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Electronic Delocalization, Energetics, and Optical Properties of Tripalladium Ditropylium Halides, [Pd3(C7H7)2X3]1- (X ) Cl-, Br-, and I-) A. Mun˜oz-Castro and R. Arratia-Pe´rez* Departamento de Ciencias Quimicas, RelatiVistic Molecular Physics (ReMoPh) group, UniVersidad Andres Bello, Republica 275, Santiago, Chile ReceiVed: February 3, 2010; ReVised Manuscript ReceiVed: February 25, 2010
Here we report relativistic electronic structure calculations employing all-electron density functional theory (DFT) including scalar and spin-orbit interaction, on the multimetallic sandwich compound [Pd3(C7H7)2X3]1(X ) Cl- (1), Br- (2), and I- (3)), which can be considered as a [Pd3X3]3- fragment flanked by two ringligands [(C7H7)2]2+. The calculations suggest that the [Pd3X3]3--ligand interaction is mainly arising from electrostatic contributions, where the formally zerovalent Pd atoms allows backdonation of charge from the halide X1- atoms to the [(C7H7)2]2+ ligands, resulting in a net charge of about +0.4 for each Pd atoms that decreases from 1 to 3. The electronic delocalization estimated via the NICS indexes and the ELF function allows us to describe a significant stabilizing σ-aromaticity at the center of the Pd3 triangle, which decreases from [Pd3Cl3]3- to [Pd3I3]3- (1 to 3) due to the softer character of the iodine counterpart, that donates extra charge to the ligands. The calculated electronic transitions via TD-DFT are in reasonable agreement with the experimental data obtained in CH2Cl2 solution, indicating that the most intense transition involves a corecentered [Pd3X3]3 transition toward the [(C7H7)2]2+ ligands, with mainly X1- character in the former molecular spinor that is responsible for the variation of the observed λmax according to the variation of X1-. Introduction Since the isolation and later recognition of the ferrocene sandwich structure (Fe(η5C5H5)2),1-3 metallocenes have constituted one of the most important subjects in organometallic chemistry because of their current and potential applications in different areas of chemistry.4-6 Most of the metallocenes are based on one redox center flanked by two aromatic carbocylic ligands exhibiting facile redox behavior5,6 and important catalytic activity.4,5 The inclusion of multiple redox centers into a single molecular unit is an active research field envisioned by the early work of Katz,7 attracting great interest due to their bonding nature and cooperative effects arising from the interaction between the metallic centers,8-10 which dramatically modify the chemical and physical behavior in comparison to its mononuclear counterpart. These metallic interactions are desirable for applications in molecular electronics,11,12 catalysis,13-15 and other areas of research.16,17 Particularly of interest is the multimetallic-monolayer motif supported between π-conjugated ligands observed for palladium compounds (for theoretical characterization see ref 18), which exhibits both metal-ligand and direct metal-metal interaction19 in diverse types of shapes, such as, linear (1D metal “wire”),21 triangular22,23 and square20,24 (2D) arrangements, among others.25-27 The novel formally zerovalent triangular Pd3 motif, depicted by the complex [Pd3(µ3-η2:η2:η3C7H7)2X3]1- (X ) Cl- (1), Br(2), and I- (3)), has been structurally characterized22,23 as a quasiequilateral triangle with an increasing Pd-Pd distance going from 1 to 3. The trimetallic moiety with three terminal X1halide ligands can be considered as a [Pd3X3]3- fragment flanked by two seven-member ring (C7H7+) in a metallocene-like array, making them attractive for studies of their similarities and novel properties in relation to usual monometallic complexes. This * To whom correspondence should be addressed. E-mail: rarratia@ unab.cl.
