0 (Bu 3 P) 2 (DMAP) 2 ] (1) and [Ru 0 (dcypm) 2 ] (1 c ) respectively (Fig. 1b). We have performed DFT calculations to construct complete catalytic pathways for both these catalyst systems. In order to elucidate the origin of the regio-and stereoselectivity of the hydroamidation reaction we have considered the active catalyst and substrate used in the experiments without going for a truncated model system. In accordance with the proposed mechanism, our calculated catalytic cycles includes the following ve steps: (1) oxidative addition of amide to ruthenium(0) to generate a ruthenium(II) complex, (2) ligand dissociation followed by alkyne coordination to furnish a p-complex, (3) alkyne insertion to the Ru-H bond to afford a vinyl intermediate, (4) vinyl-vinylidene rearrangement, (5) intramolecular nucleophilic transfer, and nally (6) reductive elimination to generate the product.
The catalytic pathway involving catalyst 1 is discussed rst in subsection C.I., followed by catalyst system 1 c in subsection C.II. Each fundamental step of the catalytic cycles is characterized by the changes in enthalpy (DH L ), Gibbs free energy (DG L ), and solvent free energy changes, with and without dispersion corrections (DG SD L , DG S L ), at the higher basis set. Only the DG SD L energy term is discussed in the text unless otherwise mentioned. The remaining energy values are collected in the ESI. † C.I. Catalyst system 1 C.I.a. Oxidative addition and hexyne coordination. The catalytic cycle for ruthenium-catalyzed hydroamidation usually starts by an oxidative addition step (Scheme 3). Fig. 2 details the energy prole of the steps studied in this sub-section, and Fig. S3 and S4 † provide 3D structures of the optimized geometries and other details of the oxidative addition and hexyne coordination steps. The active catalyst 1 is a ruthenium(0) d 8 system that possesses a typical square-planar geometry ( Fig. S4 †). The 4d z 2 orbital of ruthenium is the main contributor to the HOMO of 1 (Fig. S32a †), allowing either reactant I or II to coordinate along its axis. The N 3 -H 1 bond in II is more acidic than the C a (sp)-H 2 bond in I, as is evident from the NPA charges of the H 1 and H 2 atoms respectively (q H 1 ¼ 0.402e in II and q H 2 ¼ 0.237e in I). In fact this might be the reason that drives the electron-rich ruthenium center (q Ru ¼ À0.57e) towards participating in the oxidative addition with II, a nding that is in agreement with the deuterium labeling experiments by Gooßen et al. 37 The oxidative addition step is initiated by the formation of an encounter adduct of the type of structure 2, followed by subsequent N 3 -H 1 bond activation (see Fig. 2) leading to the cis-congured octahedral complex 3. Including dispersion corrected energy values, the encounter complex 2 is more stable than its separated reactants, a similar observation was reported in our previous calculations. 53 The oxidative addition step is exergonic and its product more stable than the starting materials 1 and II taken together (DG SD L ¼ À31.0 kcal mol À1 , Fig. 2 and S3 †). The calculated activation barrier for the transition state [2][3] ‡ is quite small (D ‡ G SD L ¼ 0.7 kcal mol À1 ). In the transition state [2][3] ‡ , ruthenium exhibits a ve-coordinated, distorted trigonal bipyramidal-like geometry (Fig. S4 †) with an N 3 -H 1 bond elongated by 1.950Å, and the imaginary mode (90i cm À1 ) involves stretching of N 3 -H 1 bond. The NPA charge at Ru 0 is decreased by 0.247e in going from 1 to 3, suggesting that oxidative addition occurs in this process.
The ruthenium(II) complex 3 represents a saturated 18-electron system with pseudo-octahedral geometry. In order to allow for hexyne coordination, a neutral ligand has to dissociate to create a vacant site at the metal center. 59 Since the metal center in 3 is more electron-decient than in 1 (q Ru ¼ À0.57e in 1 vs. q Ru ¼ À0.35e in 3), it strongly binds to the electron-donor ligands, and therefore ligand dissociation should be unfavorable. Going from 1 to 3, the NPA charge of P 1 , P 2 , N 1 and N 2 decreases by 0.088e, 0.034e, À0.019e and 0.016e respectively, indicating that phosphine ligands have contributed greater charge density to ruthenium than DMAP ligands (refer to Table S7 †) and that hence, the decoordination of DMAP will be more facile than of a phosphine. Despite the fact that the bond distance of Ru-N 1 (2.406Å) is longer than that of Ru-N 2 (2.197 A) (refer to Fig. S4 †), the Ru-N 2 bond has to be cleaved so that hexyne can coordinate to Ru in the cis position to the Ru-H 1 bond.
The particular reason for such site-specic coordination will become clear in the forthcoming sections. Following dissociation of one DMAP, the unsaturated intermediate 4 is generated ( Fig. 2 and S3 †). This step is endergonic (DG SD L ¼ 13.0 kcal mol À1 , refer to Fig. S3 †) even though it involves ligand dissociation. The energetic penalty associated with ligand dissociation when including dispersion corrected energies is not surprising. Schoenebeck et al. reported that dissociation of PdL 2 / PdL + L is endoergic upto 30 kcal mol À1 at M06L(THF)// B3LYP/{6-31+G(d), SDD (Pd)} level of theory. 60 At this stage, the charge on ruthenium (q Ru ¼ À0.284e) has depleted, creating an electronic environment suitable for hexyne coordination to occur. Inspection of the KS-LUMO of 4 reveals that the incoming hexyne will be oriented such that it can deliver electron density to the empty 4d xz orbital of ruthenium ( Fig. S32b †). Gradual progress of hexyne to the metal center results in the typical h 2cordinated ruthenium(II) intermediate 5 (Fig. 2, S3 and S4 †). The hexyne coordination step involves transition state [4][5] ‡ , with a moderate energy barrier of 20.2 kcal mol À1 (DG SD L ). [4][5] ‡ is characterized by a single imaginary frequency (39i cm À1 ), which resembles simultaneous elongations of the Ru-C a and Ru-C b bonds.
C.I.b. Hexyne insertion and vinyl-vinylidene rearrangement. Intermediate 5 is a perfect h 2 -complex as its two Ru-C (hexyne) bond lengths are similar (Ru- Fig. S4 †), and hexyne acts as two-electron donor resulting in a ruthenium(II) 18-electron system. The possibility of further oxidative addition of the hexyne via C(sp)-H bond to generate a Ru IV H 2 species was not considered in the present study, since such a reaction requires high-energy intermediates as reported by Caulton 36 and Wakatsuki 23b and is not supported by isotope labeling studies. 37 To accomplish the alkyne insertion step the Ru-H 1 should remain coplanar with the coordinated alkyne unit. Indeed, the H 1 -Ru-C a -C b dihedral angle of 12.1 in 5 fullls the geometrical criteria for effective hydride transfer to C b atom of hexyne fragment. 36 However, aer such insertion a coordinately unsaturated 16-electron vinyl complex would be generated. Therefore we made an attempt to study the hexyne insertion step by re-incorporating the DMAP, which was released during the preceding hexyne coordination step 3 / 5 (vide supra). As expected, no immediate coordination of the DMAP to the metal center took place even when placing it at the most promising position close to the metal center. So we studied the insertion step from intermediate 5 without considering the second DMAP at this stage. The vinyl complex 6 thus formed is somewhat more stable than the hexyne-coordinated complex 5 (DG SD L ¼ À4.7 kcal mol À1 ; see Calculated results show that 6 I is energetically less stable than 6 by 13.6/11.7 kcal mol À1 (DH L /DG L ) conrming that the chelating N-O type coordination plays signicant role in the stabilization of this complex.
