Organometallics 2009, 28, 3727–3733 DOI: 10.1021/om900203m
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On the Nature of the Agostic Bond between Metal Centers and β-Hydrogen Atoms in Alkyl Complexes. An Analysis Based on the Extended Transition State Method and the Natural Orbitals for Chemical Valence Scheme (ETS-NOCV) Mariusz P. Mitoraj,a,b Artur Michalak,a and Tom Ziegler*,b a
Department of Theoretical Chemistry, Faculty of Chemistry, Jagiellonian University, R.Ingardena 3, 30-060 Cracow, Poland, and bDepartment of Chemistry, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada Received March 18, 2009
We have in the present account analyzed the bonding in β-agostic alkyl complexes between the carbon chain (R) and the transition metal center. The analysis is based on a recently proposed energy decomposition scheme (ETS-NOCV). We have considered R=Et, n-Pr, i-Pr, n-Bu, attached to the cationic Ni(II)- and Pd(II)-bis-diimine Brookhart complexes (1), the cationic Ti(IV)- or Zr(IV)metallocenes (2), and the neutral Pd(II) Drent (3) complexes. We find for a given metal that the total M-R dissociation energy -ΔEtotal follows the order n-Bu>n-Pr>Et . i-Pr. For the same R-group (n-Pr), -ΔEtotal for second-row metals is larger than for first-row, as 4d forms better overlaps with the alkyl orbitals than 3d. The major stabilizing contribution to -ΔEtotal is the σ-bond between the Rcarbon and the metal. It is augmented by smaller contributions from the Cβ-M σ-interaction as well as the hyperconjugation of charge into the σCC* and σCH* alkyl orbitals. We finally have the β-agostic contribution from the interaction between a hydrogen atom on the β-carbon and the metal center. The strength of this bond is rather constant for the cationic species 1 and 2. It can be considered as originating from a (largely) Coulombic interaction between the metal center and the electron pair in the Cβ-H bond, where the density of the pair has been polarized by the positive metal charge. The neutral Drent system (3) exhibits a weaker β-agostic interaction, as the net charge on the metal center is less positive.
Introduction The term agostic bond originates from the Greek “Rγoστoζ” (which means to hold close or to clutch). The name was originally introduced by Brookhart et al. to describe the interaction between the relatively inert C-H moiety and a metal center.1,2 Since the early 1950s the number of examples has grown of coordination complexes where a β-hydrogen on a carbon chain interacts with the metal center.1-10 Moreover, it has become apparent that *Corresponding author. E-mail:
[email protected]. (1) Brookhart, M.; Green, M. L. H. J. Organomet. Chem. 1983, 250, 395. (2) Brookhart, M.; Green, M. L. H.; Wong, L. L. Prog. Inorg. Chem. 1988, 36, 1. (3) Brookhart, M.; Green, M. L. H.; Parkin, G. Proc. Natl. Acad. Sci. 2007, 104, 6908. (4) Clot, E.; Eisenstein, O. Struct. Bonding (Berlin) 2004, 113, 1. (5) Scherer, W.; McGrady, S. G. Angew. Chem., Int. Ed. 2004, 43, 1782. (6) Haaland, A.; Scherer, W.; Ruud, K.; McGrady, G. S.; Downs, A. J.; Swang, O. J. Am. Chem. Soc. 1998, 120 (15), 3762. (7) Popelier, P. L. A.; Logothetis, G. J. Organomet. Chem. 1998, 555, 101. (8) Brookhart, M.; Green, M. L. H.; Pardy, R. B. A J. Chem. Soc., Chem. Commun. 1983, 691. (9) Jordan, R. F.; Bradley, P. K.; Baenziger, N. C.; LaPointe, R. E. J. Am. Chem. Soc. 1990, 112, 1289. (10) McKean, D. C. Chem. Soc. Rev. 1978, 7, 399. r 2009 American Chemical Society