multinuclear metallocene compound is intriguing not only for the electronic structure (previously calculated22) and optical properties,23 but also for the rings currents that arise from the direct metal-metal and Pd3-ligand interaction, which plays an important stabilizing role in planar and tridimensional polyhedral clusters.28 The diatropic (aromatic) and paratropic (antiaromatic) ring currents can be estimated by calculating the nuclear independent chemical shifts (NICS) index.29-31 Recently, we extended the use of the NICS index to the relativistic two component ZORA calculations including both scalar and spin-orbit effects,32,33 depicting the variation of the aromaticity on the related [(CNT)Pd4(COT)]1+ complex, due to the spin-orbit effects.33c In this article we report the relativistic electronic structure of the [Pd3(C7H7)2X3]1- metallocene, in order to achieve a better understanding of the metal-metal and metal-ligand interactions and related optical properties. In addition, we have estimated via NICS index29,31 and the graphical representation of the electron localization function (ELF) suggested by Becke and Edgecombe34-36 the diatropic currents of the Pd3 moiety. Computational Details The relativistic density functional theory (DFT) calculations were carried out employing the ADF2008.01 code,37 incorporating both scalar and spin-orbit corrections via the twocomponent ZORA Hamiltonian.38,39 Geometry optimizations were done without any symmetry restrain, via analytical energy gradient method implemented by Verluis and Ziegler,40 within the generalized gradient approximation (GGA) of PerdewBurke-Ernzerhof (PBE) approximation for the exchange and correlation potential,41a,b employing triple-ξ Slater basis set plus polarization function (STO-TZP), obtaining structures of C1 symmetry. The inclusion of the spin-orbit effect into the calculations requires the coupling of the l and s for each electron
10.1021/jp101038u 2010 American Chemical Society Published on Web 03/19/2010
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Mun˜oz-Castro and Arratia-Pe´rez TABLE 1: Selected Bond Lengths (Å) of 1, 2, and 3 1 calc
Figure 1. Schematic Representation of [Pd3(C7H7)2X3]1- (C1).
(individual l and s coupling), hence ml and ms are no longer good quantum numbers.42a Therefore, the total angular momentum j (j ) l ( s) is used to designate the molecular spinors (MS), instead of the pure orbital angular momentum (l) molecular orbitals (MO), as is pointed out from the seminal work on the development of the relativistic self-consistent-field theory for molecules by Malli.43 Into the C1 point group, the direct product between the single valued a (Γ1 according to the Bethe’s notation42b) irreducible representation (irrep) with the double valued γ1/2 spin irrep, gives two times the extra irrep Γ2 (Bethe’s notation) according to aXγ1/2 ) 2Γ2, where Γ2xΓ2 forms the basis for φ(1/2, ( 1/2) in the C1* double-valued point group, which allows us, for simplicity, to consider the sum as γ1/2.42 The excitation energies were estimated by spin-orbit time-dependent perturbation theory (TD-DFT), using the Leeuween-Barends (LB94) functional, which possesses a correct 1/r asymptotic behavior,44a incorporating the solvent effects via a conductor-like screening model (COSMO) using CH2Cl2 as solvent.44b,c The NICS29,31 were calculated employing the GGA exchange expression proposed by Handy and Cohen41c and the correlation expression proposed by Perdew, Burke, and Ernzerhof41 (OPBE), incorporating both scalar and spin-orbit effects (OPBE/ ZORA+SO). In addition, the analysis of the Becke and Edgecombe’s ELF provides a useful tool to describe the electron delocalization in terms of the excess kinetic energy due to the Pauli repulsion.34-36 The values of the ELF (η) function are conveniently defined between 0 and 1 (0 e ELF e 1), where it is equal to 0.5 for a homogeneous electron gas at a density equal to the local density of the system. In this sense, ELF ) 1 indicates a perfect localization and 0.5 is a perfect delocalization. Values between 0.0 and 0.5 denote delocalization in low-density regions.34-36 Results and Discussion Molecular Structure. The molecular structure of [Pd3(C7H7)2X3]1- (X ) Cl- (1), Br- (2) and I- (3)) exhibits a quasiequilateral Pd3 triangle with three terminal X1- ligands in a [Pd3X3]3- motif, flanked by two seven-member rings (C7H7+) in a metallocene-like manner (Figure 1). The calculated distances depicted in Table 1 are in reasonable agreement with the experimental data22,23 and previous theoretical calculations for [Pd3(C7H7)2Cl3]1- at the B3PW91 level.22 From 1 to 3, the average Pd-Pd bond distance increases from 2.801 Å (exp, 2.763 Å) to 2.820 Å (exp, 2.782 Å), and are in the range of normal Pd-Pd bonds.19 Moreover, the distance between the centroid at the center of Pd3 ring and the centroid of C7H7+ (Pd3-C7H7) slightly increases from 1 to 3, retaining the µ3-η2: η2:η3 coordination mode to the Pd3 moiety (for a more extended discussion see refs 22 and 23). Electronic Structure. The relativistic electronic structure of the formal tris-16-electron Pd complexes,45 1, 2 and 3, are schematically depicted in Figure 2, denoting the contribution
Pd1-Pd2 Pd2-Pd3 Pd3-Pd1 average Pd3-C7H7c Pd3-C7H7′c average Pd1-X1 Pd2-X2 Pd3-X3 average
a
C1 2.800 2.795 2.808 2.801 2.105 2.104 2.105 2.486 2.478 2.482 2.482
2 exp
b
2.755 2.745 2.789 2.763 2.084 2.084 2.084 2.471 2.471 2.441 2.461
calc
a
C1 2.813 2.809 2.819 2.814 2.107 2.106 2.107 2.628 2.619 2.623 2.623
3 exp
b
2.755 2.769 2.773 2.766 2.102 2.087 2.095 2.581 2.581 2.560 2.574
calc
a
C1 2.819 2.816 2.825 2.820 2.110 2.109 2.110 2.811 2.801 2.805 2.806
expb 2.796 2.774 2.776 2.782 2.092 2.092 2.092 2.736 2.754 2.702 2.731
a PBE/ZORA+SO calculation. b Experimental data of [Pd3(C7H7)2X3]1- from refs 22 and 23. c From the centroid at the center of Pd3 to the centroid at the center of each [C7H7]+.
