In Silico Switch from Second- to First-Row Transition Metals in Olefin Metathesis: From Ru to Fe and from Rh to Co

Density functional theory (DFT) calculations have been used to investigate the behavior of different transition metals from Groups 8 (Fe and Ru) and 9 (Co and Rh) in an already well-known catalytic mechanism, which is based on an Ru(SIMes)(PPh3)Cl2=CH(Ph) complex. As expected, Ru has proven to perform better than their Fe, Co, and Rh counterparts. Even though the topographic steric maps analysis shows no difference in sterical hindrance for any of the metal centers, geometrically, the Fe-based species show a high rigidity with shorter and stronger bonds confirmed by Mayer Bond Orders. The systems bearing Co as a metallic center might present a reactivity that is, surprisingly, too high according to conceptual DFT, which would consequently be a drawback for the formation of the fundamental species of the reaction pathway: the metallacycle intermediate.


Introduction
Olefin metathesis has been a widely studied reaction due to its particular use in diverse sectors, including relevant industrial applications such as the Shell Higher Olefin Process (SHOP) [1,2] and the Phillips Triolefin Process (PTP) [3] in petrochemistry and its use in polymerization reactions. Within homogeneous catalysis, the first catalysts for this process were developed by Grubbs [4,5] and Schrock [6]. This reaction consists of the reorganization of two carbon-carbon double bonds using a metal carbene complex as the catalyst, following Chauvin's [7,8] mechanism. The nature of the metal is fundamental, ruthenium and molybdenum being the leading metals for this research [9][10][11], with scarce studies on other metals, such as rhodium [12], osmium [13], and iron [14,15].
Since Ru-and Mo-based catalysts were first discovered by Grubbs and Schrock, respectively, due to the particular nature of the reaction, the need for new catalysts to deal with more specific reactions has increased. More catalysts are being continuously developed according to the amount of enantioselective synthesis required, the polymerization process as well as the construction of different polymers, and the opening or closure of rings where double bonds are involved [16][17][18][19]. Many of these chemical reactions are mainly based on ruthenium and other second-row transition metals, especially molybdenum, despite the remarkable performance also presented by tungsten and rhenium, from the third row. Even though the vast majority of catalysts are based on the metals mentioned above, there is a growing interest in promoting first-row transition metals for the sake of lower cost and toxicity [20,21], together with similar or slightly lower efficiency, leading to a low-cost generation of catalysts. Overall, the main problem in this sector is that, as the catalysis has increased in demand, so have the catalysts and their research. This is derived from the fact that the research involves less abundant metals such as ruthenium, which results in high costs. Consequently, it has induced the need for catalysts based on cheaper and more abundant metals, such as the first-row transition metals, e.g., iron or cobalt [22], even though to date only in silico attempts have been found. This transition is required for the sustainability of the catalysts, which involves modern environment requirements, an optimization of the materials used and a reduction in toxic waste and costs [23] but, at the same time, improved efficiency [24][25][26]. As aforementioned, since experimental studies of these kinds of catalysts and their reactivity can be expensive, the use of computational tools has been gaining popularity in recent years [27,28]. In light of the experimental success of Ru-based catalysts with the SIMes N-heterocyclic carbene (SIMes = 1,3-bis(2,4,6-trimethylphenyl)-4,5-dihydroimidazole-2-ylidene), we wanted to expand our understanding of homologous Fe-based catalysts first computationally reported by Poater, Cavallo, et al. [14] and compare them with their Rh-and Co-based counterparts.

Results and Discussion
For the catalyst M(SIMes)Cl 2 (=CHPh)PPh 3 , where M = Ru, Rh, Fe, or Co, we illustrate its interaction with the essential olefin ethylene as a substrate in Scheme 1.
Catalysts 2017, 7, 389 2 of 12 generation of catalysts. Overall, the main problem in this sector is that, as the catalysis has increased in demand, so have the catalysts and their research. This is derived from the fact that the research involves less abundant metals such as ruthenium, which results in high costs. Consequently, it has induced the need for catalysts based on cheaper and more abundant metals, such as the first-row transition metals, e.g., iron or cobalt [22], even though to date only in silico attempts have been found. This transition is required for the sustainability of the catalysts, which involves modern environment requirements, an optimization of the materials used and a reduction in toxic waste and costs [23] but, at the same time, improved efficiency [24][25][26]. As aforementioned, since experimental studies of these kinds of catalysts and their reactivity can be expensive, the use of computational tools has been gaining popularity in recent years [27,28]. In light of the experimental success of Ru-based catalysts with the SIMes N-heterocyclic carbene (SIMes = 1,3-bis(2,4,6-trimethylphenyl)-4,5-dihydroimidazole-2-ylidene), we wanted to expand our understanding of homologous Fe-based catalysts first computationally reported by Poater, Cavallo, et al. [14] and compare them with their Rh-and Cobased counterparts.

