Computational Study of Cycloaddition Reactions of 16-Electron d8

ARTICLE pubs.acs.org/JPCA

Computational Study of Cycloaddition Reactions of 16-Electron d8 ML4 Complexes with C60 Jeng-Horng Sheu and Ming-Der Su* Department of Applied Chemistry, National Chiayi University, Chiayi 60004, Taiwan

bS Supporting Information ABSTRACT: The potential energy surfaces of the cycloaddition reactions M(CO)4 þ C60 f (CO)4M(C60) (M = Fe, Ru, and Os) have been studied at the B3LYP/LANL2DZ level of theory. It has been found that these reactions have two competing pathways, which can be classified as a [6,5]-attack (path A) and a [6,6]-attack (path B). Our B3LYP results suggest that, given the same reaction conditions, the [6,6]-attack is more favorable than the [6,5]-attack both kinetically and thermodynamically. A qualitative model based on the theory of Pross and Shaik has been used to develop an explanation for the barrier heights. As a consequence, the theoretical findings indicate that the singlettriplet splitting ΔEst (=Etriplet Esinglet) of the 16-electron d8 M(CO)4 and C60 species can be used as a guide to predict their reactivity toward cycloaddition. Our computational results reveal that the reactivity of d8 M(CO)4 cycloaddition to C60 decreases in the order Fe(CO)4 > Os(CO)4 > Ru(CO)4. Accordingly, we demonstrate that both electronic and geometric effects play a crucial role in determining the energy barriers as well as the reaction enthalpy.

I. INTRODUCTION Since the initial discovery1 and subsequent development of the large scale synthesis2 of buckminsterfullerene (C60), its organometallic chemistry has attracted considerable experimental and theoretical attention, especially the effect of metal coordination on the properties and reactivities of C60.3 The reason for this is that transition-metal complexes of C60 are expected to be new materials with intriguing properties.4 Many organometallic complexes of buckminsterfullerene (C60) have been synthesized and structurally characterized in the last fifteen years.5,6 Actually, synthesis, characterization, and properties of various organometallic ηnC60 (n = 16) complexes have been studied by many different groups.7 Green and co-workers were the first to provide spectroscopic evidence for the new organometallic C60 derivative of iron, namely, [Fe(CO)4(η2-C60)].8 They found that this compound is soluble in toluene, benzene, CS2, and CH2Cl2. The spectroscopic analysis indicates four bands in the carbonyl stretching region. That is, these data are completely consistent with a molecule possessing C2v symmetry, with C60 occupying an equatorial position at the iron center and with the carbonyl groups undergoing rapid exchange on the NMR time scale between axial and equatorial positions. Nevertheless, to the best of our knowledge, no other experimental data for such a reaction has been reported in the literature. No theoretical study of the cycloaddition of ML4 complexes to C60 has appeared to date, let alone a systematic theoretical study of geometrical effects on the reactivities of such ML4 species. It is these unsolved problems that provoke our interest to investigate the cycloaddition reactions in the present study. What is the mechanism for the cycloaddition of the ML4 species to C60? That is to say, what are the energies and structures of the r 2011 American Chemical Society

transition states of the reactions? In addition, if a ML4 complex containing an iron (Fe) metal center can undergo a CC bond addition with C60 resulting in a ML4 complex of a C60, would it be possible to extend this to other 16-electron d8 ML4 type complexes? If this is possible, which transition metal center containing four carbonyl ligands has the lowest activation energy and therefore can undergo the cycloaddition reaction with C60 fastest? As mentioned previously, neither experimental nor theoretical studies have been performed on these systems so far. In particular, the interest in the experimental investigation of these compounds has recently increased due to their interesting behavior in synthetic reactions and the following potential applications as well as their abilities to form effective catalysts for hydroformylation of some organic molecules.9 These questions aroused our interest to investigate the potential energy surfaces of such reactions using the density functional theory (DFT). A study of the important cycloaddition reaction, eq 1, was thus undertaken. ML4 þ C60 f precursor complex f transition state f cycloadduct

ð1Þ

For the present, we are focusing on CC cycloaddition by 16electron complexes of the form M(CO)4, where M = Fe, Ru, and Os. It was hoped in the first place that such a study would help (i) to clarify the reaction mechanism and to determine the structures and energetics of the intermediate complexes and transition states, (ii) to investigate the thermodynamics of the 16-electron Received: January 12, 2011 Revised: April 29, 2011 Published: June 14, 2011 7664

dx.doi.org/10.1021/jp200343p | J. Phys. Chem. A 2011, 115, 7664–7672

The Journal of Physical Chemistry A Scheme 1

d8 ML4 cycloaddition reactions with C60 molecule, (iii) to estimate the activation barriers and to understand the origin of the barrier heights, (iv) to establish general trends and predictions for the cycloaddition of ML4 with CC bonds, and (v) to bring out the factors that control the activation barrier for such cycloaddition reactions. As the first comprehensive examination of these systems, this paper should provide a firm basis for further study, both experimental and computational.