Figure 2. Electronic structure of [Pd3(C7H7)2X3]1-, denoting the contribution of [(C7H7)2]2+ under a C1 symmetry, where all energy levels transform according to the γ1/2 irrep. The brown rectangle denote spinors with mainly [Pd3X3]3- character.
(>10%) from both 6πej conjugated rings, C7H7+, to the molecular energy levels constituted principally by the valence shell of the [Pd3X3]3- fragment. Similarly to the electronic structure of monometallic metallocenes,46 and the multimetallic [(CNT)Pd4(COT)]1+33c complex, [Pd3(C7H7)2X3]1- exhibits the characteristic bonding, nonbonding, and antibonding46 interaction between the metallic moiety and the organic ligands, as can be seen from Figure 2. The highest occupied molecular spinor (HOMS) and HOMS-1 are composed by about ∼20% of the 5π of both C7H7+ ligands, and ∼80% of the [Pd3X3]3- fragment in a nonbonding interaction, while the lowest unoccupied molecular spinor (LUMS), LUMS+1, LUMS+2 and LUMS+3, exhibits a mainly ligand character ([C7H7]22+) with contributions of ∼75, ∼75, ∼85, and ∼85%, respectively, in an antibonding manner for 1, 2, and 3. In these symmetric metallocenes, both C7H7+ ligands contribute almost equally to the electronic structure, as can be seen from the detailed analysis of the ligands π-spinors in Table 2. The initially occupied π1, π2, and π3 transfer some electron density to the [Pd3X3]3- moiety denoting the donor capability of the ligand, while the initially unoccupied π4 and π5 (neglecting the very small amount of π6 and π7) accept charges from the [Pd3X3]3- core, denoting its acceptor capability. Hence, the [C7H7]22+ fragment can be regarded as a π-donor-πacceptor ligand, in agreement with the reported molecular orbital (MO) analyses for [Pd3(C7H7)2Cl3]1-.22 To assign the total valence population of the Pd and the formally X1- atoms, and for different fragments of [Pd3(C7H7)2X3]1-, we employed the Hirshfeld47a and Voronoi
Tripalladium Ditropylium Halides
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TABLE 2: Total Occupation (in au) of the π Spinors of the [C7H7]+ Conjugated Rings 1
2
3
levela
[C7H7]+
[C7H7′]+
[C7H7]+
[C7H7′]+
[C7H7]+
[C7H7′]+
π1 π2 π3 π4 π5 π6 π7 total π pop.
1.81 1.88 1.91 0.78 0.64 0.09 0.02 7.14
1.81 1.92 1.88 0.79 0.63 0.09 0.02 7.14
1.84 1.89 1.92 0.75 0.64 0.09 0.02 7.15
1.84 1.91 1.88 0.78 0.63 0.09 0.02 7.15
1.86 1.89 1.91 0.76 0.64 0.08 0.02 7.17
1.86 1.91 1.91 0.76 0.63 0.08 0.02 7.17
a For plot of the seven π spinors of [C7H7]+ see the Supporting Information.