such β-agostic interactions can be of vital importance in controlling chemical reactions.1-5 This is especially the case for olefin polymerization processes where β-agostic interactions often are present in the transition state for chain growth and chain termination.11-17 As a consequence, there has been a considerable interest in the β-agostic bond. However, the origin and the factors that influence the agostic interaction are still the subject of some debate.3-7,44-57 In the present study we will provide a compact, qualitative, and quantitative picture of chemical bond formation between alkyl groups and the transition metal centers in β-agostic complexes. We shall consider a selected group of β-agostic systems including the cationic Ni(II)- or Pd(II)-bisdiimine complexes (1)12 due to Brookhart, the cationic Ti (IV)- or Zr(IV)- metallocenes (2),19 and the neutral Pd(II) (11) Ziegler, T. Can. J. Chem. 1995, 73, 743. (12) Ittel, S. D.; Johnson, L. K.; Brookhart, M. Chem. Rev. 2000, 100, 1169. (13) Boffa, L. S.; Novak, B. M. Chem. Rev. 2000, 100, 1479. (14) Michalak, A; Ziegler, T. Macromolecules 2003, 36, 928. (15) Michalak, A.; Ziegler, T. J. Am. Chem. Soc. 2001, 123, 12266. (16) Cossee, P. J. Catal. 1964, 3, 80. (17) Arlman, E. J.; Cossee, P. J. Catal. 1964, 3, 99. (18) Johnson, L. K.; Mecking, S.; Brookhart, M. J. Am. Chem. Soc. 1996, 118, 267. (19) Fink, G.; Brintzinger, H. H. Ziegler Catalysts; Springer-Verlag, 1995; p 161.
Published on Web 06/15/2009
pubs.acs.org/Organometallics
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Figure 1. (A) β-Agostic model complexes studied in the present work together with their abbreviations. The considered model systems are based on the cationic Ni(II)- or Pd(II)-bis-diamine complexes (1)12 due to Brookhart, the Ti(IV)- and Zr(IV)- metallocene cations (2),19 and the neutral Pd(II) Drent (3)20 catalysts based on o-alkoxy derivatives of diphenylphosphinobenzenesulfonic acid. (B) Fragmentation employed in the bonding analysis with 1Ni-nPr as example.
Drent (3)20 catalysts based on o-alkoxy derivatives of diphenylphosphinobenzenesulfonic acid. In addition we have also analyzed one example of a negatively charged complex derived from the Brookhart catalyst (1NiBH3-nPr). The type of complexes studied here were selected due to their prominent role as polymerization catalysts, and they are displayed in Figure 1. There are many other examples of β-agostic systems that are worth investigating in subsequent studies. We can list here the systems containing the interaction between the metals (M=Ru, Nb, Ta, Li, Al) and the HβXβ subspecies (for X=Si, B). In addition the analysis of Rand γ-agostic systems present in the polymerization cycles would be of significant importance. The bonding analysis will be based on the of ETS-NOCV scheme, which combines (20) Drent, E.; van Dijk, R.; van Ginkel, R.; van Oort, B.; Pugh, R. I. Chem. Commun. 2002, 7, 744.
the extended transition state (ETS)21,22 approach with the natural orbitals for chemical valence (NOCV) method.26-30 The ETS-NOCV scheme31 allows for a decomposition of the change in density on bond formation (ΔF) into different (21) Ziegler, T.; Rauk, A. Inorg. Chem. 1979, 18, 1755. (22) Ziegler, T.; Rauk, A. Theor. Chim. Acta 1977, 46, 1. (23) Nalewajski, R. F.; Mrozek, J.; Michalak, A. Int. J. Quantum Chem. 1997, 61, 589. (24) Nalewajski, R. F.; Mrozek, J.; Michalak, A. Pol. J. Chem. 1998, 72, 1779. (25) Michalak, A.; De Kock, R.; Ziegler, T. J. Phys. Chem. A 2008, 112, 7256. (26) Michalak, A.; Mitoraj, M.; Ziegler, T. J. Phys. Chem. A. 2008, 112 (9), 1933. (27) Mitoraj, M.; Michalak, A. Organometallics 2007, 26 (26), 6576. (28) Mitoraj, M.; Michalak, A. J. Mol. Model. 2007, 13, 347. (29) Mitoraj, M.; Michalak, A. J. Mol. Model. 2008, 14, 681. (30) Mitoraj, M.; Zhu, H.; Michalak, A.; Ziegler, T. Int. J. Quantum Chem. 2008, DOI: 10.1002/qua.21910.
