Organometallics 1996, 14, 4349-4358
4349
Titanium-Ethylene Complexes Proposed To Be Intermediates in Ziegler-Natta Catalysis. Can They Be Detected through Vibrational Spectroscopy? Vidar R. Jensen" and Knut J. Bwve Department of Chemistry, University of Bergen, Allkgaten 41, N-5007 Bergen, Norway
Nina Westberg and Martin Ystenes Department of Inorganic Chemistry, The Norwegian Institute of Technology, N - 7034 Trondheim, Norway Received November 18, 1994@ Quantum chemical prediction of geometry and vibrational frequencies has been performed (1)and 4B1 (2), of Ti(C2H4)+,for a t the SCF level of theory for the two lowest states, 2 A ~ and finally, for C12Ti(CH3)(C2H4)+,for the neutral, bimetallic, A1H2Cu-C1)2TiC12(CH3)(CzH4), unperturbed C2H4 a s a reference. For the latter three species, MP2 theory and gradientcorrected density functional theory have also been applied. The titanium-ethylene bond in 1 has a distinct covalent character, with large changes in ethylene geometry upon coordination. For the rest of the complexes only minor changes in the geometry of the ethylene unit appear upon coordination. Constrained space orbital variation (CSOV) calculations on 2 reveal t h a t the titanium-ethylene bond consists of contributions from both intraunit polarization of Ti+ and C2H4 and charge transfer from C2H4 to the metal. This type of bond also seems to be present in the two larger complexes, and, in spite of the small effects on ethylene geometry, the coordination nevertheless influences the frequencies, and also the IR intensities, substantially. In two regions of the spectra, dominated by the C-C stretching vibration and the out-of-plane deformation modes of ethylene, respectively, the predicted changes are particularly distinct and should be useful for spectral identification of titanium-ethylene complexes. 1. Introduction
The many advantageous properties of Ziegler-Natta catalysts have inspired numerous scientific studies during the last decades, and researchers have suggested several mechanistic schemes for the olefin polymerization using these catalysts, see, e.g., refs 1-6. Most of the proposed mechanisms involve a metal-monomer JC complex intermediate. No direct proof for the existence of this complex has, however, been presented yet, but there are several observations that indicate its existence. Establishing whether such a complex is part of the propagation mechanism should therefore be given priority. In a study concerning the polymerization of 4-methylpentene with a vc13 catalyst, Burfield' reported several indications (e.g., from IR spectra) of the presence of an olefin complex at -78 "C. The compound was catalytically active at room temperature. Grubbs and Miyashita* reported a stereospecific isomerization of the
* To whom correspondence should be addressed.
Abstract published in Advance ACS Abstracts, August 1, 1995. (1)Cossee, P. Tetrahedron Lett. 1960, 17, 12. (2) Cossee, P. J . Catal. 1964, 3 , 80. (3)Ivin, K. J.; Rooney, J. J.;Stewart, C. D.; Green, M. L. H.; Mahtab, R. J. J . Chem. SOC.,Chem. Commun. 1978, 604. (4) Brookhart, M.; Green, M. L. H. J . Organomet. Chem. 1983,250, 395. (5) Brookhart, M.; Green, M. L. H.; Pardy, R. B. A. J . Chem. SOC., Chem. Commun. 1983, 691. (6)Ystenes, M. J . Catal. 1991, 129, 383. (7) Burfield, D. R. J . Organomet. Chem. 1978, 150, 321. (8)Grubbs, R. H.; Miyashita, A. J . A m . Chem. SOC.1978,100,1300. @
d4-labeled dicyclopentadienyl titanacyclopentane that suggests an intermediate with two ethylene molecules attached to the titanium atom. This intermediate has a structure similar to modern homogeneous ZieglerNatta catalysts. There is also indirect evidence of complex formation as the surface available for CO adsorption is reducedg when ethylene is introduced to an active Tic13 catalyst. Likewise, the retardation of the polymerization by internal olefins1°-12or even more by nonconjugated diolefins13 indicate that these olefins are able to complex and block the active center. The claims of the existence of a metal-monomer JC complex during chain propagation is supported by reports of weak charge-transfer complexes of ethylene with VOC13 and TiC14.14 In addition to these experimental observations, quantum chemical calculations also indicate the existence of a metal-monomer intermediate in Ziegler-Natta catalysis. The metal-monomer interaction is generally found to be weak in octahedral metal complexes. Novaro et al.,15J6performing ab initio restricted Hartree(9) Fries, R. W.; Mirabella, F. M. In Transition Metal Catalyzed Polymerizations; Quirk, R. P., Ed.; Cambridge Univ. Press: Cambridge,
1988; p 314. (10)Henrici-Olive, G.; Olive, S. J . Organomet. Chem. 1969,16,359. (11)Burfield, D. R. In Transition Metal Catalyzed Polymerizations; Quirk, R., Ed.; MMI Symposium Series 4; Harwood: New York, 1983; p 171. (12) Karol, F. J.; Wagner, B. E.; Cann, K. J. Lecture at the 199th ACS meeting, Boston, April 26, 1990. (13)Solli, K.-A,; Vindstad, B. K.; Wester, T.; Ystenes, M. In Catalyst design for tailor-made polyolefins; Soga, K., Terano, M., Eds.; Kodansha: Tokyo, Japan, 1994; p 35. (14)Krauss, H.-L.; Nickl, J. 2. Naturforsch. 1965,20b, 630.
0276-7333/95/2314-4349$09.QQIQ 0 1995 American Chemical Society
4350 Organometallics, Vol. 14, No. 9, 1995
Fock (RHF) calculations on A1(CH3)201-Cl)zTiC12(CH3)(C2H4), found a titanium-ethylene bond of only 3-4 kcaymol. An even weaker metal-olefin attraction, as calculated with the modified coupled pair functional (MCPF) method and reasonably large basis sets, was recently reported for a similar model c0mp1ex.l~Somewhat higher ethylene-binding energies (7- 11kcal/mol) have been calculated for Ti(II1) and Ti(IV) complexes in which the starting metal-halide fragments are frozen in a square-pyramidal configuration during ethylene coordination.ls In cationic complexes the ability to bind ethylene is expected to be much stronger as a result of the attractive charge-induced dipole force. Sodupe et aZ.19found two close-lying states for the Ti(CzH4)+complex, the highspin state 4B1being only about 5 kcaVmo1 less stable than the covalently bound 2A1. The latter has a calculated ethylene-binding energy of 24.2 kcaVmol at the MCPF level of theory. Eisch et aZa20identified the cationic titanocene monoalkyl complex, CpzTi(CH2&Me#, as the active species in a homogeneous ethylene polymerization, and others have obtained similar results.21,22These catalysts are charged entities and should therefore be expected to form relatively strong bonds with the olefin; in fact, large ethylene-binding energies (33-49 kcaVmo1) have been calculated for cationic ethylene complexes of the type [L2M(CH3)(C2H4)lf (M = Ti, Zr; L = C1 or Cp type ligand^).^^-^^ However, the ethylene-binding energies in these models are probably overestimated due to lack of counterions and solvent effects in the models. These and other problems, e.g., insufficient treatment of electron correlation, have been noted,29for many of the calculations on cationic Ziegler-Natta systems. Furthermore, recent calculations which include effects of electron corindicate that the n complex is not a stationary point on the potential energy surface due t o spontaneous insertion, while others have noted a very shallow minimum for the n complex.32 (15)Giunchi, G.; Clementi, E.; Ruiz-Vizcaya, M. E.; Novaro, 0. Chem. Phys. Lett. 1977, 49, 8. f 16)Novaro, 0.; Blaisten-Barojas, E.; Clementi, E.; Giunchi, G.; Ruiz-Vizcaya, M. E. J . Chem. Phys. 1978, 68, 2337. (17) Jensen, V. R.; B~rve, K. J.;Ystenes, M. J.Am. Chem. Soc. 1995,
117,4109. (18)Jensen, V. R.; Ystenes, M.; Warnmark, K.; hermark, B.; Svensson, M.; Siegbahn, P. E. M.; Blomberg, M. R. A. Organometallics 1994, 13, 282. (19)Sodupe, M.; Bauschlicher, C. W., Jr.; Langhoff, S. R.; Partridge, H. J . Phys. Chem. 1992,96, 2118. The state referred to as 4B1in the present work is denoted 4Bz by Sodupe et al. (20) Eisch, J. J.; Caldwell, K. R.; Werner, S.; Kruger, C. Organometallics 1991, 10, 3417. (21)Alelyunas,Y. W.; Jordan, R. F.; Echols, S. F.; Borkowsky, S. L.; Bradley, P. K. Organometallics 1991, 10, 1406. (22)Yang,X.; Stern, C. L.; Marks, T. J. J . Am. Chem. SOC.1991, 113, 3623. ( 2 3 )Kawamura-Kuribayashi, H.; Koga, N.: Morokuma, K. J . Am. Chem. SOC.1992, 114, 2359. (24)Fujimoto, H.; Yamasaki, T.; Mizutani, H.; Koga, N. J. A m . Chem. SOC.1985,107, 6157. (25) Jolly, C.; Marynick, D. S. J. Am. Chem. Soc. 1989, 111, 7968. (26)Castonguay, L. A.; Rappe, A. K. J . A m . Chem. SOC.1992, 114, 5832. (27) Kawamura-Kuribayashi, H.; Koga, N.; Morokuma, K. J . Am. Chem. SOC.1992, 114, 8687. (28) Axe, F. U.; Coffn, J. M. J . Phys. Chem. 1994,98, 2567. (29)Jensen, V. R.: Siegbahn, P. E. M. Chem. Phys. Lett. 1993,212, 353. (30)Meier, R. J.; van Doremaele, G. H. J.; Iarlori, S.; Buda, F. J. A m . Chem. SOC.1994, 116, 7274. (31)Weiss, H.; Ehrig, M.; Ahlrichs, R. J . A m . Chem. Soc. 1994,116, 4919. (32) Woo, T. K.: Fan, L.; Ziegler, T. Organometallics 1994, 13, 2252.
