Elimination and Activation of Methane and Larger Hydrocarbons

Nov 20, 1995 - Department of Chemistry, UniVersity of Memphis, Memphis, Tennessee 38152 .... moieties in the leaving group on the reaction surface. El...
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J. Phys. Chem. 1996, 100, 6475-6483

6475

Elimination and Activation of Methane and Larger Hydrocarbons Thomas R. Cundari,*,1a Nikita Matsunaga,1b and Eddie W. Moody Department of Chemistry, UniVersity of Memphis, Memphis, Tennessee 38152 ReceiVed: September 12, 1995; In Final Form: NoVember 20, 1995X

This paper describes a study of hydrocarbon activation and elimination. Important chemical conclusions include the following. There is little evidence for significant agostic interactions between Zr and C-H (or NR-HR) bonds. Replacement of small model ligands with bulkier, more realistic ligands causes the Zr coordination to pyramidalize in the putative CH activating species, which should facilitate coordination of hydrocarbon substrate. For substrates that have a π-system (ethylene, benzene, and acetylene), only acetylene showed evidence for interaction between Zr and the π-system on the leaving group in the elimination transition state, suggesting activation and elimination will be relatively insensitive to substituent effects for arenes or olefins. Following the intrinsic reaction coordinates for alkane elimination shows the substrate to remain in the coordination sphere of the d0 imido. Calculated energies for alkane binding to the d0 Zr-imido become more negative as the alkane becomes larger. In all cases, elimination of a hydrocarbon containing a π-system results in a π-complex in preference to a σ-complex. The correlation between calculated and experimental hydrocarbon elimination barriers is respectible given the approximations made in the computational models.

Zr(NHSi′)3R f (NHSi′)2Zr(dNSi′) + RH

Introduction Synthesis of solid-state materials, e.g., transition metal nitrides, from molecular precursors by chemical vapor deposition (CVD) often involves elimination of volatile organic species such as hydrocarbons, for which CH bond formation is an integral part.2 The reverse reaction, CH activation, is crucial in catalytic alkane functionalization.3 These important reactions are related, shown in eq 1 (Ln ) general ligand set; E )

(1)

activating ligand; R ) hydrocarbon substituent; M ) transition metal), in that transition metal-mediated formation (or scission) of CH bonds in a pivotal process. Recent experiments4,5 have focused on hydrocarbon (RH) elimination from high-valent Zr(NHSi′)3R and Ta(NHSi′)2(dNSi′)R to form imidos (NHSi′)2Zr(dNSi′) and (NHSi′)Ta(dNSi′)2 (Si′dSi(t-Bu)3), respectively.4,5 Three-coordinate, d0 imidos are highly reactive, demonstrating the ability to activate methane.4,5 Experimental6 and computational7 data support CH activation by [2σ + 2π] addition of H3C-H across the metalimido bond. Most computational studies of alkane elimination and activation (either oxidative addition/reductive elimination by lowvalent complexes8 or [2 + 2] addition/1,2-elimination by highvalent complexes9) have focused on methane. Methane functionalization is an attractive goal for a variety of technological reasons,10 but also the small size of methane helps keep computations tractable. The experimental RH elimination studies4a,5a employed a range of hydrocarbyls (H, Et, CtCR, Ph, etc.) to assess substituent effects on R-elimination (and hence the reverse, CH activation) as shown in eq 2.4 * Address correspondence to this author at University of Memphis. X Abstract published in AdVance ACS Abstracts, March 15, 1996.

0022-3654/96/20100-6475$12.00/0

(2)

A small linear correlation between the RH elimination rate and the C-H bond strength of eliminated RH was found, but there is no correlation between RH elimination rates and the basicity of R- or the acidity of RH.4a Finally, an excellent correlation between the proton affinity of RH and hydrocarbon elimination rates was noted.4a Equilibrium studies also point to larger energy differences in the transition state (∆∆Gq) vs the ground state (∆∆G) for these systems.4a,5 This research4,5 challenges the view of 1,2-elimination transition states (TSs) in d0 complexes as being rigidly “late” (relative to the position of reactants and products) on the reaction coordinate.11 Computational studies of HX elimination from d0 M(H)2(NH2)(X), where M ) Ti, Zr, Hf, indicate a TS flexible in its relative position along the reaction coordinate (energetically and geometrically),12 although the leaving groups (X) in the computational study12 are more electronically distinct than those studied experimentally.4 Brown13 has concluded from molecular mechanics studies of Zr(NHSi′)3R that despite the steric bulk of Si(t-Bu3), steric effects are not a prime determinant for trends in elimination rates.4a Thus, energetic differences seem related to the response of the elimination TS to electronic effects induced by R groups. As part of the continuing computational research on the reactivity of transition metal7,9c,12,14 (TM) complexes, a study of the reaction in eq 3 was undertaken.

Zr(NH2)3R f TS f (NH2)2ZRdNH + RH

(3)

where R ) H, Me, Et, i-Bu, Np, vinyl, CtCH, Ph, C(O)H, C(O)OH. Substrates correspond to those under experimental investigation.4a Formyl (C(dO)H) and carboxyl (C(dO)OH) groups were included to assess the effect of strong donor moieties in the leaving group on the reaction surface. Elimination (and activation) of H2 and CH4 have been detailed previously.7a,9c Computational Methods Three main challenges arise in computational TM chemistry: large numbers of electrons (many of them core), importance © 1996 American Chemical Society

