Computational Study on the Intramolecular Carbene-CO Coupling in M ( CH 2 ) ( CO ) 3 Radicals ( M = Co , Rh , Ir )

The intramolecular carbene-carbonyl coupling has been investigated for the simple M(CH2)(CO)3 (M = Co, Rh, Ir) radical complexes at the DFT PBEPBE/TZVP level of theory. The coupling is predicted to be very fast for the cobalt-containing system, but it is still feasible for the systems based on the other two metals. The back-way reaction, that is, the conversion of the ketene complex into carbonyl-carbene complex, cannot be excluded from the Ir-containing system in CH2Cl2, and it is even favored in gas phase. The intermolecular ketene formation by the addition of external CO onto the CH2 moiety is the favored pathway for the Ir-complex. The Laplacian distribution, as well as the natural spin density distribution of all the species, being involved in the reaction, gives explanation for the significant difference between the nature of the Co-complex and the Rh- and Ir-systems.


Introduction
Ketenes belong to the first generation of reactive intermediates [1], along with carbenes, radicals, carbocations, and carbanions [2], and are intensively studied members of the cumulene family, with a wide variety of synthetic applications [3][4][5][6].The most common method to access ketenes is from acyl halides via dehalogenation promoted by bases.Therefore, carbonylation of metal carbene provides an alternative, straightforward approach to the generation of ketene species [7][8][9][10].There are also many ketenes that cannot be synthetized by classical synthetic methods due to their high reactivity.
The formation of ketenes from carbenes usually takes place via diamagnetic pathways; therefore less attention has been paid to the reaction of mononuclear radical carbene complexes.In particular, De Bruin and coworkers have reported various transition metal carbene radicals of the cobalt group, with catalytic applications, such as cyclopropanation [11,12], carbonylation [13], and selective carboncarbon bond formation by coupling of Ir-ethene complexes with Ir-carbenoid radicals [14].The structure and the spin density distribution of mononuclear Rh(0) radical complexes were also examined experimentally and computationally [15].The results have been reviewed as well [16,17].
The main goal of this study is to further explore computationally the reactivity of simple carbonyl carbene radicals, which have already proven their applicability in the carbonylation of ethyl diazoacetate [8].The second purpose is to scrutinize the vertical trends in the cobalt group of transition metals and to investigate the reaction profile for the rhodium and iridium analogues and to check whether the equilibrium can be on the carbene side in some cases, like it was reported by Urtel and coworkers [7].

Computational Details
For all the calculations the PBEPBE gradient-corrected functional by Perdew et al. [18] was selected using the Gaussian 09 suite of programs [19].For rhodium and iridium the triple- Stuttgart/Dresden basis set (denoted as SDD) was used [20].For all other atoms the triple- basis set by Schaefer and coworkers was applied and denoted by TZVP [21].Local minima were identified by the absence of the negative eigenvalues in the vibrational frequency analyses, whereas the Hessian matrix of transition states has only one negative eigenvalue.Intrinsic reaction coordinate (IRC) analyses [22] were carried out at the same level as the geometry optimizations in order to make sure that the corresponding local minima and transition states are smoothly connected to each other.For the NBO calculations the GENNBO 5.0 program was utilized [23].For the QTAIM studies the AIMAll software was employed [24].All structures were optimized with solvent effects taking into account employing the CPCM model [25] using CH 2 Cl 2 ( = 8.93) as solvent.