Jensen et al. Nevertheless, the significant affinity for the monomer which should be present in the cationic catalysts makes them promising candidates in the search for metalmonomer complexes in Ziegler-Natta catalysts. Thus, if the mechanism of Ziegler-Natta polymerization involves x-complexation of the monomer, it should be possible to detect these complexes, e.g., through vibrational spectroscopy of systems containing active cationic species. One of the aims of the present study is to provide a theoretical vibrational analysis of metalethylene complexes whose structures are close t o what is postulated to be the case in Ziegler-Natta catalysts. The method of correlating theoretical and experimental vibrational spectra is a powerful and well-established method to detect, or to verify the structure of, molecular compounds, although so far to a lesser extent for inorganic specie^.^^-^^ Other purposes of the present calculations are to assist the characterization of the titanium-ethylene bond in complexes and, if possible, t o correlate vibrational shifts to bond characteristics. Finally, the present quantum chemical force fields of titanium-ethylene complexes are interesting as such and may be used when constructing force fields for molecular mechanics calculations. The complexes chosen for the present study were the two lowest states, 2A1and 4B1,of the simple metal cation model, Ti(CzH4)+,the more realistic cationic model, ClzTi(CH3)(C2H4)+,where ethylene has been found to insert into the titanium-methyl bond,37 and finally, the neutral, bimetallic model, A1H2Cu-C1)2TiC12(CH3)(C2H4). The latter may be described as a contact ion pair consisting of ClzTi(CH3)(CzH4)+and HzAlClz-, which mimics the experimentally detected cocatalyst counterion, A1c14-.20 The inclusion of a counterion in one of the models is interesting, as the degree of charge separation in the homogeneous catalysts is still unclear. We have thus covered a broad range of different aspects of the postulated models of the active center, such as several different coordination numbers, different oxidation states, and both mono- and bimetallic centers. No quantum chemical vibrational analyses of any related olefin complexes have so far been presented in the literature. Quantum chemical vibrational analyses of Tic14 and methylated derivative^^^ show that such calculations may lead to good predictions, although the accuracy may be slightly less than one could hope for. As neither experimental nor theoretical frequencies have been reported for titanium-ethylene complexes, we have no direct measure of the accuracy that can be expected for the present calculations. Therefore, we have tried to locate changes in the spectra upon ethylene coordination which show little dependence on the choice of model system and which are robust with respect to the method of calculation. 2. Computational Details Restricted determinants were used a s wave functions in all the present calculations. (33)Pyykko, P. J . Chem. Soc., Chem. Commun. 1990, 933. (34)Dymek, C.; Einarsrud, M.-A,; Wilkes, J.; 0ye, H. Polyhedron 1988, 7, 1139. (35)Einarsrud, M.-A.; Rytter, E.; Ystenes, M. Vib. Spectrosc. 1990, 1, 61. (36)Ystenes, M. Spectrochim. Acta 1994, 50A, 219. (37)Uppal, J. S.; Johnson, D. E.; Staley, R. H. J. A m . Chem. Soc. 1981,103,508. (38)Bauschlicher, C. W., Jr.; Taylor, P. R.; Komornicki, A. J . Chem. Phys. 1990, 92, 3982.
Ti -Ethylene Intermediates 2.1. Basis Sets. For titanium, Wachters’ primitive (14s, 9p,5d) basis39was contracted to (10s,8p,3d) with the standard modifications as implemented in GAMESS:40 The most diffise s function was removed and replaced by one s function spanning the 3s-4s region (a, = 0.209),two p functions to describe the 4p region were added (a, = 0.156, 0.06111, and one diffuse d-primitive was added (ad = 0.0743). Chlorine and aluminum were described by ECPs according to Hay and WadL41 The valence basis sets were double-5 in the 3s and 3p regions. For chlorine, a d function with exponent 0.75 was also included in the valence basis set. Hydrogen and carbon were described by 6-31G(d) basis sets.42,43For carbon, the d exponent was 0.8. In the second-order M~ller-Plesset perturbation theory (MP2) and the gradient-corrected density functional theory (DFTG) calculations, the basis set of hydrogens in ethylene and the methyl group was augmented by one p function (a, = l . l ) , yielding a 6-31G(d,p)basis. The two hydrogens attached t o Al were described by 6-31G basis sets as in the SCF calculations. The correlated calculations were performed using a spherical harmonic basis, while a Cartesian basis including the s component of the d-shells was used in all reported SCF calculations. 2.2. Geometry Optimizations and Hessian Calculations. All ethylene Hessians were calculated analytically. The Hessians for the metal-ethylene complexes were calculated by numerical differentiation of the analytically determined gradients. All geometry optimizations and Hessian calculations a t the self-consistent field (SCF) Hartree-Fock (HF) level of theory were performed using the GAMESS set of programs.40 Geometries were converged to a maximum gradient below hartreehohr. The H F numerical force field calculations were carried out with a Cartesian displacement of 0.01 bohr for each atom in the positive directions. All MP2 and DFTG calculations were performed using the Gaussian set of programs,44 and all valence electrons were correlated in the MP2 calculations. Geometries were converged to maximum gradient and displacement of 4.5 x hartreehohr and 1.8 x bohr, respectively. The numerical force field calculations were carried out with a Cartesian displacement of 0.001 A for each atom in all six directions. The DFTG method chosen was the Gaussian 92/DFT variation of Becke’s three-parameter f ~ c t i o n a l , which 4~ includes Becke’s 1988 exchange functional correction46 and the correlation functional of Lee, Yang, and Parr,47the latter consisting of both local and nonlocal terms. The exchange and correlation functionals were evaluated using the default grid of Gaussian 92/DFT. The reported SCF, MP2, and DFTG calculations were performed on local workstations a t the University of Bergen and a t the Norwegian Institute of Technology, Trondheim. Some of the larger calculations were performed on the CRAY Y-MP4D/464 and the Intel Paragon A/4 a t SINTEF, Trondheim.
