Theoretical Investigation of the Binding of Small Molecules and the

J. Phys. Chem. B 2007, 111, 6815-6821

6815

Theoretical Investigation of the Binding of Small Molecules and the Intramolecular Agostic Interaction at Tungsten Centers with Carbonyl and Phosphine Ligands† James T. Muckerman,*,‡ Etsuko Fujita,*,‡ Carl D. Hoff,§ and Gregory J. Kubas∇ Chemistry Department, BrookhaVen National Laboratory, Upton, New York 11973-5000, The Department of Chemistry, UniVersity of Miami, Coral Gables, Florida 33124, and Chemistry DiVision, MS-J582, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 ReceiVed: January 8, 2007; In Final Form: April 4, 2007

The factors controlling both the binding of small molecules to several tungsten complexes and agostic bonding in the W(CO)3(PCy3)2 complex have been examined through B3LYP hybrid density functional theory and ab initio MP2 calculations with and without basis set superposition error (BSSE) corrections. This approach attempts to isolate insofar as possible the separate effects of intrinsic bonding interactions, electron induction by ligands, and steric hindrance and strain. An important conclusion from this study is that for bimolecular reactions, BSSE corrections must be included for quantitative predictions. There is a reasonably good correlation between the BSSE-corrected B3LYP and MP2 results for bond dissociation enthalpies (BDEs) of very small molecules (H2, N2, and CO), but generally B3LYP BDEs tend to be smaller than the corresponding MP2 values. In the few cases where a comparison with experimental data can be appropriately made, it appears that the BSSE-corrected MP2 BDEs are more reliable. Using N2 as a probe molecule, the strength of the agostic bond in W(CO)3(PCy3)2 has been examined by calculating the BDE of N2 in a series of tungsten complexes with increasing electron inducing effect without agostic bonding, then extrapolating the expected trend to the case of agostically bonded W(CO)3(PCy3)2. Comparison of the extrapolated value to the calculated BDE of W(CO)3(PCy3)2(N2) yields an estimated strength of the agostic bond of from 7 to 9 kcal mol-1. Approximately 5 kcal mol-1 of the interaction is assigned to the net agostic interaction associated with moving from a nonagostic local minimum configuration of the PCy3 ligands to the agostically bonded global minimum.

Introduction The prototypical η2-dihydrogen complexes, M(CO)3(PR3)2(H2) where M ) W, Mo, Cr and R ) isopropyl (iPr) and cyclohexyl (Cy), have been extensively investigated since their discovery in 1983 and are now collectively referred to as the “Kubas complexes”.1-10 The metal center stabilizes H2 in these complexes binding by a combination of donation of the H-H σ bonding electrons to empty orbitals on the metal as well as synergistic back-donation from a filled d orbital to the empty σ* orbital of the H-H bond. The H-H bond distance is ≈20% longer than free H2 (0.74 Å), and H2 binding is reversible.1 The first H2 complexes were synthesized from agostic W(CO)3(PCy3)2 and its analogues in which a C-H σ bond of the Cy group interacts with the vacant coordination site on the W center. Small molecules such as N2, C2H4, CO, CH3CN, pyridine, etc. can bind to W(CO)3(PCy3)2 and M(CO)3(PR3)2 in general, simultaneously displacing the agostic bond.1,5 Thermodynamic and kinetic parameters for the binding of small molecules to W(CO)3(PCy3)2 have been investigated directly by time-resolved UV-vis and FTIR spectroscopy11,12 and indirectly via ligand exchange reactions using a stopped-flow technique13,14 and solution calorimetry.15 An important question is how strong is a σ C-H bond interaction of a hydrocarbon ligand (such as n-hexane or an †

Part of the special issue “Norman Sutin Festschrift”. * To whom correspondence should be addressed. J.T.M. e-mail: [email protected]. E.F. e-mail: [email protected]. ‡ Brookhaven National Laboratory. § University of Miami. ∇ Los Alamos National Laboratory.

arene) with M(CO)3(PCy3)2 versus the intramolecular agostic M‚‚‚H-C interaction in M(CO)3(PCy3)2. There is indication that hydrocarbon solvents such as toluene may assist dissociation of H2 from Cr(CO)3(PCy3)2(H2), since it appears to exhibit an unusually large difference in solution versus solid-state stability.16,17 This is one of the most weakly bound (yet isolatable) H2 complexes known. Even though the bond dissociation enthalpies (BDEs) of M-L (M ) zerovalent group 6 metal; L ) H2, N2, C2H4, etc.) complexes are not large, they can be experimentally determined. However, the experimental determination of bond strength such as the σ H-C and agostic interaction is seemingly impossible in solution for these complexes, therefore only an estimate is available. The intramolecular agostic interaction is generally believed14,15 to be 10 ( 6 kcal mol-1 based on a bond strength of 10 kcal mol-1 for Cr(CO)5(heptane).18,19 Note that the error limit seems to be assigned arbitrarily, but the bond energy is expected to be in the wide range of 4-16 kcal mol-1.15 Furthermore, in our previous publication,11 we reported that the net agostic interaction energy in W(CO)3(PCy3)2 calculated using density functional theory (DFT)20-22 is ∆H° ) -5.1 kcal mol-1, which is

