DFT calculations of NMR JC–H coupling constants: An additional tool to characterize the α-agostic interaction in high oxidation state M-alkylidene complexes (M = Re, Mo and Ta)

doi:10.1016/j.poly.2005.08.015

Polyhedron

Volume 25, Issue 2, 23 January 2006, Pages 339-348

https://doi.org/10.1016/j.poly.2005.08.015 Get rights and content

Abstract

NMR spin–spin J_C–H coupling constants have been calculated for the α-alkylidene C–H bond in several high oxidation state d⁰ transition metal-alkylidene complexes (M = Re, Mo, Ta). The DFT(B3PW91) calculations have been carried out using the GIAO method for the isolated molecules, with no solvent effect or thermal corrections. The experimental systems have been modeled either by replacing all large size ligands by ligands of smaller size with similar electronic properties or by calculating the full chemical entities. It is shown that the calculations are able to reproduce well the trends in the J_C–H values over a range of 75–150 Hz when the IGLO basis sets are used. In addition, the calculated J_C–H values differ from the experimental ones by about 10% in the case of weak α-C–H agostic interactions (pseudotetrahedral Re and Mo complexes) and by 15% in the case of strong α-C–H agostic interactions (pseudooctahedral Ta complexes). This shows that the electronic environment of the alkylidene C–H bonds, associated with the α-agostic interaction, is properly evaluated at this level of calculations for transition metal complexes of rather large size.

Graphical abstract

DFT calculations have been used to calculate the spin–spin J_C–H coupling constants for the C–H alkylidene bond in Re( triple bond CR)( double bond CHR)(X)(Y), Mo(NR′)(CHR)(X)(Y) and $Ta (C_{5} R_{5}^{'}) (CHR) (X) (Y)$ , where the experiment suggests a weak agostic interaction for Re and Mo and a strong agostic interaction for Ta. The calculated J_C–H are in good agreement with the experiment when the IGLO basis sets are used. The calculations reproduce that J_C–H is lower for the syn than for the anti isomer. They also show that J_C–H depends on the metal even in the absence of agostic interaction.

Introduction

High oxidation state (d⁰) transition metal-alkylidene complexes were discovered 30 years ago, and since this time, a large variety of them have been synthesized, in part because they are potential olefin metathesis catalysts [1], [2], [3], [4], [5], [6], [7]. In several of these complexes, the J_C–H NMR spin–spin coupling constant of the α-alkylidene C–H bond is low. This has been attributed to a weakening of the C–H bond due to the presence of an α-C–H agostic interaction, i.e., an intramolecular interaction between the C–H bond, acting as a Lewis base, and the electron deficient metal center acting as a Lewis acid [8], [9], [10], [11].

The NMR spin–spin coupling constant is a key tool to characterize the C–H⋯M agostic interactions because the J_C–H varies over a rather large range of values whereas the C–H bond length varies little. The J_C–H value of a non-agostic C(sp²)–H bond is around 160 Hz [12] whereas values as low as about 75 Hz have been observed in some complexes (see later). In contrast, the C–H bond is lengthened by 0.05 Å at most [13]. Furthermore, the C–H bond length cannot be determined experimentally with high accuracy by other techniques than the expensive and difficult neutron diffraction method. Vibrational stretching frequencies of the agostic C–H bond may be hard to identify because the band can be weak and broad [13]; computational studies are therefore very useful. The geometrical optimizations give C–H values, which usually compare very well with experiment in the few complexes whose structure has been studied by neutron diffraction [10]. Associated with the lengthening of the C–H bond, the stretching frequency is lower than that of a non-agostic C–H bond. However, direct comparison between the calculations and the experiment requires the calculations of J_C–H.