TABLE 3: Two Different Hirshfeld and VDD Charges Analysis (au): For each Pd and X1- Halide Atoms, and for [Pd3(C7H7)2X3]1- Decomposed into Three Different Fragments 1 Hirshfeld atom Pda Xa fragment [C7H7]+ [C7H7′]+ [Pd3X3]3– total
2 VDD
Hirshfeld
3 VDD
Hirshfeld
TABLE 5: NICS Values (ppm) at the Center of Each Fragment of [Pd3(C7H7)2X3]1-, from a Scalar+Spin-Orbit Calculation (OPBE/ZORA+SO)
VDD +
+0.398 –0.485
+0.393 –0.520
+0.391 –0.477
+0.381 –0.500
+0.372 –0.454
+0.352 –0.459
–0.370 –0.369 –0.261 –1.000
–0.310 –0.310 –0.380 –1.000
–0.371 –0.371 –0.258 –1.000
–0.376 –0.357 –0.267 –1.000
–0.377 –0.377 –0.247 –1.000
–0.383 –0.320 –0.297 –1.000
a Average values. For detailed analyses for each Pd and X1atoms see the Supporting Information.
TABLE 4: Energy Decomposition Analyses (EDA) for the [(C7H7)2]2+-[Pd3X3]3- Interaction Energy (Binding Energy) term
Figure 3. Isosurface (0.143 au) and cut-plane representation of the ELF function for the [Pd3X3]3- block of 1, 2, and 3, from a PBE/ZORA+SO calculation, denoting the σ-interaction inside the Pd3 triangle.
1
2
3
1160.66 1093.85 1138.88 ∆Epauli ∆Velstat –1088.03 (63%)a –1037.18 (64%)a –1052.89 (63%)a ∆Eorb –626.01 (37%)b –594.13 (36%)b –624.47 (37%)b c ∆Eint –553.38 –537.47 –538.48 a (∆Velstat /(∆Velstat +∆Eorb))%. b (∆Eorb/(∆Velstat +∆Eorb))%. c ∆Eint ) ∆Epauli + ∆Velstat + ∆Eorb.
deformation density (VDD)47b partitioning schemes (Table 3). The Hirshfeld and VDD schemes show similar results, which suggest that the [Pd3X3]3- moiety donate about ∼1.3 je to each C7H7+ fragments, in agreement with the analysis of the π-spinors of the ligands. From 1 to 3, the analysis of the valence populations suggest that the [Pd3X3]3- moiety increase the amount of the charge donated due to the softer character of the terminal halide ligands of 2 and 3. Thus, the decreasing order of softness is as follows: [Pd3I3]3- > [Pd3Br3]3- > [Pd3Cl3]3-. The analysis for each Pd and halide atoms suggest that the formally zerovalent Pd atoms (Pd(0)) can be regarded as a Pd+0.4, approximately, where 1 denotes the most electropositive (∼ +0.398) and 3 is the lease electropositive (∼ +0.372) character of the series. Binding Energy Analysis. With the aim to gain more insights into the [Pd3X3]3--ligand interaction, the [(C7H7)2]2+-[Pd3X3]3interaction energy (∆Eint) was partitioned via the energy decomposition analyses (EDA) according to the MorokumaZiegler scheme48,49 (Table 4). The interaction energy (binding energy) is calculated to be largely favorable by about -553.38 kcal/mol for 1, -537.47 kcal/mol for 2, and -538.48 kcal/mol for 3, as can be expected by the metal-ligand interaction that includes a backdonation from the ligands (see above). Within this scheme, the interaction energy term can be divided into
[C7H7] [C7H7′]+ [Pd3X3]3–
1
2
3
–10.89 –10.83 –55.95
–10.89 –10.84 –53.33
–11.22 –11.17 –50.33
three main components by the form: ∆Eint ) ∆Epauli + ∆Velstat + ∆Eorb. Where, the ∆Velstat term accounts for the stabilizing electrostatic interaction, and ∆Eorb accounts for the covalent character of the fragment-fragment interaction.48,49 In this sense, the ∆Velstat represent of about 63% of the total stabilizing energy for 1, 2, and 3 (calculated as ∆Eelstat/(∆Velstat + ∆Eorb) %). Hence, these results suggests that the electrostatic interaction plays the most important role, compared to the orbital interaction (∼37%) in the stabilization of the [Pd3(C7H7)2X3]1- complex, similarly to the [(CNT)Pd4(COT)]1+33c metallocene. Thus, the analysis suggests that the [C7H7]22+-[Pd3X3]3- interaction is mainly characterized by the electrostatic term, and is more stable for the harder [Pd3Cl3]3- core on 1. Ring Currents. The electronic delocalization interpreted as aromaticity observed in triangulo-core clusters of transition metal oxides, [Ta3O3]-,50 [M3O9]2- (M ) W, Mo),51 and variations in the aromaticity by considering the role of spin-orbit effects on [Re3X9] (X ) Cl, Br), [Re3X9]2-,32 and recently on [(CNT)Pd4(COT)]1+,33c inspired us to evaluate the aromaticity variations of [Pd3(C7H7)2X3]1- going from 1 to 3, via NICS30,31 calculations including the spin-orbit coupling at different points along the z-axis. In addition, the graphical and cut-plane representations of the ELF34-36 are used as a complementary tool (Figure 3). The negative NICS values shown in Table 5 at the center of the [Pd3X3]3- ring and at the center of each C7H7+ ligand ([C7H7]+ and [C7H7′]+) are interpreted as aromaticity, denoting a significant electronic delocalization behavior inside the Pd3 ring that leads to an increased aromaticity of each C7H7+, compared with the NICS index value for the isolated C7H7+ ring of -5.86 ppm (at the center of the C7H7+ ring at the same level of theory). The NICS indexes suggests the decrease of the amount of ring currents at the center of the [Pd3X3]3- ring going from 1 to 3 (i.e., from the harder 1 to the softer 3), which denote an increase in the aromaticity of the C7H7+ rings for 3, due to the fact that [Pd3I3]3- possess the softer character that allows to donate more charge to the ancillary ligands. The ELF function obtained for the [Pd3X3]3- block (brown square from Figure 2), exhibits a σ-type interaction between the three Pd centers denoted by a big lobule at the center of the [Pd3X3]3- moiety with decreasing ELF values of 0.36, 0.35, and
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Mun˜oz-Castro and Arratia-Pe´rez
TABLE 6: Electronic Transitions Energies for 1, 2, and 3 λ (nm) expa
λ (nm) calcb
f c (×100)
474
423
21.85
422
20.52
446
27.2
445
25.8
459
32.35
458
30.49
1
2
3
480
486
contribd 50%: HOMS-8 f LUMS 50%: HOMS-8 f LUMS+1 50%: HOMS-8 f LUMS+2 50%: HOMS-8 f LUMS+3 50%: HOMS-8 f LUMS 50%: HOMS-8 f LUMS+1 50%: HOMS-8 f LUMS+2 50%: HOMS-8 f LUMS+3 50%: HOMS-8 f LUMS 50%: HOMS-8 f LUMS+1 50%: HOMS-8 f LUMS+2 50%: HOMS-8 f LUMS+3
assignmente
polarization
CLCT CLCT CLCT CLCT CLCT CLCT CLCT CLCT CLCT CLCT CLCT CLCT
µx,y,z µx,y,z µx,y,z µx,y,z µx,y,z µx,y,z µx,y,z µx,y,z µx,y,z µx,y,z µx,y,z µx,y,z
a From ref 23 in CH2Cl2. b Scalar + Spin-Orbit calculation (LB94/ZORA+SO) including CH2Cl2 via COSMO module. c Oscillator strength (f) multiply by 100. d Percent contribution of active molecular spinors (see the Supporting Information). e Type of transition, CLCT means core ([Pd3X3]3-) to ligand ([(C7H7)2]2+) charge transfer.
0.33 for 1, 2, and 3, respectively (Figure 3), which denote a high electronic delocalization in low electronic-density regions. Accordingly, the NICS indexes for 3 suggest minor amounts of ring currents at the center of the Pd3 moiety, due to the charge transfer to the ligands. Similarly, the ELF values at the center of each Pd-Pd pair vary as 0.43 for 1, 0.39 for 2, and 0.39 for 3, respectively, denoting a low-density electronic delocalization. The aromatic character observed on [Pd3(C7H7)2X3]1-, which denotes the electronic delocalization inside the Pd3 ring, is suggested to be an important stabilizing factor for these tris16-electron Pd complexes45 that stabilizes the [Pd3X3]3- core and avoid the preference predicted by the 18-electron rule. Electronic Transitions. The calculated and experimental absorption data are summarized in Table 6. The reported absorption spectra for 1, 2, and 3, exhibit an absorption maxima (λmax) in CH2Cl2 solution, at 474, 480, and 486 nm, respectively. Denoting the influence of the X1- halide ligands into the most intense transition, which suggest that this transition involves some spinors with significant X1- character. The calculated absorption spectra including the solvent effects through the COSMO model, shows several low intense transitions in conjunction with two intense transitions that involve a [Pd3X3]3core-centered spinor (HOMO-8) with mainly X1- character, as is expected for variation of the λmax from 1 to 3. The calculated λmax is a