Results and Discussion
For initial species the complexes M(CH 2 )(CO) 3 were considered and designated as 1Co, 1Rh, and 1Ir for M = Co, Rh, and Ir, respectively.Their computed structures are depicted in Figure 1.All structures possess C s symmetry, with a structure closer to distorted tetragonal for 1Co and closer to the square planar configuration for 1Rh and 1Ir, with H 2 C-M-CO bond angles of 135 ∘ , 170 ∘ , and 165 ∘ , respectively.The carbenoid 1Rh shows closer resemblance to 1Ir than to 1Co, in terms of M-CH 2 and M-CO bond lengths as well.For instance, the metalmethylene distance is 1.821 Å in 1Co, whereas it is almost identical, 2.005 and 2.006 Å, in 1Rh and in 1Ir, respectively.The methylene carbene complex 1Co shows a significant structural difference in comparison to the ethoxycarbonyl carbene analogue, which possesses a distorted tetrahedral structure [8].
The intramolecular carbene-carbonyl coupling takes place via the methylene group and with either of the CO groups in cis position by the decrease of the H 2 C-M-CO bond angles, leading to the formation of a new carbon-carbon bond, affording ketene complexes 3Co, 3Rh, and 3Ir.All the three coordinatively unsaturated ketene complexes possess one carbonyl group lying in the H 2 C-M-CO plane and one CO ligand almost perpendicular to it.The main difference between the structure of 3Co and those of 3Rh and 3Ir is that the OC-M-CO angle is notably larger in the latter ones.In all complexes the H 2 C-M bond and the M-CO bond of the coupling carbonyl are elongated in comparison to that in the initial carbenoids.On the other hand, the M-CO bond to the two spectator carbonyl groups are somewhat contracted.
The inspection of the geometries of the transition states connecting the carbenoids with the corresponding ketene complexes (i.e., 2TSCo, 2TSRh, and 2TSIr) reveals that the H 2 C-M bond is elongated in all cases via the coupling; however, the M-CO bond of the coupling CO group is contracted first in 2TSCo and in 2TSRh.On the other hand, in 2TSIr the metal-carbonyl bond is very slightly elongated, and the H 2 C-CO distance is much smaller than that in 2TSCo and in 2TSRh.All three transition states have a single imaginary frequency, namely, −227, −235, and −282 cm −1 for 2TSCo, 2TSRh, and 2TSIr, respectively.
The reaction free energies and free energy barriers for the three complexes are presented in Table 1.The process is more exergonic for the cobalt complex in comparison to that for the ethoxycarbonyl carbene analogue (−18.3 kcal/mol as opposed to −7.0 kcal/mol) and takes place with a much smaller barrier (1.6 kcal/mol as opposed to 15.5 kcal/mol) [8].For the rhodium pathway Δ = −13.3kcal/mol has been obtained as reaction free energy with a small barrier of 5.4 kcal/mol.Finally, the reaction via 2TSIr proceeds via a barrier of 10.8 kcal/mol, and the process is still exergonic by −3.9 kcal/mol in contrast to the results of Grotjahn and coworkers, who found that the equilibrium is on the carbene side and not on the ketene side for phosphine substituted complexes [7].
Repeating the calculations in gas phase, however, provided interesting results.The reaction profile has not changed dramatically for the Co and Rh pathways, although the coupling is notably less exergonic and takes place with somewhat higher barrier in both cases.For the route 1Ir → 2TSIr → 3Ir, however, the free energy of activation remains almost unchanged, whereas the reaction profile turns into slightly endergonic by 1.4 kcal/mol.The unsaturated complexes can take up CO from the carbon-monoxide atmosphere affording coordinatively saturated ketene complexes.Flexible potential energy scan calculations revealed that this process takes place without barrier for all metals.Including solvent effects, the CO addition is exergonic for all cases with a reaction free energy of −19.3, −12.5, and −17.5 kcal/mol, leading to complexes 4Co, 4Rh,  and 4Ir, respectively (see Figure 2).In gas phase, the carbonmonoxide uptake is somewhat less exergonic.The calculated data related to the formation of saturated ketene complexes are collected in Table 2.
The ketene complexes 4Co, 4Rh, and 4Ir can liberate ketene leading to the homoleptic tricarbonyl species 5Co, 5Rh, and 5Ir, respectively.In dichloromethane the ketene elimination is predicted to be endergonic for the cobalt and somewhat less endergonic for the iridium species, with dissociation free energies of 7.7 and 5.3 kcal/mol, respectively (see Table 3).For Rh, however, the release of keten can be considered as almost an equilibrium process with a free energy of only 0.8 kcal/mol.In gas phase, the reaction is more endergonic in all cases, meaning that the strength of coordination for ketene is strongly influenced by the solvent.
In CO atmosphere it is interesting to compare the ketene displacement by CO for the coordinatively saturated ketene complexes.The equilibrium is shifted to the tetracarbonyl side for all cases with free energies of −15.7, −11.0, and −9.6 kcal/mol in CH 2 Cl 2 and −15.9, −9.7, and −7.8 kcal/mol for 5Co, 5Rh, and 5Ir, respectively.Thus, the increase of CO pressure is expected to decrease the overall rate of the reaction due to the preference for the formation of the thermodynamically more stable tetracarbonyl radicals.
