Three- and Four-Center Trans Effects in Triply Bonded Ditungsten

Nov 4, 2000 - Regla Ayala , José M. Martínez , Rafael R. Pappalardo , Adela Muñoz Páez and Enrique Sánchez Marcos. The Journal of Physical Chemis...
0 downloads 0 Views 492KB Size
Download PDF
Inorg. Chem. 2000, 39, 5553-5560

5553

Three- and Four-Center Trans Effects in Triply Bonded Ditungsten Complexes: An ab Initio Molecular Dynamics Study of Compounds with Stoichiometry W2Cl4(NHEt)2(PMe3)2 Alessandra Magistrato, Joost VandeVondele, and Ursula Rothlisberger* Laboratory of Inorganic Chemistry, ETH Zentrum, ETH Zurich, CH-8092 Zurich, Switzerland ReceiVed July 11, 2000 We have performed ab initio molecular dynamics simulations based on density functional theory to characterize the structural, electronic, and dynamic properties of the three major isomeric forms of the title compound. In agreement with experimental results, calculations with two different parametrizations of the exchange-correlation functional (BLYP and BP) both indicate the cis-C2 form as the most stable isomer. The relative energies of the different forms are, however, small (j1-2 kcal/mol), and the three compounds show overall very similar groundstate properties. Larger differences exist in their finite temperature behavior, which is dominated by the facile dissociation of one or both phosphine ligands. The calculated activation energies for phosphine dissociation differ clearly for the trans and the cis isomers and vary in the order trans , cis-C2 j cis-Ci. Analysis of the electronic structure of the transition states shows that the difference in activation energy between cis and trans isomers can be rationalized in terms of a classic trans effect caused by a molecular orbital spanning the three atomic centers N-W-P. The subtle difference between the two cis isomers, on the other hand, is likely due to an analogous four-center trans effect N-W-W-P which is mediated via metal-metal orbitals and involves ligands on both tungsten atoms.

1. Introduction Molecules of the form X4M-MX4 exhibit M-M bond orders in the full range from single to quadruple.1 Therefore, they constitute an important class of prototypical systems for the study of multiple metal-metal bonds. Furthermore, some of them have also attracted recent attention for potential applications in photochemical catalysis.2 Among the molecules of this class are the triply bonded ditungsten complexes with stoichiometry W2Cl4(NHR)2(PMe3)2 (R ) Et, Prn, Bun). 31P 1H NMR spectroscopic studies have shown that these molecules exist in solution in up to three isomeric forms: a trans and two types of cis isomers possessing Ci and C2 symmetries, respectively (Figure 1).3,4 The trans compound is formed as the initial product of the synthetic process5 while the cis-Ci isomer appears as the intermediate and the cis-C2 as the final product. Considering the high similarity of the three forms, it is not obvious what could account for the pronounced differences in their kinetic properties. A thorough experimental characterization of the relative differences on the other hand is hampered by the fact that it has not yet been possible to isolate all three isomers or to determine all three crystal structures. Ab initio molecular dynamics (AIMD) simulations combine a first-principles electronic structure calculation with a classical molecular dynamics scheme.6 This unified approach makes it possible to gain a direct view on the finite temperature behavior (1) Cotton, F. A.; Yao, Z. J. Cluster Sci. 1994, 5, 11. (2) Engebretson, D. S.; Graj, E. M.; Nocera, D. G. J. Am. Chem. Soc. 1999, 121, 868. (b) Pistorio, B. J.; Nocera, D. G. Chem. Commun. 1999, 18, 1831. (c) Nocera, D. G.; Hsu, T. L. C.; Helvoigt, S. A. Inorg. Chem. 1995, 34, 6186. (3) Chen, H.; Cotton, F. A.; Yao, Z. Inorg. Chem. 1994, 33, 4255. (4) Cotton, F. A.; Dikarev, E. V.; Wong, W. Y. Inorg. Chem. 1997, 36, 2670. (5) W2Cl4(NHR)2(PMe3)2 complexes are synthesized via reaction of W2Cl6(THF)4 with alkylamines NH2R, followed by phosphine substitution as described in ref 4.

Figure 1. Schematic representations of the trans and the two possible cis isomers. Intramolecular hydrogen bonds between the amido and chlorine ligands are indicated by thick dashed lines.