The insertion step [5][6] ‡ requires a very small activation . This is in agreement with calculations by Caulton and Eisenstein who found a value of (D ‡ H L ¼ 6.6 kcal mol À1 ) for RuHCl(HC^CH)(PH 3 ) 2 intermediate. 36 The geometry of transition state [5-6] ‡ resembles 5, albeit with elongated Ru-H 1 , Ru-C b and C a -C b bonds (refer to Fig. S6 †). Furthermore, the insertion transition state is characterized by a unique eigenmode (622i cm À1 ) that resembles the hydride transfer from Ru to the C b center. Now the DMAP can coordinate to 6 from two opposite sites, either syn or anti to the existing DMAP ligand (see Fig. 3a and b). The pathways involving anti and syn coordination of DMAP are designated as "path a" and "path b", respectively.
Path a. When bringing the second DMAP molecule closer to the metal center of 6, the Ru-O(sp 2 ) bond cleaves, and a six fold coordinated ruthenium(II) vinyl intermediate 7a forms, in which the two DMAP ligands are in trans position (Fig. 3a). 62 In vinyl complex 7a, Ru II becomes electron-decient (q Ru ¼ À0.035e in 7a), whereas C a and C b are both electron-rich centers (q C a ¼ À0.361e, q C b ¼ À0.311e refer to Table S7 †).
Electron density can be transferred to the ruthenium center by a-hydride migration, resulting in a vinylidene-type complex 8a. The importance of vinylidene intermediates in organometallic chemistry cannot be neglected, and the existence of a similar vinyl-vinylidene rearrangement in catalysis has been substantiated from experimental reports. 35,37,63 To relieve the steric strain associated with accommodating the second DMAP molecule, the Ru-C a bond in 6 rotates to a pseudo-perpendicular orientation with respect to the Ru-N 1 -N 2 -P 1 plane in 7a Fig. S6 †). Now to gain access to the vinylidene intermediate, a-hydride migration is necessary, and a coordination site at the metal center must be free. Incidentally, during the progress of the vinyl-vinylidene rearrangement step, a coordination site becomes available in the transition state [7a-8a] ‡ by decoordination of the newly added DMAP (see Fig. 3a). Interestingly, none of the phosphines undergo decoordination during the vinyl-vinylidene rearrangement, indicating that the Ru-phosphine bonds are stronger than the Ru-DMAP bonds. In [7a-8a] ‡ , the Ru-C a bond distance (2.088Å in 7a vs. 1.881Å in [7a-8a] ‡ ) has already shortened and the Ru-C a -C b bond angle attened (132 in 7a vs. 172 in [7a-8a] ‡ ), resulting a geometry similar to the vinylidene intermediate 8a ( Fig. 3a and S6 †). It is counter-intuitive that the intermediate 8a in combination with a fully dissociated DMAP is higher in free enthalpy than the transition state [7a-8a] ‡ in step 7a / 8a (see Fig. S5 †). The IRC revealed that this transition state actually connects to a loose adduct between 8a and DMAP that is lower in enthalpy than the transition state. However, in solution, this adduct will not be stable, so that we have le out this loose DMAP adduct and directly depicted the separately calculated species 8a and DMAP in Fig. 3a. Without their long-range interaction (Ru-DMAP ¼ 6.688Å), 8a and DMAP are marginally higher in energy (DH L ¼ 0.8 kcal mol À1 , refer The transition state [7a-8a] ‡ is characterized by an imaginary mode (650i cm À1 ) describing the transfer of H 2 to the ruthenium center. The activation energy of the vinyl-vinylidene rearrangement entails a moderate barrier (D , which is in agreement with the result previously reported by Caulton (D ‡ H ¼ 3.6 kcal mol À1 ). 36 The resulting intermediate, 8a is less stable than the vinyl isomer 7a (DG SD L ¼ 17.3 kcal mol À1 for 7a / 8a). The vinyl-vinylidene rearrangement step is also accompanied with a signicant change in the NPA charge on the Ru-and C acenters (Dq Ru ¼ À0.203e and Dq C a ¼ 0.554e in 7a / 8a). It is, however, intriguing to note that the C a in vinylidene 8a turns out to be an electrophilic center with a NPA charge of 0.193e, making it susceptible towards nucleophilic transfer. Similar vinylidene complexes have been reported by Dixneuf et al. 35 to play a key role in various ruthenium-catalyzed nucleophilic addition reactions (vide supra). Path b. As briey mentioned earlier, we have addressed another bifurcating reaction channel during the second DMAP addition step in intermediate 6 (see Scheme 4). Unlike "path a", the additional DMAP is added from a direction syn to the coordinated DMAP, to generate intermediate 7b (Fig. 3b). The two intermediates 7b and 7a are geometrical isomers that differ with respect to the two DMAP ligands bound to the ruthenium, the former being more stable by 5.1 kcal mol À1 (DG SD L , refer to Fig. 3a and b and S7 †). 64 Geometrical parameters and charge distributions of 7b are similar to those of 7a (refer to Fig. S6, Fig. S8 and Table S7 †).
While allowing a transfer of H 2 towards ruthenium with the aim of obtaining the vinylidene complex, our calculations revealed a new vinyl intermediate 8b, in which the vinyl hydrogens are syn to each other, unlike in structure 6 ( Fig. 3b and S8 †). This step (7b / 8b) describes a simple isomerization of the vinyl subunit with concomitant decoordination of the DMAP moiety. The activation barrier associated with the tran- which is not surprising since the negative eigenvector depicts an out-of-plane twisting motion of H 2 resulting in C a -C b rotation ( Fig. S8 †). The coordination site at the ruthenium center liberated by removal of DMAP is lled by the oxygen atom of the 2-pyrrolidinyl ligand, which now coordinates in a chelating fashion as in the isomeric intermediate 6 (vide supra).
In order to progress further from 8b, we allowed the ahydride to migrate from C a to the ruthenium center. The formation of the hydrido-vinylidene intermediate 9b from 8b represents our vinyl-vinylidene rearrangement step for "path b". The resulting vinylidene 9b is more stable than its isomer 8a (8a / 9b; DG SD L ¼ À5.4 kcal mol À1 ). Geometrical parameters for 9b differ from those for 8a in the orientation of the butyl fragment coordinated to C b ( Fig. 3a and b). However, the electron density (r(r b )) and Laplacian of the electron density (V 2 r(r b )) at the BCP (bond critical point, see computational details) for the Ru-C a (r(r b ) ¼ 0.178, 0.176; V 2 r(r b ) ¼ 0.397, 0.349 for 8a and 9b) and C a -C b (r(r b ) ¼ 0.339, 0.340; V 2 r(r b ) ¼ À0.956, À0.959 for 8a and 9b) bonds in the vinylidene intermediates are similar. In "path b", the conversion of vinyl to vinylidene (8b / 9b) requires a lower energy barrier ( Fig. 3a and b) than that of the 7a / 8a step in "path a" ( Fig. 3a and b), primarily because the vinyl complex 7a is more stable. The two isomeric hydrido-vinylidene complexes 8a and 9b may interconvert by simple rotation of the vinylidene ligand about its Ru-C a -C b axis. This type of transformation has been proposed by Oliván et al. for ruthenium and osmium vinylidene complexes. 36 However, a similar rotation of the vinylidene ligand around Ru-C a -C b in 8a surprisingly generates a new stable geometry 8az, which is reluctant to convert into the other vinylidene isomer 9b ( Fig. S14 and S15 †). Intermediate 8az is the precursor to the Z-stereoisomer, which is a minor product in the studied transformation to be discussed in the forthcoming paragraph.