6476 J. Phys. Chem., Vol. 100, No. 16, 1996 of electron correlation, and increased relativistic effects. The effects of electron correlation are mitigated to a large degree by the empty d shell in the complexes studied here. Our main approach to the challenges of computational d-block chemistry is the design, testing, and use of effective core potentials (ECPs).7,9c,12,14 Transition metal ECPs are generated from allelectron, Dirac-Fock calculations and thus include Darwin and mass velocity relativistic effects, with spin-orbit coupling averaged out in ECP generation.15 Calculations employ the parallel-GAMESS program16 on a variety of platforms: iPSC/860 (Oak Ridge); SP-1 and KSR-1 (both at Cornell Theory Center); CM-5 (Knoxville, Tennessee); parallel IBM cluster (Memphis). Effective core potentials and valence basis sets (VBSs) are used for all heavy atoms, and the -31G basis set was used for H.15 ECPs replace the innermost core orbitals for TMs and all core orbitals for main-group (MG) elements. Thus, the ns, np, and nd, (n + 1)s and (n +1)p are treated explicitly for the d block; ns and np are treated explicitly for MG elements. Transition metal VBSs are quadruple and triple zeta for the sp and d shells, respectively, while maingroup elements have a double-zeta-plus-polarization VBS. Geometries are optimized at the restricted Hartree Fock (RHF) level for closed-shell singlets. Bond lengths and angles for TM complexes are typically predicted to within 1-3% of experimental values using the present computational level (termed RHF/SBK(d)) involving complexes in a variety of geometries, formal oxidation states, and metals from the entire transition series.7,12,14 The effect of electron correlation on geometry optimization was assessed in previous studies of H27a and methane9c activation/elimination. These multiconfiguration self-consistent field (MCSCF)17 studies showed changes in stationary point geometries (including TSs) to be small,7a,9c and calculated intrinsic reaction coordinates (IRC18) at the RHF and MCSCF levels are nearly identical.7a,9c The calculations point to the appropriateness of a single-determinant description of the potential energy surfaces. Vibrational frequencies are calculated at stationary points to identify them as minima or transition states. Plotting imaginary modes is used to assess which TS connects which reactants and products, as is the calculation of the IRC.18 Although geometries are accurately predicted at the RHF level, the energetics are expected to be poor if electron correlation is ignored. Enthalpic data are determined using Møller-Plesset second-order perturbation theory (MP2)19 for energies at RHF-optimized geometries with zero point energy and temperature corrections (to 373.15 K). A simple [RHF geometry/MP2 energy] scheme yields good agreement with experimental enthalpic data subsequently provided by Wolczanski4a,5a for group IVB and group VB complexes.7b,9c Perhaps more importantly, this scheme correctly predicts trends in methane elimination barriers as a function of metal. Since our main goal is to understand trends in CH activation/alkane elimination potential energy surfaces (PESs) among related systems, the [RHF geometry/MP2] energy scheme provides an attractive choice for this research. Results and Discussion 1. Tris(Amido) Hydrocarbyl Reactants. Total energies (RHF-optimized geometries) at the RHF and MP2 levels for all species are given in Supporting Information. Pertinent metric data for optimized tris(amido)hydrocarbyl ZrIV reactants are given in Table 1. As expected, bond lengths and angles involving main group elements are in accord with standard values.20 In general, changes in the Zr(NH2)3 geometry as a function of R are minimal; amido ligands are arranged like a

Cundari et al. three-bladed propeller (when viewed along the ZrCR bond) as seen in the crystal structure of Zr(NHSi′)3Me.21 In the experimental complex the amido orientation serves to minimize steric repulsion among bulky Si(t-Bu)3 groups.21 That it is seen in smaller models studied here suggests that the amido orientation may also have an electronic component that maximizes Zr dπ-N pπ bonding. For hydrocarbyls with a π-system (R ) 1′-vinyl, 1-Ph, 1-C2H) no structural evidence (e.g., small ZrCRCβ angles) is seen that indicates direct interaction between the π-system and Zr.

a. Carbonyl-Containing Reactants. Formyl and carboxyl complexes, 1-CHO and 1-CO2H, show the greatest deviation

from normal tetrahedral Zr coordination. Formyl and carboxyl ligands coordinate η2, as seen22 and proposed21 for high-valent, early TM acyls. 1-CHO and 1-CO2H show distortions similar to those seen in the structure of Cp2Zr(Me)(C(O)Me): ZrO ) 2.290(4) Å; CO ) 1.211(8) Å; ZrC ) 2.197(6) Å.22 For 1-CHO, ZrO ) 2.22 Å; CO ) 1.25 Å; ZrC ) 2.30 Å. Large ZrCX angles are calculated for 1-CHO and 1-CO2H as observed in Cp2Zr(Me)(C(O)Me): ZrCC ) 159.8(5)°.22 b. Alkyl-Containing Reactants. Tris(amido) alkyls, 2, have tetrahedral Zr coordination (Table 1) and normal hydrocarbyl geometries.21 The structure of the isobutyl 2-i-Bu, is representative. In all cases, the distances between Cβ-Hβ and Cγ-

Hγ bonds, when available, and Zr are much greater than the closest contacts in a methane adduct of (NH2)2Zr(dNH): Zr‚‚‚C ) 3.05 Å, Zr‚‚‚H ) 2.55 Å.23 For ZrIV alkyl models there is no evidence for significant agostic Zr‚‚‚Hβ-Cβ and Zr‚‚‚HγCγ bonding. The best evidence for agostic interactions in alkyls is between Zr and CR-HR bonds. The ZrCRHR angles in the C3 symmetry minimum of 2-Me are 112°. The average ZrCRHR angle decreases as the alkyl becomes more sterically demanding: 108° (Et), 106° (i-Bu), and 105° (Np). Crabtree et al.24 have defined the metric parameter rbp

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J. Phys. Chem., Vol. 100, No. 16, 1996 6477

TABLE 1: Optimized Geometries of Zr(NH2)3 Reactantsa Zr-C (Å)

Zr-N (Å)

C-Zr-N (deg)

other

Me Et

R

2.28 2.29

2.07 2.07

N-Zr-N (deg) 111 112

108 107 ( 1

i-Bu

2.30

2.07

111 ( 1

108 ( 1

Np

2.30

2.07

110 ( 1

109 ( 3

vinyl

2.28

2.07

110 ( 1

109 ( 1

CtCH

2.27

2.06

108

111

Ph

2.29

2.07

110

109 ( 1

η2-C(dO)H η2-C(dO)OH

2.30 2.33

2.07 2.07

108 ( 3 107 ( 3

b c

C3 symmetry C-C-Zr-N ) 176° C-C-Zr ) 117° Zr-C-HR ) 108° (ave) C-C ) 1.55 Å Cβ-CR-Zr-N ) 168° Cβ-CR-Zr ) 122° Zr-C-HR ) 106° (ave) Cβ-CR-Zr-N ) -178° Cβ-CR-Zr ) 128° Zr-C-HR ) 103° (ave) CβdCR-Zr-N ) 99° Cβ-CR-Zr ) 120° Zr-C-HR ) 126° (ave) CRdCβ ) 1.36 Å CtC ) 1.24 Å C3 symmetry CC ) 1.41 ( 0.01 Å Zr-CC ) 122 ( 2° b c

a Important metric data are given for RHF-optimized minima of Zr(NH2)3R. Average values of ZrN, NZrN, and CZrN are given if there is no C3 symmetry. No range of calculated values is quoted when it is less than 0.01 Å or 1°. b See section 1a. c See section 1b.