10.1021/jp070153+ CCC: $37.00 © 2007 American Chemical Society Published on Web 05/19/2007

6816 J. Phys. Chem. B, Vol. 111, No. 24, 2007 at the lower end of the estimated range, and is comparable to the calculated binding energy of n-hexane (∆H° ) -4.4 and -6.3 kcal mol-1) to W(CO)3(PH3)2 and W(CO)5, respectively. Time-resolved IR results in the gas phase indicate that the binding energy of n-hexane to W(CO)5 is 10.8 ( 3 kcal mol-1.23 These data are lower than solution-phase values based on photoacoustic calorimetric studies17 that yielded estimates for the enthalpy of binding of n-heptane to the M(CO)5 fragments of 13.6 ( 1 kcal mol-1 (Cr) and 15.3 ( 1 kcal mol-1 (Mo). Direct comparison of the gas-phase TRIR and solution-phase photoacoustic results are made difficult due to the unknown role of solvation energies. In addition, the photoacoustic results depend on accurate assignment of the bond strength between CO and the M(CO)5 fragment19 in order to obtain a derived value.24 Computation of agostic bond strengths presents difficult challenges as well. The relatively small ∆H° values for intermolecular H-C interactions and other small-molecule binding to tungsten complexes may be exacerbated when corrected for basis set superposition error (BSSE). In the present computational study, we carefully examine factors controlling both the binding of small molecules to, and agostic bonding in, W(CO)3(PCy3)2 using both hybrid DFT (B3LYP)20-22 and MP2 (second-order Møller-Plesset perturbation theory)25 calculations with/without BSSE corrections (when appropriate). The small molecules we consider are CO, H2, N2, C2H4, CH3CN, n-hexane, pyridine, and pyrazine. Our aim is to isolate the effects of intrinsic bonding interactions, electronic effects, and steric hindrance and strain. To this end, we employ nonagostic and agostic W(CO)3(PCy3)2, and several models of W(CO)3(PCy3)2: W(CO)3(PCy3)(PH3), W(CO)3(PH2Cy)(PH3), W(CO)3(PH3)2, and WCO)3(PMe3)2, where Me ) CH3. The complexes with large alkyl substituents on the phosphine ligands are used to address agostic interactions, while those with smaller substituents are used to address bonding interactions with other molecules. Here we estimate that the strength of the agostic W‚‚‚H-C interaction in W(CO)3(PCy3)2 is 7-9 kcal mol-1 of which ∼5 kcal mol-1 is the net agostic interaction. Computational Details All calculations except as noted below were carried out with the Gaussian 03 program package26 using the LANL2DZ ECP basis27-29 for W and the 6-31G(d,p) basis30-32 for all other elements. This fixed basis size removes one of the variables in comparing the results of B3LYP hydrid DFT20-22 and MP225 calculations. It would have been possible to use a considerably larger basis for the B3LYP calculations, but for the largest system considered it was necessary to omit a number of the occupied valence orbitals from the calculation of the MP2 correlation energy even for the modest basis employed here. A vibrational frequency analysis was performed for all geometryoptimized species except the MP2 structures of W(CO)3(PCy3)(PH3) and W(CO)3(PCy3)2 (for which B3LYP frequencies were employed because MP2 frequency calculations were infeasible), and ∆H°, ∆S°, and ∆G° values were calculated using a standard state of 1 atm pressure at 298.15 K. (The conversion between the concentration and pressure standards has been discussed in our previous paper.33) For all cases of intermolecular bonding, a counterpoise calculation was also carried out to determine the basis set superposition error (BSSE). It has been noted34-39 that BSSE results are reliable only in the case of extremely large basis sets, especially in MP2 calculations, but the use of very large basis sets in some of the present MP2 calculations was infeasible. To address this issue and to assess the meaningfulness

Muckerman et al.

Figure 1. Optimized geometries of pyridine (upper left) and pyrazine (upper right) adducts of W(CO)3(PH3)2, W(CO)5(N2) (lower left), W(CO)3(PMe3)2(N2) (lower middle), and W(CO)3(PCy3)2(N2) (lower right). All are MP2 optimized except W(CO)3(PCy3)2, which is B3LYP optimized. Note that the structures of the pyridine and pyrazine complexes are similar, with both adduct molecules rotated slightly around the W-N bond axis. The B3LYP structure of W(CO)3(PH3)2(N2) has been published.11