The above calculations demonstrate the important role played by the second DMAP during the vinyl-vinylidene rearrangement steps (6 / 8a; 6 / 9b, Fig. 3a and b). Its relatively low coordinating strength permits it to reversibly occupy a Ru coordination site before the vinylidene formation steps (6 / 7a; 6 / 7b). Alternative pathways for the rearrangement leading to vinylidene formation investigated without addition of a second DMAP failed to provide the correct intermediate 8a. When vinylvinylidene rearrangement occurs directly from intermediate 6, which is devoid of the second DMAP, decoordination of the 2pyrrolidinyl unit takes place. We also investigated an alternative pathway for a vinyl-vinylidene rearrangement starting directly from 6, but without success. Upon rotating the Ru-C a bond thereby placing the hydrogen atom H 2 syn to the Ru-O bond and then shortening the distance of H 2 to the metal center, we arrived at a transition state. However, the imaginary mode seemed to resemble a movement of H 2 towards the oxygen rather than the ruthenium center, which made it unlikely that this transition state would connect to the desired product. All these calculations led us to conclude that the coordination of an additional DMAP aer the insertion step is vital for a successful vinyl-vinylidene rearrangement.
A possible line of argument against this proposed presence of a second DMAP molecule in the reaction "path a" may be that in "path b", the vinyl-vinylidene rearrangement (8b / 9b) is successful even in absence of a second DMAP molecule. However, it needs to be considered that the geometrical position of H 2 with respect to N 3 determines this rearrangement step. In case of both 7a and 8b, the H 2 remains opposite to the N 3 with N 3 -Ru-C a -H 2 dihedral of 155.2 and 148.6 respectively ( Fig. S6 and S8 †). The correct orientation of the vinyl fragment is accomplished only in presence of a second DMAP as illustrated in the step 7b / 8b. C.I.c. Nucleophilic transfer. In this section, we discuss the intramolecular nucleophilic transfer of the coordinated amide in the vinylidene complexes studied so far. "Path a" and "path b" consider the continuation of the reaction progress from intermediates 8a and 9b, respectively.
Path a. In vinylidene 8a, C a is an electron-decient center (q C a ¼ 0.193e) and quantitatively contributes to the LUMO of the molecule. The HOMO is localized on both N 3 and the carbonyl O atoms of the coordinated 2-pyrrolidinyl unit (see Fig. S32d †). 8a undergoes intramolecular nucleophilic transfer through N 3 to generate intermediate 10 via the transition state [8a-10] ‡ , which has a moderately low activation barrier (D ‡ G SD L ¼ 11.1 kcal mol À1 , Fig. 4a and S9 †). One interesting fact is that in transition state [8a-10] Fig. S10 †), and the n-butyl group is oriented anti to the incoming 2-pyrrolidinyl unit primarily due to steric hindrance. Therefore, the resulting geometry of 10 already indicates the E-selective formation of the enamide product aer the reductive elimination step. In contrast, if the butyl group is oriented syn to the 2-pyrrolidinyl unit, then the Zenamide would be the nal product. This is considered in the later sections (vide infra). Path b. Similar to "path a", we explored the nucleophilic transfer from 9b. During the progress of the nucleophilic transfer, rotation of the C b -C a -H 1 -n Bu plane occurs along the Ru-C a -C b axis, a geometrical change analogous to "path a". The geometry of the transition state [9b-10] ‡ is very similar to that of [8a-10] ‡ , while the activation barrier (D ‡ G SD L ¼ 12.5 kcal mol À1 , Fig. S9 †) is slightly higher in "path b" than in "path a" (Fig. 4a). A probable reason is the presence of slightly less charge density on C a in 9b (q C a ¼ 0.151e in 9b vs. 0.193e in 8a). However, both the vinylidene complexes 8a and 9b afford the same intermediate 10, in which the butyl group is anti to the 2-pyrrolidinyl unit. Therefore, rotation of the vinylidene plane does not depend on the orientation of the butyl fragment in the vinylidene intermediates ( Fig. 3a and b). The butyl group is placed anti to the 2-pyrrolidinyl unit because the alternative synarrangement is sterically overcrowded.
C.I.d. Reductive elimination. The nal step of the catalytic cycle is the reductive elimination, in which the desired product is liberated and the catalyst regenerated. From 10, the reductive elimination step requires the transfer of H 2 to C a to liberate the E-product VIII (Fig. 4b). Though intermediate 10 is coordinately unsaturated, the negative NPA charge on the metal center is quite high (q Ru ¼ À0.374e), making the coordination of further ligands unfavorable. Our calculations revealed that coordinating a second DMAP to the vacant site of 10 leads to an increased energetic barrier in the subsequent reductive elimination step (D ‡ E e ¼ 31.2 kcal mol À1 , D ‡ G 298 ¼ 38.4 kcal mol À1 at BP86/LANL2DZ(Ru)/6-31G*(H, C, N, O & P) level of theory). Reductive elimination of the product from 10 by gradual transfer of H 2 to C a proceeds via the transition state [10][11] ‡ . 65 The activation barrier of this step is only moderate (D ‡ G SD L ¼ 23.0 kcal mol À1 , Fig. S11 †). It leads to intermediate 11, in which the E-enamide has been formed but remains weakly bound to the metal center (Fig. S12 †).
Such weakly coordinated complexes are frequently observed in gas-phase optimizations, but can seldom be found under experimental conditions in coordinating solvents. 66 In the nal step 11 / 1, the enamide product is easily liberated from adduct 11 by coordinating a further DMAP molecule, which regenerates the Ru 0 catalyst ( Fig. 4b and S11 †).