Results and Discussion
For the catalyst M(SIMes)Cl2(=CHPh)PPh3, where M = Ru, Rh, Fe, or Co, we illustrate its interaction with the essential olefin ethylene as a substrate in Scheme 1. To unravel the olefin metathesis mechanism using a Co-based catalyst, we switched the Ru center by a cobalt atom in a known Grubbs olefin metathesis catalyst [29]. The latter consists of a ruthenium atom bonded to a SIMes-type ligand, two chlorides, a triphenylphosphine, and a phenylene group. Despite the apparent simplicity of the computational metal exchange, this leads to two problematic challenges. First, it entails switching from second to first row transition metals such as Co or Fe, which are prone to display high spin species, in agreement with Vasiliu et al. [30]. Consequently, this force screening the different multiplicity states for the first-row transition metal catalysts, not only for the first species I but through the whole reaction pathway. Second, ruthenium and iron, unlike cobalt and rhodium, bear an even number of electrons.
Based on past results with ruthenium [31], the potential energy surface was computed starting from the precatalyst I and using ethylene as substrate. The energy profile of the first cycle of the catalytic reaction, i.e., the activation of the catalyst, was calculated according to the mechanism described in Scheme 1. After the release of the labile phosphine ligand to form the 14e species II, the remaining steps are the coordination of the olefin (III), the metallacycle (IV), the generation of the second coordination intermediate (V) and finally, once the olefin is released, the second 14e species (VI). Having introduced the activation mechanism, before discussing the effectiveness depending on the metal center, the problem of the ground state for each metal and intermediate must be addressed. Differently from what happens for the first-row transition metals, ruthenium and rhodium as the ground state multiplicity only prefer the singlet and doublet states, respectively (see Table 1 and Table S3). Bearing the high qualitative similarity between the Gibbs free energies profiles in gas compared to the ones including the solvent correction with any of the exchange-correlation functionals used here, the next discussion is consistent with any methodology used for both first-row transition metal-based catalysts. Next, even though the energy profiles are nearly symmetrical for both second-row transition metals, differing by less than roughly 2-3 kcal/mol, the metallacycle for Scheme 1. Studied olefin metathesis reaction mechanism. M stands for the transition metal.
To unravel the olefin metathesis mechanism using a Co-based catalyst, we switched the Ru center by a cobalt atom in a known Grubbs olefin metathesis catalyst [29]. The latter consists of a ruthenium atom bonded to a SIMes-type ligand, two chlorides, a triphenylphosphine, and a phenylene group. Despite the apparent simplicity of the computational metal exchange, this leads to two problematic challenges. First, it entails switching from second to first row transition metals such as Co or Fe, which are prone to display high spin species, in agreement with Vasiliu et al. [30]. Consequently, this force screening the different multiplicity states for the first-row transition metal catalysts, not only for the first species I but through the whole reaction pathway. Second, ruthenium and iron, unlike cobalt and rhodium, bear an even number of electrons.