of the present MP2 calculations, we treat the W(CO)5(C2H4) system with the much larger basis (500 functions instead of 210) MWB60 ECP for W40 and 6-311+G(2df,2pd) for C, O, and H.41,42 Assuming that the MP2 results obtained with the larger basis are nearly correct, we find that the BSSE-corrected MP2 results obtained with the smaller basis are much more accurate than the uncorrected MP2 results. It is hoped that the trends in the computed BSSE values in going from system to system are correct. Results and Discussion Small-Molecule Binding. For all systems investigated we have performed a vibrational frequency analysis so that we could evaluate their enthalpy, entropy, and free energy of binding. It is often asserted that zero-point energy corrections are small and that they are essentially cancelled by BSSE in DFT B3LYP calculations.43 When the bond dissociation enthalpy is small, as in the case of an alkane σ H-C interaction or an agostic M‚‚‚H-C interaction, such a cancellation of contributions from zero-point energy and BSSE effects cannot be assumed. Therefore a counterpoise calculation for each adduct complex was performed to determine the BSSE in the computed binding energy. This was done with both the B3LYP hybrid DFT and ab initio MP2 methods to obtain a more complete description of the molecular interactions. The same basis set (limited ultimately by the size of the MP2 calculations on the largest of the systems considered here) was used throughout to minimize the number of factors that change from system to system and method to method. Unless otherwise specified, the frozen core approximation, in which all core electrons are excluded from the computation of the correlation energy, was employed in all MP2 calculations. Calculated geometries of W(CO)3(PH3)2L (L ) pyridine and pyrazine) are shown in Figure 1 along with those of W(CO)5(N2) and W(CO)3(PMe3)2(N2). Other W(CO)3(PH3)2L complexes (L ) H2, N2, C2H4, CO, n-hexane) have been published previously.11 Perhaps the only surprise about the calculated structures in Figure 1 is that the pyridine and pyrazine ligands are rotated slightly about the W-N bond axis to avoid steric hindrance. B3LYP and MP2 calculated electronic energies, enthalpies, entropies, and free

Small-Molecule Binding and Agostic Interaction

J. Phys. Chem. B, Vol. 111, No. 24, 2007 6817

TABLE 1: B3LYP Calculated Electronic Energies, Enthalpies, Entropies, and Free Energies (in kcal mol-1) of Binding of Small Molecules to Several Tungsten Complexesa system

∆E

∆H°

∆S°b

∆G°

BSSE

CO pyridine CH3CN pyrazine C2H4 N2 H2 distal dihydride cis dihydride n-hexane

-47.57 -29.21 -29.02 -28.61 -26.91 -25.71 -16.83 -11.16 -10.47 -5.43

-45.81 -27.57 -27.71 -27.01 -25.25 -24.28 -14.56 -9.87 -9.30 -4.39

-32.58 -40.83 -31.16 -40.30 -41.87 -33.97 -26.98 -28.93 -30.94 -32.64

Binding to W(CO)3(PH3)2 -36.10 -5.07 -15.40 -4.38 -18.41 -4.17 -14.99 -4.12 -12.77 -4.48 -14.15 -4.39 -6.51 -0.84 -1.24 -6.01 -0.07 -2.73 +5.34 -1.77

C2H4 N2 n-hexane

-26.86 -24.13 -7.21

-25.19 -22.86 -6.31

-39.29 -33.69 -32.10

Binding to W(CO)5 -13.47 -3.53 -12.82 -3.75 +3.26 -1.65

a

∆E - BSSE

∆H° - BSSE

∆G° - BSSE

-42.50 -24.83 -24.84 -24.49 -22.43 -21.32 -15.99 -5.15 -7.74 -3.65

-40.74 -23.19 -23.53 -22.89 -20.77 -19.89 -13.72 -3.85 -6.57 -2.62

-31.03 -11.02 -14.24 -10.87 -8.29 -9.76 -5.68 +4.77 +2.66 +7.11

-23.33 -20.38 -5.56

-21.66 -19.11 -4.66

-9.95 -9.07 +4.91

Also shown are computed BSSE and the BSSE-corrected binding energies. b Values in cal K-1 mol-1.

TABLE 2: MP2 Calculated Electronic Energies, Enthalpies, Entropies, and Free Energies (in kcal mol-1) of Binding of Small Molecules to Several Tungsten Complexesa system

∆E

∆H°

∆S°b

∆G°

BSSE

CO pyridine CH3CN pyrazine C2H4 N2 H2 distal dihydride cis dihydride n-hexane

-57.32 -51.36 -41.22 -50.23 -50.78 -34.76 -21.05 -15.96 -14.31 -18.78

-55.68 -50.01 -40.01 -48.96 -49.03 -33.54 -18.97 -14.71 -13.88 -17.93

-28.97 -39.83 -31.04 -39.57 -44.34 -33.78 -25.06 -30.49 -29.12 -37.76

Binding to W(CO)3(PH3)2 -47.04 -13.87 -38.13 -15.62 -30.76 -11.29 -37.16 -15.62 -35.81 -19.55 -23.47 -12.08 -11.50 -5.42 -5.62 -3.83 -5.20 -10.55 -6.67 -10.49