rbp ) [dZrH2 + r2dCH2 - r(dZrH2 + dCH2 - dZrC2)]1/2 - 1.454 (4) where 1.454 Å is the Zr covalent radius and r ) 0.28. Essentially, rbp is the distance from Zr to a point on the C-H bond where the covalent radii of carbon and hydrogen meet. Smaller rbp signify a larger M‚‚‚H-C agostic interaction. The rbp values for Cβ-Hβ and Cγ-Hγ bonds of the Zr alkyls are > 1.9 Å. Strongly agostic Ta alkylidenes and Ti alkyls possess rbp ≈ 0.7 Å.24 By use of calculated dZrH, dCH, and dZrC (internuclear distances), the smallest rbp for CR-HR bonds are 1.24 Å (Me), 1.19 Å (Et), 1.17 Å (i-Bu), and 1.14 Å (Np). The rbp values show agostic M‚‚‚HR-CR interaction to increase as the alkyl group increases in size and to be larger than for CβHβ and Cγ-Hγ bonds, but much less than for structurally characterized examples.24 c. Toward Study of Larger Tris(amido) Zr-Methyl Complexes. The study of compounds that more closely model experimental systems is an important goal for computational chemistry. Wolczanski et al. have reported a crystal structure for Zr(NHSi′)3Me, where Si′ ) Si(t-Bu)3,21 which has approximate C3 symmetry. However, quantum calculations on Zr(NHSi′)3Me, even with ECPs, are not currently feasible. The ZrC bond length in the C3 symmetry minimum of Zr(NH2)3Me (2-Me) is 2.28 Å and it is 2.231(7) Å in Zr(NHSi′)3Me. Zramido bond lengths average 2.04 Å,21 in agreement with results from calculations; ZrNamido ≈ 2.07 Å (see Table 1). The CZrN angles are 108° for 2-Me and 107.2(2)°, 107.5(2)°, and 108.0(2)° for Zr(NHSi′)3Me.21 NZrN angles range from 110.4(2)° to 112.2(2)°,21 in very good accord with results from calculations: NZrN ) 111°. The excellent agreement between theory and experiment, despite obvious differences in the size of Si′ and H, provide an initial clue that the structure of the ZrN3C core is determined to the largest extent by electronic effects (e.g., Zr dπ-N pπ bonding), as suggested by molecular mechanics.13,25 Larger models Zr(N(H)SiH3)3Me and Zr(N(H)TMS)3Me (TMS ) SiMe3) were optimized (RHF/SBK(d)) under C3 symmetry to more closely model Zr(NHSi′)3Me;21 bulkier substituents cause little change in pertinent bond lengths and angles (ZrC ) 2.28 Å, ZrN ) 2.08, NZrN ) 109°, CZrN ) 110°, and ZrNSi ) 133° for the N-silyl complex; ZrC ) 2.29

Å, ZrN ) 2.08 Å, NZrN ) 111°, CZrN ) 108°, and ZrNSi ) 138° for the N-TMS complex) and thus remain in very good agreement with Zr(NHSi′)3Me.21 Large (i.e., >120°) ZrNSi angles in Zr(N(H)SiH3)3Me and Zr(N(H)TMS)3Me may have an electronic cause for which two explanations seem plausible: agostic Zr‚‚‚HR-NR bonding and multiple bond character in the NSi bond. We investigated the latter by replacement of SiH3 with CH3; C3-Zr(N(H)CH3)3Me has ZrC ) 2.30 Å, ZrN ) 2.07 Å, NZrN ) 111°, CZrN ) 108°, and ZrNC ) 135°, values nearly identical to those calculated for Zr(N(H)SiH3)3Me and thus arguing against NSi π-bonding as the cause of large ZrNSi angles. The analogues C3-M(N(H)SiH3)3Me (M ) Si, Zr) possess nearly identical coordination geometries about the amido N: MNSi ) 130° (M ) Si) or 133° (M ) Zr); MNH ) 113° (M ) Si or Zr). Agostic Si‚‚‚HR-NR interactions are not expected in Si(N(H)SiH3)3Me, so the structural similarity suggests that agostic interactions are also not significant in the Zr analogue. Using a variant of eq 4 specific for Zr‚‚‚HR-NR interactions (r ) 0.29 Å and appropriate internuclear distances) yields rbp from 0.99 Å (C3Zr(N(H)TMS)3) to 1.12 Å (1-CHO). Making the amido substituent larger (H f silyl f TMS) decreases rbp and strengthens agostic interaction, but values are still suggestive of very weak agostic bonding. Extrapolating the H f silyl f TMS series to Si(t-Bu)3 yields a rough estimate of rbp ≈ 0.930.96 Å. This suggests little, if any, agostic interaction between amido protons and ZrIV. Experimental analysis (IR, NMR) of four-coordinate, ZrIV-amidos shows no evidence of agostic interactions between Zr and amido protons even at low temperature.4a Thus, it seems reasonable to infer that large ZrNSi angles are primarily steric in origin. The ZrNSi angles, although large in N-silyl and N-TMS models, are still less than in Zr(NHSi′)3Me, where ZrNSi ≈ 151°.21 We performed molecular mechanics (MM) calculations with the standard MM2 force field (for organic substituents) plus a few metal-dependent parameters chosen to reproduce the quantum chemical (RHF/SBK(d)) structure of Zr(N(H)TMS)3Me.25b Some confidence in this approach can be gained from the ability of MM to reproduce the RHF/SBK(d) structures of Zr(NH2)3Me and Zr(N(H)SiH3)3Me with no additional parameters. Finally, with the same parameters an MM optimization of Zr(NHSi′)3Me was performed and compared to experiment21

6478 J. Phys. Chem., Vol. 100, No. 16, 1996

Cundari et al.

TABLE 2: Transition-State Geometriesa ZrNi (Å)

NiHt (Å)

HtC (Å)

CZr (Å)

ZrHt (Å)

ZrNiHt (deg)

ZrNiHi (deg)

ZrHtC (deg)

H Me Et i-Bu Np vinyl CtCH

R

1.89 1.86 1.89 1.90 1.89 1.89 1.90

1.52 1.44 1.43 1.42 1.43 1.44 1.46

0.96 1.43 1.43 1.44 1.42 1.40 1.30

2.07 2.44 2.52 2.52 2.57 2.46 2.62

1.98 1.94 1.95 1.96 1.97 2.00 2.29

70 71 70 71 71 72 85

176 178 175 177 176 179 165

82 92 95 95 97 91 89

Ph η2-C(O)H

1.89 1.93

1.43 1.34

1.42 1.39

2.48 2.96

2.00 2.53

72 99

180 147

92 94

η2

1.93

1.38

1.35

2.92

2.52

98

148

93

-C(O)OH

other

CRdCβ ) 1.35 Å Zr‚‚‚Cβ ) 2.68 Å CRtCβ ) 1.24 Å CRtCβ-Hβ ) 166° CdO ) 1.26 Å Zr-O ) 2.21 Å CdO ) 1.27 Å Zr-O ) 2.22 Å

a

Important metric data are given for RHF-optimized TSs. Bond lengths and bond angles involving main group elements are in accord with standard values.20 See 4-i-Bu for definition of Ht, Hi, and Ni.

