ARTICLE pubs.acs.org/Organometallics
Nature of the Transition MetalCarbene Bond in Grubbs Olefin Metathesis Catalysts Giovanni Occhipinti* and Vidar R. Jensen Department of Chemistry, University of Bergen, Allegaten 41, N-5007 Bergen, Norway
bS Supporting Information ABSTRACT: A comparative density functional theory study of tungsten-based Fischer carbenes, tungsten- and molybdenumbased Schrock carbenes, and ruthenium- and osmium-based Grubbs-type olefin metathesis catalysts reveals that the last group of catalysts should not be taken to be intermediate between the two established categories of carbenes. Rather, the Grubbs catalysts have characteristic properties similar to those of the Schrock family of carbenes and can be viewed as an extension of the latter class. Whereas an appreciable fraction of the electrons involved in the carbene bond of Fischer carbenes are unshared, and these compounds may be classified as “ionic” or “donoracceptor” carbenes, a distinct covalent character is observed for both Schrock carbenes and Grubbs catalysts, which thus together fall into a larger category that may be termed “covalent” or “electron-sharing” carbenes. For these compounds, the energies of the atomic valence d orbitals determine the polarization of the σ and π components of the carbene bond. Whereas the early metals (as reflected in valence d orbitals of relatively high energies) W and Mo render Schrock carbenes weakly nucleophilic, the later metals Ru and Os form weakly to moderately electrophilic carbenes. Schrock carbenes may thus, more accurately, be classified as “nucleophilic covalent” or “nucleophilic electron-sharing” carbenes, while Grubbs catalysts could be termed “electrophilic covalent” or “electrophilic electron-sharing” carbenes.
’ INTRODUCTION Transition-metal (TM) carbene complexes fascinate chemists both due to their multifaceted bonding patterns and their role as catalysts.1 Their importance in fundamental and applied organic and organometallic chemistry has increased markedly over the last couple of decades. Thousands of such compounds have been recorded to date, and their number is steadily growing at a rate of a few hundred per year.2 TM carbenes are divided into two classes, defined according to a series of criteria.3 The carbene carbon atoms of Fischer carbenes4 are electrophilic and possess stabilizing π-donor groups. The metal is typically a middle or late TM in a low oxidation state ligated by strong π acceptors. In contrast, Schrock carbenes5 are nucleophilic and carry hydrogen atoms or alkyl groups as substituents on the carbene ligand. The central atom is typically an early, high-oxidation-state TM ligated by π donors. At the fundamental level, the distinction between the two is based on the nature of the TMcarbene bond,3,6 one being formed between spin triplet fragments and the other by spin singlet fragments (see Figure 1). The currently most prominent application of transition-metal carbenes is as catalysts for olefin metathesis. Whereas the Schrock molybdenum and tungsten catalysts7 can be unambiguously classified as Schrock-type carbenes, Grubbs catalysts1e apparently have properties characteristic of both classes. Even though these catalysts are often referred to as ruthenium(II) r 2011 American Chemical Society
Figure 1. Singlet and triplet cleavage of the TMdC bond.
carbenes,8 and thus clearly should fall into the Fischer class, a high RudC bond order (BO)9 and a large residual in the charge decomposition analysis (CDA),10 both suggestive of Schrock carbene character, have been noted in quantum chemical studies. Of course, loss of detail is the inevitable result when undertaking a discrete classification where nature offers a continuum of variation. Nevertheless, a useful classification scheme must be able to discern among the most prominent examples of the class of compounds for which the classification was constructed. The Received: February 26, 2011 Published: June 09, 2011 3522
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Chart 1. Metal Carbene Complexes Investigated in This Worka
Table 1. TripletSinglet Excitation Energies and Energy Differences between Singlet and Triplet Bond Cleavage, ΔBDESTa
b
compd
a
1
Abbreviations: R = tert-butyl, R = dimethylphenylmethyl, Ar = 2,6diisopropylphenyl, Ar1 = 2,6-dimethylphenyl, Cy = cyclohexyl, Mes = mesityl.
contradictory information currently available regarding the carbene classification of the Grubbs catalysts strongly suggests that a thorough characterization of their metalcarbene bonds along with a reassessment of the classification is needed. To this end, we have performed a comparative density functional theory (DFT) investigation of a series of W, Mo, Os, and Ru carbene complexes (see Chart 1).