II. COMPUTATIONAL DETAILS All geometries were fully optimized without imposing any symmetry constraints, although in some instances the resulting structure showed various elements of symmetry. DFT was employed with the three-parameter hybrid exchange functional of Becke10 and the Lee, Yang, and Parr correlation functional.11 This functional is commonly known as B3LYP. Computations were carried out using relativistic effective core potentials on the group 6 elements modeled using the double-ζ (DZ) basis sets.11 Thus, the model compounds M(CO)4 3 C60 have 634 (432 electrons) basis functions for M = Fe, Ru, and Os. Moreover, the restricted B3LYP approach was used in this work to describe all the stationary points, except for the triplet states of the reactants, which were described by unrestricted wave functions. Hence, all the B3LYP calculations are denoted by B3LYP/ LANL2DZ. Vibrational frequency calculations at the RHF/ LANL2DZ level were used to characterize all the stationary points as either minima (no imaginary frequencies) or transition states (one imaginary frequency). Subsequently, these stationary points were further calculated at the B3LYP/LANL2DZ level using the opt=readfc keyword. Due to the limitation of both CPU time and memory size, the B3LYP zero-point energy (ZPE) could not be applied to all of the M(CO)4 3 C60 systems in the present work. That is, because frequencies were not calculated for all the species at the B3LYP/LANL2DZ level of theory, ZPE corrections were not performed. Nevertheless, the addition of these corrections would not change our conclusions. All the calculations were performed with the GAUSSIAN 03 package of programs.12 III. ELECTRONIC STRUCTURE OF 16-ELECTRON D8 ML4 SYSTEMS In this section, we shall first briefly review the electronic structures of the coordinatively unsaturated electronic d8 ML4 reactant. The frontier orbitals of this fragment are known13 and are shown in Scheme 1. A block of three low lying occupied levels, a2 (xy), b1 (yz), 1a1 (z2) are primarily made up of metal d orbitals. In the

ARTICLE

somewhat higher occupied level (b2), a metal dxz orbital is hybridized with a metal px orbital in such a way that the orbital lobes point toward the missing ligands of a parent ML6 (octahedral) molecule. As a consequence, the highest occupied molecular orbital (HOMO) is b2. The lowest unoccupied molecular orbital (LUMO) is 2a1, a hybrid of metal s and pz orbitals. Those fragment orbitals in Scheme 1 are appropriate for any ligand set of σ donors. Nevertheless, π effects can be introduced to influence the ordering of the energy levels for the d8 ML4 fragment, thus allowing various configurations to occur (vide infra). As discussed previously,14 because 16-electron ML4 and CH2 are isolobal, then each should have two valence orbitals with the same symmetry properties. These are shown in 1, in which each fragment has one orbital of a0 and a00 symmetry. That is, it is the two frontier orbitals, b2 (a00 ) and 2a1 (a0 ), that allow one to view the 16 electron ML4 as an organometallic analogue of CH2.

Note that the ordering of energy levels in the metal fragment differs from that in the carbene. This is a natural consequence of the fact that in ML4 the major contribution to the a00 orbital is of metal d character, while the a0 orbital is a hybrid of metal s, p, and d characters. Therefore, for a singlet CH2 fragment, one would assign the two electrons to the a0 orbital, while for a singlet 16electron ML4 species, the two electrons are in an a00 level. In other words, the frontier orbitals of the 16-electron ML4 complex consist of an empty s/p/d hybrid orbital and a d orbital that contains a single lone pair of electrons. We shall use this concept to explain the origin of the cycloaddition barrier in a later section.

IV. GEOMETRIES AND ENERGETICS OF 16-ELECTRON D8 ML4 þ C60 The results computed for four regions on the potential energy surfaces are presented: 16-electron d8 M(CO)4 (M = Fe, Ru, and Os) plus free C60 (Rea), the precursor complex (PC), the transition state (TS), and the cycloaddition product (Pro). The fully optimized geometries for those stationary points computed at the B3LYP/LANL2DZ level of theory are shown in Figures 14, respectively. All the given energies in Table 1 are relative to the two reactant molecules, i.e., ML4 þ C60, to simplify the comparisons and to emphasize the trends. Cartesian coordinates calculated for the stationary points at the B3LYP level are available as Supporting Information. 1. Reactants (16-Electron d8 ML4 þ C60). In this study, reactants M(CO)4 (M = Fe, Ru, and Os) have been calculated both as low-spin (singlet) and as high-spin (triplet) species. It turns out that both singlet and triplet reactants M(CO)4 adopt a bent, rather than a square planar conformation, as shown in Figure 1. To the best of our knowledge, although only one experimental investigation on Fe(CO)4 has been carried out during the recent years,14 there are several theoretical calculations so far available in the literature for these M(CO)4 species.15 7665

dx.doi.org/10.1021/jp200343p |J. Phys. Chem. A 2011, 115, 7664–7672

The Journal of Physical Chemistry A

Figure 1. B3LYP/LANL2DZ optimized geometries (Å and deg) of the reactants (singlet and triplet) of Fe(CO)4, Ru(CO)4, and Os(CO)4. The experimental values in round bracket are taken from ref 14. The calculated values in square bracket are taken from ref 15a.