(MM in parentheses): ZrC ) 2.23 Å (2.28 Å); ZrN ) 2.032.05 Å (2.09 Å); NSi ) 1.74-1.75 Å (1.76 Å); NZrN ) 110°112° (111°); CZrN ) 107°-108° (108°); ZrNSi ) 151°-152° (150°). The goal of this simple exercise is to use MM to assess the steric effect on the ZrNSi angle upon substituting TMS in Zr(N(H)TMS)3Me with Si′. The agreement is quite good and supports the contention that large ZrNSi angles in Zr(NHSi′)3Me are primarily steric in origin. Taken together, the findings indicate that bonding at Zr and at its inner coordination sphere is dominated by electronic factors while the substituent geometry is largely determined by sterics. This suggests that bulky substituents (usually used to engender kinetic and thermodynamic stability) can be treated with less intensive methods (e.g., MM or smaller ab-initio basis sets) than the TM core, although this must be investigated on a case-bycase basis. “Splicing” approaches26 have been investigated for organic systems, although not systematically for TM complexes, and represent a promising route to more efficient modeling of organometallics. 2. Zr-Imido and Organic Products. Products ((NH2)2Zr(dNH) and RH) have been discussed previously.9c,14 As expected for simple organics, agreement between theoretical and experimental structures is very good and the RHF/SBK(d) results are comparable to the all-electron results, e.g., RHF/6-31G(d) calculations.20 The Cs symmetry imido (NH2)2ZrdNH has been discussed previously.14 Geometries about Zr and Namido in 3-H3 are near trigonal planar and ZrNimidoH ) 179°. For 3-H3 and the

methane-activating intermediate (NHSi′)2Zr(dNSi′) one would expect substrates to approach perpendicularly to the ZrN3 plane. Calculated ZrNimido and ZrNamido bond lengths in 3-H3 are 1.83 and 2.10 Å, respectively, in good agreement with X-ray data as discussed previously.14 It is of interest to study models more closely resembling (NHSi′)2Zr(dNSi′).4a The imido minimum, 3-H3, although close to a trigonal planar coordination geometry (Zr is 0.04 Å out of the N3 plane), has a soft vibrational mode (calculated to be 56 cm-1) for pyramidalization at Zr. Thus, the Zr coordination environment should be quite sensitive to steric effects. We “eliminated” methane (black atoms in eq 5; hydrogen atoms on TMS substituents are omitted for clarity) from C3Zr(N(H)TMS)3Me and optimized the resulting (N(H)TMS)2Zr(dNTMS), 3-TMS3, using a splicing approach26 (STO-3G for

C and H atoms in TMS methyls), since the full RHF/SBK(d) calculation is not feasible. The resulting geometry of 3-TMS3

yields ZrNamido (2.10 Å) and ZrNimido (1.84 Å) bond lengths nearly equivalent to those in 3-H3. The most interesting differences between 3-H3 and 3-TMS3 are pyramidalization in the latter (Zr is 0.04 Å and 0.32 Å out of the N3 plane in 3-H3 and 3-TMS3, respectively) and the deviation of ZrNimidoSi (165°) from linearity in 3-TMS3. It is important to assess whether differences between 3-H3 and 3-TMS3 are electronic or steric in origin. The following analysis assumes that TMS and silyl are electronically similar. Replacing methyls in 3-TMS3 with H’s yields 3-silyl3. Optimizing the structure (RHF/SBK(d)) yields a stationary point similar to 3-H3, i.e., trigonal planar Zr (Zr is coplanar with the three N atoms of the ligands), with ZrNimido ) 1.84 Å, ZrNamido ) 2.11 Å, and ZrNimidoSi ) 179°. Although an exhaustive search of conformational space for 3-TMS3 would be needed, the results suggest that pyramidalization and imido bending are relatively soft modes and that distortions seen in 3-TMS3 (relative to 3-H3) arise from steric factors. Steric repulsions among substituents in 3-Si’3 will exceed that of 3-TMS3, and thus, pyramidalization and imido bending may be greater in experimental systems. Pyramidalization of the metal is of obvious steric advantage for trapping a CH bond, since it opens up a vacant coordination site. Pyramidalization is also electronically beneficial, since it lowers the energy of the metal-based lowest unoccupied molecular orbial (a dz2 orbital with some pz and s character), which accepts C-H σ density upon methane coordination.23 In a previous study23 pyramidalization was achieved by π-loading (i.e., increasing x in d0 M(NH2)3-x(dNH)x). The present results suggest that the use of very bulky ligands may achieve similar results. 3. Transition State. Important metric data for the transition states of RH elimination (and the microscopic reverse, hydrocarbon C-H activation) are given in Table 2. a. Alkane Elimination. Transition states for alkane elimination closely resemble that for methane elimination.9c A representative example for isobutane elimination is shown in 4-i-Bu. The imaginary mode in the elimination TSs corre-

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J. Phys. Chem., Vol. 100, No. 16, 1996 6479

sponds to NH cleavage and CH bond formation, with a large angle about Ht in 4, and these results are consistent with high kinetic isotope effects.11 The ZrNi distances in TSs of 4 are closer to ZrNimido than ZrNamido bond lengths. The ZrNiHi angles are close to 180°, and the dispositions of the exocyclic NH2 groups in 4 are similar to those in 3-H3. Thus, computations support the experimental interpretation4,5 of a “late” TS for methane elimination from d0 amido(methyl) complexes and an early TS for the microscopic reverse. Using eq 4 yields rbp ) 0.54, 0.57, 0.58, and 0.60 Å for R ) Me, Et, i-Bu, and Np, respectively, signifying an earlier TS for CH activation (hence, a later TS for the microscopic reverse, elimination) of heavier alkanes. Crabtree et al.24 estimate that the TS for CH activation falls in the region of rbp ≈ 0.5 Å, consistent with the present calculations. b. Carbonyl-Containing Systems. As with reactants, the systems most unlike the rest are R ) formyl (5a) and carboxyl (5b). Using eq 4 yields nbp ) 1.13 Å (R ) C(O)H) and 1.13

Å (R ) C(O)OH) compared to values of ≈ 0.55-0.60 Å for R ) alkyl (vide supra), suggesting an earlier TS for CH activation (hence, later for elimination) of formaldehyde and formic acid vs alkanes. However, some metric data for 5a and 5b show them to be earlier (closer to tris(amido) reactants) than TSs for H2 and alkane eliminationsZrNiHi angles are much smaller, and NiHt distances shorter for 5a and 5b than the TSs for hydrocarbon elimination (see Table 2). Thus, use of rbp to probe stationary points with widely differing geometries should be done with caution. Nevertheless, calculations clearly point to donor functionalities in R having a profound influence on TS structure. It will be of interest to see if structural differences translate into energetic differences.

c. Π-Containing Systems. Phenyl and vinyl groups have the potential to interact with Zr through their π-orbitals. However, there is no geometric evidence for such interactions in the TSs for elimination of benzene and ethylene from Zr(NH2)3Ph (6) and Zr(NH2)3 vinyl (7), respectively. One can infer that elimination rates for olefins and aromatics from Zr-amidos should be relatively insensitive to leaving group substituents. Bercaw et al. conclude, based on kinetic studies of vinylic and arene C-H activation by Cp*2ScCH3, that there is little interaction between substrate π-system and Sc in the σ-bond metathesis TS.27 Similar experiments for d0 imidos would be of great interest. The TS for acetylene elimination (8) shows interesting differences from 6 and 7. The Zr‚‚‚CR distance in 8 is 2.62 Å,

much longer than those of other hydrocarbon elimination TSs, and nearly equal to the Zr‚‚‚Cβ distance of 2.68 Å. Geometry optimization of an acetylene π-complex of 3-H3 yields a Cs symmetry minimum with Zr‚‚‚C distances of ≈2.75 Å (similar to that in 8). In experimental studies of alkyne elimination from Zr(NHSi′)3(CtCR),4a no evidence is seen for elimination products. Carrying out the elimination experiments in the presence of an external alkyne shows exchange between substrates, suggesting that elimination is taking place but that the alkyne does not dissociate unless displaced by another alkyne.4a The lowest unoccupied MO for a three-coordinate d0 imido is a metal orbital ≈dz2 in character. This orbital has the appropriate symmetry to interact with π-bonding MOs, but the leaving group π MOs in 6 and 7 are not properly situated to overlap with the metal orbital. Acetylene has a pair of perpendicular CC π-orbitals so that one can interact with the vacant dσ. Note that the availability of the dσ to interact with donor functionalities on the leaving group is a direct consequence of a late, imido-like TS with significant Zr-CR bond breaking. d. Energetics. Activation enthalpies and activation free energies are calculated for hydrocarbon elimination from our model reactants (eq 3). These data are collected in Table 3. On average, calculated ∆Gqelim values are 7 ( 2 kcal mol-1 higher than the experimental values for the six hydrocarbyls (Me, Et, i-Bu, Np, vinyl, and Ph) for which there is a computational model and an experimental analogue. In a