C2H4 N2 n-hexane

-47.39 -32.50 -19.65

-45.64 -31.25 -18.82

-41.20 -34.01 -36.78

Binding to W(CO)5 -33.36 -15.95 -21.11 -9.89 -7.85 -9.63

a

∆E - BSSE

∆H° - BSSE

∆G° - BSSE

-43.45 -35.73 -29.93 -34.61 -31.23 -22.68 -15.62 -12.13 -3.76 -8.28

-41.81 -34.39 -28.72 -33.34 -29.49 -21.46 -13.55 -10.88 -3.34 -7.44

-33.17 -22.51 -19.46 -21.54 -16.27 -11.39 -6.07 -1.79 +5.35 +3.82

-31.43 -22.61 -10.01

-29.69 -21.37 -9.19

-17.41 -11.23 +1.77

Also shown are computed BSSE and the BSSE-corrected binding energies. b Values in cal K-1 mol-1.

energies (in kcal mol-1) for binding of small molecules to several tungsten complexes are summarized in Tables 1 and 2, respectively. Computed BSSE and the BSSE-corrected binding energies are also shown in these tables. Figure 2 shows the correlation between the binding enthalpies, ∆H°, calculated with the B3LYP hybrid DFT and MP2 methods for both uncorrected and BSSE-corrected values. The striking feature of the correlation of the uncorrected B3LYP and MP2 values (left panel) is that all the points fall below the ∆H°(MP2) ) ∆H°(B3LYP) reference line, some by 21 to 23 kcal mol-1, indicating that the MP2 method predicts stronger binding in all cases. Interestingly, in the correlation of the BSSE-corrected binding enthalpies (right panel) most of the points still fall below the reference line, but none by more than 12 kcal mol-1. This reflects the fact revealed in Tables 1 and 2 that the MP2 BSSE corrections are also generally larger than those from the B3LYP calculations. In general, the agreement between the binding enthalpies predicted by the two methods is much better for the BSSE-corrected values. In both the uncorrected and corrected results, the ordering of the systems by predicted binding enthalpy is almost the same, and the enthalpy differences between systems with the same method (i.e., “trends”) are in better agreement between the two methods than their absolute agreement. In the correlation of BSSE-corrected results, it is noteworthy that the smaller adduct molecules (H2, N2, and CO) lie much closer to the ideal reference line than the larger molecules,

probably as the result of DFT providing a poorer description of the longer-range interactions between bulky ligands. We will discuss several of the systems in more detail below. The binding of a number of small molecules to W(CO)3(PCy3)2, including hydrogen, nitrogen, acetonitrile, pyridine, and carbon monoxide, have been studied by solution calorimetry.15 The results are compared to those obtained with B3LYP and MP2 calculations on W(CO)3(PH3)2 in Table 3. The calculated stabilities of various adducts by both the B3LYP and MP2 methods are in the order H2 < N2 < CH3CN < pyridine < CO, which is the same as the order from the experimental measurements. Moreover, as pointed out above, the agreement between the two methods for the BSSE-corrected binding enthalpies is very good for the smaller systems, H2, N2, and CO. These systems are also easier to compare with experimental data because they should involve much weaker steric interactions. Nevertheless, there is still an electronic effect (PH3 vs PCy3 ligands) and an agostic bonding effect (in W(CO)3(PCy3)2 but not in W(CO)3(PH3)2) simultaneously at work. For H2, which is η2-bonded, there is also the possibility of a steric effect in the PCy3 complex that is not present in the PH3 complex. The experimental binding enthalpies for the three small molecules should reflect the sum of all these factors: the increase in binding energy, steric repulsion, and the energy cost of breaking the agostic bond associated with the complex with the PCy3 ligands. For the small, end-on binding ligands N2 and

6818 J. Phys. Chem. B, Vol. 111, No. 24, 2007

Muckerman et al.

Figure 2. Correlation between binding enthalpies, ∆H°, calculated with the B3LYP hybrid DFT and MP2 methods. The panel on the left correlates uncorrected binding enthalpies (red); the panel on the right correlates BSSE-corrected binding enthalpies (blue). The filled circles correspond to binding enthalpies to the W(CO)3(PH3)2 complex, while the filled squares correspond to those of other complexes, as indicated. The asterisk indicates a result obtained with the large basis (see text). The reference line in each panel corresponds to equal binding enthalpies from the two methods.

TABLE 3: Comparison of Calculated Enthalpies (in kcal mol-1) of Binding of Small Molecules to W(CO)3(PH3)2 with Experimental Values for W(CO)3(PCy3)2 Obtained by Solution Calorimetry Studies15 a

a

molecule

B3LYP

MP2

expt

H2 N2 CH3CN pyridine CO

-13.72 -19.89 -23.53 -23.19 -40.74

-13.55 -21.46 -28.72 -34.39 -41.81

-9.9 -13.5 -15.1 -18.9 -30.4

The theoretical values are corrected for BSSE.