As one can see in Figure 1, the computed structures of the singlet Fe(CO)4 compound are in reasonable agreement with the available experimental data (in parentheses).15 On the other hand, for Ru(CO)4 our B3LYP calculations predict that the Ru(CO)ax and Ru(CO)eq bond lengths in the singlet state are averagely estimated to be 1.95 and 1.94 Å, which are in agreement with available computed values (1.93 and 1.91 Å), respectively.16a Further, it is apparent from Scheme 1 that in the triplet state, one electron is situated in the 2a1 orbital, in which antibonding interactions exist between the metal and its ligands, while this orbital is empty in the singlet state. The bond length r(MLax) between the metal atom and the two axial L ligands is thus expected to be greater for the triplet state compared to that of the singlet state. This prediction is in qualitative agreement with our B3LYP/LANL2DZ results for all cases, as represented in Figure 1. For example, our DFT results demonstrate that the axial bond lengths r(MLax) are 1.813, 1.954, and 1.936 Å for singlet Fe(CO)4, Ru(CO)4, and Os(CO)4, respectively, but 1.865, 1.985, and 1.957 Å for triplet Fe(CO)4, Ru(CO)4, and Os(CO)4, respectively. On the other hand, our computational results indicate that the equatorial bond length r(MLeq) is greater for singlet than triplet ML4, except in the case of Fe(CO)4. For instance, the equatorial bond lengths r(MLeq) were calculated to be 1.787, 1.941, and 1.936 Å for singlet Fe(CO)4, Ru(CO)4, and Os(CO)4, respectively, but 1.850, 1.937, and 1.911 Å for triplet Fe(CO)4, Ru(CO)4, and Os(CO)4, respectively. As a consequence, our theoretical computations indicate that the axial bond length r(MLax) is always greater than the corresponding equatorial bond length r(MLeq), independent

ARTICLE

of the spin multiplicity adopted by the ML4 complex. This finding agrees well with predictions based on the frontier orbital theory as already shown in Scheme 1. Nevertheless, the B3LYP results indicate that both the axial and the equatorial bond angles, — Lax MLax and — Leq MLeq, are larger for singlet than for triplet ML4, except in the case of Os(CO)4. For example, our computational results estimate that the axial and equatorial bond angles for singlet M(CO)4 (M = Fe, Ru, and Os) are (158.1, 133.3), (160.4, 146.8), and (148.5, 148.0) respectively. Also, our DFT computations predict that the same bond angles for triplet Fe(CO)4, Ru(CO)4, and Os(CO)4 are (146.8, 98.56), (155.2, 98.31), and (152.8, 98.90), respectively. In spite of this we think that the main conclusions of this paper should not be altered in a significant way because the error due to the approximations made should be of a similar magnitude to the differences between the compounds studied in the present work. Additionally, the DFT results indicate that triplet Fe(CO)4 is 7.4 kcal/mol more stable than singlet Fe(CO)4. On the other hand, singlet Ru(CO)4 and Os(CO)4 are 18 and 16 kcal/mol lower in energy than triplet Ru(CO)4 and Os(CO)4, respectively. Accordingly, the B3LYP calculations suggest that the Fe(CO)4 reactant should adopt a triplet ground state. This implies that this complex might add to the unsaturated CC bond of C60 via a diradical-type mechanism. Nevertheless, it is well established that whenever a reactant contains a heavy atom center, which is not necessarily directly involved in the reaction, a strong spinorbit coupling (SOC) may occur.17 That is to say, a triplet reactant, via the agency of the heavy atom, can undergo a spin-inversion process, transforming to the singlet reactant, and then proceeding along the singlet reaction pathway. In addition, our DFT results shown above suggested that triplet Fe(CO)4 would have a small excitation energy to the first singlet state, i.e., ΔEst = 7.4 kcal/mol. Thus, due to the fact that Fe(CO)4 has a small singlettriplet splitting ΔEst and a heavy transition metal center involved, the SOC is expected to be substantial in the cycloaddition reactions with C60 and would wash out differentials based on singlet, triplet distinctions. For these reasons, it could well be that the cycloaddition reactions proceed on the singlet surface, even if the reactants start from the triplet state. Consequently, only the singlet surface was considered throughout this work.18,19 On the other hand, as discussed previously,5f,20 though every carbon atom in C60 is chemically equivalent, two different types of CC bonds within C60 can be found. One type occurs at sixfive ring fusion sites (i.e., a [6,5] bond), whereas the other occurs at sixsix ring fusion sites (i.e., a [6,6] bond). There are no fivefive ring fusion sites. As a consequence, two crystalline derivatives of C60 can be obtained by addition of organometallic fragments to the C60 (vide infra). Also, the free buckminsterfullerene molecule was optimized under Ih symmetry constraints. Our computed CC bond values are 1.464 and 1.404 Å for the [6,5] and [6,6] bonds, respectively. These values are similar to the experimental values of 1.458 and 1.401 Å from electron diffraction20a and of 1.455 and 1.391 Å from neutron powder diffraction.20b Again, due to the good agreement between B3LYP and the available experimental data on known buckminsterfullerene features, we are encouraged that the results presented in this paper should be reliable. 2. Precursor Complexes. As shown in Figures 24, all the precursor complexes (PC-Fe, PC-Ru, and PC-Os) display very similar M(CO)4---C60 bonding characteristics. Namely, the buckminsterfullerene ligand is coordinated to the transition 7666



ARTICLE

Figure 2. B3LYP/LANL2DZ optimized geometries (Å and deg) of the precursor complex, transition states, and products of Fe(CO)4 case. The heavy arrows indicate the main atomic motions in the transition state eigenvector.