of the system.7 Furthermore, it also enables the study of its reactive properties by following in situ the chemical transformations that the system can undergo.8 This method seems, therefore, particularly suited for the characterization of a complex transition metal compound with dynamic properties as intricate as those of the title complex. In this work, we have determined the ground-state structures of all three isomeric forms, which enables a direct characterization of each isomer and the relative differences between them. AIMD simulations have been applied to elucidate the essential factors governing the structural, electronic, and dynamic properties of the three isomeric forms. We have chosen this system as a test case to probe the performance of the method for the characterization of complex transition metal compounds with multiple metal-metal bonds. At the same time, this study represents also a challenging test of the performance of density functional calculations as the underlying electronic structure (6) Car, R.; Parrinello, M. Phys. ReV. Lett. 1985, 55, 2471. (7) Rothlisberger, U.; Andreoni, W. J. Chem. Phys. 1991, 94, 8129. (b) Curioni, A.; Andreoni, W.; Hutter, J.; Schiffer, H.; Parrinello, M. J. Am. Chem. Soc. 1994, 116, 11251. (c) Laasonen, K.; Klein, M. L. J. Am. Chem. Soc. 1994, 116, 11620. (d) Tsuchida, E.; Tsukada, M. J. Phys. Soc. Jpn. 1998, 67, 3844. (e) Meijer, E. J.; Sprik, M. J. Phys. Chem. A 1998, 102, 2893. (8) Rothlisberger, U.; Klein, M. L. J. Am. Chem. Soc. 1995, 117, 42. (b) Curioni, A.; Sprik, M.; Andreoni,W.; Schiffer, H.; Hutter, J.; Parrinello, M.; J. Am. Chem. Soc. 1997, 119, 7218. (c) Boero, M; Parrinello, M.; Terakura, K. J. Am. Chem. Soc. 1998, 120, 2746. (d) Doclo, K.; Rothlisberger, U. Chem. Phys. Lett. 1998, 297, 205.

10.1021/ic000754e CCC: $19.00 © 2000 American Chemical Society Published on Web 11/04/2000

5554 Inorganic Chemistry, Vol. 39, No. 24, 2000 method. As all three isomeric forms can be present in measurable quantities at ambient temperature, their relative energy differences are expected to be small, imposing large demands on the performance of a theoretical scheme. 2. Details of the Computational Scheme The Car-Parrinello method for ab initio molecular dynamics simulations has been described in detail in a number of publications.6,9 Therefore, in this section, we only give the computational details pertinent to the current study. All the calculations were performed with the program CPMD10 which is an implementation of the original CarParrinello scheme based on density functional theory (DFT), periodic boundary conditions, plane wave basis sets, and a pseudopotential formalism. In this work, we used an analytic local pseudopotential for hydrogen and nonlocal, norm-conserving soft pseudopotentials of the MartinsTrouiller type11 for all the other elements. Angular momentum components up to lmax ) 1 have been included for carbon and nitrogen and up to lmax ) 2 for phosphorus and chlorine. For tungsten, we have constructed a semicore pseudopotential with cutoff radii of rs ) 1.1 au, rp ) 1.2 au, and rd ) 1.6 au, which incorporates also scalar relativistic effects. The 14 valence electrons of the 5s25p66s26d4 shells have been treated explicitly. For all light elements, the pseudopotentials have been transformed to a fully nonlocal form using the scheme developed by Kleinman and Bylander,12 whereas for tungsten, the nonlocal part of the pseudopotential has been integrated numerically using a Gauss-Hermite quadrature. We have tested the convergence of our results with respect to the size of the plane wave basis set. Converged results for structural (j0.01 Å) and relative energetic (j0.4 kcal/mol) properties were obtained for a kinetic energy cutoff of 70 Ry which was used throughout the calculations presented here. To test the dependence of our results on the specific model used for the exchange-correlation functional, we have performed all our calculations using two different popular descriptions. In both cases, the exchange part was described with the gradient-corrected model developed by Becke (B),13 whereas the correlation part was either treated with the formulation due to Perdew (P)14 or the one due to Lee, Yang, and Parr (LYP).15 The resulting DFT models, BP or BLYP, respectively, differ solely in the description of the correlation energy. A comparison of the results obtained by these two functionals thus gives a first indication of the importance of correlation effects which can be expected to be particularly delicate for the correct description of transition metal compounds. Another point of central importance for the performance of our computational scheme is the quality of the pseudopotential for tungsten. A first probe of its accuracy was provided by a series of test calculations on the molecule WO2 for which other theoretical data at the MP2, B3LYP, and CCSD(T) levels16 are available for comparison. The structural parameters obtained in this way are summarized in Table 1. Both BLYP and BP parametrizations give very similar results in excellent agreement with coupled cluster calculations. The W-O bond length is reproduced within ∆d e 0.01 Å and the W-O-W bond angle within 1 Å, confirming the high quality of our computational scheme. (9) Car, R.; Parrinello, M. Simple Molecular System at Very High Density, Proceedings of NATO ARW, NATO ASI Series, Les Houches, France, 1988; Plenum Press: New York, 1988. (b) Galli, G.; Parrinello, M. Computer Simulation in Material Science; Meyer, M., Pontikis, V., Eds.; Fluwer: Dordrecht, The Netherlands, 1991; p 238. (c) Remler, D. K.; Madden, P. A. Mol. Phys. 1990, 70, 691. (d) Payne, M. C.; Teter, M. P.; Allan, D. C.; Arias, T. A.; Joannoppoulos, J. D. ReV. Mod. Phys. 1992, 64, 1045. (e) Marx, D.; Hutter, J. Modern Methods and Algorithms of Quantum Chemistry; Grotendorst, J., Ed.; NIC Series, 1; Forschungzentrum Juelich: Juelich, Germany, 2000; p 301. (10) Hutter J.; Ballone, P.; Bernasconi, M.; Focher, P.; Fois, E.; Goedecker, S.; Parrinello, M.; Tuckerman, M. Max-Plank-Institut fu¨r Festko¨rprforschung and IBM Zurich Research Laboratory: 1995-96. (11) Trouiller, M.; Martins, J. L. Phys. ReV. B 1991, 43, 1993. (12) Kleinman, L.; Bylander, D. M. Phys. ReV. Lett. 1982, 48, 1425. (13) Becke, A. D. Phys. ReV. A 1998, 38, 3098. (14) Perdew, J. P. Phys. ReV. B 1986, 33, 8822. (15) Lee,C.; Yang,W.; Parr, R. G. Phys. ReV. B 1988, 37, 785. (16) Pykko´, P.; Tamm, T. J. Phys. Chem. A 1997, 101, 8107.