’ RESULTS AND DISCUSSION Both classical (13)11 and non-heteroatom-stabilized (4)1d,11 complexes have been included as reference Fischer carbenes. Similarly, W and Mo Schrock alkylidene and methylidene olefin metathesis catalysts (58) and the benzylidene version of the Mo-based catalyst (9) have been included as examples of Schrock carbenes. The target Grubbs catalysts are represented by a small model of the first-generation precatalysts (14, included for validation purposes; see below) along with the actual first- and second-generation precatalysts (15 and 16), the two corresponding 14-electron methylidene catalysts (12 and 13), and their osmium analogues (10 and 11). For each of the complexes 116 the energetically most favored bond dissociation mechanism has been determined by dissociation of the TMdC bond into two sets of neutral, frozen-geometry metal and carbene fragments, one consisting of spin singlet fragments and the other of spin triplet fragments (cf. Figure 1). The spin ground state and the corresponding tripletsinglet (TS) energy gap have been identified for each such fragment using two hybrid functionals: the well-tested B3LYP functional12 and the recently developed M06 functional.13 These functionals reproduce the TS energy gaps in the carbene fragments CH2 and CF2 with very good accuracy.14 Corresponding experimental data are not available for the metal fragments, and we have thus
carbene
metal
fragment
fragment
B3LYP
M06
B3LYP
ΔBDEST M06
B3LYP
M06
1 (W)
52.6
54.0
33.1
35.2
85.7
89.2
2 (W)
29.5
31.9
30.7
32.8
60.2
64.7
3 (W)
55.4
62.2
30.6
32.8
86.0
92.8
4 (W) 5 (W)
5.8 1.3
2.5 0.2
29.2 5.6
31.3 1.2
23.4 6.9
28.8 1.0 5.2
6 (W)
9.9
6.7
2.8
1.5
12.7
7 (Mo)
0.3
0.9
13.6
9.6
13.9
8.3
8 (Mo)
10.0
6.7
13.5
9.7
23.5
16.4
9 (Mo)
0.4
1.1
13.5
9.5
13.9
10.6
10 (Os)
10.0
6.7
6.7
7.8
16.7
14.5
11 (Os)
10.5
7.2
10.1
11.6
20.6
18.8
12 (Ru) 13 (Ru)
10.6 11.1
7.3 7.8
11.9 15.4
14.2 17.9
22.5 26.5
21.5 25.7
14 (Ru)
9.6
6.4
10.8
12.2
20.4
18.6
15 (Ru)
0.1
0.4
20.0
24.2
20.9
24.6
16 (Ru)
0.3
0.1
21.8
26.0
21.5
25.9
a
All values are given in kcal/mol. See Figure 1 for a definition of ΔBDEST. A negative ΔBDEST implies that bond cleavage to singlet fragments is preferred. b The complexes are shown in Chart 1.
included a model of a metal carbene (14) for which a reliable estimate of the TS energy gap may be obtained using a highlevel wavefunction-correlated method. CCSD(T) in combination with large basis sets, including g functions on ruthenium and f functions on chlorine and phosphorus, gave a TS energy gap of 11.3 kcal/mol (see the Computational Details for more information). The corresponding predictions by B3LYP (10.8 kcal/mol) and M06 (12.4 kcal/mol) (see Table 1) are very close to this benchmark CCSD(T) value, thus boosting the confidence that can be put in the rest of the TS energy gaps reported here. The vertical tripletsinglet excitation energies and energy differences between singlet and the triplet bond cleavage for the compounds in Chart 1 are given in Table 1. As expected, the classical Fischer carbenes 13 and the non-heteroatom-stabilized carbene 4 strongly prefer dissociation to singlet fragments, whereas triplet dissociation is favored for the typical Schrock carbenes (59). Accordingly, as noted early on in quantum chemical studies of TM carbenes and their fragments,6 the TMdC bond of the Fischer and Schrock carbenes should be described by a donoracceptor mechanism for the former and by an electron-sharing mechanism for the latter compounds. Similar pictures of the bond mechanisms have later emerged also in CDA.1f,11 Turning now to the target ruthenium- and osmium-based complexes (1016), these all feature fragments in spin triplet ground states, in most cases with a relatively large TS energy gap (see Table 1). Thus, like Schrock carbenes, these compounds appear to be combinations of triplet fragments bound by electron-sharing σ and π bonds, in agreement with CDA results for the model complex (PH3)2Cl2RudCHMe.10 A more detailed picture of the bonding situation in the current complexes has been obtained in natural resonance theory 3523
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Table 2. NBO and NRT Analyses of the TMdC Bond Using the B3LYP Density compda
BONb
BON,Ic
BON,Cd
CBOe
CBOσf
CBOπg
C2pπh
1 (W)
1.62
0.93
0.68
0.55
0.39
0.16
0.61
2 (W) 3 (W)
1.97 1.66
1.27 0.77
0.70 0.89
0.70 0.79
0.41 0.45
0.29 0.34
0.61 0.61
4 (W)
1.76
0.66
1.10
1.00
0.48
0.51
0.55
5 (W)
1.89
0.35
1.53
1.46
0.62
0.83
1.10
6 (W)
1.89
0.36
1.53
1.46
0.65
0.81
1.14
7 (Mo)
1.94
0.2
1.66
1.50
0.65
0.84
1.01
8 (Mo)
1.93
0.24
1.69
1.57
0.68
0.89
1.04
9 (Mo)
1.94
0.28
1.66
1.46
0.66
0.80
1.02
10 (Os) 11 (Os)
1.71 1.86
0.14 0.19
1.57 1.68
1.57 1.53
0.81 0.81
0.76 0.73
0.90 0.84
12 (Ru)
1.69
0.17
1.51
1.51
0.81
0.70
0.83
13 (Ru)
1.85
0.24
1.61
1.46
0.80
0.66
0.77
14 (Ru)
1.82
0.39
1.43
1.47
0.82
0.65
0.79
15 (Ru)
1.61
0.29
1.33
1.27
0.78
0.49
0.73
16 (Ru)
1.89
0.53
1.36
1.22
0.79
0.44
0.72
The complexes are shown in Chart 1. b The natural BO as obtained from NRT analysis.15 c The ionic component of BON. d The covalent component of BON. e The covalent bond order index;17 cf. see the Computational Details for more information. f The approximate σ component of the CBO. g The approximate π component of the CBO. h The natural population of the carbene carbon 2pπ atomic orbital.