combination of two transitions, which are the result of a 50% of HOMS-8 f LUMS and 50% of HOMS-8 f LUMS+1, and 50% HOMS-8 f LUMS+2 and 50% of HOMS-8 f LUMS+3 transition (Table 6). Where the LUMS, LUMS+1, LUMS+2, and LUMS+3 are centered in the [(C7H7)2]2+ fragment (π4 and π5) as can be seen from Figure 2 (see the Supporting Information). Thus, the transition can be regarded as a core ([Pd3X3]3-) to ligand ([(C7H7)2]2+) charge transfer (CLCT). The calculated energies of λmax (active in the x, y, and z axis, µx,y,z) at 423 and 422 nm for 1, 446 and 445 nm for 2, and 459 and 458 nm for 3, respectively, are in reasonable agreement with the experimental data and clearly reproduce the observed λmax trend. 4. Conclusions The electronic structure has been analyzed via the relativistic two component ZORA Hamiltonian including spin-orbit coupling. The calculated data suggest that the multimetallic complexes [Pd3(C7H7)2X3]1- exhibits similar electronic structure with typical monometallic metallocenes. The calculations suggest that the [Pd3X3]3--ligand interaction is mainly arising from electrostatic contributions, where the formally zerovalent Pd
atoms allows backdonation of charge (covalent contribution) from the halide X1- atoms to the [(C7H7)2]2+ ligands, resulting in a net charge of about +0.4 for each Pd atoms which decrease from 1 to 3, as is expected. The ring currents were estimated via NICS indexes and the electronic delocalization via the ELF function, which suggests highly diatropic currents (interpreted as aromaticity), as result of an extended electronic delocalization at the center of the Pd3 core, forming a big lobule that increases the amount of diatropic rings currents at the center of each (C7H7)+ ligand. The calculated electronic transitions of 1, 2, and 3, are in reasonable agreement with the experimental data in CH2Cl2, showing that the transition is a [Pd3X3]3- core centered to [(C7H7)2]2+ ligands, with a mainly X1- character in the former responsible for the variation of the observed λmax. Acknowledgment. The authors thank the reviewers for their useful comments. This work has been supported by FONDECYT Grants 1070345, UNAB-DI-02-09/R, UNABDI-09-09/I, Project Millennium No. P07-006-F, and Conicyt Fellowship 21100513. Supporting Information Available: Plot of the seven π spinors of [C7H7]+, detailed charge analysis for each Pd and X1- atoms, and active molecular spinors involved in the maxima absorption of 1. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) (a) Kealy, T. J.; Pauson, P. L. Nature 1951, 168, 1039. (b) Miller, S. A.; Tebboth, J. A.; Tremaine, J. F. J. Chem. Soc. 1952, 632. (2) (a) Fischer, E. O.; Pfab, W. Z. Naturforsh. 1952, 7b, 377. (b) Wilkinson, G.; Rosenblum, M.; Whiting, M. C.; Woodward, R. B. J. Am. Chem. Soc. 1952, 74, 2125. (c) Wilkinson, G. J. Am. Chem. Soc. 1952, 74, 6146–6149. (3) (a) Kauffman, G. B. J. Chem. Educ. 1983, 60, 185. (b) Laszlo, P.; Hoffmann, R. Angew. Chem., Int. Ed. 2000, 39, 12. (c) Ferrocenes; Togni, A.; Hayashi, T., Eds.; VCH Publishers: New York, 1995. (4) Metallocenes: Synthesis, ReactiVity, Applications; Togni, A. Halterman R. L., Eds.; Wiley-VCH: Weinheim, 2006. (5) Long, N. J. Metallocenes: An Introduction to Sandwich Complexes; Blackwell Science: Oxford, U.K., Malden, MA, 1998. (6) (a) Stepnicka, P. Ferrocenes: Ligands, Materials and Biomolecules; Wiley: Hoboken, NJ, 2008. (b) Yasin, T.; Fan, Z.; Feng, L. Polyhedron 2005, 24, 1262. (7) (a) Katz, T. J.; Schulman, J. J. Am. Chem. Soc. 1964, 86, 3169. (b) Katz, T. J.; Balogh, V.; Schulman, J. J. Am. Chem. Soc. 1968, 90, 734. (c) Katz, T. J.; Acton, N. J. Am. Chem. Soc. 1972, 94, 3281. (8) (a) Braunstein, P., Oro, L. A., Raithby, P. R., Metal Clusters in Chemistry; Wiley-VCH: Weinheim, 1999. (b) Shriver, D. F., Kaesz, H. D., Adams, R. D. The Chemistry of Metal Cluster Complexes; VCH: New York, 1990.
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