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components (ΔFk) with an appealing chemical representation. Additionally, for each deformation density contribution (ΔFk), it is possible not only to visualize ΔFk but also to provide the energy contributions to the bond energy from ΔFk.31
Computational Details All the DFT calculations presented here were based on the Amsterdam Density Functional (ADF) program.32-36 The Becke-Perdew exchange-correlation functional37,38 was applied. A standard double-ζ STO basis with one set of polarization functions was adopted for the elements H, C, N, O, S, B, and Si, while a standard triple-ζ basis set was employed for the transition metals, Ni, Pd, Ti, and Zr. Auxiliary s, p, d, f, and g STO functions, centered on all nuclei, were used to fit the electron density and obtain accurate Coulomb potentials in each SCF cycle. Relativistic effects were included using the ZORA approximation.39-41 In our analysis each of our complexes R-MF (1-3) is divided into a radical (R) and a metal fragment (MF), as shown in Figure 1b. Subsequently we use the ETS-NOCV scheme to study the interaction between R and MF as they are brought together to form R-MF containing both a M-R bond and a M-Hβ β-agostic interaction. Thus, our analysis is based on the bonding between the two open-shell molecular fragments, each holding one unpaired electron with the opposite spin polarizations.
Computational Methods Our analysis is based on the ETS-NOCV approach, which is a merger of the extended transition state (ETS)21,22 method with the natural orbitals for chemical valence (NOCV)26-30 scheme. (31) Mitoraj, M.; Michalak, A.; Ziegler, T. J. Chem. Theory Comput. 2009, 5, 962. (32) TeVelde, G; Bickelhaupt, F. M.; Baerends E. J.; Fonseca Guerra C.; Van Gisbergen S. J. A.; Snijders, J. G.; Ziegler T. J. Comput. Chem. 2001, 22, 931, and references therein. (33) Baerends, E. J.; Ellis, D. E.; Ros, P. Chem. Phys. 1973, 2, 41. (34) Baerends, E. J.; Ros, P. Chem. Phys. 1973, 2, 52. (35) te Velde, G.; Baerends, E. J. J. Comput. Phys. 1992, 99, 84. (36) Fonseca, C. G.; Visser, O.; Snijders, J. G.; te Velde, G.; Baerends, E. J. In Methods and Techniques in Computational Chemistry; METECC-95; Clementi, E., Corongiu, G., Eds.; STEF: Cagliari, Italy, 1995; p 305. (37) Becke, A. Phys. Rev. A 1988, 38, 3098. (38) Perdew, J. P. Phys. Rev. B 1986, 34, 7406. (39) van Lenthe, E.; Baerends, E. J.; Snijders, J. G. J. Chem. Phys. 1993, 99, 4597. (40) van Lenthe, E.; Baerends, E. J.; Snijders, J. G. J. Chem. Phys. 1993, 101, 9783. (41) van Lenthe, E.; van Leeuwen, R.; Baerends, E. J.; Snijders, J. G. Int. J. Quantum Chem. 1996, 57, 281. (42) L€ owdin, P. O. J. Chem. Phys. 1950, 18, 365. (43) Rado n, M. Theor. Chem. Acc. 2008, 120, 337. (44) Ruiz, E.; Salahub, D. R.; Vela, A. J. Phys. Chem. 1996, 100, 12265. (45) Vidal, I.; Melchor, S.; Alkorta, I.; Elguero, I.; Sundberg, M. R.; Dobado, J. A. Organometallics 2006, 25, 5638. (46) Cotton, F. A.; LaCour, T.; Stanislowski, A. G. J. Am. Chem. Soc. 1974, 96, 754. (47) Trofimenko, S. J. Am. Chem. Soc. 1968, 90, 4754. (48) Thakur, T. S.; Desiraju, G. R. Chem. Commun. 2006, 5, 552. (49) Eisenstein, O.; Jean, Y. J. Am. Chem. Soc. 1985, 107, 1177. (50) Jaffart, J.; Etienne, M.; Maseras, F.; McGrady, J. E.; Eisenstein, O. J. Am. Chem. Soc. 2001, 123, 6000. (51) Etienne, M. Organometallics 1994, 13, 410. (52) Cho, H.-G.; Andrews, L. J. Phys. Chem. A 2004, 108, 6294. (53) Cho, H.-G.; Andrews, L. J. Am. Chem. Soc. 2004, 126, 10485. (54) Cho, H.-G.; Andrews, L. Organometallics 2004, 23, 4357. (55) Cho, H.-G.; Andrews, L. Inorg. Chem. 2004, 43, 5253. (56) Pantazis, D. A.; McGrady, J. E.; Besora, M.; Maseras, F.; Etienne, M. Organometallics 2008, 27, 1128. (57) Scheins, S.; Messerschmidt, M.; Gembicky, M; Pitak, M; Volkov, A. Coppens, P.; Harvey, B. G.; Turpin, G. C.; Arif, A. M.; Ernst, R. D. J. Am. Chem. Soc. 2009, ASAP DOI: 10.1021/ja807649k.