2.3. Constrained Space Orbital Variations (CSOV). The CSOV approach facilitates the decomposition of the energy (39) Wachters, A. J. H. J . Chem. Phys. 1970, 52, 1033. (40) Schmidt, M. W.; Baldridge, K. K.; Jensen, J. H.; Koseki, S.; Gordon, M. S.; Nguyen, K. A.; Windus, T. L.; Elbert, S. T. Q . C. P. E . Bull. 1990, 10, 52. (41)Hay, P. J.;Wadt, W. R. J . Chem. Phys. 1985, 82, 284. (42)Ditchfield, R.; Hehre, W. J.; Pople, J. A. J . Chem. Phys. 1971, 54, 724. (43)Hehre, W. J.; Ditchfield, R.; Pople, J. A. J . Chem. Phys. 1972, 56, 2257. (44)Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Wong, M. W.; Foresman, J. B.; Robb, M. A.; HeadGordon, M.; Replogle, E. s.;Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.;Baker, J.; Stewart, J . J. P.; Pople, J. A. Gaussian 92/DFT, Revision F.4; Gaussian Inc.: Pittsburgh, PA, 1993. (45)Becke, A. D. J . Chem. Phys. 1993,98, 5648. (46)Becke, A. D. Phys. Reu. A 1988, 38, 3098. (47)Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785.
Organometallics, Vol. 14, No. 9, 1995 4351 of interaction between two molecules and is thoroughly described by Bagus et a1.48.49 A detailed study of ligand and metal charge rearrangements i s thus enabled, and in particular, it is possible to distinguish between energetic contributions from intraunit polarization and interunit charge transfer and covalent bonding. This is achieved through the partitioning of the occupied and virtual orbital space in subsets belonging to each molecule and then optimizing the combined system by allowing orbitals in different subsets to interact according to a careful and systematic procedure. An orbital set for the combined system was prepared from frozen, SCF-optimized orbitals for the isolated reactant molecules. The open shell orbitals on Ti+ were chosen in accordance with their orientation in the complex. The two sets of frozen orbitals were orthogonalized in a Schmidt procedure, according to the following order of the orbitals: ocdethylene), occ(Ti), virt(Ti), virt(ethylene), where occ(x) (virt(x)) are the occupied (virtual) orbitals of x. The CSOV calculations were thus carried out as described in ref 48 for the study of metalligand bonding in &co and AlDH3. The CSOV calculations were performed with the STOCKHOLMSoset of programs. 2.4. Vibrational Analysis. All frequencies were calculated within the harmonic approximation. The MOLVIB and GAMFORCE programs were applied51,52in assignment of the vibrations. To aid the interpretation of the force field, the Cartesian Hessian matrix was transformed to a n M-dimensional valence force field matrix. Such a transformation is only unique when M = 3N - 6 ( N is the number of atoms). This requires a set of coordinates which often does not describe the physical situation well. For example, angles may obtain no intrinsic resistance toward deformation. This often leads to valence force matrices with very large interaction constants, and render an interpretation of the force constants close to impossible. A more appropriate set of valence coordinates can normally be obtained with M 7 3N - 6. However, this leads to a force field matrix which is not uniquely defined. Tests with several different coordinate sets gave stretching force constants that were almost invariant to the choice of the other coordinates. The only significant variations were found when the sets were unphysical, which was easily detected as some off-diagonal constants became larger t h a n the corresponding diagonal force constants. The force field used in this work included all stretching and bending coordinates between bonding atoms plus a torsion of the Al-CI-Ti-C1 ring. No large off-diagonal force constants were found in the force field matrix. For assignment of the ethylene modes the valence force constants were transformed to a set of symmetry force constants within the D 2 h symmetry. When the potential energy distribution (PED) is calculated in terms of these symmetry constants, the D2h symmetry of the vibration is found. In this way it is also possible to assign the ethylene modes to a dominating D2h symmetry species even when the D2h symmetry is lost. It is then possible to follow the changes in the individual modes upon complexation, although some precautions must be taken as this approach is a n approximation. Nevertheless, for all ethylene modes in this work significantly more t h a n 50% of the PED could be attributed to symmetry force constants of the given symmetry, and hence the assignments were obvious. (48) Bagus, P. S.; Hermann, K.; Bauschlicher, C. W., Jr. J . Chem. Phys. 1984, 80, 4378. (49)Pettersson, L. G. M.; Bagus, P. S. Phys. Reu. Lett. 1986, 56, 500. (50) STOCKHOLM is a general purpose quantum chemical set of programs written by P. E. M. Siegbahn, M. R. A. Blomberg, L. G. M. Pettersson, B. 0.Fbos, and J. Almlof. Contact Prof. Per E. M. Siegbahn at the Department of Physics, University of Stockholm, Stockholm, Sweden, for further information. (51) Sundius, T. J . Mol. Struct. 1990, 218, 321. (52)Bache, 0. GAMFORCE; Department of Inorganic Chemistry, Norwegian Institute of Technology, Trondheim, Norway, 1991.
4352 Organometallics, Vol. 14, No. 9, 1995
Jensen et al.
1
3
W
2 Figure 1. Two states, 2A1(1)and 4B1 (2), of the complex Ti(CzH4)- as optimized at the RHF level. Table 1. Structural Parameters for Ethylenea RHF MP2 DFTG exptb
params
c-c C-H LHCH
1.317 1.076 116.4
1.336 1.081 116.9
1.331 1.087 116.3
1.339 1.085 117.8
3' Figure 2. Complex Cl2TiCH3(C2H4)+as optimized at the RHF (3)and MP2 (3)levels. As is evident from Table 3, the DFTG-optimized structure (3")is close to 3'.
Units: distances, A;angles, deg. From ref 72.
3. Results and Discussion The first part of this section presents the calculated structures in terms of geometrical parameters. Attempts are also made, through the use of geometrical parameters, bond energies, CSOV energies of interaction, and population analyses, to characterize the titanium-ethylene bond in the various complexes. In the last part of this section, the vibrational spectra analyses are presented, with focus on the monomer modes and the modes due to the metal-monomer interactions. 3.1. Structures. The structures of the two states, 2A1 (1)and 4B1(2), of Ti(C2H4)+are shown in Figure 1. In both of these complexes, the midpoint of the C-C bond is kept a t the origin, the C-C bond is directed along the x axis, and the titanium atom is located on the negative z axis. The structures (3and 4)of the two larger complexes C12Ti(CH3)(C2H4)+and AlH2@-C1)2TiC12(CH3)(C2H4)are shown in Figures 2 and 3. The wave functions of 3 and 4 transform according to the fully symmetric irreducible representation of the corresponding point groups. The structures were found to possess C, symmetry, except for the MP2- and DFTGoptimized geometries of C12Ti(CH3)(C2H4)+(3and 3", C1 symmetry). In all cases, the presented structures are the ones which were found to have the lowest energy
n
I
4' Figure 3. Complex AIH201-C1)2TiC12(CH3)(C2H4) as optimized at the MP2 (4') level. As is evident from Table 4, the RHF-optimized structure (4) is similar to 4'. in the region of the potential energy surface where ethylene is parallel, or close to parallel, to the metalmethyl bond. From the ethylene C-C and the Ti-ethylene distances in Tables 1-4, it is evident that a regular covalent bond to ethylene is found only in the 2A1state of Ti(C2H4)+. The 2A1state of Ti(C2H4)+has, by far, the shortest metal-monomer bond of the complexes studied, the Ti-C distance being 2.192 a t the RHF level. The
Ti -Ethylene Intermediates
Organometallics, Vol. 14,No. 9, 1995 4353
Table 2. Selected Structural Parameters from ROHF Geometry Optimization of the Two Lowest-Lying States of Ti(Cz&)+ distances 2A1 4B1 angles 2A~ 4B1 Ti-C
c-c C-H
2.192 1.394 1.080
2.872 1.333 1.078
LTiCH LHC H LH-bend"
110.2 114.6 13.0
99.6 116.6 3.0
Units: distances, A; angles, deg. LH-bend denotes the outof-plane bending of the hydrogen atoms. [I
Table 3. Selected Structural Parameters from RHF (31, MP2 (3'1, and DFTG (3") Geometry Optimization of ClzTi(CH3)(Cz&)+ distances 3 3' 3 angles 3 3' 3" Ti(l)-C(2) 2.776 2.607 2.712 LTi(l)C(2)H(7) 104.2 98.9 101.8 Ti(l)-C(3) 2.472 2.489 2.421 LTi(l)C(P)H(B) 104.2 105.0 106.9 Ti(l)-C(4) 2.000 2.022 2.005 LTi(l)-C(3)H(9) 97.6 96.0 94.7 Ti(l)-H(11) 2.555 2.509 2.553 LTi(l)C(3)H(10) 97.6 101.6 99.3 Ti(l)-H(12) 2.555 2.546 2.552 LTi(l)C(4)H(11) 108.0 103.0 106.9 Ti(l)-H(13) 2.563 2.688 2.616 LTi(l)C(4)H(12) 108.0 105.6 106.9 C(2)-C(3) 1.345 1.358 1.355 LTi(l)C(4)H(13) 108.7 116.2 111.6 C(3)-C(4) 3.403 3.478 3.495 LC1(5)Ti(l)C(4) 106.4 106.6 106.9 C(2)-H(7) 1.077 1.085 1.089 LC1(6)Ti(l)C(4) 106.4 106.6 106.8 C(2)-H(8) 1.077 1.084 1.088 LC1(5)Ti(l)C1(6) 120.8 113.3 115.0 C(3)-H(9) 1.081 1.087 1.093 LTi(l)C(2)C(3) 62.9 79.4 87.0 C(3)-H(10) 1.081 1.086 1.092 LC(2)C(3)C(4) 123.7 110.3 117.2 C(4)-H(11) 1.088 1.100 1.100 LH(7)C(2)H(8) 117.0 117.3 116.7 C(4)-H(12) 1.088 1.097 1.100LH(9)C(3)H(10) 117.3 117.6 117.2 C(4)-H(13) 1.087 1.091 1.097 LH(ll)C(4)H(12) 111.5 111.4 111.5 Ti(l)-C1(5) 2.179 2.135 2.160 LH(12)C(4)H(13) 110.0 110.4 109.9 Ti(l)-Cl(G) 2.179 2.134 2.160 LC(4)Ti(l)C(2)C(3) 0.0 34.9 33.9 Units: distances, A; angles, deg.