In general, calculations of NMR chemical shifts and spin–spin coupling constants require considerable computational effort [14], [15], [16], [17], [18]. However computations of NMR parameters for transition metal complexes have been made possible because of the successful development of the DFT methods as described in the recent review by Autschbach [17]. The key point is that calculations using the GIAO [19], [20] or IGLO [21], [22] methods, along with extended basis sets, give NMR chemical shifts and spin–spin coupling constants that can be reasonably compared with experiment. In the case of the spin–spin coupling constant, the calculated values differ from the experimental ones by 10–20% [17], [23]. Because of the computational effort involved, spin–spin C–H coupling constants have so far only been calculated for various relatively small organic molecules [23], [24], [25], [26] and few metal complexes [27], [28], [29]. In the case of transition metal complexes, NMR spin–spin coupling constant calculations have been focused on ligand–ligand, metal–ligand and metal–metal coupling constants [30], [31], [32], [33], [34], [35], [36], [37].

It has been shown that the spin–spin coupling constant is influenced both by the solvent and by vibrational effects [23], [38], [39] and that the solvent effect is especially important in the case of electron deficient complexes [33], [34], [40]. In the case of transition metal complexes, the solvent effect has been shown to be due in large part to the coordination of molecule of solvent, which changes the coordination number of the metal center. Anharmonicity and vibrational effects have been shown to be most important in the case of two atoms with distance that are far from usual distance. For instance these effects will be more important in the case of compressed dihydride and stretched dihydride complexes than in the case of regular dihydrogen or dihydride complexes [30], [37]. In such cases, a temperature effect is expected [41].

These limitations being known, it should be possible to calculate J_C–H for agostic C–H bonds. An agostic interaction requires an electron deficient metal but is usually observed in weakly or non-coordinating solvent. The C–H bond is only very slightly elongated by the agostic interaction so that the vibrational effect should be negligible since temperature effects have never been reported. We can thus study if the calculations reproduce, with reasonable computational effort (DFT with electronic core potential on heavy atoms and limited basis sets), the changes in the J_C–H values in systems where it should be acceptable to neglect the temperature and solvent effects. To better test the validity of the computational method, we have studied two sets of complexes. One set is the pseudotetrahedral series, Re( triple bond CtBu)( double bond CHtBu)(X)(Y) (X = Y = CH₂tBu; X = Y = OtBu; X = CH₂tBu, Y = OSiPh₃) [42], [43], [44], [45], [46] and Mo(NR)(CHtBu)(X)(Y) (R = 2,6-iPr₂-(C₆H₃) or CPh₃; X = Y = CH₂tBu; X = Y = OtBu) [47], [48], [49], [50], [51] where the agostic interaction is weak and has been observed only in one of the two isomers. The second set is the pseudooctahedral cyclopentadienyl tantalum alkylidene series, Ta(C₅R₅)( double bond CHtBu)(X)(Y) (R = H (Cp) or CH₃(Cp*), X = Y = Cl; X = Y = CH₂tBu) where the alkylidene C–H α-agostic interaction is strong [52]. The alkylidene group has a relatively high barrier for rotation in all these complexes [1], [27], [44], [48], [53], [54], which avoids averaging problems. The following pattern emerges from the experimental results. Changing the metal and the coordination number changes J_C–H significantly but changes of only a few hertz result from a substitution of ligands in a given complex. Experimentalists consider, nevertheless, these small changes as meaningful and it is therefore of interest to establish if the computations are able to reproduce the detailed changes in J_C–H as well as the absolute values in a quantitative way.

The GIAO method with basis sets including functions with large exponents for accurate representation of the core electrons such as the IGLO-II and IGLO-III basis sets, elaborated by Kutzelnigg et al. [55] give very good results for NMR properties including spin–spin coupling constants. Good results have been also obtained with aug-cc-pXVZ basis sets after addition of supplementary core functions [14], [23]. However, the vast number of calculations of transition metal complexes have been carried out with 6-31G(d,p) Pople type basis set on the organic ligand [56]. We will thus compare the results obtained with the Pople basis set and the IGLO basis set in the case the rhenium complexes. Only the IGLO basis sets will be used for the other systems.