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We start by presenting the basic concepts of the ETS method. In this scheme, the total bonding energy between the interacting fragments (ΔEtotal) is divided into four chemically meaningful components (eq 1):
ΔE total ¼ ΔE dist þ ΔE elstat þ ΔE Pauli þ ΔEorb
ð1Þ
The first component, referred to as the distortion term, ΔEdist, represents the amount of energy required to promote the separated fragments from their equilibrium geometry to the structure they will take up in the combined molecule. The second term, ΔEelstat, corresponds to the classical electrostatic interaction between the promoted fragments as they are brought to their positions in the final complex. The third term, ΔEPauli, accounts for the repulsive Pauli interaction between occupied orbitals on the two fragments in the combined complex. Finally, the last term, ΔEorb, represents the stabilizing interactions between the occupied molecular orbitals on one fragment and the unoccupied molecular orbitals of the other fragment as well as mixing of occupied and virtual orbitals within the same fragment (intrafragment polarization) after the two fragments have been united. We can write the change in density that gives rise to ΔEorb as
ΔFð1Þ ¼
XX
ΔΡμν λð1Þνð1Þ
ν
λ
ð2Þ
where the sum is over all the occupied and virtual molecular orbitals on the two fragments. It now follows from the ETS scheme that the ΔEorb term is given by21,22
ΔEorb ¼
XX μ
λ
ΔΡλμ F TS λμ
ð3Þ
where FTS λμ is a Kohn-Sham Fock matrix element that is defined in terms of a (transition state) potential that is midway between that of the combined fragments and the final molecule, hence the word transition state. Turning next to the NOCV approach, we note that historically the natural orbitals for chemical valence (NOCV)23-28 have been derived from the Nalewajski-Mrozek valence theory.23-25 However, from a mathematical point of view the NOCVs, ψi, are simply defined as the eigenvectors,
ψi ð1Þ ¼
M X
C i, λ λð1Þ
ð4Þ
λ
that diagonalizes the deformation density matrix ΔP introduced in eq 2. Thus,
ΔPCi ¼ vi Ci ; i ¼ 1, M
ð5Þ
where M denotes the total number of molecular orbitals on the fragments and Ci is a column vector containing the coefficients that defines the NOCV ψi of eq 4. It follows further26-31 that the deformation density ΔF of eq 2 can be expressed in the NOCV representation as a sum of pairs of complementary eigenfunctions (ψ-k, ψk) corresponding to the eigenvalues vk and -vk with the same absolute value but opposite signs:
ΔFðrÞ ¼
M =2 X k ¼1
vk ½ -ψ2-k ðrÞ þ ψ2k ðrÞ ¼
M =2 X k ¼1
ΔFk ðrÞ
ð6Þ
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Table 1. ETS Energy Decomposition of the Bond between the Alkyl Groups and the Metal-Based Fragmentsa Together with the M-Cr-Cβ Angles ΔEPauli
ΔEelstat
ΔEstericb
ΔEorb
ΔEdist
ΔEtotalc
M-CR-Cβd
Brookhart (1) 1Ni-Et 126.3 -92.9 33.4 -107.8 6.3 -68.1 76.5 1Ni-nPr 127.4 -95.1 32.3 -109.6 6.2 -71.1 77.7 1Ni-iPr 128.4 -97.0 31.4 -106.6 6.9 -68.3 75.5 1Ni-Bu 128.8 -97.4 31.4 -111.7 8.4 -71.9 78.4 159.9 -119.1 40.8 -117.2 7.7 -68.7 75.4 1NiBH3-nPr 1Ni-MeAcr 139.1 -100.1 39.0 -118.8 11.4 -68.4 78.2 1Pd-Et 154.5 -113.8 40.7 -119.7 7.4 -71.6 78.9 1Pd-nPr 155.2 -116.4 38.8 -121.7 7.8 -75.1 80.2 1Pd-iPr 156.1 -117.2 38.9 -118.6 7.9 -71.8 78.3 Metallocenes (2) 2Ti-nPr 98.3 -61.1 37.2 -99.2 8.1 -53.9 83.1 2Zr-nPr 94.6 -59.6 35.0 -109.5 8.3 -66.2 84.9 Drent (3) 3Pd-Et 166.1 -124.1 42.0 -108.6 6.3 -60.3 81.9 3Pd-nPr 166.0 -125.4 40.6 -108.4 6.7 -61.1 82.7 3Pd-iPr 170.8 -128.8 42.0 -106.9 6.9 -58.0 81.2 a kcal/mol. b The total steric repulsion, ΔEsteric = ΔEPauli + ΔEelstat. cΔEtotal = ΔEsteric + ΔEorb + ΔEdist. d The angle defined as M-CR-Cβ.