C.I.e. Regio-and stereoselective products. Up to this point, we have described two different pathways ("path a" & "path b") for the formation of the E-enamide. Both originate from intermediate 5 and merge at intermediate 10 later in the catalytic cycle (Scheme 4). However, we have also endeavored to explore pathways for generating hydroamidation products with different regio-and stereoselectivities. In this section, we discuss the mechanism of formation of both the Markovnikov and the Z-congured enamides. The Markovnikov products form if the amide nucleophile attacks at the hexyne C b . We found that Markovnikov addition can proceed prior to alkyne insertion and, in our case, can initiate from intermediate 5. The C b center in intermediate 5 bears a greater positive charge than the free alkyne I (q C b ¼ 0.063e in 5 vs. q C b ¼ 0.001e in I), inciting the electron-rich N 3 center (q N 3 ¼ À0.532e in 5) to undergo an intramolecular nucleophilic transfer (see Fig. S13 †) leading to the Markovnikov product VI (Fig. 1). However, under experimental conditions, no Markovnikov product was observed. 33,34 Gratifyingly, our calculated results reveal that the formation of the Markovnikov product involves very high transition barriers for both the nucleophilic transfer 5 / 6m (D ‡ G SD L ¼ 25.8 kcal mol À1 ) and subsequent reductive elimination steps from 6m via the transition state [7m-1] ‡ (D ‡ G SD L ¼ 37.1 kcal mol À1 ; Fig. S13 †). Such high energy barriers can be explained on the grounds of a low NPA charge on the C b carbon in 5. A similar justication was provided above, when comparing the activation barriers for the nucleophilic transfer in "path a" and "path b" (vide supra). Furthermore, molecular orbital analysis reveals that the KS-HOMO of 5 is the bonding p-orbital of the C a -C b bond, which repels the nucleophilic 2-pyrrolidinyl unit (Fig. S32c †).
The vinylidene complexes (8a and 9b) discussed so far involve a nite contribution of electron density from the carbonyl oxygen as seen from their KS-HOMO (Fig. S32d-e †). Hence, a fair possibility exists for oxygen to attack the electrophilic C a center in both the vinylidene complexes from "path a" and "path b". Indeed, such a nucleophilic transfer of the sp 2 oxygen from the coordinated 2-pyrrolidinyl unit results in a stable isomer 8az, which is more stable by À33.6 kcal mol À1 (DG SD L ) than the starting materials (Fig. S14 †). An interesting observation during these transformations (8a / 8az/9b / 8az) is that the butyl substituent at C b arranges syn to the 2-pyrrolidinyl fragment, predetermining the stereoselectivity towards the Z-enamide product (Fig. S15 †). Progressing from 8az, we have explored the potential energy surface with the aim of creating an N 3 -C a bond, resulting in intermediate 10z. Complex 10z can undergo reductive elimination in a similar fashion to furnish the Z-enamide product. The activation barrier for the step 8az / 10z via the transition state [8az-10z] ‡ (D ‡ G SD L ¼ 25.4 kcal mol À1 , refer to Fig. S14 †) requires substantially higher energy values, precluding the formation of the Z-enamide product in high yields, as substantiated by the experimental ndings. 34 The calculated route for Z-enamide formation overrules any possibility of H 2 migrating to the oxygen atom of 2pyrrolidinyl unit. Apart from the fact that they are well separated (H 2 -O ¼ 2.641Å in 8a), the same H 2 is necessary to accomplish a successful reductive elimination step (Fig. S11 †). If coordinated, not only the transfer of H 2 to C a will be difficult, the reduced nucleophilicity at oxygen center will also affect adversely the Z-enamide route.
The overall catalytic cycle and reaction energetics for the different pathways originating from the catalytic system 1 are represented in Scheme 4 and Fig. 5, respectively. From intermediate 5, three different reaction channels can emanate. "Path a" and "path b" involve the formation of isomeric vinylidenes (8a and 9b), which can undergo nucleophilic addition to furnish the common intermediate 10. From 10, the E-product is selectively formed by reductive elimination (Scheme 4).
However another possibility remains in which the energetically unfavorable (Fig. 5) Markovnikov addition product is liberated following the step 5 / 6m / VI as discussed in the previous section. A pathway to the Z-product can also be connected from the vinylidene intermediates 8a and 9b via nucleophilic addition of the sp 2 oxygen.
Closer inspection of the reaction prole (Fig. 5) reveals that the selective formation of E-products is more facile than its other stereo-and regio-chemical variants. This nding is supported by the experimental observations for the studied catalytic system 1. For all investigated pathways, the oxidative addition and hexyne coordination steps (1 / 5, black lines) follow a common reaction route (Scheme 4, Fig. 5). For the pathway leading to anti-Markovnikov E-enamides, "path a" is more facile than "path b", the latter involving a substantially higher barrier of 46.2 kcal mol À1 (D ‡ G SD L ) for the step 6 / 8b (green lines, Fig. 5) compared to 20.7 kcal mol À1 (D ‡ G SD L ) for 6 / 8a (blue lines). Undoubtedly, this signies that "path a" is the most accessed route.
For the Markovnikov addition, the highest barrier of 37.1 kcal mol À1 (D ‡ G SD L ) is encountered along step 6m / 1 (red line in Fig. 5). Obviously, this regio-isomer will not be detected under the given reaction condition. Hence, from 5, the reaction will proceed along "path a" and refrain to follow the alternative 5 / 6m route. Considering the Z-selective pathway from 8a, the highest energy-demanding transformation (D ‡ G SD L ¼ 27.8 kcal mol À1 ) occurs for step 10z / 11z (magenta lines, Fig. 5). Even though the energy for the reductive elimination step is higher in the Z-selective pathway than for the analogous step (10 / 11; D ‡ G SD L ¼ 23.0 kcal mol À1 ) in the E-selective pathway (black lines), we believe that this barrier can be surmounted under the reaction conditions, giving rise to the Z-enamide as a minor product, which is supported by experimental results. The energetic span model proposed by Amatore and Jutand, 67 later rened by Shaik and Kozuch, 68 says that the largest rate and hence the highest turnover is obtained from the lowest Gibbs energy span in a catalytic cycle. The energy span is the difference between the highest transition state and lowest intermediate of the entire catalytic cycle. In this study, the computed cycle deals with the formation of different stereo-and regiochemical enamide isomers branching out from a small number of key intermediates of the hydroamidation pathway (Scheme 4 and Fig. 5). For both the stereoisomeric pathways, the energy span model designates intermediate 6 as the lowest, and thus, turnover frequency-determining intermediate (TDI). The turnover frequency-determining transition state (TDTS) is different for E-and Z-selective pathways. In the former case, the TDTS is [10][11] ‡ , and in the latter it is [8az-10z] ‡ , with a relative TOF of 10.0 in favor of the E-enamide isomer. In order to assess the maximum inuence of individual steps in contributing to the relative TOF of product formation, we have considered those steps following vinylidene intermediate 8a from which the Eand Z-enamide pathways originate. The highest activation barrier in case of E-product formation is associated with the reductive elimination step 10 / 11 (D ‡ G SD L ¼ 23.0 kcal mol À1 ).
Similarly, for the other stereoisomer, the highest surmountable energy barrier is also associated with the reductive elimination step 10z / 11z (D ‡ G SD L ¼ 27.8 kcal mol À1 ). Therefore, on the level of individual reaction steps, it is also clear that the Eenamide formation route is more favorable by 4.8 kcal mol À1 than that leading to the Z-isomer, concurring with the experimental observation towards the preference for the E-product.

C.II. Catalyst system 1 c
In order to understand the inuence of ligands in determining the selectivity of product formation, we have performed a similar mechanistic investigation for [Ru 0 (dcypm) 2 ] (1 c ) as the catalyst system instead of [Ru 0 (Bu 3 P) 2 (DMAP) 2 ] (1) (vide supra, Fig. 1b). The fundamental reaction steps originating from 1 c are similar to those corresponding to catalyst system 1. In the following section, we briey discuss the mechanism of the catalytic cycle with the three following subsections: (a) oxidative addition, hexyne coordination and insertion, (b) vinyl-vinylidene rearrangement and nucleophilic transfer, and (c) reductive elimination.