CO, the energetic cost of breaking the agostic bond is expected to be the dominant factor. The case of C2H4 binding is complicated by the fact that it binds η2 to the metal center in W(CO)3(PH3)2 with its CdC bond nearly parallel to the P-W-P “axis”. This is expected to give rise to steric effects in W(CO)3(PCy3)2 if not in W(CO)3(PH3)2. For the latter complex the calculated binding is rather strong with both methods, even with BSSE corrections. The calculated MP2 BSSE (-20 kcal mol-1) is particularly larges the largest BSSE among all the systems listed in Tables 1 and 2. Although the η2 mode of binding along the P-W-P axis is favored electronically and in reality the crystal structure of W(CO)3(PCy3)2(C2H4) shows this orientation, it is disfavored sterically, especially in such complexes with phosphines containing bulky alkyl groups.44 Indeed, experimental studies of C2H4 binding to W(PCy3)2(CO)3 indicate that it binds weakly (Keq ) 60 ( 10 M-1 in toluene estimated from Keq ) kf/kr, where kf and kr are the forward and reverse rate constants for C2H4 binding, respectively).11 As shown in Tables 1 and 2, C2H4 has the most negative entropy of binding of all the ligands studied. Interestingly, solution calorimetric studies indicate that in spite of these steric factors, C2H4 has a more exothermic enthalpy of binding to W(CO)3(PCy3)2 than does N2. The entropy of binding, however, is more unfavorable for C2H4 than for N2.45 It is noteworthy that the binding of C2H4 to W(CO)5 is quite similar to that to W(CO)3(PH3)2. Also shown in Figure 2 are the analogous results from B3LYP and MP2 calculations on W(CO)5(C2H4) with the larger (500

Figure 3. B3LYP optimized geometries of W(CO)3(PH3)2(H2): distal dihydride (left) and cis dihydride (right).

function) basis. Even in this case it was necessary to calculate the MP2 frequencies of the adduct at the MP2/MWB60/6-311G(d,p)//MP2/MWB60/6-311G(d,p) level of theory to make the computation tractable. The uncorrected binding enthalpies for each method with the two basis sets are quite similar; the B3LYP enthalpy is 3.5 kcal/mol smaller and the MP2 enthalpy 1.3 kcal/ mol-1 larger with the larger basis. Both the B3LYP and MP2 BSSEs are smaller (by 3.6 and 5.1 kcal/mol-1, respectively, with the larger basis. This results in the BSSE-corrected binding enthalpies being 0.9 kcal/mol-1 smaller and 6.3 kcal/mol larger for the B3LYP and MP2 methods, respectively. These changes are considerably smaller, even for the MP2 method, than the calculated BSSEs using the smaller basis, and represent only about -4% (B3LYP) and +14% (MP2) of the uncorrected binding enthalpies calculated with the smaller basis. It is interesting to note that according to this analysis, the BSSEcorrected MP2 test calculation with the smaller basis surprisingly appears to underestimate the binding enthalpy by 17.5%. Previous theoretical work by Toma`s et al.46 on dihydrogen binding to W(CO)3(PH3)2 showed the dihydrogen complex to be more stable than either of two dihydride complexes resulting from oxidative addition. Their B3LYP and MP2 results placed the energy of the distal dihydride (where the H atoms are located at either side of one of the phosphine ligands, see Figure 3) and the cis dihydride about 5 and 6 kcal mol-1 above that of

Small-Molecule Binding and Agostic Interaction

J. Phys. Chem. B, Vol. 111, No. 24, 2007 6819

TABLE 4: Selected Thermodynamic Properties (in kcal mol-1) from the Calculation of Dihydrogen Binding to W(PH3)2(CO)3 Using the B3LYP and MP2 Methods with and without BSSE Corrections B3LYP

MP2

product

∆H°

∆G°

∆H° - BSSE

∆G° - BSSE

∆H°

∆G°

∆H° - BSSE

∆G° - BSSE

H2 distal dihydride cis dihydride

-14.56 -9.87 -9.30

-6.51 -1.24 -0.07

-13.72 -3.85 -6.57

-5.68 +4.77 +2.66

-18.97 -14.71 -13.88

-11.50 -5.62 -5.20

-13.55 -10.88 -3.34

-6.07 -1.79 +5.35

TABLE 5: Calculated N2 Binding Enthalpies to Various Tungsten Complexes Using the B3LYP and MP2 Methods with and without BSSE Correction B3LYP