metal (M) in a η2 fashion via two MC σ bonds. That is, the positions of metals (Fe, Ru, and Os) are all on the CC bond between two 6,6-rings. In addition, the MC distances to C60 in the precursor complexes PC-Fe, PC-Ru, and PC-Os are 3.690, 3.707, 3.684 Å, respectively. The M(CO)4---C60 bond distances are exceptionally long, indicating little, if any, energy stabilization by reactant complexation. In other words, the longer MC distances correlate with a smaller value for the intermediate stabilization energy. The simplest explanation of such long bond distances is that it is a steric effect. It seems unlikely that the species exist in gas-phase M(CO)4/C60 mixtures at room temperature, because the stabilization energies of PC-Fe, PCRu, and PC-Os are 11, 5.5, and 6.4 kcal/mol at the B3LYP/ LANL2DZ level of theory, respectively, which are too low. Indeed, to our knowledge, no experimental detection of M(CO)4---C60 complexes formed during the reaction has been reported.21 3. Transition States. The TS geometries for the additions of d8 M(CO)4 (M = Fe, Ru, and Os) to buckminsterfullerene are

given in Figures 24, respectively. As mentioned earlier, because C60 has two different types of chemical bonds, the approaching M(CO)4 may attack either of these two kinds of bonds. That is, it rearranges further either into a [6,5] cycloadduct via a [6,5] attack (i.e., path (A)) or into a [6,6] cycloproduct via a [6,6] attack (i.e., path (B)). It has to be noted that, as mentioned previously, the 16-electron ML4 and carbene is isolobal. This means that the two fragments should have similar valence orbitals with the same symmetry properties. Therefore, the interactions between valence orbitals of ML4 and C60 should be quite similar to those between valence orbitals of carbene and ethylene. Interested readers can find excellent reviews in ref.22 For reaction path A, we have located the transition state ([6,5]-TS-Fe, [6,5]-TS-Ru, and [6,5]-TS-Os) for each M(CO)4 species at the B3LYP/LANL2DZ level of theory, along with the imaginary frequency eigenvector (see Figures 24). These transition states at the RHF/LANL2DZ level of theory are confirmed by calculation of the energy Hessian, which shows only one imaginary vibrational frequency: 368i cm1 ([6,5]-TS-Fe), 7667



ARTICLE

Figure 3. B3LYP/LANL2DZ optimized geometries (Å and deg) of the precursor complex, transition states, and products of Ru(CO)4 case. The heavy arrows indicate the main atomic motions in the transition state eigenvector.

237i cm1 ([6,5]-TS-Ru), and 402i cm1 ([6,5]-TS-Os). Decomposition of the imaginary mode into internal coordinate displacements shows the major component to be a MC bond vibration, as one would expect for a true cycloaddition TS (see Figures 24). Apparently, the transition states connect the corresponding precursor complexes to the cycloaddition products. It should be mentioned that the primary similarity among the transition states is a three-center pattern involving the group 8 transition metal and two connected carbon atoms of the buckminsterfullerene. For reaction path B, the TS geometries for the [6,6] attack are depicted in Figures 24, respectively. All these TSs possess one imaginary frequency and are true first-order saddle points. Our RHF/LANL2DZ frequency calculations indicate that the single imaginary frequency values are 121i, 351i, and 318i cm1 for [6,6]-TS-Fe, [6,6]-TS-Ru, and [6,6]-TS-Os, respectively. Again, as already shown in Figures 24, the major component of the [6,6]-TS vibrational mode is located at the transition metal and two connected carbon atoms.

According to our computational results, one can readily see that, of the two possible routes for buckminsterfullerene cycloaddition reactions with M(CO)4, the most promising one is path (B) ([6,6] attack), which has a lower activation energy than path (A) ([6,5] attack). For example, at the B3LYP level of theory, comparing the barrier heights between path (A) and path (B), the energetic trend decreases in the order [6,5]-TS-Fe (4.7 kcal/mol) > [6,6]TS-Fe (1.7 kcal/mol), [6,5]-TS-Ru (16 kcal/mol) > [6,6]-TS-Ru (3.3 kcal/mol), and [6,5]-TS-Os (12 kcal/mol) > [6,6]-TS-Os (2.1 kcal/mol). As a consequence, our model calculations strongly suggest that the cycloaddition of M(CO)4 to C60 should produce the major [6,6] cycloadduct via [6,6] attack, with a minority of [6,5] cycloproduct via [6,5] attack. Considering now the nature of the metal center, it is apparent from Figures 24 and Table 1 that the calculated activation energy for cycloaddition is substantially lower for Fe than for Ru and Os. For example, at the DFT level of theory, the barrier height for M(CO)4 addition decreases in the order (kcal/mol) [6,5]-TS-Ru (16) > [6,5]-TS-Os (12) > [6,5]-TS-Fe (4.7) and 7668



ARTICLE

Figure 4. B3LYP/LANL2DZ optimized geometries (Å and deg) of the precursor complex, transition states, and products of Os(CO)4 case. The heavy arrows indicate the main atomic motions in the transition state eigenvector.

[6,6]-TS-Ru (3.3) > [6,6]-TS-Os (2.1) > [6,6]-TS-Fe (1.7). Consequently, our theoretical calculations strongly indicate that the Fe reaction is the most favorable. On the other hand, we also note that at the [6,5]-TSs in Figures 24 the forming MC bond is stretched by an average of 2.1%, 2.9%, and 12% for [6,5]-TS-Fe, [6,5]-TS-Ru, and [6,5]TS-Os, respectively, relative to its corresponding threemembered ring cycloadduct. Likewise, the forming MC bond is stretched by an average 28%, 25%, and 27% relative to its equilibrium value as the M(CO)4 changes for [6,6]-TS-Fe, [6,6]-TS-Ru, and [6,6]TS-Os, respectively. That is, the barrier is encountered earlier in the reactions with Fe(CO)4 than for the reaction with Ru(CO)4 and Os(CO)4. In addition, these values also suggest that the [6,6]-TS transition state structures are of a more reactant-like character, whereas those for [6,5]-TS are of a more product-like character. Taken together, a M(CO)4 complex with a less massive central metal atom reaches the TS relatively early, whereas a M(CO)4 with a more massive central metal element arrives relatively late.