Figure 2. Bond dissociation energy (zero-point corrected) of the TMdC bond for the carbene complexes shown in Chart 1.
a
(NRT)15 and natural bond orbital (NBO)16 analyses of the B3LYP electron densities (see Table 2). The covalent character was evaluated as the covalent contribution (BON,C) to the natural bond order, BON. Approximate separation of the σ and π bond components was achieved using a covalent bond order index,17 in the following termed CBO, which is seen to agree well with the covalent part of the natural BO (see Table 2). The low symmetry of most of the present complexes does not formally exclude mixing of σ and π components. In practice, however, the σ and π bonds were found to be well separated in different natural bond orbitals and the index may thus be resolved into σ and π components. The NBO analysis was performed using the same spatial orientation of the TMdC bond for all complexes.18 Fischer-type carbenes (14) display a TMdC bond with a low covalent character (BON,C = 0.681.10) and an elevated ionic contribution (3864% of the BON). In contrast, clear Schrock carbenes (59) and Os and Ru 14-electron catalyst complexes (1013) feature a TMdC bond dominated by the covalent contribution (8192% of the BON). The covalent bond orders (BON,C and CBO) are in the range 1.51.7 and reflect the presence of more than one covalent component in the carbene bond. Indeed, both the σ and π components of the CBO (0.60.9, cf. right-hand side of Table 2) are significant in all these complexes (513). Whereas the Schrock carbenes are seen to possess π BOs close to unity (BOπ = 0.80.9), the carbene bonds of the Os and Ru complexes (1016) feature comparably high σ components (BOσ = 0.8). Hence, the π bond in the Os- and Ru-based Grubbs catalysts is somewhat less covalent than that of the Schrock carbenes. This is particularly evident for the two benzylidene precursors (15 and 16), in which π donation from the conjugated phenyl ring polarizes the π bond toward the metal, effectively reducing the π BO, analogous to the effect of other π donors.10 The horizontal orientation of
Figure 3. Percentage of metal character in the σ and π NBOs of the TMdC bond for the carbene complexes shown in Chart 1.
the benzylidene group, imposed by steric factors, enhances this effect.19 That the present approach is capable of discerning among the different carbene bonds is underlined by the low RuNHC CBOσ (0.47) in the Grubbs second-generation catalyst 16, thus clearly distinguishing this Fischer carbene from the much higher CBOσ (0.79) of the RudCHPh bond in the same complex. Finally, it should also be noted that the aforementioned trends do not appear to be dependent on a particular formulation of the BO.20 The bond dissociation energy (BDE) of the TMdC bond, with respect to the relaxed neutral fragments in their spin ground state, has been calculated using the B3LYP-D21 and M06 functionals (see Figure 2). Despite the fact that many factors contribute to the BDE,22 and that the correlation with the BO is therefore often modest (see, e.g., ref 11), the strongest bonds in the present work are seen to also have the highest covalent characters and vice versa. For example, the BDEs for the Schrock carbenes 59 (92106 kcal/mol) are nearly twice those of the Fischer carbenes 13 (5363 kcal/mol) and the order of the BDEs (511 > 1216 > 4 > 13) reflects roughly that of the covalent BOs. Turning now to the polarization of the various bond components, the percentage of metal character in the σ and π TMdC natural bonding orbitals is shown in Figure 3. The σ and π bonds of the Fischer-type carbenes 14 are strongly polarized toward the carbene carbon atom and the metal atom, respectively. In contrast, the carbene bonds of the Schrock carbenes (59) are more equally polarized, as also observed previously for Fischerand Schrock-type carbenes of tungsten.11 Although the Os and Ru 14-electron catalysts (1013) and the model of the firstgeneration precatalyst (14) clearly group together with the Schrock-type carbenes in showing smaller differences in polarization between the σ and π components, some important distinctions should be noted. For example, the σ and π bonds 3524
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Organometallics of W-based Schrock-type carbenes are both polarized toward the carbene carbon atom, whereas the σ bonds in the Ru catalysts are only slightly polarized toward the carbene and the π bond is weakly polarized toward the metal atom. In general, it can be observed that the polarization of both the σ and the π bond increases toward the metal in the order W < Mo < Os < Ru, a trend which can be explained by the fact that the energies of the atomic orbitals participating in the TMdC bonds increase in the order C2s < Ru4d < Os5d < C2p ≈ Mo4d < W5d.23 Accordingly, the π component of a Wcarbene double bond constructed from two triplet fragments should be polarized toward the carbon atom, whereas the opposite polarization should be expected for a Ru complex. These orbital energies also explain why the σ bond is less polarized in Os and Ru than in W and Mo complexes. Considered together with classical electronegativity scales, the covalent nature of the RudC bond implies that the formal oxidation state of Ru in Grubbs catalysts is þ4. On the basis of the