Magistrato et al. Table 1. Test Calculations for WO2, W-O Bond Distances Are Given in Å and W-O-W Bond Angles Are Given in Degreesa W-O O-W-O

LDA

BLYP

BP

MP2

B3LYP

CCSD(T)

1.624 101.1

1.651 102.8

1.636 100.6

1.657 101.3

1.636 101.5

1.649 101.4

a Corresponding results from MP2, B3LYP, and CCSD(T) calculations are taken from ref 16.

Figure 2. Superposition of X-ray data4 and calculated structure (BP functional) for the cis-Ci isomer. The use of a plane wave basis set implies the presence of periodic boundary conditions. All our calculations on the ditungsten complexes were therefore performed in periodically repeated face-centered cubic supercells. In initial calculations, a cell of edge a ) 30 au was used, whereas final results are given for a ) 35 au. Molecular dynamics runs at elevated temperatures were also performed in the larger cell of a ) 35 au. The classical equations of motion were integrated with a velocity Verlet algorithm with a time step of 0.145 fs and a fictitious mass for the electronic degrees of freedom of µ ) 1000 au.

3. Results and Discussion A quick inspection of all possible permutational isomers with stoichiometry Cl2(NHEt)PMe3W-WCl2(NHEt)PMe3 shows that the three experimentally observed forms in Figure 1 are the only structures that fulfill two conditions: (i) They form two hydrogen bonds between the amido protons and chloride ligands of the opposite coordination sphere NH‚‚‚Cl. (ii) They avoid having two of the bulky phosphine ligands at opposite coordination sites. These two structural properties emerge, therefore, as potentially important stability-governing factors. Indeed, the importance of intramolecular hydrogen bonds has been pointed out previously.3 From our calculations on the trans isomer, we estimate a stabilization energy of 16 kcal/mol due to the two amido hydrogen bonds.17 The placement of the two bulky phosphine ligands on top of each other leads to close steric contacts of ∼1 Å between the hydrogens of the methyl groups. It seems, therefore, likely that the manifold of thermally relevant isomeric forms of the complexes of stoichiometry Cl2(NHEt)PMe3W-WCl2(NHEt)PMe3 is indeed represented by the three forms of Figure 1 only, and we have focused all our subsequent studies solely on these molecules. 3.1. Structural Properties and Energetics at T ) 0 K. The starting point of our calculations was the crystal structure of the cis-Ci isomer.4 Figure 2 shows a superposition of the crystallographic data with the fully optimized gas-phase geometry.18 (17) The h-bond stabilization energy was estimated from the energy difference between the h-bonded ground-state structure and a conformation without hydrogen bonds that was generated via a rotation around the N-C bond in such a way that the two hydrogens were pointing in the opposite direction of the Cl atoms.

Triply Bonded Ditungsten Complexes

Inorganic Chemistry, Vol. 39, No. 24, 2000 5555

Table 2. Comparison of Crystallographic and Calculated (BP and BLYP Functionals) Values for Selected Bond Distances (Å), Bond Angles (deg), and Torsional Angles for the cis-Ci, the Trans, and the cis-C2 Isomers of W2Cl4(NHEt)2(PMe3)2a cis-Ci W(1)-W(1a) W(1)-N(1) W(1)-Cl(2) W(1)-P(1) W(1)-Cl(1) N(1)-H‚‚‚Cl(1a) N(1a)-H‚‚‚Cl(1) N(1)-H‚‚‚Cl(2a) N(1a)-H‚‚‚Cl(2) P(1)-W(1)-N(1) P(1)-W(1)-Cl(2) N(1)-W(1)-Cl(2) W(1a)-W(1)-P(1) W(1a)-W(1)-Cl(1) P(1)-W(1)-Cl(1) N(1)-W(1)-Cl(1) Cl(1)-W(1)-Cl(2) W(1a)-W(1)-N(1) W(1a)-W(1)-Cl(2) P(1)-W(1)-W(1a)-Cl(1a) Cl(1)-W(1)-W(1a)-P(1a) N(1)-W(1)-W(1a)-Cl(2a) Cl(2)-W(1)-W(1a)-N(1) a

cis-C2 BLYP

BP

trans

exp

BP

BLYP

2.31 1.91 2.43 2.50 2.40

2.31 1.93 2.44 2.53 2.38

2.32 1.94 2.47 2.57 2.40

2.32 1.92 2.43 2.54 2.38

2.32 1.93 2.45 2.58 2.40

2.51 2.51 87.5 80.18 155.6 95.69 114.4 148.8 95.1 85.07 99.2 102.9 -8.37 8.37 -10.4 10.4