The former is therefore predicted to undergo a more exothermic addition, which is borne out by our B3LYP calculations (see below).23 Furthermore, as one can see in Table 1 and Figures 24, transition states for both path (A) (i.e., [6,5] attack) and path (B) (i.e., [6,6] attack) lie lower in energy than the corresponding reactants only in the iron case. In fact, as stated earlier, the activation energies for the [6,6] attack are quite small (less than 4.0 kcal/mol). This strongly implies that d8 M(CO)4 will undergo cycloaddition to C60 in a concerted manner, particularly in the case of Fe(CO)4. Consequently, the stereochemistry of the final three-membered ring cycloproduct should be preserved on the basis of the present theoretical study. 4. Cycloadducts. The optimized product structures ([6,5]Pro-Fe, [6,5]-Pro-Ru, [6,5]-Pro-Os, [6,6]-Pro-Fe, [6,6]-Pro-Ru, and [6,6]-Pro-Os) are summarized in Figures 24. To simplify comparisons and to emphasize the trends, the calculated reaction enthalpies for cycloaddition are collected in Table 1. 7669



ARTICLE

Table 1. Relative Energies for Singlet and Triplet 16-Electron d8 ML4 Fragments with C60 and for the Process ML4 þ C60 f Precursor Complex f Transition State f Cycloadduct.a ΔEst

b

ΔEcpx

c

(kcal/mol)

ΔETS

d

(kcal/mol)

ΔH

e

systems

(kcal/mol)

(kcal/mol)

[6,5]-attack

7.37

10.9

6.19

[6,6]-attack

7.37

10.9

9.12

22.4

þ10.6 2.14

2.71 13.5

Fe(CO)4 9.34

Ru(CO)4 [6,5]-attack [6,6]-attack

þ17.5 þ17.5

5.46 5.46

[6,5]-attack

þ16.3

6.38

þ5.38

[6,6]-attack

þ16.3

6.38

4.27

Os(CO)4 5.30 22.0

a

At the B3LYP/LANL2DZ level. See the text. b Energy relative to the corresponding singlet state. A negative value means the triplet is the ground state. c The stabilization energy of the precursor complex, relative to the corresponding reactants. d The activation energy of the transition state, relative to the corresponding reactants. e The reaction enthalpy of the product, relative to the corresponding reactants.

From Table 1 and Figures 24, it is readily seen that the order of reaction enthalpy for the cycloaddition of C60 to d8 M(CO)4 follows the same trend as the activation energy. For instance, the enthalpy for path A (i.e., [6,5] attack) increases in the order [6,5]-Pro-Fe (9.3 kcal/mol) < [6,5]-Pro-Os (5.3 kcal/mol) < [6,5]-Pro-Ru (2.7 kcal/mol). Likewise, for path B (i.e., [6,6] attack) the reaction enthalpy increases in the order [6,6]-Pro-Fe (22 kcal/mol) < [6,6]-Pro-Os (22 kcal/mol) < [6,6]-Pro-Ru (14 kcal/mol). Accordingly, our computational results indicate that the [6,6] attack should be more exothermic than the [6,5] attack. Moreover, from both a kinetic and a thermodynamic viewpoint, it is obvious that the reactivity toward C60 cycloaddition decreases in the order Fe(CO)4 > Os(CO)4 > Ru(CO)4. That is to say, a d8 M(CO)4 with a less massive central metal atom will react faster with C60 than a d8 M(CO)4 with a more massive central metal element. As there are no relevant experimental and theoretical data on such systems, the above conclusion is a prediction.24

V. CONFIGURATION MIXING MODEL In this section, an interesting model for interpreting the relative reactivity of the reactants is provided by the configuration mixing (CM) model, which is based on the work of Pross and Shaik.25,26 According to the conclusions of this model, the energy barriers governing processes as well as the reaction enthalpies should be proportional to the energy gaps in the reactants, that is, ΔEst (=Etriplet Esinglet for ML4) þ ΔEππ* (=Etriplet Esinglet for C60). Accordingly, if a reactant ML4 has a singlet ground state with a small excitation energy to the triplet state, this will allow more opportunity for the participation of the triplet state in the singlet reaction. Such systems can readily undergo single-step bond additions. We thus conclude that both the order of the singlet and triplet states and their energy separation are responsible for the existence and the height of the energy barrier.25,26 Bearing these analyses in mind, we shall now explain the origin of the following observed trends:

1. Why Is the Fe Reaction More Favorable than the Ru and Os Reaction in the Cycloaddition of C60 to d8 M(CO)4? The

driving force for this can be traced to the singlettriplet energy gap (ΔEst) of the 16-electron d8 M(CO4) complex. As already discussed in the previous section, 16-electron M(CO)4 is isolobal to the carbene (CH2) species. As a result, its reaction pattern should be analogous. As seen in Table 1, our B3LYP/LANL2DZ results indicate that the singlettriplet energy splitting ΔEst increases in the order Fe(CO4) (7.4 kcal/mol) < Os(CO4) (þ16 kcal/mol) < Ru(CO4) (þ18 kcal/mol). This implies that the cycloaddition of C60 to a d8 M(CO4) is easier and more exothermic for the Fe system than for either its Ru or Os counterpart. Indeed, this is what we observed in the present work. Our theoretical findings are therefore in good accordance with the CM model. 2. Given Identical Reaction Conditions, Why Is the Cycloaddition Reaction of C60 for the [6,6]-Attack More Favorable than That for the [6,5]-Attack Both Kinetically and Thermodynamically? The reason for this can be traced back to the singlettriplet energy splitting (ΔEst) of C60.27,28 According to the CM model discussed above, we know that a smaller ΔEst for the fused two-ring system results in a lower barrier height and a larger exothermicity. Because the buckminsterfullerene species is too large and complicated for calculations, one may reduce it to a smaller size for theoretical study. We therefore chose the C10H8 (naphthalene) and C9H71 to mimic the fusion of two six-membered rings (i.e., [6,6]) and the junction of sixand five-membered rings (i.e., [6,5]), respectively. Our B3LYP/ LANL2DZ results demonstrate that the singlettriplet energy splitting ΔEst is 59 and 55 kcal/mol for the C10H8 and C9H71 species, respectively. This correlates well with the trend in both barrier heights and reaction enthalpies for both [6,6] and [6,5] attacks, as demonstrated in the previous section.