relative order of the atomic orbital energies (C2s < Ru4d < C2p) and the observed polarization of the π bond toward the metal, it could also be argued that the effective “π electronegativity” of the carbon atom is in fact lower than that of ruthenium. Such nontraditional reasoning would suggest an oxidation state of þ2 for Ru. Our results illustrate that the carbene reactivity is determined by the polarization of the π bond. The natural population (NP) of the carbene C2pπ orbital11 indicates electron excess (NP > 1) or deficiency (NP < 1) in the region most exposed to electrophilic or nucleophilic attacks (see Table 2). Fischer-type carbenes 14 have a population for the C2pπ orbital just above half an electron and are therefore electrophilic. In contrast, in Schrock carbenes this population is seen to be higher than unity, making these compounds appear as weakly nucleophilic, in agreement with previous studies of Fischer and Schrock carbene complexes of tungsten.11 Finally, for Os and Ru Grubbs catalysts, the corresponding population is between 0.72 and 0.90 electron, suggesting that these compounds should be classified as weakly to moderately electrophilic. The latter result is in agreement with the observed reactivity pattern for these compounds. It is indeed known that ruthenium-based Grubbs catalysts tolerate the presence of various nucleophiles24 but can, under particular conditions, react with water,25 N-heterocyclic carbenes,26 phosphines,27 or amines.28 Osmium alkylidenes, on the other hand, are predicted to be less electrophilic than those of ruthenium (cf. Table 2) and in some cases display ambivalent nucleophilic/electrophilic29 or even simple nucleophilic30 reactivity at the carbene. It should be stressed that the polarization of the π bond toward the metal in Grubbs catalysts does not have the same cause as the corresponding polarization in Fischer carbenes. For Fischer carbenes the polarization is the result of the donoracceptor mechanism of the carbene bond, while in Grubbs catalysts it is the consequence of the relatively late nature of the transition metals involved (as reflected in the relatively low energies of the atomic valence d orbitals; vide supra). Summarizing the results from the above comparison of individual molecular properties for the various carbenes, the Grubbs catalysts seem to group together with the Schrock carbenes rather than the Fischer carbenes. However, before proceeding to simply classify the Grubbs catalysts as Schrock carbenes, this grouping-together tendency should be confirmed and more systematically analyzed using multivariate classification techniques. Similarly, the property that best seems to distinguish the Grubbs catalysts from the Fischer carbenes is the degree to which
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Table 3. Molecular Descriptors Used in the Multivariate Analysesa 1
percentage of metal character in the σ NBO of the TMdC bond
2
percentage of metal character in the π NBO of the TMdC bond
3
ionic component of the natural bond order, BON,I
4
covalent component of the natural bond order, BON,C
5
natural population of the carbene carbon 2pπ atomic orbital, C2pπ
6
TS energy gap in the carbene fragment
7
TS energy gap in the metal fragment
8 9
energy difference between singlet and triplet bond cleavage, ΔBDEST bond dissociation energy (M06) of the TMdC bond
a The mutual correlation coefficients (R2) of descriptors 19 are in all cases e0.9, and the descriptors may thus be considered nonredundant,31 as explained in the Computational Details.
Figure 4. Dendrogram illustrating the cluster analysis based on the standardized Euclidean distance.
the corresponding carbene bonds are covalent. However, a modified or extended classification of the transition-metal carbenes based on this, or any other, property should quantitatively address the border between the classes. Also, for the latter quantification task, multivariate analysis is a useful tool. To this end, we have selected, from the above calculated properties, nine descriptors with low internal redundancy (mutual correlation coefficient R2 e 0.9)31 (see Table 3) and used them in a k-means clustering analysis.32 The optimal number of and separation between clusters were determined by using the silhouette function.33 The dendrogram from the cluster analysis (Figure 4) and the silhouette test reveal the presence of two well-separated clusters (averaged silhouette value S = 0.84),34 the first consisting of Fischer heteroatom- and non-heteroatom-stabilized carbenes (rendered in black in Figure 4) and the second containing both Grubbs catalysts (violet) and Schrock carbenes (pink). To obtain further insight into the clustering pattern, and in particular to gain understanding as to the role of the individual descriptors (given in Table 3), we have also performed a principal component analysis (PCA).32 Following standard procedures,35 two principal components (PCs), together explaining 92.8% of the total variance, were retained in the PCA model. The scores plot (Figure 5) illustrates how the samples (the carbene complexes) are related to each other, and, similarly to what could be observed in the dendrogram (Figure 4), the plot 3525
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Figure 5. Scores plot: t1 versus t2.
