We have investigated the performance of eight popular density functionals, four of which are "standard" functionals not including dispersion (B3LYP, BP86, PBE, and TPSS) and four of which have been constructed to account for dispersion (B97D, wB97XD, M06, and M06L), in reproducing 18 molecular structures derived from single-crystal X-ray diffraction experiments on ruthenium-based olefin metathesis catalyst precursors. Our analysis of all the internuclear distances reveals that standard DFT predicts systematically expanded structures. In contrast, all the methods accounting for dispersion give rise to more compact structures, removing the systematic overestimation of internuclear distances. The contracting effect of dispersion is general and also affects chemical bonds, thus reducing the general overestimation of bond lengths. The best overall performance is observed for wB97XD, which offers relatively small statistical errors when considering the overall structure as well as selected distances. Only for the coordination center geometry is the accuracy of wB97XD matched by standard functionals such as PBE and TPSS, whereas M06 and M06L are associated with larger errors. At the other end of the scale, B3LYP is seen to give the largest statistical errors in general, both when considering the complete structures and the geometries of the coordination centers alone. For the organic ligands, however, B3LYP performs clearly better than the other standard functionals although not as well as the functionals accounting for dispersion. Extending the basis sets is seen to improve the structures in particular of the coordination center, thus underlining the importance of using sufficiently flexible basis sets if highly accurate geometries are to be obtained. Similar conclusions to those obtained for the ruthenium catalysts can be drawn from comparisons of the X-ray crystal structures of 10 other organometallic complexes of relevance to homogeneous catalysis, covering first (Ti, Fe, Co, Ni), second (Zr, Mo, Rh, Pd) and third (W, Ir) row transition metals, with those of DFT. The latter analyses thus offer a first indication that the picture obtained for the ruthenium alkylidene complexes may be extended to other classes of relatively large transition metal complexes.
A quantitative structure-activity relationship (QSAR) model is presented in which both the independent and dependent (response) variables are derived from density functional theory (DFT) calculations on a large set of 14-electron complexes, LCl(2)Ru=CH(2), with different dative ligands, L. The multivariate model thus correlates the properties of the 14-electron complexes with a calculated measure of activity, with modest computational cost, and reproduces the experimental order of activity for the Grubbs ruthenium catalysts for olefin metathesis. The accuracy and applicability of the model is to a large extent due to the use of highly specific geometric and electronic molecular descriptors which establish a direct connection between activity and chemically meaningful donor ligand properties. The ligands that most efficiently promote catalytic activity are those that stabilize the high-oxidation state (+4) metallacyclobutane intermediate relative to the ruthenium-carbene structures dominating the rest of the reaction pathway. Stabilization of the intermediate is ensured, among others, through ligand-to-metal sigma donation, whereas metal-to-ligand pi back-donation destabilizes the intermediate and lowers catalytic activity. A bulky dative ligand drives the reaction toward the less sterically congested metallacyclobutane species and thus contributes to catalytic activity. The multivariate model and the high-level descriptors furthermore provide practical handles for catalyst development as exemplified by the suggestion of several new donor ligands predicted to give more active and functional group tolerant ruthenium-based catalysts. The present strategy holds great promise for broader screenings of olefin metathesis catalysts as well as for development of homogeneous transition metal catalysts in general.
Development of functional inorganic and transition metal compounds is usually based on ad hoc qualified guesses, with computational methods playing a lesser role than in drug discovery. A de novo evolutionary algorithm (EA) is presented that automatically generates transition metal complexes using a search space constrained around chemically meaningful structures assembled from three kinds of fragments: a part shared by all structures and typically containing the metal center itself, one or several parts consisting of ligand skeletons, and unconstrained parts that may grow and vary freely. In EA optimizations, using a cost-efficient fitness function based on a linear quantitative structure-activity relationship model for catalytic activity, we demonstrate the capabilities of the method by retracing the transition from the first-generation, phosphine-based Grubbs olefin metathesis catalysts to second-generation catalysts containing N-heterocyclic carbene ligands instead of phosphines. Moreover, DFT calculations on selected high-fitness, last-generation structures from these evolutionary experiments suggest that, in terms of catalytic activity, the structures arrived at by virtual evolution alone compare favorably with existing, highly active catalysts. The structures from the evolution experiments are, however, complex and probably difficult to synthesize, but a set of manually simplified variations thereof might form the leads for a new generation of Grubbs catalysts.