Table 4. Selected Structural Parameters from RHF (4) and MP2 ( 4 ) Geometry Optimization of
A~Hz(I~-C~)ZT~C~Z(CH~)(CZ&)~ distances
4
4
Ti(l)-C(2) Ti(l)-C(3) Ti(l)-C(4) Ti(l)-H(16,17) Ti( l)-H( 18) C(2)-C(3) C(3)-C(4) C(2)-H(12,13) C(3)-H(14,15) C(4)-H(16,17) C(4)-H(18) Ti(l)-C1(5,6) Ti(7)-C1(7) Ti(l)-C1(8) C1(7)-Al(9) C1(8)-Al(9) Al(9)-H(lO,ll)
3.046 3.048 2.037 2.600 2.549 1.330 3.693 1.074 1.075 1.081 1.087 2.278 2.390 2.860 2.527 2.289 1.578
2.771 2.798 2.079 2.712 2.410 1.351 3.585 1.081 1.082 1.086 1.104 2.239 2.412 2.600 2.409 2.333 1.594
angles
4
LTi(l)C(2)H(12,13) 97.4 LTi(l)C(3)H(14,15) 98.0 LTi(l)C(4)H(16,17) 109.0 LTi(l)C(4)H(18) 105.3 LC1(7)Ti(1)C(2) 153.3 74.4 LC1(8)Ti(l)C(2) 169.5 LC1(8)Ti(l)C(4) 77.3 LTi(l)C(2)C(3) LC(2)C(3)C(4) 110.8 LC(3)C(4)H(16,17) 124.0 LC(3)C(4)H(18) 49.6 LH(12)C(2)H(13) 117.0 LH(14)C(3)H(15) 117.3 LH(16)C(4)H(17) 111.8 LC1(5)Ti(l)C1(6) 157.5 LC1(7)Ti(l)C1(8) 78.9 LC1(7)A1(9)C1(8) 88.2 LH(lO)Al(9)H(ll) 128.5 LC1(5)Ti(l)Cl(6)C1(7)164.0
4 98.0 99.3 114.2 93.3 156.6 75.9 162.6 74.9 110.2 123.2 42.0 117.7 117.9 112.7 160.7 80.7 86.6 127.8 179.5
Units: distances, A, angles, deg.
C-C bond of the ethylene moiety is also very long (1.394 Hence the ethylene n bond is significantly weakened. Ethylene C-C bonds of this length are normally found in the transition state of olefin insertion, see, e.g., refs 23 and 24. In the other complexes, ethylene C-C bond distances of 1.330-1.345 A are found at the RHF level, indicating only a minor weakening of the ethylene n bond. Theoretically predicted geometries of the cationic n complex C12Ti(CH3)(C2Hd+ have been presented by several authors.23-25,28,31 The most relevant studies for comparison are perhaps the recent papers by Axe and Coffin28and Weiss et ~ 1 since . optimized ~ ~ geometries at the MP2 level are presented in both of these papers
A at the RHF level) compared to free ethylene.
and, in ref 28, also at the DFTG level. The structures optimized at the HF, MP2, and DFTG levels of theory in refs 28 and 31 are close to ours, although some differences may be noticed. The present HF and MP2 metal-ligand distances, and in particular the titaniummethyl distances (2.000-2.022 A) are somewhat longer than their reported distances (1.95-1.99 A), probably due to the use of a larger metal basis set in the present calculations. The difference between the two TiC(ethy1ene) distances (0.12 A) is also smaller than reported at the MP2 level (-0.4 A) in refs 28 and 31. The present bond distances calculated at the DFTG level are close to the distances reported by Axe et al. for their DFTG calculations using combined nonlocal corrections by B e ~ k and e ~ ~P e r d e ~ (Becke-Perdew) ~~ as well as a combination of the nonlocal corrections by Perdew and and P e r d e ~ (Perdew-Perdew). ~~ The present MP2- and DFTG-optimized structures are of C1 symmetry while C, symmetry was imposed by Axe and Nevertheless, the Ti-ethylene distances in ref 28 are close to the present distances, and in particular this is true for the calculations with the Becke-Perdew corrections. The calculations involving the Perdew-Perdew nonlocal corrections are seen to predict somewhat longer bond distances (-0.01-0.03 A) than the present DFTG results. The longest Ti-ethylene distance (Ti-C above 3 A at the SCF level) is found for the neutral model complex 4, shown in Figure 3. The bonding interaction probably involves dipole-induced dipole forces and o-donation from ethylene (-0.2e, from Mulliken population analysis a t the MP2 level). The binding forces are weak, as illustrated by the fact that no stationary point due to x coordination of ethylene was located for this complex a t the DFTG level. As expected when including treatment of dynamical correlation, MP2 predicts shorter bond distances for the weak bonds in 4 than does SCF. In particular this is the case for the Ti(l)-C(2,3) distances, which are shortened by almost 0.3 A. The asymmetry of the double Ti-C1-AI bridge is also reduced, through shortening of the longest Ti-C1 distances. Finally, Ti(l)-H(18) is reduced to 2.410 A (comparedt o the SCF result of 2.549 A) when including effects of electron correlation at the MP2 level, and this may be due t o a very weak agostic interaction from methyl. Transition metal compounds generally offer many close-lying states, a fact which constitutes a challenge for theorists in the field. Rigorous treatment of correlation effects is often deemed necessary. However, the HF approximation may be able to provide reasonable geometries in cases where near degeneracies are absent, as has been seen in a series of studies involving transition metals.19,55-64The HF configuration is a good zeroth-order wave function for the two states of Ti(53)Perdew, J. P. Phys. Rev. B 1986,33,8822. (54)Perdew, J. P.; Wang, Y. Phys. Rev. B 1986,33,8800. (55) Dobbs, K. D.; Hehre, W. J. J . Comput. Chem. 1987,8, 861. (56) Dobbs, K. D.; Hehre, W. J. J . Comput. Chem. 1987,8, 880. (57) Blomberg, M. R. A,; Siegbahn, P. E. M.; Svensson, M. J . Am. Chem. SOC.1992,114, 6095. (58)Siegbahn, P. E. M. Chem. Phys. Lett. 1993,205,290. (59) Siegbahn, P. E. M. J . A m . Chem. SOC.1993,115, 5803. (60) Siegbahn, P. E. M. Theor. Cheim. Acta 1993,86, 219. (61) Siegbahn, P. E. M.; Blomberg, M. R. A.; Svensson, M. J . A m . Chem. SOC.1993,115, 4191. (62) Blomberg, M. R. A,; Siegbahn, P. E. M.; Svensson, M. J . Phys. Chem. 1993,97,2564.