highlights that Fischer carbenes (black) are very different from both Grubbs catalysts and Schrock carbenes, which in contrast appear as relatively similar to each other. Indeed, along PC1, which accounts for almost 80% of the total variance, Grubbs catalysts and Schrock carbenes are indistinguishable and are tightly clustered together, clearly separated from Fischer-type carbenes. The separation between Grubbs catalysts and Schrock carbenes into two contiguous clusters is handled by PC2, but it should be kept in mind that the latter principal component explains much less of the variance (only 13.9%) than does PC1. These results further demonstrate that Grubbs catalysts should not be classified as compounds that fill the gap between Fischer and Schrock carbenes but rather appear as an extension of the latter family of carbenes. The analysis of the loadings plot (Figure 6) reveals that the covalent component of the natural bond order (descriptor 4) contributes the most to PC1 and shows the best correlation (R2 = 0.95) with the scores on PC1 and is thus the single property that best describes the variation among the investigated carbene complexes. By applying k-means clustering and silhouette algorithms to descriptor 4, two monodimensional and well-separated clusters (averaged silhouette value S = 0.89), similar to those identified by the scores on PC1 (Figure 5), appear. The cluster of Fischer carbenes has a mean value for the covalent component of the natural bond order (descriptor 4) equal to 0.84, which corresponds to 48.4% of the total natural bond order (BON). Such a low value, which implies a significant fraction of unshared electrons in the TMdC bond (i.e., high ionic components of the natural bond order), suggests that these compounds may, in a more systematic fashion, be classified as “ionic” or “donoracceptor” carbenes. In contrast, Grubbs catalysts and Schrock carbenes together, with a mean value for the covalent component at 1.55 (84.4% of BON), may be classified as “covalent” or “electron-sharing” carbenes. The point of separation between “ionic” and “covalent” carbenes, determined by a single variable (descriptor 4), can be estimated at ca. 1.18 (65.3% of BON). Indeed, the silhouette value, s(i), for this point is basically zero, indicating an intermediate position between the two clusters.33 Finally, as highlighted by the score values on PC2, important differences still exist among the covalent carbenes. The loadings plot (Figure 6) shows that the natural population of the carbene carbon 2pπ atomic orbital (descriptor 5) and the percentage of
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Figure 6. Loadings plot: p1 versus p2. The plot shows the contribution from the individual descriptors (19, listed in Table 3) to the first two principal components, PC1 and PC2.
metal character in the σ NBOs of the TMdC bond (descriptor 1) are the two most discriminating properties, with opposite signs for the loading values on PC2. For the subset of covalent carbenes these two properties are strongly negatively correlated to each other (R2 = 0.88), and as illustrated above by the scores values, both properties are strongly dependent on what extent the central metal atom is an early or late TM (reflected in the energies of the TM atomic valence d orbitals). The degree to which the σ and π components of the carbene bond become polarized toward the metal increases in the order W < Mo < Os < Ru (vide supra). The most visible consequence of this polarization is that Schrock carbenes, which involve relatively early transition metals (W and Mo), take on a weak nucleophilic reactivity at the Ccarbene atom, while Grubbs catalysts, which involve relatively late transition metals (Ru and Os), display weak to moderate electrophilic reactivity.
’ CONCLUSIONS Multivariate comparison of molecular-level computational results for classic Fischer and Schrock carbenes with those of ruthenium- and osmium-based Grubbs catalysts shows that the latter should not be taken to be intermediate between the two established categories of carbenes. Rather, the Grubbs catalysts have characteristic properties similar to those of the Schrock family of carbenes and can be viewed as an extension of the latter class. Fischer carbenes are characterized by a significant fraction of unshared electrons in the TMdC bond (as judged from high ionic components of the natural bond order) and may be classified as “ionic” or “donoracceptor” carbenes. In contrast, a prominent covalent character for the TMdC bond is observed for both Schrock carbenes and Grubbs catalysts, which thus together fall into a larger category that may be termed “covalent” or “electron-sharing” carbenes. Whereas the relatively early transition metals (W and Mo) render the Schrock carbenes weakly nucleophilic, the later metals (Ru and Os) give weakly to moderately electrophilic carbenes. Accordingly, Schrock carbenes may, more accurately, be classified as “nucleophilic covalent” or “nucleophilic electron-sharing” carbenes, while Grubbs catalysts may be termed “electrophilic covalent” or “electrophilic electronsharing” carbenes. In a more conservative classification scheme, the classic Fischer and Schrock categories could be maintained, 3526
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Organometallics with the Grubbs catalysts entered into a new subcategory, termed “electrophilic Schrock” carbenes.