VI. CONCLUSION This work represents an attempt to apply the CM model to understand the origin of barriers for the activation of C60 by 16-electron d8 M(CO)4. As already mentioned in section III, 16-electron ML4 (M = Fe, Ru, and Os) and X(CH3)2 (X = C, Si, Ge, Sn, and Pb) are isolobal. This means that each has two valence orbitals with the same symmetry properties. As a result, the topology of their reaction patterns should be quite similar. For instance, both calculations21 show that the 6,6-addition is preferred to the 6,5-addition. Also, it was found that the CM model can well rationalize the computational results and build up a model to explain the whole reaction pattern. That is, our work has shown that the singlettriplet splitting ΔEst (=Etriplet Esinglet) based on the CM model can provide a useful basis for understanding and rationalizing the relative magnitude of the activation barriers for the cycloaddition reactions of C60. From the analysis in the present study, we are confident in predicting that for the 16-electron ML4 systems, a lighter transition metal center (i.e., the first-row) will lead to a smaller ΔEst and will facilitate the cycloaddition reactions to double bonds of C60. Despite the fact that the estimated magnitude of the barrier and the predicted geometry of the transition state for such reactions appears to be dependent on the calculational level applied, our qualitative predictions are in accordance with the results presented here and with the available experimental observations. In spite of its simplicity, our approach can provide chemists with important insights into the factors controlling the activation of unsaturated 7670


The Journal of Physical Chemistry A CC bonds and thus permits them to predict the reactivity of, as yet unknown, reactive ML4 intermediates. It is hoped that the present work will stimulate further research into this subject.

’ ASSOCIATED CONTENT

bS

Supporting Information. B3LYP/LANL2DZ optimized geometries. This material is available free of charge via the Internet athttp://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT We are grateful to the National Center for High-Performance Computing of Taiwan for generous amounts of computing time. We also thank the National Science Council of Taiwan for the financial support. We thank Mr. Jun Hsiao for useful discussions. Special thanks are also due to reviewers 1 and 2 for very helpful suggestions and comments. ’ REFERENCES (1) Kroto, H. W.; Heath, J. R.; O’Brien, S. C.; Curl, R. F.; Smalley, R. E. Nature 1985, 318, 354. (2) Kr€atschmer, W.; Lamb, L. D.; Fostiropoulos, K.; Huffman, D. R. Nature 1990, 347, 354. Kr€atschmer, W.; Lamb, L. D.; Fostiropoulos, K.; Huffman, D. R. Chem. Phys. Lett. 1990, 170, 167. (3) For recent reviews, see: (a) Hawkins, J. M. Acc. Chem. Res. 1992, 25, 150. (b) Fagan, P. J.; Calabrese, J. C.; Malone, B. Acc. Chem. Res. 1992, 25, 134. (c) Balch, A.; Olmstead, M. M. Chem. Rev. 1998, 98, 2123. (d) Kee, K.; Song, H.; Park, J. T. Acc. Chem. Res. 2003, 36, 78. (e) Fagan, P. J.; Calabrese, J. C.; Malone, B. Acc. Chem. Res. 1992, 25, 134. (f) Hirsch, A. The Chemistry of the Fullerenes; Thieme: Stuttgart, 1994. (4) For instance, see: Matsuo, Y.; Nakamura, E. Organometallics 2003, 22, 2554 and references therein. (5) (a) Hawkins, J. M.; Meyer, A.; Lewis, T. A.; Loren, S.; Hollander, F. J. Science 1991, 252, 312. (b) Fagan, P. J.; Calabrese, J. C.; Malone, B. Science 1991, 252, 1160. (c) Balch, A. L.; Catalano, V. J.; Lee, J. W. Inorg. Chem. 1991, 30, 3980. (d) Fagan, P. J.; Calabrese, J. C.; Malone, B. J. Am. Chem. Soc. 1991, 113, 9408. (e) Balch, A. L.; Catalano, V. J.; Lee, J. W.; Olmstead, M. M. J. Am. Chem. Soc. 1992, 114, 5455. (f) Balch, A. L.; Lee, J. W.; Noll, B. C.; Olmstead, M. M. J. Am. Chem. Soc. 1992, 114, 10984. (g) Bashilov, V. V.; Petrovskii, P. V.; Sokolov, V. I.; Lindeman, S. V.; Guzey, I. A.; Struchkov, Y. T. Organometallics 1993, 12, 991. (h) Balch, A. L.; Lee, J. W.; Noll, B. C.; Olmstead, M. M. Inorg. Chem. 1993, 32, 3577. (i) Mavunkal, I. P.; Chi, Y.; Peng, S.-M.; Lee, G.-H. Organometallics 1995, 14, 4454. (j) Lee, K.; Hsu, H.-F.; Shapley, J. R. Organometallics 1997, 16, 3876. (k) Sawamura, M.; Kuninonu, Y.; Nakamura, E. J. Am. Chem. Soc. 2000, 122, 12407. (l) Park, J. T.; Song, H.; Lee, K.; Lee, C. H. Angew. Chem., Int. Ed. 2001, 40, 1500. (m) Sawamura, M.; Kuninonu, Y.; Taganoh, M.; Matsuo, Y.; Yamanaka, M.; Nakamura, E. J. Am. Chem. Soc. 2002, 124, 9354. (n) Matsuo, Y.; Mitani, Y.; Zhong, Y.-W.; Nakamura, E. Organometallics 2006, 25, 2826. (6) (a) Stephens, A. H. H.; Green, M. L. H. Adv. Inorg. Chem. 1997, 44, 1. (b) Green, M. L. H.; Stephens, A. H. H. J. Chem. Soc., Chem. Commun. 1997, 793. (c) Chernega, A. N.; Green, M. L. H.; Haggit, J.; Stephens, A. H. H. J. Chem. Soc., Dalton. Trans. 1998, 755. (7) For instance, see: (a) Hawkins, J. M.; Lewis, T. A.; Loren, S. D.; Meyer, A.; Heath, J. R.; Shibato, Y.; Saykally, R. J. J. Org. Chem. 1990, 55, 6250. (b) Koefod, R. S.; Hudgens, M. F.; Shapley, J. R. J. Am. Chem. Soc. 1991, 113, 8957. (c) Schreiner, S.; Gallaher, T. N.; Parsons, H. K.