4354 Organometallics, Vol. 14, No. 9, 1995 (C2H4)+,l9and certainly is expected t o be so also in 3 and 4, which formally are do complexes. The weight of the reference configuration (square of the coefficient) was found to be as low as 0.67 in a MCPF calculation on H2Al(p-C1)2TiCl2CH3(C2H4).l7However, this rather low value is caused by the large number of correlated electrons in the c a l ~ u l a t i o nrather ~ ~ than by important competing configurations, as illustrated by the fact that no excited configuration has a coefficient larger than 0.06. With the HF configuration being a good zeroth-order representation of the wave function in all the present complexes, multireference treatment of correlation effects should not be required in order to obtain reasonable descriptions of geometries and relative energies in these complexes. For further evaluation of the SCF-optimized geometries it is useful to compare some parts of the neutral structures 4 and 4' with experimentally determined structural parameters of related compounds. The RHFand MP2-optimized Ti(l)-C1(5) distances of 2.278 and 2.239 fi, respectively, are in excellent agreement with X-ray diffraction data for terminal Ti-C1 bonds, 2.222.31 in titanium tetrachloride ester complexes. Likewise, the calculated Ti-methyl distances, 2.037 and 2.079 A, agree well with the Ti-C distance of 2.042 fi found in electron diffraction studies of T i C l s c H ~ The .~~ calculated Al-H distances of 1.578 and 1.594 A fit well in between the Al-H bond lengths in [CpzTi@-H)2A1H21(CH3)2NC2H4N(CH3)2CsHs,which were determined by X-ray crystallography to be 1.459 and 1.659 A.67
3.2. Characterization of the Titanium-Ethylene Bond. Information about the calculated metal-ethylene-binding energies may add to the understanding of the mechanism involved in the coordination. Ethylenebinding energies, relative to ground state reactants, of 24.2 and 19.0 kcal/mol have been reported for the complexes 1 and 2,9respectively (calculated using the modified coupled pair functional method (MCPF)). Formation of the 2A1state complex (11,with an electron . orbital (5bl), repair present in the ~ t back-donation quires pre-excitation of Ti+. The 4B1state (21, however, needs no rearrangements of the metal electrons upon ethylene coordination and thus turns out to have almost as large an ethylene-binding energy as 1. As expected, the HF approximation fails to compensate for the loss of exchange energy when forming the low-spin state (11, which is thus 23.6 kcal/mol less stable than the ground state reactants at this level (ROHF). The corresponding value (15.7 kcaL"o1) for 2 is more in line with the MCPF result. Reducing the amount of repulsive valence electrons compared to 2 will tend t o increase the strength of the (63) Bauschlicher, C. W., Jr.; Langhoff, S.R. J . Phys. Chem. 1991,
95,2278.
( 6 4 ) Rosi, M.; Bauschlicher, C. W., Jr. Chem. Phys. Lett. 1990,166, 189. (65)Rytter, E.; Kvisle, S.; Nirisen, 0.; Ystenes, M.; 0ye, H. A. In
Transition Metal Catalyzed Polymerizations: Ziegler-Natta and Metathesis Polymerzzations; Quirk, R., Ed.; Cambridge University Press, U.K., 1988; p 292. 166) Berry, A,; Dawoodi, Z.; Derome, A. E.; Dickinson, J. M.; Downs, A. J.;Green, J. C.; Green, M. L. H.; Hare, P. M.; Payne, M. P.; Rankin, D. W. H.; Robertson, H. E. J. J . Chem. SOC.,Chem. Commun. 1986,
520. (67)Lobkovskii, E. B.; Soloveichik, G. L.; Sisov, A. I.; Bulychev, B. M.;Gusev, A. I.; Kirillova, N. I. J . Orgunomet. Chem. 1984, 265, 167.
Jensen et al. Table 5. Interaction Energies Given Relative to Separated Ti+ and Ethylene, Elnt[kcaYmoll, and Dipole Moments (Calculated with Ti at the Origin),p [Dl, for the CSOV SCF Wave Functions for the 4B1 State of Ti(C2H4)+at the SCF Equilibrium Geometry" ~~~~
frozen orbital interaction -6.4 +0.64 Ti+ polarization, Ti basis only -1.2 +5.2 +1.78 Ti+ donation, Ti -0.7 +0.5 f1.70 virtual CzH4 basis 3. C2H4 polarization, C2H4 +3.5 +4.2 f2.29 basis only 4. C2H4 donation, C2H4 +13.3 +9.8 +3.50 virtual Ti basis +15.4 +2.1 +4.22 5. C2H4 donation, CzH4 virtual and active Ti bases full SCF +15.7 +0.3 +4.29 0. 1. 2.
+
+ +
a
+1.14 -0.08 +0.59 f1.21 +0.72 +0.07
Energies are given relative to separated Ti+ and ethylene.