’ COMPUTATIONAL DETAILS Geometry Optimizations. All geometry optimizations were performed using Becke’s three-parameter hybrid density functional (B3LYP)12 as implemented in Gaussian 03.36 Whereas a restricted formalism was used in the case of spin singlet states, an unrestricted formalism was adopted for triplet spin states. Wavefunction stability tests were routinely carried out. All stationary points (minima) were characterized by the eigenvalues of the analytically calculated Hessian matrix. Numerical integrations were performed using the default “fine” grid of Gaussian 03, and the Gaussian 03 default values were also adopted for the selfconsistent-field (SCF) and geometry optimization convergence criteria. Zero-point corrections were computed within the harmonic-oscillator, rigid-rotor, and ideal-gas approximations. The DunningHuzinaga double-ζ basis set,37 contracted (4s)/[2s], was used for hydrogen. The Stuttgart 2-electron (first row) and 10-electron (P, Cl) effective core potentials (ECPs) were used with accompanying (4s2p)/[2s2p]-contracted basis sets for carbon, nitrogen, and phosphorus and (4s5p)/[2s3p]-contracted basis sets for oxygen, fluorine, and chlorine.38 A single set of polarization p functions (H) or d functions (other elements) were added for all atoms directly bound to the metal center or to the carbene/alkylidene carbon atom.39 A d polarization function was also added to the oxygen atom of CO ligands, to the N atoms of H2IMes ligands, and to the sp2-hybridized carbon atom of the aryl ring directly bound to the nitrogen atom of imido ligands.39 The Stuttgart 28-electron (Mo, Ru) and 60-electron (W, Os) relativistic effective core potentials (ECP) were used with accompanying (8s,7p,6d)/ [6s,5p,3d]-contracted basis sets.40 Conformational Issues. Complexes 116 were chosen in such a way as to easily handle conformational issues. Most of the complexes are symmetrically substituted and possess symmetric ligands with a relatively low number of rotatable bonds. Moreover, all these ligands show the same or at the most only a couple of different conformations in complexes for which the X-ray structure is available.2 Therefore, the number of reasonably low-lying conformers is very limited in all cases. For complexes 5, 7, and 16 the available X-ray conformations were used as starting structures41 in the geometry optimization. For complex 15 the conformation of the analogous X-ray structure of the p-chlorobenzylidene complex was used instead. The methylidene complexes 6 and 8 were obtained from complexes 5 and 7 by replacement of the alkyl group R of the alkylidene moiety CHR by a hydrogen atom. The benzylidene complex 9 was obtained from 7 by using a phenyl group for the substituent R. The conformations of the 14-electron Ru complexes 12 and 13 were obtained from the X-ray structures of 15 and 16 by removing a tricyclohexylphosphine ligand and replacing the benzylidene moiety by a methylidene moiety in the most stable upright orientation.19 The starting structure of complex 14 was obtained from 15 by replacing the cyclohexyl groups of the phosphine ligands by hydrogen atoms and the benzylidene group by a methylidene group in its upright orientation. The starting structures of the two Os complexes 10 and 11 were obtained from the geometry-optimized Ru analogues 12 and 13. For complexes 3 and 4 the previously reported staggered conformations of the carbene ligand11 were prepared in the starting structures. Finally, complexes 1 and 2 were obtained from 4 by replacing one of the hydrogen atoms of the methylidene moiety by N(CH3)2 and OCH3, respectively. The carbene and metal fragments were geometry optimized (to obtain the bond dissociation energies) by starting from the corresponding fragment structures of the geometry-optimized metal carbene complexes. For some of the compounds, alternative conformers were generated, either by chemical intuition or in conformational searches at the molecular mechanics level using the PCModel 9.2 software,42 but these
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alternative conformers were always found to be less stable than those derived in the aforementioned procedure. Single-Point (SP) DFT Energy Evaluations. The total energy and the electronic properties were re-evaluated at the optimized geometry, using the B3LYP12 and M0613 density functionals as implemented in the Gaussian 0336 and NWChem suite of programs,43 respectively. Restricted and unrestricted formalisms have been employed for singlet and triplet spin states, respectively. The solutions thus obtained were routinely subjected to stability tests. The basis sets used in the SP energy calculations were improved in comparison to those used in geometry optimization. For hydrogen, the DunningHuzinaga double-ζ basis set plus polarization (DZP)37 was decontracted and extended with a single diffuse even-tempered s function, resulting in a (5s,1p)/[4s,1p]-contracted basis set. The basis sets of the p-block elements38 were decontracted to triple-ζ quality and extended with a single set of polarization d functions,39 and for elements that did not already have diffuse p functions (C, N, and P), a single set of such functions, obtained in an even-tempered manner, were added, resulting in (4s,5p,1d)/[3s,4p,1d]-contracted basis sets. Finally, for the metals a set of f polarization functions was added to the basis sets described above, resulting in (8s,7p,6d,2f)/[6s,5p,3d,2f]-contracted basis sets.40 For the calculation of TMdC bond dissociation energies, an empirical dispersion term proposed by Grimme21a was added to the B3LYP energies, thus affording B3LYP-D energies. SP Coupled-Cluster Energy Evaluations. The tripletsinglet energy gap (ΔETS) of the neutral frozen (PH3)2Cl2Ru fragment of the geometry-optimized (PH3)2Cl2RudCH2 complex 14 was re-evaluated using coupled cluster singles and doubles