In the combined ETS-NOCV scheme31 the orbital interaction term (ΔEorb) is expressed in terms of NOCVs as
ΔEorb ¼
M=2 X k ¼1
TS vk ½ -F TS -k, -k þ Fk, k
ð7Þ
TS where FTS -k,-k and Fk,k are diagonal Kohn-Sham matrix elements defined over NOCVs with respect to the transition state (TS). The advantage of the expression in eq 7 for ΔEorb over that of eq 2 is that only a few complementary NOCV pairs normally contribute significantly to ΔEorb. We see above (eqs 6 and 7) that for each complementary NOCV pair, representing one of the charge delocalization ΔFk, we can not only visualize ΔFk but also provide the energy contributions to the bond energy from ΔFk.31
Results and Discussion Let us first discuss the total bond formation energy, ΔEtotal, due to the creation of one of the alkyl complexes in Figure 1a from the corresponding alkyl radical chain and a metal radical fragment, as illustrated in Figure 1b. The bond energy ΔEtotal is decomposed in Table 1 according to eq 1 into four components. We note that the orbital interaction stems not only from the direct M-C bond formation but also from any other stabilizing interaction between the alkyl radical and the metal radical fragment such as β-agostic interactions. With respect to a given alkyl chain (n-propyl), Table 1 reveals that -ΔEtotal is larger for 4d metals than 3d elements. This is the case for both the Brookhart complexes (1) and the metallocenes (2), where our data allow such a comparison. The trend is set by ΔEorb and stems from the fact that 4dorbitals form stronger overlaps with the carbon ligand orbitals than 3d-orbitals. This makes the bonding interaction between the singly occupied orbitals on the two fragments stronger in the 4d case. In the Pd systems this trend is opposed by ΔEsteric due to repulsive interactions between occupied d- and alkyl orbitals. Now the better overlap in the case of the heavier metal makes for a more repulsive interactions. However, for the metallocenes all d-orbitals interacting with occupied alkyl orbitals are empty. The interactions are as a consequence stabilizing and add to the trend in ΔEorb, whereas ΔEsteric is quite similar for the two metallocenes.
Within the 4d metals, -ΔEtotal involving n-propyl is smaller for the neutral Drent complex (3) than for the cationic Brookhart (1) and metallocene (2) systems. As we shall see shortly, this is due to a weaker β-agostic bond to the metal center in the neutral Drent complex (3). Among the two cationic alkyl complexes, -ΔEtotal is larger for 1 than 2. This is mostly due to ΔEorb and reflects better overlaps between 4d and the relevant alkyl orbitals for palladium compared to zirconium. With respect to different alkyl groups, we note that linear alkyl chains give rise to a larger -ΔEtotal contribution than branched alkyls (i-Pr vs n-Pr) for all the different metal systems. This is due to ΔEorb, and to some degree also ΔEsteric. Within the series of linear alkyls the trend in -ΔEtotal follows Et