metal-alkene bond.29 This is the case in 3, for which the present value of the MP2 binding energy is 42.6 kcal/mol. And finally, removing the positive charge on the metal fragment by including a counterion, as in 4, reduces the bond strength considerably. The present MP2 result for the ethylene-binding energy in 4 is 1.5 kcal/mol, and no stationary point due to i~ coordination of ethylene was located for this complex with a DFTG method. To obtain more insight into the nature of the apparently noncovalent metal-monomer bonds, it was decided to perform CSOV c a l c ~ l a t i o n(cf. s ~ Computa~~~~ tional Details) on the smallest of these complexes, the 4B1state of Ti(C2H4)+. The titanium-ethylene-binding energy for the 4B1state, as calculated using the ROHF method, is seen to be fairly well in agreement with the MCPF value. ROHF is the level of theory used in the CSOV calculations. By means of the CSOV approach, it is possible to decompose the interaction energy between ethylene and titanium into a sum of chemically significant terms. It is of particular interest to distinguish between contributions from intraunit polarization, leading to a charge-induced dipole bond, and charge transfer, leading to a donationhack-donation bond. The interaction energy, Elnt,relative to separated Ti+ and ethylene is given along with the dipole moments, p, in Table 5 for each CSOV step. The interaction energy is defined as Eint = E(Ti+) E(C2H.4 - E(Ti(C2H4If),and thus E i n t > 0 indicates attraction. The CSOV calculations were initiated, CSOV step 0, by using the frozen orbitals for the two noninteracting units Ti+ and C2H4 at the equilibrium geometry. The orbitals were, however, properly orthogonalized. The negative value of Eint indicates that the interaction between the two frozen subsystems is repulsive. Then, in CSOV step 1, the Ti+ orbitals were allowed t o vary while the ethylene part of the orbital space was kept fixed, thus accounting for polarization of Ti+ in the field of a frozen ethylene molecule. In step 2, the Ti orbitals were also allowed to mix with the virtual orbitals of ethylene, permitting charge transfer from Ti+ to ethylene. Then, in step 3, the relaxed orbitals of Ti+ were fixed and the ethylene orbitals were optimized within the ethylene orbital space. Since no virtual titanium orbitals were included in the variation, this should give a measure of the polarization of ethylene. In step 4, the virtual orbitals of Ti+ were also included in the variation, and thus charge transfer from ethylene to Ti+
+
Ti-Ethylene Intermediates
Organometallics, Vol. 14, No. 9, 1995 4355
Table 6. Ethylene Frequencies Intensities as Calculated at Various Levels of Theorp modeb
description r (C-H stretch) r r
r R (C=C stretch), a (C-C-H bend)
a
a, R a r (ethylene torsion) r , p (C-C-H2 out-of-plane bend) /J
a
SCF
MP2
DFTG
exptc
exptd
307911.0 305610 301010 298910.6 167010 144910.14 134710 121810 104010 98612.4 98910 80710.0
3 16610.6 314510 307210 305610.3 162710 1434l0.09 133110 119210 102710 93411.9 88410 79610.0
324710.7 322110 316110 314610.4 171410 148410.13 138810 124110 106710 97411.9 95910 83110.02
3106 s 3103 3026 2989 s 1623 1444 s 1342 1236 1023 949 vs 943 826 vw
3234 3232 3153 3147 1655 1473 1370 1245 1044 969 959 843
The calculated frequencies are for harmonic modes. The SCF frequencies are scaled by a factor 0.9 and the MP2 frequencies by 0.9434.73 Frequencies in cm-’; IR intensities in D2 u-l A-2. Intensities below 0.01 are given as 0.0. The ethylene molecule is oriented with the C-C bond along the z-axis and with the x-axis normal to the plane containing the molecule. Observed anharmonic frequencies taken from ref 74. Intensities are visual estimates, v = very. w = weak, s = strong. The harmonic frequencies are those recommended by Duncan et al.75
was accounted for. Finally, in step 5 , the singly occupied orbitals of Ti+ were included in the variational procedure, accounting for covalency between these orbitals and the ethylene orbitals. According to the values of Eint,and the corresponding changes between successive CSOV steps, M i n t , the dominating contributions t o the interaction energy are intraunit polarization of Ti+ and C2H4 (9.4 kcallmol), and charge transfer (donation) from C2H4 to Ti+ (11.9 kcallmol). It is evident that donation from the metal to ethylene (step 2) is unimportant. The corresponding values of p and Ap show that, for all the significant contributions, the dipole moment, as calculated with Ti at the origin, increases. The change in p is either a result of the polarization of metal electrons away from ethylene, as in CSOV step 1, or of the polarization of ethylene charge toward the metal, as in steps 3-5. In step 1,most of the polarization can be attributed t o the two unpaired electrons located in a1 orbitals on titanium. The 4s orbital is seen to cause most of the increase in p occurring in this step, while both orbitals experience a marked contraction in the z-direction which reduces the repulsive interaction with ethylene. The reason for nonzero dipole moment of the superimposed frozen orbital systems (step 0) is that the orbital orthogonalization procedure removes some electron density from the intermolecular region. To conclude, the metal-alkene bonding in 2 seems to consist of intraunit polarization and ethylene donation, both being equally important. A Ti-C distance of 2.872 A may seem unexpectedly long when compared to 2.192 A in 1 and is a consequence of the rather repulsive high-spin coupled valence electrons of the metal, essentially the 3d24s1configuration. Addition of covalent ligands t o titanium results in a shorter bond toward ethylene, as seen in 3 (Figure 2, Table 31, where the Ti(l)-C(3) distance is below 2.5 A for all the three methods used for optimization. Only a slight prolongation of the ethylene C-C bond (-0.02 A) takes place upon coordination. The formal electron configuration of the metal (do),in 3 and 4, hinders the formation of a covalent type donationback-donation bond. The relatively strong metal-ethylene bond probably involves both ethylene donation and chargeinduced dipole forces, as found in 2. The relaxation due to polarization of the metal electron is expected to be less than in 2 as there are no unpaired electrons
present. The Mulliken population analysis indicates that the ethylene donation should be significant for this system, with an estimated reduction in ethylene charge of -0.3e at the MP2 level. Significant asymmetric coordination of ethylene is seen to be preferred at all three levels of theory (3,3’, and 3’7, the Ti(l)-C(3) distance being 0.1-0.3 A longer than Ti(l)-C(2). 3.3. Vibrational Frequencies. The main results from the vibrational analysis are summarized in Tables 6-9. Table 6 gives the ethylene frequencies as calculated at the various levels of theory, as well as the observed ethylene frequencies. Tables 7 and 8 compare the vibrational frequencies, which can be attributed to the ethylene unit, and also frequencies which can be assigned to translation (liberation) and rotation (torsion) of the ethylene unit relative t o the titanium fragment. In addition, for 3,3’,and 3” the section of the spectrum most suitable for detection (800-1800 cm-l) is given in Figure 4 and is compared with the ethylene spectrum calculated a t the corresponding level of theory. These spectra, based on the calculated frequencies and intensities, are simulated as Lorentzian functions with a common fwhm of 20 cm-l. In Table 9, the most important force constants (as calculated at the SCF level) are compared. The SCF frequencies are scaled by a factor of 0.9, and the force constants are accordingly scaled by 0.81 = 0.g2. Figure 5 gives the stretching force constants (scaled) for 4. The scaled SCF and MP2 frequencies in ethylene (Table 6) show expected and tolerable deviations from the experimental fundamentals, while the rather new DFTG functionals employed lead to frequencies that are generally close to the experimental harmonic ones. Except for vz (calculated 1714, experimental harmonic 1655 cm-l), DFTG performs very well in all regions of the spectrum. The overestimation of v2 at both the SCF and DFTG levels is caused by the incompleteness of the one-particle basis sets.68 Tables 7 and 8 list the frequencies of the various complexes, as calculated at the SCF and the two correlated levels, respectively. In both tables the calculated frequencies of ethylene are given as reference. The modes that can be attributed to the ethylene molecule, have been labeled according to the symmetry of the corresponding mode in isolated (68) B~rve,K. J.; Jensen, V. R. Manuscript in preparation.
4356 Organometallics, Vol. 14, No. 9, 1995
Jensen et al.
Table 7. Ethylene Frequencies in the Various Complexes, as Calculated at the SCF Levela.*
modeC v11
v5
v1
vs v2 VlO
v3 "6 V4
v7 v8 v12
description B3u B1, A, Bzu A, B2u A, B1, Au B1u B2g B3u B3g B2g B1u B3u B z ~ B1,
r r
r
r
R, a
a a, R a r 5 , rlc
P
a
frequencyAR intensitv' 2 4B1
ethylene 'A,
1 'Ai
307911.0 305610 301010 298910.6 167010 1449/0.14 1347/0 1218/0 1040/0 98612.4 98910 80710.0
302410.02 300310 294710.2 29340.01 1505/0.05 142710.3 116711.4 120610 84110 90310.7 98212.0
rot., /3 rot., T (asym) trans., T (sym) trans., y (wag)r trans. (rocky rot. (twisty
306510.04 3046/0 298210.01 296810.1 161710.8 145110.2 133010.6 122210 105210 105715.0 102410.03 82210.01 29710.08 14310.4 12310.1
801/0.0
53810.4 29210.5 27210.8
3 'A
4 'A
308310.2 302110.07 299510.05 293510.2 159411.0 143910.4 131511.2 122210.01 103310.0 99414.4 1119/1,3 820/0.03 33510.1 13910.4 24910.6 10410.1 15010.0 6210.03
309410.03 307210.01 300910.02 299310.02 163210.6 145010.2 133810.3 122410.4 104410.0 104413.3 102011.2 81910.01 31410.2 17110.1 4310.2 13710.2 13310.01 11410.01
a The calculated frequencies are for harmonic modes, scaled 0.9 relative to the SCF16-31ad) frequencies. Compounds 1-4 are ethylenetitanium complexes, see Figures 1-3. The symmetries refer to the framework of a n unperturbed ethylene molecule. For the titaniumethylene complexes, where the symmetry is lower and mixing may occur, the modes are assigned according to the main contribution to the vibration. The valence coordinates given are the ones responsible for the main contributions to the potential energy distribution. The ethylene valence coordinates are defined in Table 6. "Rot." and "trans" refer to rotation (torsion) or translation (liberation) of the whole ethylene molecule. T. Ti-C (ethylene) stretch; T,, Ti-C (methyl) stretch; /j', Ti-C-H (ethylene) bend; y , C(ethy1ene)-Ti-C(methy1) bend; (twist),(rock) and (wag) refer to the whole ethylene unit vs the rest of the complex. e Frequencies in cm-l; IR intensities in D2 u-l A-2. Intensities below 0.01 are given as 0.0. f The assignment of these modes is tentative due to extensive coupling with other vibrations.