Based on past results with ruthenium [31], the potential energy surface was computed starting from the precatalyst I and using ethylene as substrate. The energy profile of the first cycle of the catalytic reaction, i.e., the activation of the catalyst, was calculated according to the mechanism described in Scheme 1. After the release of the labile phosphine ligand to form the 14e species II, the remaining steps are the coordination of the olefin (III), the metallacycle (IV), the generation of the second coordination intermediate (V) and finally, once the olefin is released, the second 14e species (VI). Having introduced the activation mechanism, before discussing the effectiveness depending on the metal center, the problem of the ground state for each metal and intermediate must be addressed. Differently from what happens for the first-row transition metals, ruthenium and rhodium as the ground state multiplicity only prefer the singlet and doublet states, respectively (see Table 1 and Table S3). Bearing the high qualitative similarity between the Gibbs free energies profiles in gas compared to the ones including the solvent correction with any of the exchange-correlation functionals used here, the next discussion is consistent with any methodology used for both first-row transition metal-based catalysts. Next, even though the energy profiles are nearly symmetrical for both second-row transition metals, differing by less than roughly 2-3 kcal/mol, the metallacycle In Table 2, the activation mechanism in olefin metathesis for the series M(SIMes)Cl 2 (=CHPh)PPh 3 (M = Fe and Co) is displayed (see Table S2). For these cobalt and iron structures, the complexity increases since both metals are prone to favor high spin multiplicities. Table 2 includes the energy values comparing their reaction pathways with different multiplicities to find out which is the ground state for each intermediate. It should be pointed out that, for some multiplicities, there are structures that cannot be located since some metal-carbon bonds break. The discussion on the solvent energy calculations is based on the BP86 functional [34][35][36] for the sake of consistency with the choice of multiplicity for each computed species, since the single-point energy calculations with the Truhlar functionals M06L [37] and M06 [38] may change the order of multiplicity, even though M06 was found to provide the right energy values for ruthenium as a metal center [39]. It is also important to point out that, for cobalt, the doublet state predominates, since the next quadruplet multiplicity is found to be from 10 to 20 kcal/mol higher in energy in all cases. Switching to iron, we can see a variety of multiplicities in the reaction mechanism ranging from singlet up to quintuplet, for the metallacycle IV, whereas triplet is the ground state of the other intermediates. Bearing the importance of the metallacycle in the olefin metathesis pathway [8,40], it is necessary to remark that for cobalt the metallacycle IV is not located since no multiplicity supports the four-membered ring, consequently breaking any of both Ru-C bonds.
Moving to the comparison between Fe-, Ru-, Co-, and Rh-based complexes, as shown in Tables 1 and 2 and summarized in Figure 1, it appears that, for Co and Fe, the first step that consists of the phosphine dissociation was more facile. This is promising since, for Ru, this is a drawback [41] and usually turns out to be the limiting step [42,43]. The energy cost is 23.1 kcal/mol for Ru but only 6.6 kcal/mol for Co. However, for the dissociative first step I→II, the trend is clear, favored by roughly 15 kcal/mol for both first-row transition metals [44]. Next, for the II→III step, only ruthenium and rhodium displayed a favorable coordination intermediate III, even if for Fe and Co this species is still achievable. Next, the central issue of the reaction pathway was found at Complex IV since for Co we were not able to locate the optimized geometry, which is the fundamental intermediate of the general reaction pathway described by Chauvin [7,8], leading us to think that this intermediate is not readily achievable for Co. We further tried to locate unsuccessfully a concerted transition state linking III directly with V, since all attempts to locate IV converged to either of these two coordination intermediates. As for the Fe-based complex, this metallacycle IV is very stable in agreement with previous studies, which is a drawback in olefin metathesis. The latter fact, together with the quintuplet multiplicity of species II and VI, may be the main reasons for the limited effectiveness of iron as an olefin metathesis catalyst [45]. Indeed, the fact that, for the whole Ru-based reaction pathway, the singlet is the most stable spin state, together with its relatively unstable metallacycle IV, probably explains the experimental failure to obtain active Co-or Fe-based olefin metathesis catalysts. Table 2. Computed stationary points (Gibbs free energies in kcal/mol) for the olefin metathesis reaction pathway for M(SIMes)Cl 2 (=CHPh)PPh 3 (M = Fe and Co) with ethylene as substrate (m = multiplicity; 1 = singlet; 2 = doublet; 3 = triplet; 4 = quadruplet; 5 = quintuplet; 6 = sextuplet; g = gas; s = solvent) at the BP86-D3BJ/TZVP~sdd level of theory.

Fe Co
Species Geometrically, the facile phosphine dissociation cannot be explained directly by the elongation of the metal-P bond, as observed in Figure 2, but it requires the analyses of the latter bond using bond orders to take into account the different radius of each metal (see Table 3 and Table S1).
The structural data for the different molecules involved in the reaction mechanism for the four metals collected in Table 3 include the bonds between the respective metal and the nearby ligands. From the analysis of these data, we determined that, for Fe, the majority of the bonds are shorter; however, since the radius of the metals is fundamental to compare the strength of bonds bearing different metals, we further studied the Mayer Bond Orders (MBOs). It is possible to conclude that M-C and M=C bonds are stronger for Ru and Rh than for Fe and Co, respectively, in agreement with previous studies by Vasiliu et al. [30] and De Brito Sá et al. [45] related to the binding energy of the metal-carbene bond.