Previous promising tests of the new M06 family of functionals in predicting ruthenium-metal phosphine bond dissociation energies (Zhao, Y.; Truhlar, D. G. Acc. Chem. Res. 2008, 41, 157) have been extended to a series of phosphine complexes of chromium, molybdenum, nickel, and ruthenium for which relevant experimental data are available. In addition to the M06 family of functionals, bond dissociation enthalpies have been calculated using a selection of density functionals and hybrid functionals based on the generalized gradient approximation (GGA), and with or without an empirical term (i.e., DFT-D) accounting for long-range dispersion. For the ruthenium complexes, second-order Møller-Plesset perturbation theory (MP2) has also been applied. Electrostatic and nonelectrostatic solvent effects have been estimated using the polarizable continuum model (PCM), allowing for comparison with experimental data obtained for dissociation reactions in organic solvents. Whereas the GGA and hybrid-GGA functionals grossly underestimate the absolute metal-phosphine bond enthalpies, with mean unsigned errors (MUEs) for a set of 10 phosphine dissociation reactions in the range 13-27 kcal/mol, the recently developed DFT-based methods for inclusion of attractive noncovalent interactions and dispersion (the DFT-D and M06 functionals) dramatically improve upon the situation. The best agreement with experiment is observed for BLYP-D (MUE = 2.2 kcal/mol), and with the exception for M06-2X, all these methods provide MUEs well below 5 kcal/mol, which should be sufficient for a broad range of applications. The improvements in predicted relative bond enthalpies are less convincing, however. In several cases the GGA and hybrid-GGA functionals are better at reproducing substitution effects than the DFT-D and M06 methods.
Whereas a number of homoleptic metal(III) tetramethylaluminates M(AlMe(4))(3) of the rare earth metals have proven accessible, the stability of these compounds varies strongly among the metals, with some even escaping preparation altogether. The differences in stability may seem puzzling given that this class of metals usually is considered to be relatively uniform with respect to properties. On the basis of quantum chemically obtained relative energies and atomic and molecular descriptors of homoleptic tris(tetramethylaluminate) and related compounds of rare earth metals, transition metals, p-block metals, and actinides, multivariate modeling has identified the importance of ionic metal-methylaluminate bonding and small steric repulsion between the methylaluminate ligands for obtaining stable homoleptic compounds. Low electronegativity and a sufficiently large ionic radius are thus essential properties for the central metal atom. Whereas scandium and many transition metals are too small and too electronegative for this task, all lanthanides and actinides covered in this study are predicted to give homoleptic compounds stable toward loss of trimethylaluminum, the expected main decomposition reaction. Three of the predicted lanthanide-based compounds Ln(AlMe(4))(3) (Ln = Ce, Tm, Yb) have been prepared and fully characterized in the present work, in addition to Ln(OCH(2)tBu)(3)(AlMe(3))(3) (Ln = Sc, Nd) and [Eu(AlEt(4))(2)](n). At ambient temperature, donor-free hexane solutions of Ln(AlMe(4))(3) of the Ln(3+)/Ln(2+) redox-active metal centers display enhanced reduction to [Ln(AlMe(4))(2)](n) with decreasing negative redox potential, in the order Eu ≫ Yb ≫ Sm. Whereas Eu(AlMe(4))(3) could not be identified, Yb(AlMe(4))(3) turned out to be isolable in low yield. All attempts to prepare the putative Sc(AlMe(4))(3), featuring the smallest rare earth metal center, failed.
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