Table 8. Ethylene Frequencies in the T w o Largest Complexes, at the MP2 and DFTG Levelsa frequencyAR intensity ethylene 3' 3" 4 MP2 MP2 DFTG MP2 mode' descriptiond 'A, 'A 'A 'A Bs" r 316610.6 314610.2 325510.2 317910.01 314510 311710.06 3199/0.09 316110.0 BI, r A, r 307210 304010.2 315610.13 307210.01 BzU r 3056/0.3 301710.3 3105/0.3 3063/0.0 A, R , a 162710 157310.3 164010.5 158510.3 Bzu a 143410.09 1424/0.3 147510.4 1426/0.2 A, a , R 133110 131310.3 136310.3 1319/0.2 B1, a 1192/0 119710.0 124110.0 119710.0 Au 5 102710 103510.01 105410.01 1024lO.O B1, r,bi 93411.9 97910.6 100512.1 996/3.1 BZk- u 88410 104612.1 110211.0 953/0.09 Bsu a 796/0.0 80410.02 840/0.03 80510.0 bg rot.,B 29310.12 31010.05 32010.4 BP, rot., T(asym) 16210.11 14W0.2 20810.4 BI, trans., T (sym) 26210.10 269/0.2 6410.04 12910.13 13610.08 16210.03 B3" trans., y (wag) Bzu trans. (rocky 15510.02 16010.02 15710.0 BI, rot. (twistY 2310.0 1210.0 12710.0 a The calculated frequencies are for harmonic modes. The MP2 frequencies have been scaled by a factor 0.9434.73 Compounds 3 , 3 " , and 4 are ethylene-titanium complexes, see Figure 2 and 3. The symmetries refer to the framework of an unperturbed ethylene molecule. For the bound ethylene, where the symmetry is lower and mixing may occur, the modes are assigned according to the main contribution to the vibration. The valence coordinates given are the ones responsible for the main contribution of the potential energy distribution, and are based on the SCF calculations. See Table 6 for the definition of the valence coordinates. e Frequencies in cm-', IR intensities in DZu-l A-2. Intensities below 0.01 are given as 0.0. f T h e assignment of these modes is tentative due t o extensive coupling with other vibrations. See Table 7.
ethylene (cf. Computational Details). As the D2h symmetry is destroyed upon complexation, modes that are IR inactive in ethylene may show up with considerable IR intensity in the complexes. The mode descriptions given in the tables are in all cases mainly based on the SCF calculations. The comparison between SCF results
Table 9. Selected Force Constants (SCF/6-31G(d)/ Scaled 0.81) for the Ethylene Group and the Titanium-Carbon Bondsa ethylene
1
9.29 5.00 0.94 0.17 0.15
5.45 4.88 0.69 0.12 0.13 0.72 0.16
8.47 5.00 0.87 0.11 0.10 0.13 0.07
0.08 0.23
0.06 0.11 0.29 -0.07
0.07 0.17 0.01 -0.02
2
3
4
7.97 5.0614.88 0.8810.78 0.13 0.1410.09 0.3 110.24 0.09/0.10 1.89 0.35 0.1010.06 0.17/0.15 -0.12/0.07 0.06
8.65 5.0815.09 0.8810.90 0.11 0.0910.09 0.1510.17 0.07/0.07 1.85 0.31 0.0910.08 0.19 0.0610.00 --0.08
a F and f in mdyn kl, H in mdyn A rad-2, and h in mdyn rad-'. When the two ethylene carbons are not equivalent, two values are given for each parameter. The first value is then associated with the ethylene carbon closest to the methyl group. See Table 6 for the a definition of the valence coordinates in ethylene. The other valence coordinates are as follows: T, Ti-C (ethylene) stretch; T,, Ti-C (methyl) stretch; 0,Ti-C-H (ethylene) bend; y , C(ethy1enel-Ti-C(methy1) bend.
and the correlated calculations is difficult for the lowest frequencies reported, as it was not always possible to correlate unambiguously these modes from the various complexes. In particular, this is a problem for 3' and 3", as the complex lost the mirror plane in the correlated calculations. These difficulties, however, hardly influence the internal ethylene vibrations. The modes suitable for detection of ethylene coordination are mainly related to the out-of-plane deformation or to the C-C stretch in ethylene. In all the present complexes there is found a lowering of YZ,an A, mode dominated by the C-C stretch, which for 1 is reduced by 165 cm-'. This reduction is predicted to be in the range 53-76 cm-l for the charged complexes and close t o 40 cm-l for the neutral complex, 4. The predicted change in v z is thus in accordance with the correspond-
Ti -Ethylene Intermediates
Organometallics, Vol. 14, No. 9, 1995 4357
~
l e100
1700
1600
1500
1400
1300
1200
1100
1000
900
800
1
v lcm
1
Figure 4. Simulated IR absorption (arbitrary units) spectra of ClzTiCH3(CzH*)+based on the harmonic frequencies and intensities as calculated at SCF, MP2 and DFTG levels. SCF frequencies have been scaled by 0.90 and MP2 frequencies by 0.9434. The corresponding simulated ethylene spectra (dashed lines) are given for comparison. The highest peaks have been cut in order to reduce their dominance in the spectra. The spectra are simulated as Lorentzian functions with a common fwhm of 20 cm-l.