From the analysis of these data, we determined that, for Fe, the majority of the bonds are shorter; however, since the radius of the metals is fundamental to compare the strength of bonds bearing different metals, we further studied the Mayer Bond Orders (MBOs). It is possible to conclude that M-C and M=C bonds are stronger for Ru and Rh than for Fe and Co, respectively, in agreement with previous studies by Vasiliu et al. [30] and De Brito Sá et al. [45] related to the binding energy of the metal-carbene bond.   Bearing in mind that the olefin metathesis mechanism involves the coordination of a CH2=CH2 molecule to the metal center, which occurs between II and III, we performed an analysis of the accessibility for the metal center using the SambVca 2.0 web tool [46]. To view the occupied region close to the bonding distance of ethylene, we chose Complex I, without the phosphine, instead of II, since it better represents the real structure. In II (see the Supplementary Materials) [47], without the phosphine yet, the chloride atoms may alter the accessibility to the metal environment, rotating further from the SIMes ligand. Overall, it is evident from Figure 3 that, for the studied M-based complexes (M = Co, Fe, or Ru), all initial species I present sterics that are quite similar. Even though the bond distance with the ylidene moiety is shorter for Co and Fe than it is for Ru, neither the metal   Table 3. Bond lengths (in Å) and Mayer Bond Orders (MBOs) for all the molecules involved in the mechanism for the Fe, Ru, Co, and Rh transition metals. (F = front and R = rear position of the chlorides according to the orientation in Figure 1, and the labeling Ru=C and Ru-C is maintained throughout the whole reaction pathway for the sake of clarity). Bearing in mind that the olefin metathesis mechanism involves the coordination of a CH 2 =CH 2 molecule to the metal center, which occurs between II and III, we performed an analysis of the accessibility for the metal center using the SambVca 2.0 web tool [46]. To view the occupied region close to the bonding distance of ethylene, we chose Complex I, without the phosphine, instead of II, since it better represents the real structure. In II (see the Supplementary Materials) [47], without the phosphine yet, the chloride atoms may alter the accessibility to the metal environment, rotating further from the SIMes ligand. Overall, it is evident from Figure 3 that, for the studied M-based complexes (M = Co, Fe, or Ru), all initial species I present sterics that are quite similar. Even though the bond distance with the ylidene moiety is shorter for Co and Fe than it is for Ru, neither the metal center with Co nor that with Fe are significantly more sterically congested than that with Ru, according to Figure 3. There are no vast differences at a glance [48,49]. Quantifying the percent buried volume (%VBur), we collected 46.0%, 46.1%, 46.2%, and 46.1% of buried volume for Fe, Co, Ru, and Rh, respectively. The data confirm that the metal site accessibility does not differ in any of the metals. Thus, we can exclude it from being a possible cause for the different performance of the three catalysts.

Fe
Catalysts 2017, 7, 389 7 of 12 Figure 3. Topographic steric maps for the Co-and Ru-based catalyst I. The metal is at the origin, and the P atom is on the z-axis (Bz = benzylidene). The isocontour curves of the steric maps are given in Å. The radius of the sphere around the metal center was set to 3.5 Å; the Bondi radii were scaled by 1.17 for all the atoms, and a mesh of 0.1 Å was used to scan the sphere for buried voxels.
To round up all the obtained steric data, from an electronic point of view, we collected the data for the frontier molecular orbitals for each metal mechanism, and we used them for a conceptual DFT analysis. As shown in Table 4, Co-based complexes appear not to be exceptionally hard, which might induce to their non-existence, or at least to the difficulty in finding them due to their high reactivity. As for Ru and Fe, Ru appears to be a bit less reactive than Fe since it has a higher chemical hardness than the Fe-based catalysts. On the other hand, the higher electrophilicity of the Ru-based complex recognizes that it is more prone to react with nucleophiles such as olefins. In agreement with this hypothesis, the Natural Bond Orbital (NBO) charges confirm that the charge on the metal become much more negative on the metallacycle IV for Ru (−0.144) with respect to Fe (−0.025) and with Rh (−0.078) in between. Table 4. Highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO), chemical hardness (η), and electrophilicity (ω) for the computed stationary points for the olefin metathesis reaction pathway for M(SIMes)Cl2(=CHPh)PPh3 (M = Ru, Co, and Fe).  To round up all the obtained steric data, from an electronic point of view, we collected the data for the frontier molecular orbitals for each metal mechanism, and we used them for a conceptual DFT analysis. As shown in Table 4, Co-based complexes appear not to be exceptionally hard, which might induce to their non-existence, or at least to the difficulty in finding them due to their high reactivity. As for Ru and Fe, Ru appears to be a bit less reactive than Fe since it has a higher chemical hardness than the Fe-based catalysts. On the other hand, the higher electrophilicity of the Ru-based complex recognizes that it is more prone to react with nucleophiles such as olefins. In agreement with this hypothesis, the Natural Bond Orbital (NBO) charges confirm that the charge on the metal become much more negative on the metallacycle IV for Ru (−0.144) with respect to Fe (−0.025) and with Rh (−0.078) in between.