2.38 2.38 88.1 79.3 156.5 96.7 114.2 147.9 94.8 85.9 98.9 102.1 -8.3 8.8 -10.0 10.3

2.42 2.44 87.9 79.4 155.7 97.9 113.6 147.8 94.6 85.7 99.5 102.7 -6.9 10.4 -8.2 11.3

2.32 2.32 86.0 79.4 145.4 97.0 102.3 159.8 97.0 87.2 98.0 114.7 -78.4 -78.0 101.3 101.3

2.38 2.37 86.2 79.5 145.0 97.7 102.5 159.0 96.3 86.9 98.6 114.8 -78.9 -78.6 100.9 100.9

BP

BLYP

2.31 1.93 2.37 2.66 2.37 2.42 2.43

2.31 1.93 2.39 2.71 2.39 2.48 2.48

162.4 78.6 95.3 97.0 112.4 80.2 95.2 141.1 100.4 102.3 -24.5 -24.5 -4.3 -4.8

159.9 78.4 95.1 99.2 111.1 80.1 94.6 142.2 100.7 102. -25.7 -25.3 -6.5 -7.2

The same labeling scheme was applied as in ref 4.

Specific structural parameters obtained with the BP and the BLYP functionals are compared in Table 2 with the corresponding experimental values. With a root-mean-square deviation of only 0.024 Å per atom, the agreement between the measured and calculated structure is excellent, reconfirming once more the adequacy of our computational method. Consistent with other studies on organometallic transition metal complexes, the BP functional performs slightly better.19 All bond lengths are reproduced within e0.04 Å (1-2% relative error), whereas we find a maximal difference of ∆d e 0.07 Å (3% relative error) using the BLYP functional. The largest deviation occurs for the tungsten-phosphorus bonds for which also the largest variations are observed when changing the exchange-correlation functional. The comparison between BP and BLYP results indicates clearly that this interaction is distinctly sensitive to correlation effects. This holds also for the lengths of the intramolecular hydrogen bonds and, even though to a lesser extent, for the W-Cl bonds of the chlorines in trans position to the amido ligands (Cl(2) in Table 2). For the other two isomeric forms, no experimental structural data are available for this complex. Starting from the geometry of the cis-Ci isomer, we have thus generated analogous structures for the cis-C2 and the trans form and determined their equilibrium geometries. The resulting characteristic structural parameters are also given in Table 2. No major structural differences can be detected between the calculated ground-state geometries of the three isomers. The largest variations occur for the tungsten-phosphorus bonds that decrease in the order trans (2.655 Å) . cis-C2 (2.540 Å) J cis-Ci (2.530 Å) parallel to the observed trend in the JW-P NMR coupling constants of 115, 308, and 340 Hz. 4 The W-P bond elongation in the trans with respect to the cis isomers can be rationalized in terms of the (18) Due to the absence of strong electrostatic interactions (the cis-Ci isomer has no monopole and no dipole moment) and the relatively large intermolecular separation (the shortest distance between two molecules in the crystal is 3 Å), crystal packing effects can be expected to be small and the crystallographic structure should be very similar to the molecular geometry in the gas phase. (19) Ziegler, T Density Functional Methods in Chemistry and Material Science; Wiley: New York, 1997; p 69.