MP2

complex

∆H°

∆H° BSSE

∆H°

∆H° BSSE

W(CO)5 W(CO)3(PH3)2 W(CO)3(PMe3)2 W(CO)3(PCy3)2

-22.86 -24.28 -24.67 -16.91

-19.11 -19.89 -20.14 -12.87

-31.25 -33.54 -35.14 -

-21.37 -21.46 -22.63 -

the dihydrogen complex, respectively. No correction was made for BSSE. The present uncorrected B3LYP binding enthalpies are in the same order as found by Toma`s et al.:46 H2 > distal dihydride > cis dihydride in strength of binding, but the BSSEcorrected values predict the cis dihydride to be more strongly bound than the distal dihydride (see Table 4). In fact, the BSSE correction, coupled with rather large negative entropy changes, causes the ∆G° value for both dihydrides to be positive by several kcal mol-1, with that for the cis dihydride still lower. This result appears to be incorrect in view of the experimental values for the W(CO)3(PR3)2(H2) f W(CO)3(PR3)2(H)2 equilibrium reaction at 298 K:7 ∆H° ) 1.2 ( 0.6 kcal mol-1, ∆S° ) 1.2 ( 2.6 cal K-1 mol-1, and ∆G° ) 0.80 ( 0.12 kcal mol-1 for R ) iPr; and ∆H° ) 1.5 ( 0.4 kcal mol-1, ∆S° ) 2.4 ( 1.4 cal K-1 mol-1, and ∆G° ) 0.75 ( 0.12 kcal mol-1 for R ) cyclopentyl. In the uncorrected MP2 calculations the binding is somewhat stronger, but it is in the same order as the uncorrected B3LYP calculations. The BSSE-corrected MP2 results not only preserve this order, but place the cis dihydride about 7.5 kcal mol-1 above the distal dihydride. For the W(CO)3(PH3)2(H2) f distal W(CO)3(PH3)2(H)2 reaction at 298 K we obtain ∆H° ) 2.67 kcal mol-1, ∆S° ) -5.43 cal K-1 mol-1, and ∆G° ) 4.28 kcal mol-1. In view of the expected electronic effect, this computed enthalpy of reaction is in reasonably good agreement with the experimental data obtained for larger alkyl ligands. The large discrepancy in the entropy of reaction (-5.43 vs +1.2 or 2.4), which could possibly be due to a solvation effect not considered here, is responsible for the difference between computed and measured ∆G° values. The binding of n-hexane resembles an agostic interaction in that it involves a σ H-C interaction with the metal center, but since the binding of n-hexane to the metal is a bimolecular (as opposed to unimolecular) process, the binding entropy is much more negative (less than -30 compared to nearly zero cal K-1 mol-1). This causes the BSSE-corrected values of ∆G° to be positive for all the cases of binding of n-hexane. Zari and Hall47 have previously carried out a theoretical study of hydrocarbon binding energies to W(CO)5 employing three different sizes of basis set and several ab initio methods. Our BSSE-corrected MP2 result for n-hexane of -9.19 kcal mol-1 is in good agreement with their values of -9.12 and -10.40 kcal mol-1 for the η2(3) binding (in their notation) of propane, the largest hydrocarbon they considered, with their basis sets I and II, respectively. Their results further suggest that primary H-C binding to W(CO)5 increases slightly with increasing hydrocarbon size.

A comparison of experimental and calculated values of ∆H° for n-hexane binding to W(CO)5 is enlightening. The experimental BDE23 of 10.8 ( 3 kcal mol-1 obtained using timeresolved IR in the gas phase (using a standard state of 1 atm. at 298 K) agrees well only with the value obtained by the MP2 method with BSSE correction, -9.2 kcal/mol-1. The other predictions, -6.3 (B3LYP, without BSSE correction), -4.7 (B3LYP with BSSE correction), and -18.8 (MP2 without BSSE correction), are in significant disagreement. Table 5 summarizes the results for N2 binding to a number of tungsten complexes. The calculated binding enthalpies for a given method, especially the BSSE-corrected values, are rather tightly clustered except for W(CO)3(PCy3)2(N2). The BSSEcorrected MP2 values are about 2 kcal mol-1 stronger than the BSSE-corrected B3LYP values. Note that the strength of the binding of N2 increases slightly with increasing electron induction power of the ligands (PMe3 > PH3 > CO) except for PCy3. According to the characterization by Tolman48 based on CO stretching frequencies in Ni(CO)3L and an estimate for PH3, the electronic effect for PCy3 should be only slightly larger than for PMe3. On this basis, extrapolated enthalpy values for PCy3 would be about -25.0 and -20.5 kcal mol-1 for the uncorrected and BSSE-corrected B3LYP method, respectively. The actual computed values for W(CO)3(PCy3)2 are about -16.9 and -12.9 kcal mol-1. Note that the experimental enthalpy of binding15 of N2 in toluene is -13.5 kcal mol-1, similar to the calculated value obtained with BSSE correction. There are two additional factors at play in the case of the PCy3 ligands: (1) there is an agostic bond in the complex that is not present in the other complexes in Table 5 that must be broken in order to accommodate the incoming nitrogen molecule; and (2) the bulkiness of the three cyclohexyl groups around the two substituted phosphine ligands may cause steric and strain effects that influence the initial complex and its N2 adduct to different extents. The latter effect should be minimized by the choice of N2 as the adduct molecule because it binds end-on and requires minimal space. So neglecting steric and strain effects, it appears that the energetic cost of breaking the agostic bond in W(PCy3)2(CO)3 is on the order of 7 to 9 kcal mol-1. This conclusion is supported to some extent by considering the N2 binding energy of the “nonagostic” W(PCy3)2(CO)3 complex. Assuming the same adduct geometry and energy, the uncorrected and BSSEcorrected B3LYP nonagostic complex binding enthalpies are -22.0 and -17.9 kcal mol-1, respectively. These are only about 3 kcal mol-1 short of the extrapolated values, but they suggest that even the nonagostic W(PCy3)2(CO)3 complex has some residual stabilization. Agostic Interaction. The strength of an agostic bond in HCH ‚‚‚TiHF has been investigated using HF, MP2, CCSD(T) (coupled cluster theory with single and double substitutions with noniterative triple excitations), and DFT with large all-electron basis sets.49 One of the principal conclusions of that work is that MP2 dramatically overestimates the agostic interaction strength, whereas GGA and hybrid DFT methods yielded results in better agreement with their CCSD(T) benchmark calculations. The present results suggest that the poor perfor-