TABLE 3: Reaction Energeticsa R

∆Hqelim

∆Sqelim

∆Gqelim

∆Hrxn

∆Srxn

∆Grxn

∆Hqact

∆Sqact

∆Gqact

H Me Et i-Bu Np vinyl CtCH phenyl C(O)H C(O)OH

27.3 34.0 34.2 33.5 33.1 30.9 36.4 29.3 28.4 27.4

-2.872 -5.160 -8.630 -5.942 -4.855 -7.448 -4.102 -3.150 -6.339 -7.163

28.4 35.9 37.5 35.7 34.9 32.7 37.9 30.5 30.8 30.1

18.8 19.7 18.0 19.3 19.3 25.9 46.3 27.0 30.5 34.3

22.258 21.997 20.248 27.495 24.297 23.110 23.292 25.141 27.813 28.335

10.4 11.5 10.4 9.0 10.2 17.2 37.6 17.6 20.1 23.7

8.5 14.3 16.2 14.2 13.8 5.0 -9.9 2.3 -2.1 -6.9

-25.130 -27.157 -28.878 -33.437 -29.152 -30.558 -27.394 -28.281 -34.152 -35.498

17.9 24.4 27.1 26.7 24.7 16.4 0.3 12.9 10.6 6.4

a Enthalpies and free energies are given in kcal mol-1 and were calculated using MP2 energies. Entropic data is in units of cal mol-1 K-1. For definition of energetic quantities see eq 3. ∆Hqelim ) HTS - HZr(NH2)3R; ∆Hrxn ) HRH + H(NH2)2Zr(dNH) - HZr(NH2)3R; ∆Hqact ) ∆Hqelim - ∆Hrxn. Entropies and free energies are calculated similarly. All data assume a temperature of 373.15 K.

6480 J. Phys. Chem., Vol. 100, No. 16, 1996

Cundari et al. expected to possess near-degenerate conformers separated by small energy barriers.23,29 Following the IRCs for elimination TSs 4 in the direction of products shows the alkanes to remain coordinated to imido 3-H3 indicative of stabilizing substratecomplex interaction (geometries are given in Supporting Information). A typical example is shown for isobutane, 9-i-BuH.

Figure 1. Plot of experimental ∆Gqelim(RH) from Zr(NHSi′)3R vs calculated ∆Eqelim, ∆Hqelim and ∆Gqelim for RH elimination from Zr(NH2)3R. Equations for the best-lines are given (R is the linear correlation coefficient).

previous study of methane elimination from group IVB methyl(amido) complexes9c it was found that going to higher levels of theory (in particular, adding polarization functions to hydrogen) reduces calculated elimination barriers by 3-4 kcal mol-1. In Figure 1 experimental ∆Gqelim values for hydrocarbon elimination from Zr(NHSi′)3R are plotted vs calculated ∆Eqelim, ∆Hqelim, and ∆Gqelim for hydrocarbon elimination from Zr(NH2)3R. Inspection of Figure 1 shows that the correlation between theory and experiment is nearly equivalent for ∆Hqelim and ∆Eqelim, which is better than the correlation for ∆Gqelim. This may be due in large part to the difficulties in accurate calculation of entropies.20 Despite differences in model and experimental systems, the correlations in Figure 1 are reasonable, although not spectacular. Calculations show that elimination barriers for π- and COcontaining hydrocarbons (average ∆Hqelim ≈ 30 kcal mol-1) are lower than for alkane elimination (average ∆Hqelim ≈ 34 kcal mol-1). Inspection of the experimental data shows a similar trend, although differences are smaller.4a Caution should be exercised in attaching undue quantitative significance to a correlation between leaving group donor ability and elimination barriers for two reasons. First, ∆Hqelim(acetylene) is higher than those of other substrates although there is clear evidence of an interaction between Zr and the leaving group in TS 8. Second, ∆Hqelim(ethylene) is consistent with those of other systems with a potential donor functionality despite the fact that the geometry of TS 7 suggests no interaction between vinyl and Zr. Given a late TS for elimination, one can propose that a donor in the leaving group will play a bigger role in stabilizing the TS than reactants, since the former is more electronically unsaturated, leading to a lower elimination barrier. 4. Intrinsic Reaction Coordinate and Substrate-Imido Interaction. Increasing interest has focused on interactions between very weak ligands (e.g., alkanes) and TM complexes and on their importance in catalysis.28 Calculations23 suggest that the right combination of geometry and ancillary ligands can yield appreciable (g10 kcal mol-1) methane-binding enthalpies. This work raises several questions. First, how does the binding of larger alkanes compare with that of methane? Second, what are the binding modes of substrates like ethylene and benzene with π-donor ability? Third, given the nature of the models, can we address the likelihood of d0-alkane adduct formation in more sterically congested experimental complexes? a. Intrinsic Reaction Coordinate for Alkane Elimination. Elimination of methane from Zr(NH2)3Me yields a (NH2)2Zr(dNH)‚‚‚CH4 adduct with a binding enthalpy of 6.3 kcal mol-1 relative to those of imido and methane.23 Alkane adducts are

Replacing one of the methane H’s in 9-MeH with larger alkyls causes only slight changes in the geometry of the Zr‚‚‚η2-CH moiety in the adducts obtained from the IRC calculations. The Zr‚‚‚C and Zr‚‚‚H distances for adducts of larger alkanes are 3.02 ( 0.01 Å and 2.51 ( 0.04 Å, respectively, comparable to those in 9-MeH: Zr‚‚‚C ) 3.05 Å, Zr‚‚‚H ) 2.55 Å.22 Calculated binding energies, relative to those of separate 3-H3 and alkane, increase as the alkane becomes larger: ∆Eadd (kcal mol-1) ) -7.6 (MeH), -9.3 (EtH), -10.0 (i-BuH), -11.4 (NpH). Gas-phase acidity30 (∆H°acid (for the reaction RH(g) f R-(g), ∆H°acid (kcal mol-1) ) 416.6 (MeH), 420.1 (EtH), 412.9 (i-BuH), 408.9 (NpH)) of the alkanes shows a very poor linear correlation with ∆Eadd. Alkane properties that measure their intrinsic basicity show reasonable linear correlation with ∆Eadd, e.g., ionization potentials31 (IP(eV) ) 12.6 (CH4), 11.5 (EtH), 10.6 (i-BuH), 10.4 (NpH)). b. Intrinsic Reaction Coordinate for Elimination of Π-Containing Hydrocarbons. Following the IRC for elimination of π-containing hydrocarbons is of interest, since two potential donor functionalities exist on the substrate and it is not clear for d0 complexes which is preferred.32 The IRCs for elimination of acetylene, ethylene, and benzene lead to approximate Cs symmetry adducts (10-12, respectively) best described as π-complexes. Adducts 10 and 11 are best described as η2-CC,

