Hydride Complexes - American Chemical Society

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Dynamic Behavior of Hydrogen in Transition Metal Bis(silyl) Hydride Complexes Yevhen Horbatenko and Sergei F. Vyboishchikov* Institut de Química Computacional i Catàlisi and Departament de Química, Campus de Montilivi, Universitat de Girona, 17071, Girona, Spain S Supporting Information *

ABSTRACT: A series of rhodium complexes CpRh(SiMe2X)2(SiMe3)(H) (X = Me, Cl, Br, I), Cp1−Cp4, CpRh(SiMe2X)2(PMe3)(H)+ (X = Me, Cl, Br, I), Cp5− Cp8, CpRh(SiMe3)2(SiF3)(H), Cp9, CpRh(SiMe3)2(SiH3)(H), Cp10, TpRh(SiH 3 ) 2 (SiMe 3 )(H), Tp1, TpRh(SiH3)2(PMe3)(H)+, Tp2, and TpRh(SiF3)2(PMe3)(H)+, Tp3, were studied computationally to understand the hydrogen behavior in the Si···H···Si moiety. The hydride ligand interacts with at least one of the silyls, and in many cases with both, but is located asymmetrically with regard to them, giving rise to a double-well potential energy surface (PES) for hydrogen motion. The hydrogen transfer barriers ΔE vary from 0.03 to 3 kcal·mol−1. For selected complexes Tp1, Tp2, Tp3, and Cp9 the three-dimensional PESs were constructed and the vibrational Schrödinger equation was solved. The PES is highly anharmonic in all four cases. The hydrogen is delocalized between two silicons in complexes Tp1, Tp3, and Cp9, but localized around the energy minima in complex Tp2. Complex Tp3 is an intermediate case with a substantial tunneling. The delocalized behavior is pertinent to systems with ΔE < 0.25 kcal·mol−1. For complexes Tp1, Tp2, Tp3, and Cp9 the J(Si−H) spin−spin coupling constants were calculated taking into account the vibrational motion of hydride. For Tp1, Tp3, and Cp9 both J(Si1−H) and J(Si2−H) are negative due to simultaneous Si1···H···Si2 interactions, while for Tp2 J(Si2−H) is positive, indicating a single Si···H interaction only. Negative J(Si−H) values were obtained even for Si···H distances as large as 2.3 Å (complex Tp3). A possible effect of vibrations on the J(Si−H) values is also discussed.

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Complexes can exist in isolated form,12−16 but also play a role as intermediates in oxidation addition reactions. Complexes with nonclassical interactions were studied both experimentally and computationally. The experimental methods used include X-ray diffraction,10,11,17−22 NMR,17−22 IR,17−19,21,22 and, in a few cases, neutron diffraction.23−29 Major differences between nonclassical complexes, including σcomplexes, and agostic and interligand hypervalent interactions (IHI)11 were reviewed by Nikonov.17,30 The Si−H distance in the range 1.7−1.8 Å clearly indicates σ-coordination,31,32 while longer Si−H separations are harder to interpret. Nevertheless, for distances up to 2.1 Å there is at least some degree of Si···H interaction almost always.32,33 Some authors even claim that the interaction can still exist for Si···H separations as large as 2.4 Å.32,34 Theoretical interpretation of Si−H interactions is based on a kind of the Dewar−Chatt−Duncanson model. These interactions involve the donation of the silane (Si−H) σ-orbital to the metal center and the back-donation from the metal to the (Si−H) σ*-antibonding orbital, which has strong acceptor properties.2 These two effects weaken the Si−H bond and

INTRODUCTION

Transition metal−silyl chemistry originated in 1956 with a synthesis of the iron complex Cp(CO) 2 Fe(SiMe3 ) by Wilkinson.1 By now, silyl complexes [LnM−SiR3] are known for nearly all transition metals.2,3 Transition metal silyl complexes play an important role as intermediates in various silylation reactions4−6 and even in industrial applications.7−9 One of the most widely used approaches for the synthesis of transition metal−silyl complexes is oxidative addition of silanes.2 An oxidative addition of a hydrosilane to a metal center can yield a classical complex with two-center twoelectron M−Si and M−H bonds (Figure 1a). However, if silane coordination occurs without oxidative addition, the Si−H bond remains intact, leading to a nonclassical η2-silane σ-complex with a three-center two-electron bond (Figures 1b).10,11 σ-