Computational Details
All the DFT static calculations were performed with the Gaussian09 set of programs (Gaussian09.D01, Gaussian, Inc., Wallingford, CT, USA, 2009) [50]. The electronic configuration of the molecular systems was described with the triple zeta valence polarization function of Ahlrichs and co-workers for H, C, N, P, and Cl (TZVP keyword in Gaussian) [51]. Cobalt, iron, and ruthenium were described by the small-core, quasi-relativistic Stuttgart/Dresden effective core potential, with an associated valence basis set, contracted (standard SDD keywords in Gaussian09) [52][53][54]. The geometry optimizations were performed without symmetry constraints, and the characterization of the located stationary points was achieved by analytical frequency calculations, using the BP86 functional of Becke and Perdew [32][33][34], together with the Grimme D3BJ correction term to the electronic energy [55,56].
Single-point calculations of the BP86-D3BJ optimized geometries were performed using the BP86 [32][33][34], M06L and M06 functionals [37,38], and, were performed again with the triple-z basis set of Weigend and Ahlrichs for main-group atoms (TZVP keyword in Gaussian), whereas the SDD basis set was employed for ruthenium. Solvent effects were included with the polarizable continuous solvation model (PCM) using CH 2 Cl 2 as solvent [57,58]. The reported free energies in this work include energies obtained at the M06/TZVP level of theory corrected with zero-point energies, thermal corrections, and entropy effects evaluated at 298 K.
%VBur Calculations: The buried volume calculations were performed with the SambVca package developed by Cavallo et al. [59]. The radius of the sphere around the origin placed 2 Å below the metal center was set to 3.5 Å, while for the atoms we adopted the Bondi radii scaled by 1.17, and a mesh of 0.1 Å was used to scan the sphere for buried voxels. The steric maps were evaluated with a development version of the SambVca package [46,60].
The electrophilicity of the complexes was evaluated as the Parr electrophilicity index (ω) calculated as ω = µ 2 /2η, where µ and η are the chemical potential and the molecular hardness, respectively [61]. In the framework of DFT, µ and η for an N-electron system with total electronic energy E and subject to an external potential are defined as the first and second derivatives of the energy concerning N at a fixed external potential. In numerical applications, µ and η are approximated with the finite difference formulas (µ = 0.5(ε L + ε H ) and η = 0.5(ε L − ε H )), which are based on Koopmans' theorem. The ε H and ε L are the energies of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), respectively [62].

Conclusions
We have studied a well-known olefin metathesis mechanism with Ru, and that of homologous Rh, using two other abundant metals, Fe and Co. Rh, for the sake of complete comparison, was taken into account to cover the first two metal elements from Groups 8 and 9. Co-based catalyst turns out to be very reactive, but the location of the metallacycle IV is not feasible. Experimental research with this metal has not yet yielded any results, and here we argue a hypothesis. For Fe-based complexes, we have determined that Fe in fact presents stronger bonds than the Ru counterpart, even though, for the vital bond, which is the M=C bond, ruthenium bears stronger bonds. Analysis of the topographic steric maps data showed that, for all metals, the sterical hindrance is not an issue since they resemble each other, and therefore, there should not be sterical impediments for the entering olefin. On the other hand, electronically, Fe-based catalysts vary their ground state multiplicity throughout the mechanism, going from singlet up to quintuplet, which may be a drawback for their effectiveness, apart from the relatively exaggerated stability of its metallacycle, which is also partially a problem for the Rh-based counterpart. Chemical hardness analyses determined that Ru is more prone to react with a nucleophilic olefin than Fe-based catalysts. Still, ruthenium continues leading the list for new generations of olefin metathesis catalysts [63][64][65]. However, we have to keep going on the research to stabilize the metallacycle bearing Co as a metal center, which was the only drawback found for this metal in this study.