since ZrC distances are equivalent. Designation of hapticity for 12 is not straightforward; ZrC distances range from 2.89 to 3.88 Å. The distance from Zr to the centroid of the six C atoms is 3.11 Å, and the distance from Zr to the centroid of the three C atoms closest to Zr is 2.88 Å. The former is much longer than the distances to the centroids of the CC bonds for acetylene (2.69 Å, 10) and ethylene (2.75 Å, 11), so we represent 12 as (NH2)2Zr(dNH)(η3-C6H6). Calculated energies for coordination to (NH2)2Zr(dNH) are -23.8 (C2H4), -23.8 (C2H2), and -23.5 (C6H6) kcal mol-1, much greater than those for alkane adducts. This is plausible result, since a π-orbital is expected to be a much better donor than a CH σ-bond. Analysis of the IRCs shows the preferred elimination pathways for ethylene, acetylene, and benzene and does not lead to a η2-CH coordinated adduct (or σ-complex) but rather to a π-complex. Feher and Jones32a have studied arene reductive elimination by low-valent Rh complexes and conclude that an η2-arene is the preferred elimination product, although for a related Ir system Stoutland and Bergman32b suggest that a

Elimination and Activation of Hydrocarbons

J. Phys. Chem., Vol. 100, No. 16, 1996 6481

π-complex does not lie along the reaction coordinate for ethylene CH activation. It is not possible to isolate an η2-CH-coordinated ethylene adduct of (NH2)2Zr(dNH) in C1 symmetry. A Cs symmetry TS, 13, is calculated to have a complexation energy

of -5.2 kcal mol-1 (cf. the methane complexation energy of -7.6 kcal mol-1 in 9-MeH).22 However, 13 is a TS (as determined by calculation of the energy Hessian) with an appreciable imaginary frequency (114i cm-1), which breaks Cs symmetry and leads to π-complex 11 18.6 kcal mol-1 lower in energy. Thus, although some points along the IRC for ethylene elimination from 1-vinyl may resemble η2-CH-coordinated ethylene, no minimum corresponding to this coordination mode was found. In the absence of steric constraints the IRCs show a clear electronic preference for R-elimination of π-containing substrates, leading to π-complexes in preference to σ-complexes. Analysis of IRCs for benzene elimination from 1-Ph and acetylene elimination from 1-C2H supports similar conclusions. Hence, for the microscopic reverse (vinylic, acetylenic and arene CH activation) IRC results imply that the reaction does not proceed through initial formation of an η2-CH adduct (or conversion of a π-complex to an η2-CH adduct) but rather proceeds directly from π-complex to product. c. Toward the Study of Adducts of Larger Model Complexes. Studies of hydrocarbon coordination to models such as (NH2)2Zr(dNH) provide valuable insight into the bonding of alkanes to TM complexes in the absence of steric influences.22 However, it is valid to inquire whether hydrocarbon coordination can occur in the presence of Si(t-Bu)3 substituents. For ethylene one must address the preference of different coordination modes (13 vs 11) for the full ligand set. To address these issues, we proceeded as follows. Starting with RHF/SBK(d)-optimized23 9-MeH, three Si(t-Bu)3 groups were grafted on in place of two amido and one imido protons.35 With the ZrN3‚‚‚η2-CH core frozen, the remaining atoms were optimized using molecular mechanics.25,343 The MM-optimized (NHSi′)2Zr(dNSi′)‚‚‚CH4 adduct is shown schematically in 14 (amido protons omitted for clarity). Although no exhaustive search of conformational

space was done for 14, the main interest is in finding that Si′ can relax so that there are no close contacts (defined as nonbonded atoms closer than the sum of their van der Waals radii) between atoms in methane and atoms in NSi′ and NHSi′. Adduct 14 is also very interesting since a conformation such as this is consistent with selectivity patterns: primary C-H bonds are activated by Zr-imido, but secondary and tertiary C-H bonds are not.4a From methane to primary C-H bond

Figure 2. Molecular-mechanics-calculated structures 15a and 15b are σ- and π-complexes of ethylene, respectively, with (NHSi′)2Zr(dNSi′), Si′ ) Si(t-Bu)3. Most H atoms on the Zr complex are omitted for clarity except amido protons and methyl protons on Si′, which have close contact with ethylene H’s.

activation, it seems plausible that the distal proton (Hd in 14) could be replaced by an alkyl. Activating a secondary (tertiary) C-H bond would entail replacement of one (both) of the proximal protons (Hp in 14) with an alkyl group and would cause significant steric repulsion with amido Si′ substituents. It is not feasible at this time to address the energetics of methane coordination to (NHSi′)2Zr(dNSi′) with quantum mechanical calculations. If we assume a ∆Hadd(MeH) equal to that for (NH2)2Zr(dNH),22 ≈6-7 kcal mol-1, this may be insufficient to overcome the unfavorable T∆S term to yield a negative ∆Gadd(MeH) for (NHSi′)2Zr(dNSi′). It is also unclear what energetic barriers must be surmounted (e.g., arising from ligand reorganization due to intramolecular agostic bonding in the three-coordinate imido) to coordinate methane. Wolczanski and co-workers28b have addressed similar issues in their experiments. However, the MM calculations show that from a steric viewpoint there is sufficient room to access the Zr-imido active site in (NHSi′)2Zr(dHSi′) and to permit coordination and activation of methane and primary alkanes. Another point of interest concerns ethylene coordination to (NHSi′)2Zr(dNSi′). The quantum calculations show a preference for π-complex 11, which is 19 kcal mol-1 lower in energy than σ-complex 13. However, steric considerations may lessen this energy difference. Methane adduct 14 was modified by replacement of two noncoordinated protons (Hd and Hp2) with methylene to yield (NHSi′)2Zr(dNSi′)‚‚‚η2-CH(ethylene); see 15a in Figure 2. As before, the ZrN3-η2-CH core geometry was fixed and all other metric parameters optimized with molecular mechanics. A second MM optimization was performed by taking 15a and setting the Zr‚‚‚Calkene distances to those for RHF/SBK(d)-optimized π-complex 11 to yield (NHSi′)2Zr(dNSi′)‚‚‚η2-CC(ethylene), 15b in Figure 2, and by optimizing the entire complex apart from the ZrN3-η2-CC core.