C.II.a. Oxidative addition, hexyne coordination and insertion. In analogy to the initiating step starting from 1, axial addition of II to catalyst 1 c leads to the stable adduct 2 c , followed by N-H 1 bond activation via the transition state [2 c -3 c ] ‡ to generate the oxidatively added Ru II intermediate 3 c (Fig. 6, S18 and 19 †). The NPA charge on ruthenium in 2 c is more negative than that in 2 (q Ru ¼ À1.056e in 2 c vs. À0.656e in 2), indicating a more facile oxidative addition step. However, the calculated activation barrier is higher (D ‡ G SD L ¼ 12.5 kcal mol À1 , Fig. 6 and S18 †) than in the step corresponding to catalytic system 1 (D ‡ G SD L ¼ 0.7 kcal mol À1 , for step 2 / 3, Fig. 2), suggesting the transformation to be governed to a greater extent by the steric environment around the metal center.
Further progress of I towards the ruthenium center resulted in h 2 -hexyne complex 4 c via the transition state [3 c -4 c ] ‡ . In the transition state [3 c -4 c ] ‡ , the P 1 2 atom has already moved away from ruthenium to create a vacant side for the incoming alkyne to coordinate (Fig. S18 †). Unlike in catalytic system 1 (Fig. 2), the alkyne coordination step (3 c / 4 c ) is endoergic (DG SD L ¼ 8.7 kcal mol À1 ) and has a higher activation barrier (D ‡ G SD L ¼ 29.5 kcal mol À1 ). An important point to consider here is that the charge on ruthenium increases by 0.219e during hexyne coordination (3 c / 4 c ). However, a similar increase was not observed during the transformation 3 / 5, suggesting a superior electron-donating capability of the phosphorus atoms of the ligand dcypm (V) compared to the nitrogen atoms of DMAP (Tables S7 and S8 †).
The next step should be the usual insertion of the h 2 -coordinated hexyne to the Ru-H 1 bond. Migration of the H 1 atom from ruthenium to C b in 4 c generates the vinyl intermediate 5 c (refer to Fig. 6, S18 and S19 †). The activation barrier (D ‡ G SD L ¼ 7.9 kcal mol À1 , Fig. 6) for the transition state [4 c -5 c ] ‡ is lower than in the insertion step 5 / 6 (D ‡ G SD L ¼ 8.8 kcal mol À1 , Fig. 3a) calculated for catalytic system 1. Since the electronic charge on the metal is further reduced (Dq Ru ¼ 0.185e, for the step 4 c / 5 c , Table S8 †), this insertion step can be characterized as hydride migration similar to the previously studied steps 5 / 6 (Table S7 †).
C.II.b. Vinyl-vinylidene rearrangement and nucleophilic transfer. In the previous catalytic system 1, we have observed that two different vinyl isomers 6 and 8b can be generated depending on the orientation of the additional, incoming DMAP ligand to intermediate 6. A similar possibility can be ruled out for catalytic system 1 c . In order to obtain two isomeric vinyl structures, we have performed direct C a -C b bond rotation from intermediate 5 c . Unsurprisingly, the activation barrier for this step is high (D ‡ G SD L ¼ 68.0 kcal mol À1 , Fig. S20 and S22 †) due to rotation around the carbon-carbon double bond, and hence, this pathway will not be followed. An alternative, more facile pathway consisting of H 2 migration followed by C a -C b rotation and nally retro-transfer of H 2 to C a was calculated. The resulting vinyl isomer 9b c is less stable than 5 c by 8.7 kcal mol À1 (DG SD L ). These isomeric intermediates (5 c and 9b c ) lead to two different reaction channels which referred as "path a c " and "path b c " from now onwards. Both these intermediates possess a Ru-O(sp 2 ) interaction similar to that observed in the vinyl complexes 6 and 8b ( Fig. 3a and b, S6, S8, S19 and S26 †). Path a c . Intermediate 5 c is not suitable for vinyl-vinylidene rearrangement because H 2 migration to the ruthenium center is accompanied with dissociation of 2-pyrrolidinyl unit. Previous experience with catalytic system 1 led us to expect that a successful transfer of H 2 occurs only when the C a -H 2 bond faces syn to the Ru-O(sp 2 ) bond (refer intermediate 6 c in Fig. S24 †). In search of such an intermediate, we have performed a rotation of N-Ru-C a -H 2 dihedral angle in 5 c by about 180 , leading to a less stable isomer 6 c (DG SD L ¼ 4.3 kcal mol À1 , Fig. S23 and S24 †). Now from 6 c , further migration of H 2 from C a to the ruthenium center furnished the desired vinylidene intermediate 7a c (Fig. 7 and S23 †). Also from previous experience, we were aware that the vinyl-vinylidene rearrangement step requires a hydride ion transfer in which the metal center in the resulting vinylidene complexes acquires more electron density (Table S7 †). It is important to note that the ruthenium center in 6 c is more electron-rich (q Ru ¼ À0.233e) than the other calculated vinyl intermediates 7a (q Ru ¼ À0.035e) and 9b (q Ru ¼ À0.027e, Table S8 †), suggesting that the hydride transfer will be less favorable, with a higher activation barrier (D ‡ G SD L ¼ 24.5 kcal mol À1 , for 6 c / 7a c , 20.7 kcal mol À1 for 7a / 8a and 10.1 kcal mol À1 for 8b / 9b) for the step 6 c / 7a c . The geometry of 7a c is similar to that of 8a, in which the two hydrogen atoms (H 1 and H 2 ) are oriented trans to each other (Fig. 7, S23 and S24 †). Like 8a and 9b, the C a atom is electron-decient in 7a c (Table S7 and S8 †) creating a suitable electronic environment for intramolecular nucleophilic transfer to occur. The activation barrier of this step (7a c / 8a c ) is moderately low (D ‡ G SD L ¼ 11.2 kcal mol À1 ), similarly to that of 8a / 10 (D ‡ G SD L ¼ 11.1 kcal mol À1 ) and 9b / 10 (D ‡ G SD L ¼ 12.5 kcal mol À1 ). In contrast to [8a-10] ‡ and [9b-10] ‡ (see Fig. 4a, 7 and S24 †), the vinylidene plane (C b -C a -H 1 -Bu) in the transition state [7a c -8a c ] ‡ rotates into an orientation in which the 2-pyrrolidinyl unit is syn to the butyl fragment, predicting the nal product to be the Z-enamide. The N-C a -C b -H 2 dihedral angle is 174.7 already in 8a c , which will now undergo reductive elimination to liberate product VII.