ARTICLE

Inorg. Chem. 1994, 33, 3021. (d) Park, J. T.; Cho, J.-J.; Song, H. J. Chem. Soc., Chem. Commun. 1995, 15. (e) Sawamura, M.; Iikura, H.; Nakamura, E. J. Am. Chem. Soc. 1996, 118, 12850. (f) Sawamura, M.; Iikura, H.; Hirai, A.; Nakamura, E. J. Am. Chem. Soc. 1998, 120, 8285. (g) Sawamura, M.; Iikura, H.; Hirai, A.; Nakamura, E. J. Am. Chem. Soc. 1998, 120, 8285. (h) Park, J. T.; Song, H.; Cho, J.-J.; Chung, M.-K.; Lee, J.-H.; Suh, I.-H. Organometallics 1998, 17, 227. (i) Sawamura, M.; Toganoh, M.; Kuninobu, Y.; Kato, S.; Nakamura, E. Chem. Lett. 2000, 29, 270. (j) Sawamura, M.; Iikura, H.; Ohama, T.; Hackler, U. E.; Nakamura, E. J. Organomet. Chem. 2000, 599, 32. (k) Nakamura, E.; Sawamura, M. Pure Appl. Chem. 2001, 73, 355. (l) Sawamura, M.; Toganoh, M.; Kuninobu, Y.; Kato, S.; Nakamura, E. Chem. Lett. 2000, 270. (m) Sawamura, M.; Iikura, H.; Ohama, T.; Hackler, U. E.; Nakamura, E. J. Organomet. Chem. 2000, 599, 32. (n) Sawamura, M.; Toganoh, M.; Suzuki, K.; Hirai, A.; Iikura, H.; Nakamura, E. Org. Lett. 2000, 2, 1919. (o) Sawamura, M.; Kuninobu, Y.; Nakamura, E. J. Am. Chem. Soc. 2000, 122, 12407. (p) Zanello, P.; Laschi, F.; Cinquantini, A.; Fontani, M.; Tang, K.; Jin, X.; Li, L. Eur. J. Inorg. Chem. 2000, 1345. (q) Nakamura, E.; Sawamura, M. Pure Appl. Chem. 2001, 73, 355. (r) Sawamura, M.; Toganoh, M.; Iikura, H.; Matsuo, Y.; Hirai, A.; Nakamura, E. J. Mater. Chem. 2002, 12, 2109. (s) Lee, K.; Song, H.; Kim, B.; Park, J. T.; Park, S.; Choi, M.-G. J. Am. Chem. Soc. 2002, 124, 2872. (t) Sawamura, M.; Kuninobu, Y.; Toganoh, M.; Matsuo, Y.; Yamanaka, M.; Nakamura, E. J. Am. Chem. Soc. 2002, 124, 9354. (u) Toganoh, M.; Matsuo, Y.; Nakamura, E. J. Am. Chem. Soc. 2003, 125, 13974. (v) Lee, K.; Song, H.; Park, J. T. Acc. Chem. Res. 2003, 36, 78. (w) Kim, K. H.; Jung, J.; Han, Y.-K. Organometallics 2004, 23, 3865. (8) Douthwaite, R. E.; Green, M. L. H.; Stephens, A. H. H.; Turner, J. F. C. J. Chem. Soc., Chem. Commun. 1993, 1522. (9) For instance, see: (a) Jiao, Q.; Huang, Y.; Lee, S. A.; Gord, J. R.; Freiser, B. S. J. Am. Chem. Soc. 1992, 114, 2726. (b) Baronov, V.; Bohme, D. K. Int. J. Mass Spectrom. Ion Processes 1997, 165/166, 249. (c) Thompson, D. M.; Jones, M.; Baird, M. C. Eur. J. Inorg. Chem. 2003, 175. (d) Kamat, P. V.; Haria, M.; Hotchandani, S. J. Phys. Chem. B 2004, 108, 5166. (e) Zheng, L. A.; Barrera, E. V. J. Appl. Phys. 2005, 97, 094309. (f) Malic, N.; Nichols, P. J.; Makha, M.; Raston, C. L. Cryst. Growth Des. 2009, 9, 863. (10) (a) Becke, A. D. Phys. Rev. A 1988, 38, 3098. (b) Becke, A. D. J. Chem. Phys. 1993, 98, 1372. (c) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (11) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785. (12) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian03; Gaussian, Inc.: Wallingford, CT, 2003. (13) Albright, T. A.; Burdett, J K.; Whangbo, M. H. Orbital Interactions in Chemistry; Wiley: New York, 1985; pp 358 (see also references therein). (14) Hoffmann, R. Angew. Chem., Int. Ed. Engl. 1982, 21, 711. (15) (a) Ihee, H.; Cao, J.; Zewail, A. H. Angew. Chem. Intl. Ed. 2001, 113, 1580. (b) Poliakoff, M.; Turner, J. J. J. Chem. Soc., Dalton 1974, 2276. (16) (a) Ziegler, T.; Tschinke, V.; Fan, L.; Becke, A. D. J. Am. Chem. Soc. 1989, 111, 9177. (b) Gonzalez, O.; Branchadell, V. J. Chem. Phys. 1999, 110, 778. (c) Cirera, J.; Alemany, P.; Alvarez, S. Chem.—Eur. J. 2004, 10, 190. 7671