6482 J. Phys. Chem., Vol. 100, No. 16, 1996 The MM exercise shows π-complex 15a to suffer more steric repulsion with Si′ substituents than the σ-complex; there are three H(ethylene)‚‚‚H(Si′) close contacts in 15b but only one such close contact in 15a. The MM calculations predict that 15a is 21 kcal mol-1 lower in energy than 15b. Although it would be unwise to put quantitative faith in the calculated MM (or quantum mechanical) energies, the combination of calculations suggests that the electronic preference for a π-complex is counteracted by a steric preference for a σ-complex. Hence, although calculations on simple models indicate that an olefin π-complex precedes vinylic C-H activation, η2-CH coordination may be more competitive in the experimental system. Summary This paper describes a computational study of hydrocarbon activation and elimination by high-valent Zr complexes, a process of importance in the design of advanced materials precursors and catalytic alkane functionalization. Several important conclusions were reached as a result of this study and are summarized below. (1) For the tris(amido)-ZrIV-alkyl model reactants, Zr(NH2)3R (R ) alkyl) there is no evidence of agostic interactions between Zr and C-H bonds for C atoms not covalently bonded to Zr. The best evidence for agostic interactions in alkyls is between Zr and CR-HR bonds, but these interactions are still considerably less than in characterized high-valent, agostic complexes. Similarly, agostic interactions between Zr and NRHR bonds are very weak. (2) Calculations indicate that for complexes of the type Zr(N(H)X)3CH3 the geometry of the ZrN3C core is dominated by electronic considerations (e.g., Zr dπ-N pπ bonding), while substituent orientation is largely determined by steric factors. This suggests computational approaches whereby less intensive methods can be used to describe steric interactions on the periphery with more sophisticated methods used to describe the inner coordination sphere, a potentially valuable tool in the modeling of more realistic organometallics. (3) Replacement of NH and NH2 in the parent imido, (NH2)2Zr(dNH), with more realistic NTMS and N(H)TMS groups causes the imido ligand to coordinate in an increasingly bent fashion (i.e., ZrNimidoR , 180°) and the coordination geometry of Zr to distort from trigonal planar to pyramidal. Calculations suggest that the origin of these changes is steric and thus would presumably be greater in the experimental CH-activating transient (NHSi′)2Zr(dNSi′). These geometric changes should facilitate coordination of substrate (RH) to Zr-imido. Calculated complexation energies increase as the alkane becomes larger. A combination of quantum and molecular mechanical calculations suggest that even with the experimental Si(t-Bu)3 substituents alkane coordination is possible. It is uncertain in light of an expected unfavorable T∆S term whether alkane complexation enthalpies (estimated to be 6-9 kcal mol-1) are large enough to yield a negative ∆Gadd(RH) for alkane coordination to (NHSi′)2Zr(dHSi′). Calculations suggest coordination may be most favorable for primary carbons of a large alkane. (4) Calculated elimination TSs can best be described as “late” or closer to imido/RH products. Transition states for elimination of formaldehyde and formic acid showed substantial interaction between Zr and the carbonyl O. For substrates that have a π-system (ethylene, benzene, and acetylene), only acetylene showed any structural evidence for interaction between the metal and the π-system on the leaving group in the elimination transition state. Complexes with donor functionalities in the leaving group (π- and carbonyl-systems) have elimination

Cundari et al. barriers that are calculated to be ≈4 kcal mol-1 lower than those for which R ) alkyl. Such a result may be rationalized as being consistent with a coordinatively unsaturated Zr in the late TS being stabilized preferentially (vs the tetrahedral ground state) and yielding a lower ∆Hqelim. (5) In all cases, elimination of a hydrocarbon containing a π-system results not in a σ-complex (i.e., η2-CH coordinated to the metal) but rather in a π-complex. In the case of ethylene, quantum calculations show the π-complex to be 19 kcal mol-1 below the σ-complex. As mentioned above, there is no evidence for interaction between the Zr and the π-system in the TS for ethylene elimination, so π interaction between the Zr and substrate must come into play very late in the elimination process. Molecular mechanics calculations suggest that steric factors favor the σ-complex over the π-complex for the full (NHSi′)2Zr(dNSi′)‚‚‚(ethylene) by 21 kcal mol-1. Thus, in the experimental system π- and σ-complexes may be more energetically competitive and an equilibrium between the two may occur prior to C-H activation. (6) The correlation between the calculated RH elimination barrier for Zr(NH2)3R and the experimentally determined ∆Gqelim(RH) for Zr(NHSi′)3R, although not perfect, is respectable given the difference in steric bulk between the Si(t-Bu)3 substituents studied experimentally and the H used in computational models. The computational results further support experimental inferences about the nature of the transition state and that the main energetic expense in reaching the elimination TS is not dominated by steric considerations brought about by bulky Si′ groups. Acknowledgment. T.R.C. acknowledges the Petroleum Research Fund (administered by the American Chemical Society), National Science Foundation (CHE-9314732), and Air Force Office of Scientific Research (93-10105) for support of ECP studies at Memphis. T.R.C. also thanks Professor Pete Wolczanski (Cornell) and his group for numerous discussions concerning experimental aspects of hydrocarbon activation/ elimination. The major portion of the calculations described here were carried out using the resources of the Cornell Theory Center, which receives major funding from NSF and New York State. Addtional funding comes from ARPA, NIH, IBM, and other members of the center’s Corporate Research Institute. T.R.C. gratefully acknowledges the Cornell Theory Center staff for their help and hospitality during his stay at Cornell. Supporting Information Available: Tables of energies (RHF and MP2) for all products and reactants, enthalpic and entropic corrections (at 373.15 K) needed to convert from energies to enthalpies to free energies, and Cartesian coordinates (in Å) for alkane adducts (4 pages). Ordering information is given on any current masthead page. References and Notes (1) (a) E-mail: [email protected]. (b) Address: Department of Chemistry, Johns Hopkins University. E-Mail: [email protected]. (2) (a) Dubois, L. H.; Zegarski, B. R.; Girolami, G. S. J. Electrochem. Soc. 1992, 139, 3603. (b) Saeki, Y.; Matsuzaki, R.; Yajima, A.; Akiyama, M.; Yokohama, N.; Hinode, K.; Homma, Y. J. Electrochem. Soc. 1989, 136, 882. (c) Fix, R. M.; Gordon, R. G.; Hoffman, D. M. J. Am. Chem. Soc. 1990, 112, 7833. (d) Winter, C. H.; Sheridan, P. H.; Lewkebandara, T. S.; Heeg, M. J.; Proscia, J. W. J. Am. Chem. Soc. 1992, 114, 1095. (e) Weiller, B. H. Mater. Res. Soc. Symp. Proc. 1993, 282, 605. (3) ActiVation and Functionalization of Alkanes; Hill, C. L., Ed.; Wiley: New York, 1989. (4) (a) Bis(amido) Zr-imido. Cummins, C. C.; Baxter, S. M.; Wolczanski, P. T. J. Am. Chem. Soc. 1988, 110, 8731. Wolczanski, P. T. (Cornell). Personal communication. (b) Bis(amido) Ti-imido. Cummins, C. C.; Schaller, C. P.; Van Duyne, G. D.; Wolczanski, P. T.; Chan, A. W.