stronger trans influence of the amido as compared to the chlorine ligand.4 In the detailed analysis of the electronic structure presented in section 3.3, we demonstrate that a possible explanation for the difference in the W-P bond length of the two cis isomers is provided by an analogous four-center trans influence N-W-W-P in cis-C2 versus Cl-W-W-P in cisCi, which is mediated via metal-metal bonds. A similar effect, but less pronounced, occurs for the W-Cl(2) bond length. For the trans isomer, the ligand in trans position to Cl(2) is Cl(1), while for the two cis isomers it is the amido ligand. The shorter W-Cl(2) bond length of 2.37 Å in the trans isomer in comparison with the ones in the two cis isomers of 2.43 and 2.44 Å can thus be rationalized once again in terms of the difference in trans influence between the amido and the chlorine ligand. A calculation of the bond orders (BOs)20 shows the same trends, i.e., a weakening of the W-P (and to a lesser extent of the W-Cl(2)) bond in trans position to the amido ligand. In addition, increased values for the W-N bond order confirm the previously proposed4 double bond character of this interaction. Slightly enhanced values for the BOW-W also suggest that the metal-metal interaction in the trans isomer is somewhat stronger than in the cis complexes. An alternative way to make contact with intuitive chemical bonding concepts is the transformation of the Kohn-Sham wave functions to maximally localized (Wannier) functions.21 In Figure 3, we show the centers of the Wannier functions in the case of the trans isomer as a representative example for the general bonding situation in all three complexes. Single bonds such as the C-C or C-H bonds of the ethyl groups are represented by a single Wannier center. The triple bond character of the W-W interaction and the double bond nature of the W-N bond are clearly manifested through the presence of three and two Wannier centers, respectively.22 (20) For the calculation of the bond orders according to the scheme proposed by Mayer (Mayer, I. Chem. Phys. Lett. 1983, 97, 270.), the plane wave representations of the total wave functions were projected onto an atom-centered minimal basis of atomic pseudo-wave-functions. (21) Silvestrelli, P. L.; Marzari, N.; Vanderbilt, D.; Parrinello, M. Solid State Commun. 1998, 107, 7.

5556 Inorganic Chemistry, Vol. 39, No. 24, 2000

Magistrato et al.

Figure 3. Centers of the Wannier orbitals (indicated by small balls) for the trans isomer. Note the three Wannier centers located around the midpoint of the W-W bond (consistent with a triple-bond character) and the two Wannier centers present at the tungsten-amido bonds (indicating a double-bond character). Table 3. Energy Differences (kcal/mol) for the Three W2Cl4(NHEt)2(PMe3)2 Isomers isomer

BLYP

BP

trans cis-Ci cis-C2

0.3 2.8 0.0

1.4 2.4 0.0

As mentioned before, all three isomers form two intramolecular hydrogen bonds between the amido proton and a chlorine ligand which locks the structure into an essentially eclipsed geometry. The hydrogen bonds in the cis-C2 isomer are slightly shorter (2.32 Å) than the ones in the cis-Ci (2.38 Å) and trans (2.42 Å) isomers. In Table 3, we report the relative energies of the three isomers. Both functionals result in the same energy ordering with cisC2 < trans < cis-Ci. The energy difference to the trans isomer depends strongly on the exchange-correlation functional. The relative energy with respect to the ground-state cis-C2, for instance, changes from an almost degenerate value of ∆E ) 0.3 kcal/mol with the BLYP functional to ∆E ) 1.4 kcal/mol using BP. These results indicate that subtle correlation effects are playing an especially crucial role for the stability of this form. In particular, we have already seen in the analysis of the structural properties that the trans isomer is characterized by a pronounced trans influence of the N-W-P centers. The electronic distribution of such an extended state is easily influenced by the specific description of the correlation energy, and the relative stabilization energy of the trans form can therefore be expected to be especially delicate. The relative energies between the two cis isomers on the other hand is less affected upon changing of the correlation energy functional. To first order, the coordination of the two tungsten centers are identical for both cis isomers and structural differences enter only at a secondary level through correlations between the two coordination spheres. In view of its superior performance for the description of transition metal complexes,19 the values obtained with the BP functional are the best estimate of the relative stability of the three isomers that we can give at the (22) The location of the Wannier center along the bond is a function of the electronegativity difference of the constituent atoms and the ratio of their van der Waals radii (Alber, F.; Folkeis, G.; Carloni, P. J. Phys. Chem. B 1999, 103, 6121.).