Figure 1. Classical silyl complex (a) and nonclassical silane complex (b). © XXXX American Chemical Society

Received: October 19, 2012

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dx.doi.org/10.1021/om300981y | Organometallics XXXX, XXX, XXX−XXX

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If an Si−H interaction is possible, the two silicons can compete for it, giving rise to a silyl−silane complex, in which case interconversion between the two forms can take place (Figure 2b) and the PES for hydrogen transfer has two minima. In this case the vibrational wave function can have either one or two maxima (Figure 3b). If the barrier is low enough to ensure

eventually give rise to a wide range of structures discussed above, from nonclassical to classical silyl hydride complexes.34 A very valuable tool for assessing nonclassical interactions is provided by NMR, the spin−spin coupling constants 1J(Si−H) being of particular importance. In a free silane, J(Si−H) is about 150−200 Hz,2,35 while for classical silyl hydride complexes it is vanishing or very small (below 20 Hz). In the presence of nonclassical interactions |J(Si−H)| is in the range 20−140 Hz, more typically from 40 to 80 Hz.36−39 It is commonly accepted that |J(Si−H)| > 20 Hz corresponds to a direct Si−H interaction,2,35 although the strength of the interaction was shown to not always correlate with |J(Si−H)|.40 A more unequivocal indication of a direct Si···H interaction is given by the sign of J(Si−H). Due to a negative gyromagnetic ratio of the 29Si nucleus, J(Si−H) is negative if the direct Si···H interaction prevails, whereas through-bond interactions, such as Si−M−H, provide a positive contribution to the total J(Si−H). While in most cases only the absolute value |J(Si−H)| is easily available experimentally, the sign is harder to obtain, but the sign of computed J(Si−H) serves as a valuable indicator of the direct Si−H interaction.22,41−43 Useful data are also supplied by IR spectra. When nonclassical interactions are present, the Si−H stretching frequency is broadened and red-shifted with respect to values of 2100−2200 cm−1 typical of a free silane. For σ-complexes, the Si−H vibrations, often coupled with M−H stretching, are observed in the region 1600−1950 cm−1. In the case of βagostic interactions the frequency is about 1690−2100 cm−1.3 From the computational viewpoint, a very informative indicator of an Si···H interaction is the Mayer bond order (MBO),44 which can be computed at virtually no additional cost. For a full covalent bond, it reflects the bond multiplicity, with typical values for the Si−H bond of about 0.9. For weaker Si···H interactions, the MBO exhibits lower positive values. We usually consider MBOs of 0.05 or below as insignificant, while higher values are regarded as indicative of an Si···H interaction,33 albeit a weak one. This work is focused on complexes with two silicon ligands and one hydride ligand. In the absence of interactions between ligands, this corresponds to a bis(silyl) hydride complex (Figure 2a). A tantalum complex of this kind, Cp2Ta(SiMe2H)2H, was

Figure 3. Schematic representation of various types of hydrogen motion potentials in transition metal complexes with two silicon ligands and one hydride. The solid lines represent PES profiles, and the dashed lines are the ground-state vibrational wave functions.