Elimination and Activation of Hydrocarbons E.; Hoffmann, R. J. Am. Chem. Soc. 1991, 113, 2985. (c) Bis(alkoxy) Tiimido. Bennett, J. L.; Wolczanski, P. T. J. Am. Chem. Soc. 1994, 116, 2179. (5) (a) Bis(amido) Ta-imido. Schaller, C. P.; Wolczanski, P. T. Inorg. Chem. 1993, 32, 131. (b) A related system in which the putative methaneactivating species is (NHSi′)2V(dNSi′) is described in the following. de With, J.; Horton, A. D. Angew. Chem., Int. Ed. Engl. 1993, 32, 903. (6) Transamination has been seen in WVI chemistry (Chan, D. M. T.; Fultz, W. C.; Nugent, W. A.; Roe, D. C.; Tulip, T. H. J. Am. Chem. Soc. 1985, 107, 251.), but there is no evidence for coordinated amines in ZrIV chemistry.4a (7) (a) Cundari, T. R. Int. J. Quantum Chem., Proc. Sanibel Symp. 1992, 26, 793. (b) Cundari, T. R. Organometallics 1994, 13, 2987. (8) (a) Hoffmann, R.; Saillard, J. Y. J. Am. Chem. Soc. 1984, 106, 2006. (b) Low, J. J.; Goddard, W. A. J. Am. Chem. Soc. 1986, 108, 6115, and references therein. (c) Koga, N.; Morokuma, K. J. Chem. Phys. 1990, 94, 5454. (d) Ziegler, T. L.; Tschinke, V.; Fan, L.; Becke, A. D. J. Am. Chem. Soc. 1989, 111, 9177. (e) Silvestre, J.; Calhorda, M. J.; Hoffmann, R.; Stoutland, P. O.; Bergman, R. G. Organometallics 1986, 5, 1841. (9) (a) Goddard, W. A.; Steigerwald, M. L. J. Am. Chem. Soc. 1984, 106, 308. (b) Hoffmann, R.; Saillard, J.-Y.; Rabaaˆ, H. J. Am. Chem. Soc. 1986, 108, 4327. (c) Cundari, T. R. J. Am. Chem. Soc. 1992, 114, 10557. (10) (a) Periana, R. A.; Taube, D. J.; Evitt, E. R.; Lo¨ffler, D. G.; Wentrcek, P. R.; Voss, G.; Masuda, T.; Science 1993, 259, 340. (b) Parkyns, N. D. Chem. Br. 1990, 9, 841. (11) An examination of the literature for C-H activation by d0 transition metal complexes up to 1988 can be found in Rothwell, I. P. in ref 2, p 151. (12) Cundari, T. R.; Gordon, M. S. J. Am. Chem. Soc. 1993, 115, 4210. (13) Brown, T. L. (Illinois). Personal communication. (14) Cundari, T. R. J. Am. Chem. Soc. 1992, 114, 7879. (15) (a) Krauss, M.; Stevens, W. J.; Basch, H.; Jasien, P. G. Can. J. Chem. 1992, 70, 612. (b) Stevens, W. J.; Basch, H.; Krauss, M. J. Chem. Phys. 1984, 81, 6026. (c) -31G basis set. Ditchfield, R.; Hehre, W. J.; Pople, J. A. J. Chem. Phys. 1971, 54, 724. Hehre, W. J.; Ditchfield, R.; Pople, J. A. J. Chem. Phys. 1972, 56, 2257. (16) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Jensen, J. H.; Koseki, S.; Matsunaga, N. M.; Gordon, M. S.; Nguyen, K. A.; Su, S.; Windus, T. L.; Elbert, S. T. J. Comput. Chem. 1993, 14, 1347. (17) Ruedenberg, K.; Schmidt, M. W.; Dombek, M. M.; Elbert, S. T. Chem. Phys. 1982, 71, 41, 51, 65. (18) Gonzalez, C.; Schlegel, H. B. J. Chem. Phys. 1989, 90, 2154.

J. Phys. Chem., Vol. 100, No. 16, 1996 6483 (19) (a) Carsky, P.; Hess, B. A.; Schaad, L. J. J. Comput. Chem. 1984, 5, 280. (b) Pople, J. A.; Binkely, J. S.; Seeger, R. Int. J. Quantum Chem. 1976, S10, 1. (20) Experimental values for numerous organic species can be found in Pople, J. A.; Hehre, W. J.; Radom, L.; Schleyer, P. v. R. Ab-Initio Molecular Orbital Theory; Wiley: New York, 1986, and references therein. (21) Cummins, C. C.; van Duyne, G. D.; Schaller, C. P.; Wolczanski, P. T. Organometallics 1991, 10, 164. (22) Fachinetti, G.; Fochi, G.; Floriani, C. J. Chem. Soc., Dalton Trans. 1977, 1946. (23) Cundari, T. R. Organometallics 1993, 12, 1998. (24) Crabtree, R. H.; Holt, E. M.; Lavin, M.; Morehouse, S. M. Inorg. Chem. 1985, 24, 1986. (25) (a) A description of the MM2 force field can be found in Burkert U.; Allinger, N. L. Molecular Mechanics; ACS Monograph 177, American Chemical Society: Washington, DC, 1982. (b) The few force constants and equilibrium bond distances and angles involving Zr were estimated from RHF/SBK(d) calculations of the energy Hessian for Zr(N(H)TMS)3Me. Torsional barriers about metal-ligand bonds were set to zero. Cundari, T. R.; Moody, E. W. Unpublished results. (26) Jensen, J. H.; Gordon, M. S. J. Comput. Chem. 1991, 12, 421. (27) Thompson, M. E.; Baxter, S. M.; Bulls, A. R.; Burger, B.; Nolan, M. C.; Santarsiero, B. D.; Schaefer, W. P.; Bercaw, J. E. J. Am. Chem. Soc. 1987, 109, 203. (28) (a) Wasserman, E. P.; Moore, C. B.; Bergman, R. G. Science 1992, 255, 315. (b) Schaller, C. P.; Bonnano, J. B.; Wolczanski, P. T. J. Am. Chem. Soc. 1994, 116, 4133. (29) Koga, N.; Morokuma, K. J. Phys. Chem. 1990, 94, 5454. (30) DePuy, C. H.; Gronert, S.; Barlow, S. E.; Bierbaum, V. M.; Damrauer, R. J. Am. Chem. Soc. 1989, 111, 1968. (31) CRC Handbook 64th ed.; Weast, R. C., Ed.; CRC Press: Boca Raton, FL, 1983; p E-70. (32) (a) Jones, W. D.; Feher, F. J. Acc. Chem. Res. 1989, 22, 91. (b) Stoutland, P. O.; Bergman, R. G. J. Am. Chem. Soc. 1985, 107, 4581. (33) The Chem 3D+ program was used as a graphical user interface. All Si′ groups have local C3 symmetry. All C-Si-C-C, Si-C-C-H, and C-C-C-H torsional angles start out at standard values to make the conformation about Si-C and C-C bonds staggered.

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