including a perturbative triples correction (CCSD(T))44 as implemented in the Gaussian 0336 program. The basis sets were modified and extended compared to those described above for the DFT SP calculations. Hydrogen atoms were described by a Dunning triple-ζ basis set45 augmented by a diffuse s function (Rs = 0.043 152), obtained in an even-tempered manner, and a polarization p function (Rp = 1.00). Phosphorus and chlorine basis sets were extended with a single set of diffuse s and p functions chosen in a even-tempered manner, and the single d polarization function was replaced by two primitive d functions and one primitive f function (Rd = 0.216 and 0.652, and Rf = 0.452 for P; Rd = 0.344 and 1.046, and Rf = 0.706 for Cl), resulting in a (5s,5p,2d,1f)/[4s,4p,2d,1f]-contracted (P) and a (5s,6p,2d,1f)/[4s,5p,2d,1f]-contracted (Cl) basis set, respectively.46 Finally, for ruthenium the s, p, and d functions were partially decontracted and complemented by addition of a single polarization g function (Rg= 1.057),40b resulting in a (8s,7p,6d,2f,1g)/[7s,6p,4d,2f,1g]-contracted basis set. The SP energies calculated for the singlet and the triplet states were 141.455 349 11 and 141.473 426 88 au, respectively, corresponding to ΔETS value of 11.3 kcal/mol. The obtained T1 diagnostic values, 0.0305 and 0.0241 for the singlet and triplet states, respectively, were both below the recommended maximum (0.04) for the CCSD(T) method,47 indicating that the latter single-reference method is applicable to the present tripletsinglet gap. NBO and NRT Analyses. Natural bond orbital (NBO)16 and natural resonance theory (NRT)15,48 analyses of the B3LYP electron densities were performed using the NBO 5.0 program.49 The geometry of each complex was oriented in such a way as to have the TM located in the origin, the TMdC bond along the z axis and the carbene plane in the xz plane. Approximate separation of the σ and π bond components (see Table 2) was achieved using a covalent bond order (CBO) index17 as defined in eq 1. 0 0 ! ! 1 1 1 1 @ @ CBOi ¼ nocc;i fM;i nocc;i f 2 2 2 M;i 2 3527
ð1Þ
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Organometallics In eq 1, the index i is either σ or π; nocc,i and fM,i are the population and the fraction of the metal character in the natural orbital, respectively. The asterisk (*) signifies the corresponding antibonding (non-Lewis) natural orbital. The total CBO (the sum of the σ and π contributions) is seen to agree very well with the covalent part of the natural bond order (BON,C) (see Table 2). For complexes 316, the optimal NBO Lewis structures located all involved a double bond between the metal and the carbene carbon atom and the percentage of Lewis character was similar (97.699.1%) for all these complexes. See Table S1 in the Supporting Information for more details. These optimal Lewis structures were used for both the NBO analysis and as the single reference structure (with the keyword $NRTSTR) in the subsequent NRT analysis. For the Fischer carbene complexes 1 and 2, the best Lewis structure found by the NBO search involves a carbene ligand dissociated from the metal, the natural bonding orbitals of the Wcarbene double bond being highly polarized and thus better described by two lone pairs localized on the W and Ccarbene atoms, respectively. In order to quantify the bond polarization and to compare the results with the other complexes 316, a Lewis structure involving a double bond between W and the carbene carbon atom was used also in these complexes (keyword $CHOOSE) for the NBO analysis. The Lewis character percentages for 1 (97.7%) and 2 (96.9%) using these structures were only slightly lower than those of the optimal Lewis structures found by the NBO search and were comparable to those of the other complexes above. These WdCcarbene double bond Lewis structures were also used as reference structures for the single-reference NRT analyses of 1 and 2. The accuracy of a NRT description can be quantified by the root-mean square deviation, d(w), of the idealized resonance superposition with respect to the true density or by the fractional improvement, f(w), compared to the best single-term description, d(0).15,48 Whereas for complex 1 the accuracy was comparable to that found for complexes 316, and the NRT results reported for 1 are those of the singlereference analysis, the accuracy was lower for complex 2. In order to improve the accuracy of the NRT treatment of 2, the two most important Lewis structures found in the single-reference NRT analysis, one involving a WdCcarbene double bond and the other a WCcarbene triple bond, were employed as reference structures in a multireference NRT analysis of this complex (see the Supporting Information for further details. The natural bond order (BON)48a was calculated as part of the NRT analysis and was obtained by adding the contributions from the individual resonance structures (see Table 2). The default energy threshold (NRTTHR = 1 kcal/mol) was applied to generate the list of secondary structures involved in the calculation of the MdC natural bond order of the various complexes. Multivariate Data Analysis. For the selection of descriptors, we have applied the concept of nonredundant descriptors introduced by Katritzky and Gordeeva,31 which consists in pruning off one variable from each pair that has an intercorrelation R2 value above 0.9. k-means clustering and the principal component analysis (PCA) were carried out by means of the PLS Toolbox 3.550 written for MATLAB51 and performed using autoscaled data (mean centered and scaled to unit variance). The default (standardized) Euclidean distance has been used to build the dendrogram of the clustering. Analysis and validation of the k-means clustering models were performed by means of the silhouette function available in MATLAB,51 using the default (standardized) squared Euclidean distance.