ARTICLE

(17) (a) McGlynn, S. P.; Azumi, T.; Kinoshita, M., The Triplet State; Prentice-Hall: New York, 1969: pp 190198. (b) El-Sayed, M. A. J. Chem. Phys. 1963, 36, 2834. (c) El-Sayed, M. A. Acc. Chem. Res. 1968, 1, 8. (18) Our computational results showed that, for instance, the ground state of Fe(CO)4 is the triplet state. Moreover, Fe(CO)4 can be generated from Fe(CO)5. As a result, the reaction of Fe(CO)4 with C60 must be preceded by a ligand loss. The ligand substitution by C60 can be associative or dissociative depending on the crossing regions between the singlet and triplet potential energy surfaces. However, the furthermore discussion is beyond the scope of the present work. Interested readers can be found an excellent paper: Carreon-Macedo, J.-L.; Harvey, J. N. J. Am. Chem. Soc. 2004, 126, 5789. (19) Our computational results demonstrated that there is another possibility that should be considered: the spin could also change during the reaction through a minimum energy crossing point. However, the systems studied in the present work are rather large to try to locate crossing points. But it still has the possibility. See: (a) Referenc 17. (b) Harvey, J. N.; Aschi, M. Faraday Discuss. 2003, 124, 129. (c) Harvey, J. N. Faraday Discuss. 2004, 127, 165. (20) (a) David, W. I. F.; Ibberson, R. M.; Matthewman, J. C.; Prassides, K.; Dennis, T. J. S.; Hare, H. W.; Taylor, R.; Walton, D. R. M. Nature 1991, 353, 147. (b) Hedberg, K.; Hedberg, L.; Bethune, D. S.; Brown, C. A.; Dorn, H. C.; Johnson, R. D.; de Vries, M. Science 1991, 254, 410. (21) We also checked the precursor complex, which are formed by the triplet Fe(CO)4 with C60. However, the present computational method (B3LYP/LANL2DZ) cannot locate such a Van der Waals adduct or a true complex. (22) Su, M.-D. Chem.—Eur. J. 2004, 10, 5877. (23) One reviewer suggested that it would be better to calculate the entrance complexes, transition states, and products for M(CO)4 and C60 systems, which are performed in the triplet state. However, our theoretical investigations indicate that no such stationary points can be found at present computations (B3LYP/LANL2DZ). Also see ref 20. (24) After this paper was submitted, one reviewer suggested to discuss the possibility of the CO þ MC60, CO þ (CO)MC60, CO þ (CO)2MC60, and CO þ (CO)3MC60 reactions, if MC60 other than M(CO)4 is formed in the first place. We thus used the B3LYP/ LANL2DZ method to optimize these stationary points. We selected the Fe metal in the present calculations. Comparing their corresponding reactants, the relative energies (kcal/mol) were calculated to be 2.42, 14.2, 17.5, and 17.3 for CO þ MC60, CO þ (CO)MC60, CO þ (CO)2MC60, and CO þ (CO)3MC60 reactions, respectively. Accordingly, our theoretical findings indicate that these reactions should not be easily observed experimentally. (25) For details, see: (a) Shaik, S.; Schlegel, H. B.; Wolfe, S. Theoretical Aspects of Physical Organic Chemistry; John Wiley & Sons Inc.: New York, 1992. (b) Pross, A. Theoretical and Physical principles of Organic Reactivity; John Wiley & Sons Inc.: New York, 1995. (c) Shaik, S. Prog. Phys. Org. Chem. 1985, 15, 197.(d) Shaik, S.; Hiberty, P. C. A Chemist’s Guide to Valence Bond Theory; Wiley, Interscience: New York, 2008. (26) (a) The first paper that originated the CM model: Shaik, S. J. Am. Chem. Soc. 1981, 103, 3692. (b) About the most updated review of the CM model, one can see: Shaik, S.; Shurki, A. Angew. Chem., Int. Ed. 1999, 38, 586. (27) Sheu, J.-H.; Su, M.-D. Chem.—Eur. J. 2007, 13, 6171. (28) Su, M.-D.; Chu, S.-Y. J. Am. Chem. Soc. 1999, 121, 1045.

7672


Computational Study of Cycloaddition Reactions of 16-Electron d8

Recommend Documents