Path b c . During step 6 c / 7b c , H 2 undergoes migration to C b via a high-energy transition state [6 c -7b c ] ‡ (D ‡ G SD L ¼ 57.2 kcal mol À1 , Fig. 8 and S25 †), in which the imaginary mode depicts the hydride transfer between the carbon centers. A similarly Fig. 6 Energy profile for the oxidative addition and hexyne insertion steps for catalytic system 1 c . Ball and stick structures of the computed species with labeling of atoms, geometrical parameters and energy profiles are collected in Fig. S18 and S19. † high activation barrier was reported by Oliván and Clot during their study of the 1,3 H-migration in MHCl(CCH 2 )(PH 3 ) 2 (M ¼ Ru, Os) complexes. 36 Intermediate 7b c formed in the hydride transfer shows a short Ru-C a bond (1.743Å, Fig. S26 †), which is even more contracted than the calculated Ru-C a vinylidene bond (1.833Å) in 7a c . NBO analysis reveals that one sand two p-bonds are possible between the ruthenium and C a atoms (Fig. 9a). The orbitals participating in the overlap between the metal d-orbitals and the orthogonal p-orbitals of C a are depicted in Fig. 9a. Additionally, the C a -C b bond in 7b c is elongated by 0.11Å compared to 6 c , allowing an extra exibility of this bond. Now, an easy C a -C b bond rotation can give rise to intermediate 8b c , in which the orientation of H 1 is different to its immediate predecessor 7b c (Fig. S25 and S26 †). Subsequent migration of H 2 to C a furnished the vinyl intermediate 9b c , which differs from 6 c in that the vinyl hydrogens are oriented in a syn fashion. The calculated activation barrier for the retro-hydrogen transfer through [8b c -9b c ] ‡ is lower than the previous barrier by 28.7 kcal mol À1 (DG SD L , Fig. 8 and S25 †). The optimized vinyl isomer 9b c is less stable than 6 c by 4.4 kcal mol À1 (DG SD L ). Subsequent hydride transfer from C a to the ruthenium generates the isomeric vinylidene 10b c via transition state [9b c -10b c ] ‡ , which is isoenergetic to [6 c -7a c ] ‡ (refer to Fig. 7 and 8). Similarly to 9b, the two hydrogens (H 1 and H 2 ) of the vinylidene ligand in intermediate 10b c are syn to each other (Fig. S26 †). From 10b c , we allowed the intramolecular nucleophilic transfer of the 2-pyrrolidinyl unit to occur from ruthenium to the C a . In contrast to "path a c ", the butyl fragment in transition state [10b c -11b c ] ‡ is oriented anti to the 2-pyrrolidinyl unit (Fig. 8). A similar orientation was visible during the analogous transition states in steps 8a / 10 and 9b / 10 for catalytic system 1 (see Fig. 4a). Intermediate 11b c (see Fig. 8) is more stable by 2.8 kcal mol À1 (DG SD L ) than 8a c and will undergo reductive elimination to liberate the E-enamide product VIII.  Fig. S21 and S22. † At this point, we opined that during the nucleophilic transfer step, the rotation of the C b -C a -H 1 -Bu plane is controlled by the orientation of the butyl fragment in the presence of the cyclohexyl groups on the P 1 2 atom, as discussed in the forthcoming section. In contrast, in the previous catalytic cycle (Scheme 4), the vinylidene isomers 8a and 9b gave the same intermediate 10 due to the presence of less bulky monodentate phosphine ligands (vide supra).
It is important to mention that the isomerization step 6 c / 10b c calculated so far to connect vinylidene intermediate 10b c is still energetically highly demanding. The overall activation energy for step 6 c / 10b c is 61.6 kcal mol À1 (D ‡ G SD L ), which raises doubts as to its ability to surmount the barrier even at the elevated reaction temperature of 373 K. Hence, we explored an alternate route in which the isomerization can be achieved in a single step via rotation of the C b H 1 (Bu) unit around the Ru-C a axis (Fig. 9b). A similar type of rotation was suggested by Oliván and Clot to be facile for Ru(II) hydrido-vinylidene complexes. 36 Gratifyingly, a similar rotation from 7a c via transition state [7a c -10b c ] ‡ (see Fig. 9b and S21 †) entails a low activation barrier of 8.1 kcal mol À1 (D ‡ G SD L ). In transition state the ruthenium is more negative (q Ru ¼ À1.121e vs. À0.340e in 7a c and 10b c ) than vinylidines 7a c and 10b c , suggesting a lack of back bonding with C a whereas C a -C b p-bond remains intact during rotation. This nding unambiguously point towards the existence of a singlestep, easily accessible route for the interconversion of the vinylidenes in presence of dcypm ligands. 69 C.II.c. Reductive elimination Path a c . In reductive elimination step, the C a -H 2 bond forms and the ruthenium(0) catalyst is regenerated (Fig. 10a). Therefore, from 8a c , H 2 was transferred from ruthenium to C a to generate intermediate 9a c (Fig. S27 and S28 †). The activation barrier for the step 8a c / 9a c is quite small (D ‡ G SD L ¼ 3.7 kcal mol À1 , Fig. 10a and S27 †) compared to the analogous reductive elimination step (D ‡ G SD L ¼ 23.0 kcal mol À1 , for 10 / 11) for catalytic system 1. In [8a c -9a c ] ‡ , the electron density on ruthenium has increased by 0.136e (Table S8 †) from 8a c , characterizing this step as proton rather than hydride transfer.
Intermediate 9a c already reveals the product formation, with the enamide weakly bound to the coordinatively unsaturated ruthenium center ( Fig. 10a and S28 †). Subsequent coordination of already dissociated P 1 2 atom of dcypm to the ruthenium center will allow liberating the Z-enamide (VII) product and regenerating the ruthenium(0) catalyst 1 c . Path b c . Similarly to "path a c ", we proceeded from 11b c by transferring the H 2 atom from ruthenium to C a in order to accomplish the reductive elimination step. Unfortunately, we were unable to nd converging intermediates along this reaction pathway aer constraining geometrical features to t the expected structures along the way. Therefore, we sought for an alternative mechanism for the reductive elimination. First, we modied the orientation of the decoordinated phosphine (P 1 2 part) by rotation along the Ru-P 1 1 bond to generate intermediate 12b c (see Fig. 10b, S29 and S30 †), which is less stable than 11b c by 1.2 kcal mol À1 (DG SD L ). Next, the H 2 atom was transferred from ruthenium to furnish intermediate 13b c . The enamide that is already formed is bound to the ruthenium center in a h 2 -fashion, while P 1 2 still remains uncoordinated. The activation barrier for reductive elimination is higher by 13.2 kcal mol À1 than that for 8a c / 9a c in "path a c " (D ‡ G SD L ¼ 16.9 kcal mol À1 vs. 3.7 kcal mol À1 ). The ruthenium center in 13b c is more electron-decient than 1 c (q Ru ¼ À0.439e in 13b c vs. À0.903e in 1 c ) due to the presence of a p-accepting, h 2 -coordinated enamide. Gradual elongation of the Ru-C a and Ru-C b distances in 13b c leads to E-enamide with regeneration of the initial catalyst 1 c . This step is very facile with a small activation barrier (D ‡ G SD L ¼ 7.7 kcal mol À1 , Fig. 10b and S29 †). Interestingly, during the removal of enamide from 13b c , there was an abrupt shortening of the Ru-P 1 2 bond resulting the formation of a covalent Ru-P bond (Ru-P 1 2 ¼ 4.662Å and 4.003Å in 13b c and [13b c -1 c ] ‡ ).