6820 J. Phys. Chem. B, Vol. 111, No. 24, 2007

Muckerman et al.

TABLE 6: Calculated Net Agostic Interaction (in kcal mol-1) in Various Tungsten Complexes Using the B3LYP and MP2 Methods B3LYP

MP2

species

∆E

∆H°

∆S°a

∆G°

∆E

∆H°

∆S°a

∆G°

W(PH2Cy)(PH3)(CO)3 W(PCy3)(PH3)(CO)3 W(PCy3)2(CO)3

-0.52 -5.19 -4.66

-0.90 -5.41 -5.05

-7.38 -2.14 +0.64

+1.31 -4.77 -5.24

-4.78 -4.79 -5.31c

-5.05 -5.01b -5.69b

-0.41 -2.14b +0.64b

-4.93 -4.37b -5.88b

a Values in cal K-1 mol-1. b B3LYP vibrational frequencies used in the calculation of thermodynamic properties. c There are 184 occupied orbitals of which 52 are core orbitals. Only orbitals 176-800 were used in the calculation of the MP2 correlation energy.

is defined as the difference between the enthalpy at the global (agostically bonded) minimum (see Figure 4, right column) and a local minimum at which the nearest W-H distance is longer than 3.0 A, the generally accepted cutoff for an agostic bond (see Figure 4, left column). It is noteworthy that only the W(CO)3(PH2Cy)(PH3) complex exhibits a β-agostic interaction; all others form an R-agostic bond. This suggests that in the absence of steric crowding by other bulky cyclohexyl ligands, strain is minimized by forming a β-agostic bond. The B3LYP net agostic interaction in W(CO)3(PH2Cy)(PH3) seems anomalously small (∆H° ) -0.90 kcal mol-1) compared to the other entries in Table 6, where it is seen that the MP2 ∆H° value for the same complex is -5.05 kcal mol-1. The computed net agostic enthalpy for W(CO)3(PCy3)2 with the B3LYP method is -5.05 kcal mol-1. This is consistent with the argument presented above that ∼3 kcal mol-1 of the 7-9 kcal mol-1 energy cost of breaking this agostic bond in order to form a bond with N2 may be attributed to overcoming the residual stabilization in the nonagostically bonded complex (e.g., van der Waals interactions involving the bulky cyclohexyl ligands). This would leave ∼5 kcal mol-1 for breaking the net agostic bond, in agreement with the directly calculated value presented in Table 6. In this regard, it is also of interest to note that for the related complex W(CO)3(PiPr3)2 the strength of the agostic interaction is estimated to be ∼1 kcal mol-1 weaker than in the W(CO)3(PCy3)2 complex based on comparative enthalpies of binding of N2.45 Conclusions

Figure 4. B3LYP structures of nonagostic (left column, local minima) and agostic (right column, global minima) W(CO)3(PR3)2 complexes: W(CO)3(PH2Cy)(PH3), top; W(CO)3(PCy3)(PH3), middle; and W(CO)3(PCy3)2, bottom.

mance of the MP2 method in the previous study by von Frantzius et al.49 arises from their model for agostic interactions not allowing for BSSE corrections. They49 used their conclusion to justify the further use of DFT with smaller basis sets to characterize the agostic W‚‚‚H-C interaction in W(tCCMe3)(dCHCMe3)(CH2CMe3)(dmpe) where dmpe is dimethylphosphinoethane. Their DFT calculations conclude that the strength of the R-agostic bond is in the range of a typical hydrogen bond (e10 kcal mol-1) in both systems. Table 6 shows the computed strength of the net agostic interaction in three different tungsten complexes at both the B3LYP and MP2 levels of theory. The net agostic bond enthalpy