current state. The cis-C2 isomer is predicted to be the most stable form while the trans isomer is 1.4 kcal/mol higher in energy and the cis-Ci isomer 2.4 kcal/mol higher in energy. Relative energy differences as small as e1 kcal/mol are certainly at the limit of accuracy that we can expect for such a delicate system. From the experimental equilibrium concentrations of the three isomers,4 the relative free energy differences at room temperature can be estimated to be 0.0 kcal/mol for the cis-C2 form, ∼1.2 kcal/mol for the cis-Ci form, and ∼1.8 kcal/mol for the trans form in fairly good agreement with the calculated relative energies at 0 K. The inversion of the relative stabilities of the trans and the cis-Ci isomer can be caused by differences in the free energy or by the presence of solvent effects. Experimental observations also confirm that the relative stability of the cisCi isomer is a very delicate issue as subtle changes in the structure of the three complexes or in the experimental conditions can distinctly influence its stability.4 3.2. Dynamic Processes at Elevated Temperatures. To gain further insight into the dynamic behavior of the system, we performed molecular dynamics (Car-Parrinello) simulations at different temperatures. A simulation of the system at elevated temperatures allows for an enhanced sampling of the potential energy surface. In such a way, it becomes possible to observe events within the limited time of our simulations of a few tens of picoseconds that would normally only happen on a much longer time scale. The first dynamic feature that we have observed for all three isomers is the rotation of one of the coordination planes of the two tungsten atoms by 90°. This process takes place most easily for the cis-C2 isomer for which the total number of intramolecular hydrogen bonds can be maintained during the rotation by a simple switch to adjacent centers. The higher temperature properties of all three isomers are characterized by the breaking of the tungsten-phosphorus coordination bond and, consequently, the dissociation of the phosphine ligands. We have observed this process at increasingly higher temperatures for the trans (∼600 K), cis-Ci (∼1200 K), and cis-C2 (∼1500 K) compounds. One specific example of such a dissociative trajectory is depicted in Figure 4 for the cis-C2 isomer at 1500 K. The series of representative snapshots in Figure 4 reveals a rich variety of dynamic processes that take place almost concurrently. The first frame in Figure 4 shows the conformation that the molecule adapts just before the first dissociation event, which is quite severely distorted with respect to the groundstate geometry. The breaking of the W-P(1a) bond takes place in the second frame, while in the third frame the Cl(2) ion moves to a bridging position between the two tungsten atoms. The formation of this bridged intermediate is plausible in view of the fact that the system will try to stabilize the coordinatively unsaturated species formed via dissociation of the PMe3 ligand.23 In the fourth frame, the Cl(2) atom passes on to the other tungsten atom W(1a). In this way, a short-lived unsaturated heptacoordinated ditungsten complex with three Cl ligands on the W(1a) is formed temporarily. After only 650 fs, another chlorine Cl(2a) forms a new bridge and passes to the undercoordinated tungsten atom W(1) (frame e), leading to a scrambling of the chlorine ligands followed by the dissociation of the second phosphine (frame f). We were able to observe similar dissociation events for several runs for all three isomers. Clearly, the number of reactive trajectories that we can sample in this way is far too small to be able to describe the dissociation (23) This bridged intermediate does not correspond to a minimum on the 0 K potential energy surface.

Triply Bonded Ditungsten Complexes

Inorganic Chemistry, Vol. 39, No. 24, 2000 5557

Figure 4. Dissociation events of the W-PMe3 bonds for the cis-C2 isomer at 1500 K. Only snapshots of the most representative frames a-f are shown. The chlorine and PMe3 ligands have been labeled for the sake of clarity: (a) configuration of the molecule just before the first dissociation event (510 fs); (b) dissociation of the PMe3 (1a) (552 fs); (c) Cl(2) in bridging position between the two tungsten atoms (586 fs); (d) Cl(2) passes to W(1a) (618 fs); (e) Cl(2a) forms a new bridge between the two tungsten atoms (650 fs); (f) dissociation of the P(1)Me3 and formation of an unsaturated hexacoordinate intermediate (670 fs). Table 4. Reaction Energies and Barriers for Dissociation of the W-PMe3 Bond Obtained with the BP and BLYP Functionalsa Efaw b

Eba w c

∆E1 d

∆E2 e

isomer

BP

BLYP

BP

BLYP

BP

BLYP

BP

BLYP

trans cis-Ci cis-C2

18.2 24.3 22.7

12.6 18.6 17.4

2.5 9.3 4.9

3.2 9.4 6.7

15.7 15.0 17.7

9.4 9.2 10.7

31.9 30.9 33.2

20.1 17.8 20.5

Values are given in kcal/mol. b Efaw is the value of the activation energies of the forward reaction (dissociation). c Eba w is the value of the back reaction (association). d ∆E1 is the reaction energy for dissociation of one PMe3. e ∆E2 the reaction energy for dissociation of both PMe3. a

reaction in a statistically meaningful way. However, the fact that the phosphine dissociation was observed at very different temperatures suggested that the three isomeric forms might exhibit large differences in the corresponding activation barriers. We have determined the activation energies for phosphine dissociation by performing molecular dynamics runs in which the system was constrained to follow an approximate reaction coordinate.24 A W-P distance constraint was applied and varied in steps of 0.1 Å. The transition state was localized by the change of sign of the average constraint force. The resulting activation energies are summarized in Table 4 together with the overall reaction energies for phosphine dissociation ∆E1 ) E(complex) - E(PMe3) - E(complex - PMe3) and ∆E2 ) E(complex) - 2E(PMe3) - E(complex - 2PMe3). For both functionals, the calculated activation energies vary in the order trans , cis-C2 j cis-Ci. Even though the relative trends are very similar, the absolute values obtained by the BP and BLYP functionals differ distinctly by almost 6 kcal/mol. The best estimates of the activation energies that we can give at the moment are the values calculated with the BP functional (24) Sprik, M.; Ciccotti, G. J. Chem. Phys. 1998, 109, 7737.