Whenever the reaction steps constitute electron-rich metal complexes, the oxidative addition will generally be more facile than reductive elimination. In a similar line of argument, Negishi et al. proposed that in palladium-catalyzed C-C bond-forming reactions, the reductive elimination rate is inversely proportional to the ligand basicity. 70 Fig. S33 † depicts the NPA charges on ruthenium centers for all calculated saddle points (see Table S8 †) present in "path a", "path a c " and "path b c ", respectively. The plot shows that the ruthenium complexes with cyclic phosphines are more electron-rich than their monophosphine counterparts. This observation can directly point to more facile oxidative addition and more difficult reductive elimination steps for the catalytic system 1 c compared to the catalytic system 1. However, to our surprise, the calculated thermodynamics showed a reverse trend. This was ascribed mainly to the dominant role of sterics in the proximity of the metal center in governing the reaction energetics.
Overall, the catalytic cycle and reaction energies calculated for catalytic system 1 c are depicted in Scheme 5 and Fig. 11 respectively. Similarly to the previous catalytic system, two different pathways exist that both originate from a common intermediate 6 c but do not share a common reductive elimination route. Unlike 5, which is a hexyne-coordinated h 2 complex, 6 c is the vinyl intermediate formed aer the hexyne insertion step ( Fig. 2 and 6). For the catalytic system 1 c , the calculated pathways "path a c " (blue lines) and "path b c " (green lines) furnished exclusively two different stereoisomeric enamides (Z-and E-), that are contrary to those observed for the catalytic system 1 (Scheme 4, Fig. 5). "Path a c " and "path b c " involve two isomeric vinylidene complexes 7a c and 11b c in which the two hydrogen atoms (H 1 and H 2 ) are oriented anti and syn with respect to each other, which correspond to those observed in intermediates 8a and 9b. Closer inspection of the energy prole reveals that the major hydroamidation product for the catalytic system 1 c will be the Z-enamide VII. This result is in agreement with the experimental observation.
Neither the energetic span model nor the concept of a ratedetermining highest transition state (HETS) can be used in unmodied form to decide which of the two possible stereoisomers will preferentially form, since both the highest energy span (step 3 c / 4 c ) and the HETS [3 c -4 c ] ‡ are identical for the pathways leading to the two isomers. They bifurcate only aer reaching the vinylidene intermediate 7a c , at a stage where the energy prole is relatively at. In order to compare the rate of formation of the E-and Z-isomers, one must instead apply the models only to the pathways emanating from the bifurcation point 7a c . This is a reasonable strategy since one can assume that the surrounding medium will fully absorb any excess energy of the common intermediate 7a c .
Starting from the bifurcation point, formation of the Zenamide involves a single activation barrier amounting to 11.2 kcal mol À1 , so that the corresponding step 7a c / 8a c becomes rate-determining for this partial pathway. The largest energy span for this part of the cycle is between the TDI 7a c and the TDTS [7a c -8a c ] ‡ (11.2 kcal mol À1 ). Alternatively, formation of the E-enamide requires three activation barriers, among which that for step 11b c / 13b c (D ‡ G SD L ¼ 18.1 kcal mol À1 ) is ratedetermining. For this partial pathway, the largest energy span is between the TDI 11b c and the TDTS [12b c -13b c ] ‡ (18.1 kcal mol À1 ).
Thus, both models predict that the formation of the Z-isomer should be favored, which is in excellent agreement with the experimental ndings.
In their mechanistic investigation of olen metathesis reactions using ruthenium(II) carbene complexes, 49 Thiel and Bühl found a dissociative pathway involving liberation of one phosphine to be the most favorable route. Since the hydroamidation pathway investigated herein has some mechanistic similarity, intermediates with only one dcypm ligand had to be considered. Fig. S34 † depicts the reaction route containing dcypm decoordination, hexyne coordination and subsequent insertion from intermediate 3 c . Whereas the dissociation of the chelating phosphine is indeed exergonic by À15.4 kcal mol À1 (DG S L ), the next hexyne coordination step involves a particularly high-energy intermediate 3 c _I_P that is 40.0 kcal mol À1 above 3 c _I (Fig. S34 †), which renders this dissociative pathway unfavorable overall. A pair of isomeric 16e À ruthenium(II) vinylidene complexes 7a c -D and 10b c -D (Fig. S35 †), obtained aer removal of the dangling dcypm unit from 7a c and 10b c complexes, were also considered as starting points for the subsequent intramolecular nucleophilic attack of the amide moiety ( Fig. 7 and 8). The activation energies for the steps 7a c -D / 8a c -D and 10b c -D / 11b c -D are as high as 23.1 and 21.3 kcal mol À1 (DG S L , Fig. S35 †), values that are far greater than those for the analogous steps involving saturated 18e À ruthenium(II) intermediates (Scheme 5, 7a c / 8a c , 11.1 kcal mol À1 ; 10b c / 11b c , 11.7 kcal mol À1 ). It also has to be taken into account that regeneration of 1 c by re-coordination of the second dcypm ligand has a considerable entropic penalty (see Fig. S35, † 8a c -D / 8a c , 11b c -D / 11b c ). Overall, the investigation of pathways involving coordinatively unsaturated ruthenium(II) species did not lead to more favorable energy proles.
The groups of Grubbs and Hoffmann have reported that deactivation of ruthenium alkylidene complexes can occur by various means including external phosphine attack or intramolecular coordination from a dangling nucleophilic center. 71 Herein, the possibility for a similar deactivation route was considered, where the dangling phosphorus atoms in intermediates 7a c and 11b c were allowed to undergo intramolecular attack to the C a of the vinylidene fragments. The intramolecular coordination of the P 1 2 following the steps 7a c / Pa c and 11b c / Pb c is facile with activation barriers below 11 kcal mol À1 (DG S L ; refer to Fig. S36 †). Similar reactivity was reported for N-phosphino-functionalized N-heterocyclic carbenes at RuCl 2 (PCy 3 )py 2 (CHPh) complexes. 71c In the resulting C a -P 1 2 coordinated intermediates Pa c and Pb c , the butyl group is in the orientation required for a stereo-selective nucleophilic attack of the 2-pyrrolidinyl unit (Pa c / 8 0 a c , Pb c / 11 0 b c ; Fig. S36 †). However, this step requires an excessive activation barrier of 34-37 kcal mol À1 (Fig. S36 †). Therefore, Pa c and Pb c may be present in rapid equilibrium with 7a c and 11b c , but the nucleophilic attack to the vinylidene complexes is likely to proceed as depicted in Scheme 5.

C.III. Steric and electronic factors inuencing the stereoselectivity
The stereoselectivity of product formation for both catalytic systems (1 and 1 c ) is controlled in the intramolecular nucleophilic transfer step from the computed vinylidene intermediates. The KS-HOMO of vinylidenes (8a, 9b, 7a c and 10b c , Fig. S32 †) is mostly localized in the 2p y orbital of nitrogen and oxygen of the 2-pyrrolidinyl unit, whereas the KS-LUMO resides in the 2p x orbital of C a atom ( Fig. 12a and b for 8a, 7a c ).