’ ASSOCIATED CONTENT Supporting Information. Tables and figures giving total energies, thermochemical and dispersion corrections, additional information from NBO and NRT analyses, results from the
bS
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multivariate data analysis, and Cartesian coordinates of the optimized structures. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT The Norwegian Research Council is acknowledged for financial support through the KOSK program (Grant No. 177322/V30) as well as for CPU resources granted through the NOTUR supercomputing program. The University of Bergen is acknowledged for financial support through the Nanoscience program and the Meltzer Foundation. ’ REFERENCES (1) (a) Herrmann, W. A. Angew. Chem., Int. Ed. 2002, 41, 1290. (b) Schrock, R. R. Dalton Trans. 2001, 2541. (c) Cundari, T. R. Chem. Rev. 2000, 100, 807. (d) de Fremont, P.; Marion, N.; Nolan, S. P. Coord. Chem. Rev. 2009, 253, 862. (e) Trnka, T. M.; Grubbs, R. H. Acc. Chem. Res. 2001, 34, 18. (f) Frenking, G.; Sola, M.; Vyboishchikov, S. F. J. Organomet. Chem. 2005, 690, 6178. (2) The Cambridge Structural Database (CSD) of the Cambridge Crystallographic Data Centre (CCDC), version 5.32, updated Nov 2010. (3) Crabtree, R. H. The Organometallic Chemistry of the Transition Metals; Wiley: New York, 2005. (4) Fischer, E. O.; Maasb€ol, A. Angew. Chem., Int. Ed. 1964, 3, 580. (5) Schrock, R. R. J. Am. Chem. Soc. 1974, 96, 6796. (6) Taylor, T. E.; Hall, M. B. J. Am. Chem. Soc. 1984, 106, 1576. (7) Schrock, R. R.; Hoveyda, A. H. Angew. Chem., Int. Ed. 2003, 42, 4592. (8) (a) Hoveyda, A. H.; Zhugralin, A. R. Nature 2007, 450, 243. (b) Ulman, M.; Grubbs, R. H. Organometallics 1998, 17, 2484. (c) Volland, M. A. O.; Hansen, S. M.; Rominger, F.; Hofmann, P. Organometallics 2004, 23, 800. (9) Occhipinti, G.; Bjørsvik, H.-R.; Jensen, V. R. J. Am. Chem. Soc. 2006, 128, 6952. (10) Coalter, J. N.; Bollinger, J. C.; Huffman, J. C.; Werner-Zwanziger, U.; Caulton, K. G.; Davidson, E. R.; Gerard, H.; Clot, E.; Eisenstein, O. New J. Chem. 2000, 24, 9. (11) Vyboishchikov, S. F.; Frenking, G. Chem. Eur. J. 1998, 4, 1428. (12) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (13) Zhao, Y.; Truhlar, D. G. Acc. Chem. Res. 2008, 41, 157. (14) Whereas the B3LYP functional overestimates the tripletsinglet energy gap in the CH2 and CF2 carbene fragments by 1.9 and 6.9 kcal/ mol, respectively, M06 underestimates these relative energies by 0.5 and 1.5 kcal/mol, respectively. A description of the basis sets is given in Computational Details. (15) Glendening, E. D.; Weinhold, F. J. Comput. Chem. 1998, 19, 593. (16) (a) Foster, J. P.; Weinhold, F. J. Am. Chem. Soc. 1980, 102, 7211. (b) Reed, A. E.; Weinstock, R. B.; Weinhold, F. J. Chem. Phys. 1985, 83, 735. (17) Sparta, M.; Børve, K. J.; Jensen, V. R. J. Phys. Chem. A 2006, 110, 11711. (18) The geometry of each complex was orientated in such a way to have the TM located in the origin, the TMdC bond along the z axis, and the carbene plane in the xz plane. (19) Tsipis, A. C.; Orpen, A. G.; Harvey, J. N. Dalton Trans. 2005, 2849. (20) (a) The Wiberg bond index20b for the TMdC bonds (see the Supporting Information) follows a trend very similar to that of the two covalent bond orders given in Table 2 (correlation coefficient R2 > 0.95). (b) Wiberg, K. B. Tetrahedron 1968, 24, 1083. 3528
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