of 18 kcal/mol for trans, 23 kcal/mol for cis-C2, and 24 kcal/ mol for cis-Ci. The ground-state W-P bond has already proven to be sensitive to correlation contributions, and this effect is further enhanced in the transition states for phosphine dissociation. In analogy to the discussion of the trans influence on the W-P bond in the ground state, the distinctly lower activation energy of the trans isomer can be rationalized in terms of a classic trans effect. This is also confirmed by the detailed analysis of the electronic structure performed in section 3.3. A comparison of the dissociation energies involved in breaking the W-P bond shows that the first dissociation energy ∆E1 is very similar for the three isomeric forms. The same holds true for the energy involved in the dissociation of the second phosphine ∆E2. Furthermore, ∆E2 is essentially double ∆E1, indicating that the dissociations of the two PMe3 ligands are nearly independent of each other. Despite the similarity of the relative values, the absolute values obtained with the BP and the BLYP functionals differ again strongly (∼16 kcal/mol for BP vs ∼10 kcal/mol for BLYP). The relative magnitude of the variation between BP and BLYP results is even larger than that for the activation energies. The calculation of ∆E1 and ∆E2 involves the energy differences of subsystems with a varying number of atoms and bonds (therefore, also with different correlation contributions) for which a fortuitous error cancellation can be expected to be even less effective than in the calculation of the activation barriers. In summary, our finite temperature studies identify the dissociation of the phosphine ligands as the fastest reactive process at finite temperature.25 This is in agreement with experimental suggestions that a dissociation/association mechanism contributes at least in part to the observed isomerization (25) This does not exclude that slower processes are also present. With the approach used herein, we are not able to detect any slower reactive processes because the dissociation, as the fastest channel, occurs with the highest statistical probability and therefore prevents the observation of alternative events.

5558 Inorganic Chemistry, Vol. 39, No. 24, 2000

Magistrato et al.

Figure 5. Kohn-Sham eigenvalues of the 19 highest occupied states for the tree isomers in the (a) ground state and (b) at the transition state. The labels characterize the approximate nature of the singleparticle orbitals.

process.3,4 The much lower kinetic barrier of the trans isomer calculated here is consistent with such a possible reaction channel. However, the actual isomerization process is most probably even more complicated.26 3.3. Analysis of the Electronic Structure. To further identify the specific electronic properties of the three isomeric forms that lead to the large differences in their thermodynamic and kinetic stability, we have performed a detailed analysis of the electronic structure for the ground states as well as for the transition states for phosphine dissociation. In a first attempt to classify the overall electronic properties of the three isomers, we have determined their dipole moments. The cis-C2 isomer has a dipole moment of µ ) 1.1 D and the trans has a dipole moment of µ ) 1.5 D, whereas, for symmetry reasons, the cisCi isomer has a vanishing dipole moment. This suggests that the former two might dominate in more polar solvents, but overall there are no striking differences between the three forms. To characterize their specific electronic properties, we proceeded with a detailed analysis of the Kohn-Sham one-electron states. The Kohn-Sahm eigenvalues of the 19 highest lying states were plotted for the ground (Figure 5a) and transition states (Figure 5b) in order to pinpoint the major differences. For the ground states, the largest variations occur between the eigenvalues of the trans and those of the two cis isomers. (26) VandeVondele, J.; Magistrato, A.; Rothlisberger, U. To be published.

Figure 6. HOMO-2 of the (a) cis-Ci isomer and (b) the trans isomer in the ground state. Contours are shown at (3.0 au.

The deviations are particularly pronounced for the region between the HOMO-6 and HOMO-12. For the trans isomer, we observe delocalized molecular orbitals (HOMO-3 and HOMO-4) involving the three centers N-W-P. These form the molecular orbital basis for the observed trans influence that manifests itself in the elongation of the W-P bond. Some differences also exist for the three highest occupied states that are localized molecular orbitals representing the three metalmetal bonds. For the two cis isomers, the HOMO-2 is a superposition of the two dz2 orbitals that form an isolated metalmetal dσ bond without any direct interaction with ligand orbitals (Figure 6a). The corresponding orbital for the trans isomer instead exhibits a bonding interaction of the metal-metal bonds with the phosphorus lone pair and a p-orbital of the nitrogen atom of the amido ligand (Figure 6b) contributing to the trans influence on the W-P bond.

Triply Bonded Ditungsten Complexes

Figure 7. (a) HOMO-1 and (b) HOMO of the cis-Ci isomer in the ground state. Contours are shown at (3.0 au. The corresponding orbitals for the trans and the cis-C2 isomer are qualitatively very similar.

In contrast, both the HOMO-1 (Figure 7a) and the HOMO (Figure 7b), which corresponds to the combination of the two dxy and dyz orbitals of the tungsten atoms (i.e., the two metalmetal dπ bonds), are very similar for all three isomers. In Figure 8, the HOMO-2 of the trans isomer at the transition state for phosphine dissociation is shown. Clearly, a pronounced delocalization of the molecular orbital from the phosphine to the amido ligand is present. In general, a strong mixing takes place at the transition state. This is in contrast to the electronic structure in the ground state in which metal-ligand and metalmetal orbitals are largely separated. This is also the case for the HOMO-2 and the HOMO-1 states of the cis isomers, which are pure metal-metal orbitals in the ground state whereas at the transition state they show significant interactions with phosphine ligand orbitals (Figure 8b). This mixing becomes