The factors controlling both the binding of small molecules to several tungsten complexes and agostic bonding in the W(CO)3(PCy3)2 complex have been examined through B3LYP hybrid DFT and ab initio MP2 calculations, both with and without BSSE correction. This approach attempts to isolate insofar as possible the separate effects of intrinsic bonding interactions, electron induction by ligands, and steric hindrance and strain. An important conclusion from this study is that for bimolecular reactions, BSSE corrections must be included for quantitative predictions. There is a reasonably good correlation between the BSSE-corrected B3LYP and MP2 results for enthalpies of binding of very small molecules (H2, N2, and CO), but B3LYP BDEs tend to be smaller than the corresponding MP2 values. In the few cases where a comparison with experimental data can be appropriately made, it appears that the BSSE-corrected MP2 BDEs are more reliable. Using N2 as a probe molecule, we have examined the strength of the agostic bond in W(CO)3(PCy3)2 in a manner that allows a BSSE correction. By calculating the BDE of N2 in a series of tungsten complexes with increasing electron inducing effect without agostic bonding, we extrapolated the expected trend to the case of agostically bonded W(CO)3(PCy3)2. Comparison of the extrapolated value to the calculated BDE of W(CO)3(PCy3)2(N2) yields an estimated strength of the agostic bond of from 7

Small-Molecule Binding and Agostic Interaction to 9 kcal mol-1. Approximately 5 kcal mol-1 of the interaction is assigned to the net agostic interaction associated with moving from a nonagostic local minimum configuration of the PCy3 ligands to the agostically bonded global minimum. The relatively weak nature of the agostic bondsso weak that the local minimum configuration of the PCy3 ligands is calculated to play a significant role in its formationsis in keeping with its fluxional character as well as its ready displacement by other weak ligands such as H2. Considering all data currently available, including calculations reported here, a value of 9 ( 3 kcal mol-1 seems valid for assignment of the total strength of the agostic interaction in W(CO)3(PCy3)2. Theoretical estimates tend toward lower, and experimental estimates toward higher, ends of these limits, but they are in reasonable accord. Acknowledgment. The work at Brookhaven National Laboratory and Los Alamos National Laboratory is funded under contract DE-AC02-98CH10886 and 07SCPE501, respectively, with the U.S. Department of Energy and supported by its Division of Chemical Sciences, Geosciences, & Biosciences, Office of Basic Energy Sciences. Support from the National Science Foundation grant number CHE-0615743 is gratefully acknowledged (C.D.H.). Supporting Information Available: Complete ref 26 and tables containing MP2 and B3LYP optimized Cartesian coordinates. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Kubas, G. J. Metal Dihydrogen and σ-Bond Complexes: Structure, Theory, and ReactiVity; Kluwer Academic/Plenum Publishers: New York 2001. (2) Kubas, G. J.; Ryan, R. R.; Swanson, B. I.; Vergamini, P. J.; Wasserman, H. J. J. Am. Chem. Soc. 1984, 106, 451-452. (3) Kubas, G. J.; Unkefer, C. J.; Swanson, B. I.; Fukushima, E. J. Am. Chem. Soc. 1986, 108, 7000-7009. (4) Kubas, G. J.; Ryan, R. R.; Wrobleski, D. A. J. Am. Chem. Soc. 1986, 108, 1339-1341. (5) Wasserman, H. J.; Kubas, G. J.; Ryan, R. R. J. Am. Chem. Soc. 1986, 108, 2294-2301. (6) Kubas, G. J. Acc. Chem. Res. 1988, 21, 120-128. (7) Khalsa, G. R. K.; Kubas, G. J.; Unkefer, C. J.; Vandersluys, L. S.; Kubatmartin, K. A. J. Am. Chem. Soc. 1990, 112, 3855-3860. (8) Heinekey, D. M.; Oldham, W. J. J. Chem. ReV. 1993, 93, 913926. (9) Morris, R. H.; Jessop, P. G. Coord. Chem. ReV. 1993, 121, 155289. (10) Heinekey, D. M.; Law, J. K.; Schultz, S. M. J. Am. Chem. Soc. 2001, 123, 12728-12729. (11) Grills, D. C.; van Eldik, R.; Muckerman, J. T.; Fujita, E. J. Am. Chem. Soc. 2006, 128, 15728-15741. (12) Grills, D. C.; Huang, K.-W.; Muckerman, J. T.; Fujita, E. Coord. Chem. ReV. 2006, 250, 1681-1695. (13) Zhang, K.; Gonzalez, A. A.; Hoff, C. D. J. Am. Chem. Soc. 1989, 111, 3627-3632. (14) Gonzalez, A. A.; Zhang, K.; Hoff, C. D. Inorg. Chem. 1989, 28, 4285-4290. (15) Gonzalez, A. A.; Zhang, K.; Nolan, S. P.; Delavega, R. L.; Mukerjee, S. L.; Hoff, C. D.; Kubas, G. J. Organometallics 1988, 7, 24292435. (16) Eckert, J.; Kubas, G. J.; White, R. P. Inorg. Chem. 1992, 31, 15501551.

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