Section snippets

Computational details

In one set of calculations, the experimental rhenium Re( triple bond CtBu)( double bond CHtBu)(X)(Y) (X = Y = CH₂tBu, Re-1; X = CH₂tBu, Y = OSiPh₃, Re-2; X =Y = OtBu, Re-3) complexes, the molybdenum Mo(NR)(CHtBu)(X)(Y) (R = 2,6-iPr₂-(C₆H₃), X = Y = CH₂tBu, Mo-1; R = CPh₃, X = Y = CH₂tBu, Mo-2; R = 2,6-iPr₂-(C₆H₃),X = Y = OtBu, Mo-3) complexes and the tantalum Ta(C₅R₅)( double bond CHtBu)(X)(Y) (R = CH₃, X = Y = CH₂tBu, Ta-1; R = CH₃, X = Y = Cl, Ta-2 and R = H, X = Y = CH₂tBu, Ta-3; R = H, X = Y = Cl, Ta-4) complexes have been represented by small models, constructed by substitution

The Re(CtBu)(CHtBu)(X)(Y) complexes: methodology and calibration

The geometries of Re complexes, presented in Fig. 1, have been discussed at length in our previous contribution [27]. Thus, only key points will be mentioned here when needed. The overall geometries of the complexes for the small models are in good agreement with the available experimental data. The presence of the full ligands introduced only minor changes in the structures, the main difference residing in a slight change in the difference in the energy between the syn and anti isomers, the

Conclusion and perspective

This study shows that NMR J_C–H coupling constants can be calculated accurately without excessive computational effort. B3PW91 NMR calculations with IGLO-II basis sets for main group atoms on geometries optimized with the same functional and 6-31G(d,p) basis sets is accurate enough to reproduce the experimental J_C–H values associated with either weak or strong α-C–H agostic interactions in d⁰ metal–alkylidene complexes (Re, Mo and Ta). It appears that the computed values with the full systems

Acknowledgements

It is my great pleasure to thank Malcolm Chisholm, an old friend, who initially attracted me to Indiana University as visiting professor. He has always been an enthusiastic supporter of the dialogue between experimental and computational chemists. The present work is far removed from the simple MO pictures that we used to draw over a cup of tea in his office while looking out at the autumn foliage turning red during an Indian summer.

X.S.M. thanks the CNRS for a post-doctoral fellowship. We are

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DFT calculations of NMR JC–H coupling constants: An additional tool to characterize the α-agostic interaction in high oxidation state M-alkylidene complexes (M = Re, Mo and Ta)

Abstract

Graphical abstract

Introduction

Section snippets

Computational details

The Re(CtBu)(CHtBu)(X)(Y) complexes: methodology and calibration

Conclusion and perspective

Acknowledgements

J. Organomet. Chem.

Prog. Nucl. Magn. Res. Spectrosc.

Chem. Phys. Lett.

J. Organomet. Chem.

Chem. Rev.

J. Chem. Soc., Dalton Trans.

New J. Chem.

Angew. Chem. Int. Ed.

Top. Organomet. Chem.

Chem. Rev.

New J. Chem.

Prog. Inorg. Chem.

Angew. Chem. Int. Ed.

The Organometallic Chemistry of the Transition Metals

Metal Dihydrogen and σ-Bond Complexes: Structure, Theory and Reactivity

Chem. Rev.

Chem. Rev.

Struct. Bond.

J. Chem. Phys.

J. Chem. Phys.

J. Chem. Phys.

J. Am. Chem. Soc.

Magn. Reson. Chem.

J. Chem. Theory Comput.

J. Am. Chem. Soc.

Organometallics

Chem. Commun.

Dalton Trans.

J. Am. Chem. Soc.

J. Am. Chem. Soc.

Organometallics

J. Am. Chem. Soc.

J. Am. Chem. Soc.

J. Am. Chem. Soc.

Magn. Reson. Chem.

J. Chem. Theory Comput.

DFT calculations of NMR J_C–H coupling constants: An additional tool to characterize the α-agostic interaction in high oxidation state M-alkylidene complexes (M = Re, Mo and Ta)