Inorganic Chemistry, Vol. 39, No. 24, 2000 5559

Figure 8. Electronic structure of the transition states. (a) HOMO-4 of the trans isomer. Note the presence of a delocalized molecular orbital between the amido and the phosphine ligands that is responsible for the trans effect on the W-P bond. Contours are drawn at (3.5 au. (b) HOMO-1 of the cis-C2 complex. Contours are drawn at (3.0 au.

possible through the fact that at the transition state for phosphine dissociation, the W-P bond orbitals are strongly raised in energy and start to interact with the high-lying metal-metal orbitals. For the trans isomer the one-electron orbitals that contribute to the W-P coordination bond lie higher in energy than for the cis forms, consistent with the weaker W-P bond in the former. Therefore, the mixing with high-lying, reactive metal-metal orbitals sets in much earlier. Already in the ground state, W-P bond orbitals can interact with the lowest lying metal-metal orbital (the dσ orbital) via delocalized three-center orbitals involving the N-W-P atoms (Figure 6b). The same orbital (Figure 8a) leads to a classic trans effect, i.e., weakening of the W-P bond, in the transition state. This provides a first electronic

5560 Inorganic Chemistry, Vol. 39, No. 24, 2000

Magistrato et al. possible existence of such second-order effects has not been pointed out so far and there might be other systems for which effects such as the one described here may have indeed important consequences. 4. Summary and Conclusions

Figure 9. Contour plot of the HOMO-5 of the cis-C2 isomer at the transition state indicating the presence of a four-center (N-W-W-P) trans effect. The contours are drawn at (3.0 au.

rationalization for the large variation in dissociation barriers of the trans with respect to the cis isomers. The differences between the two cis isomers on the other hand are more subtle. A difference in the electronic properties that we have been able to detect between them is the presence of delocalized states connecting the amido and the phosphine ligands of the two different coordination spheres. These extended four-center states are mediated via metal-metal dz2 orbitals and occur only for the cis-C2 isomer (Figure 9). This corresponds to a four-center analogue of the trans effect in which delocalized states are formed via two metal centers instead of only a single one. For the cis-C2 isomer, the amido ligand on the second tungsten atom is in pseudo-trans-position to the phosphine group, while for the cis-Ci isomer it is a chlorine. This second-order effect provides a first rationale for the slightly lower dissociation barrier of the cis-C2 with respect to the cis-Ci isomer. Moreover, this four-center trans effect is also consistent with the experimentally observed trend in the rates of isomerization of the cisCi isomer to the thermodynamically more favored cis-C2 form that follows the order Bun > Prn > Et. Due to their higher inductive effect, the four-center trans effect that stabilizes the cis-Ci isomer toward dissociation is diminished for larger amido substituents. The energy differences involved are very small, and we cannot establish with certainty that this four-center trans effect plays a decisive role in determining the dynamic properties of this system. However, to the best of our knowledge, the

In this report, we describe our recent ab initio molecular dynamics studies of triply bonded ditungsten complexes with stoichiometry W2Cl4(NHEt)2(PMe3)2. We have characterized the structural, energetic, and electronic properties of the three main isomeric forms, a trans and two cis isomers of Ci and C2 symmetry. Gradient-corrected density functional calculations with the BP parametrization for exchange and correlation predict the cis-C2 isomer as the most stable form. However, the relative energy differences between the three isomers are only of the order of ∼1-2 kcal/mol. Furthermore, the relative energy of the trans isomer is especially sensitive to correlation effects due the presence of delocalized multicenter states that form the molecular basis for a classic trans influence on the tungstenphosphine coordination bond. The dissociation of the phosphine ligands is the fastest reactive process that we are able to observe at finite temperature. Due to the larger trans effect of the amido group with respect to the chlorine ligand, the W-P bond dissociation is greatly facilitated for the trans isomer. This confirms the experimental suggestion that the lowest energy channel that contributes at least in part to the cis/trans isomerization involves dissociation and association of the phosphine ligands.3,4 To characterize the differences between the three isomeric forms in more detail, we have performed an extended analysis of the electronic structure for the ground states and for the transition states involved in phosphine dissociation. An inspection of the one-electron orbitals suggests that the W-P bond orbitals in the trans isomer lie at higher energy and can easily mix with the higher lying reactive metal-metal orbitals facilitating thereby the dissociation of the phosphine ligands. The three-center N-W-P states that contribute to this effect form the electronic basis of the strong trans effect that manifests itself in the large differences of the dissociation barriers of the trans and the cis isomers. We suggest that the small difference in the activation energies of the two cis isomers is due to an analogous four-center N-W-W-P trans effect that is mediated via metal-metal orbitals on the two tungsten centers. Such second-order effects have been overlooked so far and could be operational in many systems with metal-metal bonds. Acknowledgment. We thank F. A. Cotton for suggesting this study. A.M. and J.V. acknowledge funding from ETH internal grants. IC000754E