For the formation of coordinatively saturated ketene complexes an alternative, intermolecular pathway was found, when the CH 2 group is attacked by an external carbon monoxide.The related transition states (6TSCo, 6TSRh, and 6TSIr) undergo some minor geometrical distortions in comparison with the carbenoids (1Co, 1Rh, and 1Ir) with somewhat smaller bond angles between the equatorial CO ligands.The distance between the carbon of the incoming CO and that of the CH 2 group is the smallest for 6TSIr and the largest for 6TSCo.The transition states have a single imaginary frequency, namely, −85i, −131i, and −176i cm −1 for 6TSCo, 6TSRh, and 6TSIr, respectively (see Figure 3).This one-step pathway is strongly exergonic with a reaction free energy of −37.5 kcal/mol for cobalt.Smaller magnitude of Δ  From the electron density distribution within a molecule, detailed information can be obtained by the Laplacian of electron density, ∇ 2 (r) < 0, which indicates charge concentrations or charge depletions.The Laplacian distribution of all structures, involved in this study, is depicted in Figure 4 along with the molecular graphs with critical points.
The comparison of the carbenoid radicals 1Co, 1Rh, and 1Ir reveals no significant difference in electron density distribution.A distortion around the cobalt atom is somewhat greater than that around the Rh and Ir atoms which may be attributed to the more compact structure of 1Co with shorter Co-C bond distances.Even less difference can be observed by the inspection of the ketene complexes 3Co, 3Rh, and 3Ir.The transition states 2TSRh and 2TSIr differ significantly from the structure 2TSCo.In the rhodium and iridium containing transition structures a bond path can be found between the coupling CH 2 and CO groups.Neither bond path nor bond critical point, however, has been computed in this region of 2TSCo which means that 2TSCo is an early transition state, whereas 2TSRh and 2TSIr are also early transition states by geometry but late transition states according to their electronic structures.
The spin density distribution between atoms has been computed within the framework of Natural Bond Orbital (NBO) analysis (see Table 4).The three systems can be again divided into two groups, as the Rh and Ir based species show similar behavior, whereas the spin density distribution is remarkably different in the cobalt-containing structures.In the carbenoids, the methylene carbons carry the majority of spin density; however, it is also not negligible on the cobalt atom with a value of 0.224.In 1Rh and 1Ir the unpaired electron is mostly located on the methylene carbon.In the transition states less difference can be obtained, as the spin density of C methylene is significantly increased in 2TSCo.Although some spin density has remained on cobalt, the spin density distribution is fairly similar for all transition structures.Among the ketene complexes, however, the cobalt-containing complex differs remarkably again from its Rh and Ir complex analogues.The spin density is mainly concentrated on cobalt, whereas it is somewhat evenly distributed between the central atom and the carbonyl ligands.This different behavior of the cobalt-containing systems may be in conjunction with the different reaction profile associated with it, that is, the more exergonic reaction profile and the very low activation barrier.For Rh complexes, however, the moderate spin density on the metal is in accordance with the observation reported by de Bruin and coworkers, where the spin density on Rh never exceeded 45% for mononuclear rhodium-complexes [15].
It is concluded that transition metal carbonyl radicals of the cobalt group, especially the cobalt-complex 1Co itself, can serve as effective catalysts in the carbene-carbonyl coupling step resulting in ketene complexes which after the uptake of one CO can presumably dissociate the ketene ligand.Although the equilibrium is on the ketene side for the Ircontaining system, the conversion of ketene into carbene cannot be excluded even in this case.The metal carbenoids, however, can form coordinatively saturated ketene complexes by a direct CO addition onto the carbene carbon.For cobalt and rhodium the intramolecular pathway is preferred; however, for the Ir-containing radical both reaction channels are feasible, with a slight preference for the intermolecular pathway.

Figure 2 :
Figure 2: Computed structures of the genuine minima, involved in the formation of coordinatively saturated ketene complexes.Bond lengths are given in Å.

Figure 3 :Figure 4 :
Figure 3: Computed structures of the transition states involved in the formation of coordinatively saturated ketene complexes with external CO.Bond lengths are given in Å.

Table 1 :
Reaction Gibbs free energies and free energy barriers for the carbene-carbonyl couplings.

Table 3 :
Table ReactionGibbs free energies and free energy barriers for the formation of coordinatively saturated ketene complexes via CO uptake (top 6 rows) and via the concerted mechanism (bottom 6 rows).Reaction Gibbs free energies for the ketene elimination step.

Table 4 :
Natural spin density for all complexes and transition states within this study.