Therefore, whenever we brought the nitrogen atom closer to C a , the Ru-C b -H 1 -Bu plane underwent rotation to match the HOMO-LUMO symmetry. This rotation allowed the incoming 2pyrrolidine unit to move into the vinylidene plane with N-C a -C b -Bu dihedral angle of either 0 or 180 for products VII and VIII, respectively. For catalytic system 1, intermediates 8a and 9b were found to be equally likely to rotate the vinylidene plane during the nucleophilic transfer. However, in both cases, the butyl group turned anti to the nucleophile (N-C a -C b -Bu angle À174.4 in Scheme 5 Computed catalytic cycle for the catalyst system 1 c . The energy values (D ‡ G SD L , in kcal mol À1 ) represent the highest barrier for a given step. Blue ("path a c ") and green ("path b c ") lines indicate the anti-Markovnikov Z-product and anti-Markovnikov E-product formation pathways respectively. 10), allowing us to predict that the steric interaction with the 2pyrrolidinyl unit is more dominant than the n-butyl phosphine (P 2 ). In contrast, in the case of oxygen attack to C a , the steric interaction of the butyl chain with the 2-pyrrolidinyl is greatly reduced compared to n-butyl phosphine, eventually generating the Z-product (see Fig. 12c and S14 †).
For catalytic system 1 c , our calculated results showed the formation of different stereoisomeric products from the vinylidene intermediates 7a c and 10b c (Scheme 5). Although vinylidenes 10b c and 9b gave the same E-product, different stereoisomeric enamides were obtained from intermediates 7a c and 8a (Scheme 4 and Scheme 5). Formation of Z-and Eenamides from 7a c and 10b c can be explained aer considering the steric interaction between the butyl chain with the decoordinated phosphine ligand (P 1 2 ) containing two bulky cyclohexyl groups (Cy) lying just under the vinylidene plane (Ru-C b -H 1 -Bu; Fig. 7 and 8). To conclusively prove the presence of such steric effects, we moved the decoordinated phosphine (P 1  2 ) from the vinylidene side to the H 2 side by simple rotation along the Ru-P 1 1 bond to generate another isomer, which is isoenergetic to 7a c (0.6 kcal mol À1 stable than 7a c ). Unfortunately, this gave the same Z-enamide aer the nucleophilic transfer and reductive elimination steps. Our efforts in replacing the cyclohexyl groups of the dangling P 1 2 to methyl groups or hydrogens also resulted in the same Z-enamide product (7a c -I, 7a c -II, Scheme S1 †). We then reasoned that the presence of the -CH 2 P 1 2 (R) 2 (R ¼ -Cy, -Me, -H) fragment may hinder the butyl chain to rotate into the position opposite to the incoming 2pyrrolidinyl moiety. Hence, we replaced the -CH 2 P 1 2 (Cy) 2 by -Me (7a c -V, Scheme S1 †), but to our surprise, we obtained the same stereoisomer. These ndings prompted us to suspect the existence of steric inuence from the other set of coordinated dcypm ligands (P 1 , P 2 ). To this end, we modied structure 7a c -V by replacing all the -Cy groups by -Me, and then performed the  nucleophilic transfer step. Gratifyingly, the E-enamide product was formed justifying the absence of any spatial hindrance for the butyl group to bend downwards. These results suggest that the stereoselective outcome of the nucleophilic addition can be controlled by adjusting the steric bulk of the substituents at the phosphorous atoms.
We can also consider the steric inuence of dcypm ligands from a different perspective. Closer inspection of the geometries of vinylidenes 7a c and 10b c reveals that the 2-pyrrolidinyl unit is inclined towards H 2 atom (<N-Ru-P 1 1 ¼ 151.1 , 154.6 for 7a c and 10b c vs. 171.8 , 171.5 for 8a and 9b respectively) due to steric congestion by the bulky cyclohexyl groups present at the P 1 and P 2 atoms of the dcypm ligand (see Fig. 7 and 9a). Therefore, during the nucleophilic transfer, the 2-pyrrolidinyl unit turns to the xy plane and attacks the C a atom, at which the 2p x orbital comprising the LUMO is situated. Thus, the butyl fragments in 7a c remain syn to the 2-pyrrolidinyl unit (dihedral angle N-Ru-C b -Bu ¼ 5.6 in 8a c ) and anti in 10b c (dihedral N-Ru-C b -Bu ¼ À173.9 in 11b c ).

C. Conclusion
Using DFT calculations, catalytic pathways for the rutheniumcatalyzed hydroamidation of 1-hexyne with pyrrolidinone were modeled both for a ruthenium catalyst bearing tri-n-butylphosphine and a complementary one bearing the sterically demanding bis(dicyclohexylphosphino)methane (dcypm) ligand. These two catalysts had been reported to give complementary stereoselectivities in catalytic hydroamidation reactions, an observation that could not be explained by spectroscopic investigations. The DFT calculations resulted in the discovery of plausible catalytic pathways for all possible regio-and stereoisomeric enamide products, which could then compared to each other to assess their relative rates.
For a catalyst generated in situ from [(cod)Ru(met) 2 ], tri-nbutylphosphine and DMAP, both the energy span model and the concept of a rate-determining highest transition state predict that the reaction pathway leading to the E-congured anti-Markovnikov product should be favored over the competing pathway leading to the Z-congured enamide. This is in good agreement with the experimental ndings. Pathways leading to the anti-Markovnikov product were found to involve highly endergonic steps, which are unlikely to proceed at the low reaction temperatures. This explains why in contrast to the addition of carboxylates to alkynes not even traces of anti-Markovnikov products are detected in Ru-catalyzed hydroamidations. The experimentally observed decisive inuence of the DMAP additive on the catalyst activity was found to result from its unique ability to reversible coordinate to the ruthenium center facilitating a vinyl-vinylidene rearrangement.
Similar catalytic cycles were also computed for a catalyst bearing sterically demanding, chelating dcypm ligands. The pathways leading to E-and Z-congured anti-Markovnikov products were found to bifurcate relatively late aer formation of a ruthenium vinylidene complex. The overall rate determining step and energy span were found to be within the common part of the catalytic cycle, namely within the initial hexyne coordination step. In order to allow us to compare the rates of E-and Z-product formation, we, thus, had to adapt the standard models to this rather unusual situation. This was done by comparing only the parts of the complementary pathways aer the bifurcation. Applying this restriction, the model of the highest transition state and the energy span model both predicted the Z-selective pathway to be favorable for this catalyst system. This is in excellent agreement with experimental results.
The calculations for the rst time provide an explanation why the stereoselectivity of ruthenium catalyzed hydroamidations can be controlled so remarkably well by the ligand system. They revealed that a strong steric interaction between the dcypm ligand and the vinylidene group is the key factor that causes the reversal of the stereoselectivity when substituting nbutylphosphine with chelating dcypm ligands. During the nucleophilic attack of the amide to the vinylidene carbon 7a c , the carbon side chain, which was previously oriented syn to the hydride substituent, is forced into a Z-conguration by the steric bulk of the chelating ligand. This effect is not observed for the sterically less crowded tri-n-butylphosphine.
This detailed understanding of the reaction mechanism will serve as the basis for the rational design of hydroamidation catalysts with a new level of activity and stereoselectivity.

D. Conflict of interest
The authors declare no competing nancial interests.