H
1.68
I
I
H CI
Figure 5. Stretching force constants in 4 calculated at the SCF level, scaled by a factor 0.81. The asymmetry of the Al-C1-Ti-C1 ring is evident. For 3 the Ti-C1 stretching force constant is 2.38 mdyn A-1. ing reduction (-50 cm-l) reported by Burfield7 for a VC13-bmethylpentene complex. Except for complex 1, the IR intensity for this mode seems t o be large enough for detection, especially as there are no other modes in this region of the spectrum. For the strongest complexation (11, the calculations also predict a significant effect on v3, due t o a strong coupling between the v2 and v3 modes in ethylene. In 3, v3 also gives rise to one of the strongest bands in the IR spectrum, and should thus be easily identified. The modes related to the out-of-plane deformation in ethylene are especially useful as they seem to give information about the strength and type of the metalethylene bond in question. For these modes, there seem to be two opposing effects; a weakening of the n bond of ethylene gives softer force constants for these modes, and a direct interaction with titanium gives higher frequencies. As a consequence, a weak or noncovalent metal-ethylene bond leads to increased frequencies for two of these modes, v7 and vg. The total shift may be evenly distributed among the two modes, as in 4, or
unevenly, as in 3. The large shifts to shorter wavelengths calculated for vg in 3 are particularly evident in Figure 4, where it is also seen that this mode obtains significant IR intensity upon coordination. The changes in v7 and vg are distinct even for the weakest metalethylene bond studied, with upward shifts of 62 and 69 cm-l calculated at the MP2 level for 4. In contrast, a strong bond with a covalent character leads to a substantial reduction in the frequencies of v4 and V I , 83 and 199 cm-’, for 1. The significant shifts predicted for the out-of-plane deformation modes, together with the strong IR intensity seen for v7 in particular, make these modes good candidates for detection of titaniumethylene n complexes. The C-H stretching region may reflect the existence of strong titanium-ethylene complexes. For 1, a significant reduction in frequency is seen for all of these four modes. For the weaker complexes, only small or no changes are seen. A specific problem is that the modes appear to get a lower IR intensity after coordination, and hence detection may be difficult. The low-frequency modes, especially those connected to rotation or translation of the ethylene entity, are probably less useful for the detection of the complexation. Their frequencies are uncertain and cannot be checked against known modes, and they would probably produce much weaker bands in the far IR spectrum than modes related to the rest of the complex. The Ti-C1 stretching modes may dominate this part of the spectrum, with strong and broad band^.^^,^^ Significant differences may be noticed when comparing the various methods mode by mode. For example, the SCF calculation predicts (Figure 4) that the CH3 umbrella vibration should be observable as a significant band at 1217 cm-1 in the IR spectrum. The correlated calculations predict that this mode should have a lower frequency (1117 and 1179 cm-l) and also a much lower IR activity. In hydrocarbons, this mode normally has a frequency a t about 1375 cm-l, while it is close to 1200 cm-’ in trimethylaluminum and t r i m e t h y l g a l l i ~ m . ~ ~ Some differences in the region 1300-1400 cm-l are also evident from Figure 4. This region contains three overlapping peaks; two CH3 deformation modes in addition to v3. All the calculations predict that the two CH3 deformation modes are close to degenerate and have higher frequencies than v3. The latter difference is seen to be larger at the SCF level than for the two correlated methods. In spite of some differences between the results from the various methods, the directions of the shifts which have been found suitable for detection of n complex (69)Ystenes, M.; Rytter, E. Spectrosc. Lett. 1987,20, 519. (70)Ystenes, M.; Rytter, E. Spectrochim. Acta 1992,48A, 543. (71)Kvisle, S. Aluminum Alkyls in Low Temperature Matrices. Ph.D. Thesis, Department of Inorganic Chemistry, The Norwegian Institute of Technology, Trondheim, Norway, 1983. (72)Duncan, J. L.; Wright, I. J.;Van Lerberghe, D. J.Mol. Spectrosc. 1972,42, 463. (73)Pople, J. A.; Scott, A. P.; Wong, M. W.; Radom, L. Isr. J. Chem. 1993,33,345. A scale factor of 0.9427 is reported for full MP2/6-31G(d)fundamental frequencies. Anthony P. Scott reports in an electronic mail posting to the Computational Chemistry List (gopherd/infomeister.osc.edu:73/1m/archived-messaged94/08/10~ that the scale factor for frozen core MP2/6-31G(d)has been estimated at 0.9434. (74)Shimanouchi, T., Ed. Tables of Molecular Vibrational Frequencies. National Bureau of Standards: Washington, DC, 1972; Consolidated Volume 1,NSRDS-NBS-39. (75)Duncan, J. L.; McKean, D. C.; Mallison, P. D. J. Mol. Spectrosc. 1973,45, 221.
Jensen et al.
4358 Organometallics, Vol. 14, No. 9, 1995
formation are seen to be independent of the methods applied in the present study. The applied computational methods are also seen to predict roughly the same magnitude for the shifts. An exception is the two outof-plane ethylene deformation modes in 3, V I and V S , where the SCF calculation predicts that most of the shift occurs in the v g mode, probably because the complex has C, symmetry at this level of theory. However, the good agreement between the shifts calculated for 3 at the two correlated levels is encouraging. None of the shifts calculated for v2, V I , and V8 differs by more than 20 cm-l between the MP2 and DFTG methods. The fact that no titanium-ethylene n complex was found for 4 with the DFTG method is taken as a reminder that it is still not clear whether these complexes, proposed to be intermediates in Ziegler-Natta catalysis, represent local minima on the potential energy surface of ethylene insertion reaction. Even if such local minima exist, it is an open question whether the lifetimes of the complexes are sufficient for experimental detection. 3.4. Important Features of the Force Field. The calculated force constants in Table 9 reflect the changes that appear in ethylene upon coordination. The changes are particularly clear for 1: the C-C bond becomes weaker, and the C-C-H angle is less rigid. The Ti-C stretching constants increase with shorter Ti-ethylene bond lengths, and this is accompanied by an increasing force constant for the Ti-C-H bend. The large and positive fRT (C-C/C-Ti interaction) is also expected, as a shortening of the Ti-ethylene bond leads to a longer C-C bond. A negative f T T (C-Ti/C-Ti interaction) shows that the Ti-ethylene bond is best described as a nonclassic bond to the center of the n bond and not as independent Ti-C bonds. The nonclassic bond character is not that evident for 3, where the asymmetric complexation leads to different effects for the two carbon atoms. The two FT constants differ with more than 25%, which is also reflected in a difference of 0.3 between the lengths of these two bonds at both the SCF and DFTG levels. Furthermore, the two f R T constants have different signs, and fm is positive. This means that shortening the Ti-ethylene bond should cause the ethylene entity to rotate (Bz,), and a rotation should cause shortening or lengthening of the C-C bond, depending on the direction of rotation. The explanation is probably that the complex is approaching a classic bond situation for the Ti-C bond closest to the methyl group. A further strengthening of this bond causes a weakening of the metal-ethylene n bond and thus a shortening of the ethylene C-C bond. A feature that reflects the positive value of f m is that the frequency of the asymmetric Ti-ethylene stretch is significantly lower than for the symmetric counterpart. The force field for 4 behaves more as expected, with a negative fTT and positive fRT for both Ti-C bonds. However, one of the latter interactions is reduced to nil, probably because of the very weak metal-ethylene interaction, with Ti-C distances above 3 A. The weak titanium-ethylene interaction is reflected in the low calculated frequencies (43 and 64 cm-') for the symmetric Ti-ethylene stretch.
4. Conclusions
Ethylene was found to be covalently bound in the 2A1 state of Ti(C2H4)+. For the other complexes studied, the olefin geometry is much closer to that of free ethylene, with only a small weakening of the ethylene n bond during coordination. In the 4B1 state of Ti(CzH4)+, detailed CSOV calculations show that the bond t o ethylene is composed of intramolecular polarization and ethylene-to-metal donation. The rather weak metalmonomer interaction in this complex is caused by the repulsive high-spin coupled valence electrons of the metal. Adding covalent ligands t o titanium results in a stronger donatiodpolarization bond toward ethylene as calculated for C ~ Z T ~ ( C H ~ ) ( C The ~ H ~weakest )+. titanium-ethylene bond, apparently also of the donation/ polarization type, was found for the neutral, bimetallic A1H20c-C1)2TiC12(CH3)(C2H~). At the DFTG level, no stationary point due to ~t coordination of ethylene was found for this system. The calculations show that detection of metalmonomer complexes by means of vibrational spectroscopy should be feasible mainly in two frequency domains. (i) The changes in the fundamental dominated by the ethylene C-C stretching vibration (v2) may be substantial. For a strong, covalent type titaniumethylene bond, the shift may be so large that the mode becomes difficult t o identify in the vibrational spectrum of the complex. This mode is not IR-active in free ethylene, but it should be easily detected in Raman, and it is significantly activated for IR even for the weakest coordination studied in this work. (ii) Modes related t o out-of-plane deformations of ethylene, in particular v7 and Y E , are especially useful as they seem to contain information about the strength and type of metalethylene bond in question. A donatiodpolarization type metal-ethylene bond leads to increased frequencies for one or both of these modes, whereas a strong, covalent type bond gives a substantial reduction of v7. The latter mode is among the strongest in the IR spectrum of ethylene and maintains its intensity in the complexes. In case of a strong, covalent type titanium-ethylene bond, the C-H stretching region is also significantly affected. If the metal-ethylene bond is dominated by donation and polarization, the shifts are small, and the intensities of these bands in the complexes are also reduced. Acknowledgment. A scholarship from the Norwegian Institute of Technology is gratefully acknowledged (V.R.J.), as is financial support from The Norwegian Academy of Science and Letters and Den norske stats oljeselskap a s . (VISTA, Grant No. V6415)and a grant of computing time from the Norwegian Supercomputing Committee (TRU). The authors want t o thank Intel Corporation for support through the SINTEMntel Paragon SupercomputerPartnership Agreement. V.R.J. also appreciates additional funding from Anders Jahres Fond. Finally, we would like to thank Dr. Bjorn K. Alsberg for help with visualization of the IR spectra. OM940879P