an interconversion rapid on the NMR time scale, the situation is referred to as hydrogen fluxionality. The rhodium complexes [Cp*Rh(PMe3)(SiR3)(HSiR3)]BAr437 (R = Me or Et, Ar = 3,5C6H3(CF3)2) are examples of such fluxionality. For both complexes hydride resonance shows 29Si satellites in the 1H NMR spectra and the J(Si−H) coupling constants are 28.5 and 27.8 Hz, respectively, which supports the assignment of these complexes as η1-silyl-η2-silane complexes. The observation in the 1H NMR spectra of a single resonance for the SiMe3 groups is in agreement with this fluxional nature. On the other hand, the hydrogen can interact with both silicon atoms simultaneously but be located closer to one of them (Figure 2c), with the entire R3Si···H···SiR′3 moiety behaving as a single ligand.33,41,42 The potential energy surface (PES) is of double-well character as well, with a small barrier. In this case the vibrational wave function has a single maximum above the transition state (Figure 3c). In the extreme case, the barrier may vanish altogether, giving rise to a single-well PES and a vibrational wave function with a single maximum. Experimentally found structures of certain iron complexes such as CpFe(CO)(SiF2Me)2(H)46 and CpFe(CO)(SiCl3)2(H)47 can be consistent with this description. A more recent computational study41 also supports the symmetric configuration of CpFe(CO)(SiR3)2(H) complexes with weak Si···H···Si interactions. In general, it is not always easy to distinguish between the fluctional behavior and the simultaneous triple Si···H···Si interactions. In a previous study, Vyboishchikov and Nikonov33 obtained an indication that the PES of hydride motion along the Si−Si vector in complexes CpRh(SiR3)2H2 and CpRh(SiR3)3H can be quite shallow. Hence, a static description of such complexes may be inadequate. The purpose of this work is to study the hydrogen dynamic behavior in complexes of this kind. To understand the hydrogen dynamics, we will obtain and analyze the vibrational wave function by solving the vibrational Schrödinger equation on a given PES. Since the hydrogen transfer can be coupled to the Si−Si motion, a single hydrogen transfer coordinate is not sufficient to adequately describe the system. Thus, the Si−Si and the Rh−H coordinates must also be taken into account. We expect that these three coordinates can reasonably describe the hydrogen motion in these complexes. Here we will apply a formalism similar to that used by us for proton sponge cations.48 Although quite different chemically, the Si···H···Si

Figure 2. Bonding patterns in transition metal complexes with two silyl and one hydride ligand. (a) Pure bis(silyl) hydride complex. (c) Dynamic equilibrium in a silyl−silane complex. (b) Complex with simultaneous Si···H···Si interactions.

studied by neutron diffraction27 and exhibits a Ta−H distance of 1.785 Å and two Si−H distances of 2.189 and 2.190 Å, which were deemed nonbonding. The NMR data show that the two dimethylsilyl ligands are equivalent. Another example is rhodium complex Cp*Rh(SiEt3)2(H)2.45 A neutron diffraction study also shows the presence of classical hydride ligands with an average Rh−H distance of 1.581 Å and with an average Si− H distance of 2.27 Å. The NMR spectrum shows the presence of two hydride ligands as well. B


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Figure 4. Cp complexes in this work (Cp = cyclopentadienyl).

Figure 5. Tp complexes in this work (Tp = hydridotris(pyrazolyl)borate). quality PESs by the DFT can be challenging. The second-order Møller−Plesset perturbation theory (MP2) may sometimes fail as well. In order to have reliable results, a high-level (preferably a coupledclusters) reference is needed. Since geometry optimization at a higher correlated level is virtually impossible, we adopted the following strategy to assess the reliability of the methods. Initially, the geometry optimizations for a given complex were done with a number of density functionals and MP2. With the resulting structures, single-point CCSD energies were computed. It is reasonable to assume that the structure yielding the lowest CCSD energy is closer to the (unknown) CCSD minimum and, hence, should be trusted more than the others. For the CCSD calculations the Orca 2.8 package70 was employed, taking advantage of the LPNO formalism.71 For geometry optimizations, the full-electron 6-311G** basis set72−74 was used for all atoms except rhodium and iodine, for which “Stuttgart” pseudopotentials were employed75,76 in conjunction with a [311111/22111/411] basis for Rh and a [31/311] basis for I. Harmonic vibrational frequencies were computed at the DFT level for all the stationary points found (minima and transition states). For single-point CCSD calculations, the full-electron cc-pVTZ basis set77−79 was used for all atoms, except for rhodium and iodine. For Rh and I, the same pseudopotentials as for geometry optimizations were employed, but more extensive “def2-TZVPP” ([211111/4111/411/ 11/1] contraction)80 and “def-TZVPP” ([31/311/11/1] contraction)81 basis sets were applied for Rh and I, respectively. Spin−spin coupling constants J(Si−H) were calculated using the B3LYP functional in conjunction with the aug-cc-pVTZ-J basis set.82−85 This basis was shown to give spin−spin coupling constants quite close to the converged values.86 Potential Energy Surfaces. Each of the three-dimensional PESs was obtained by a series of constrained geometry optimizations at the TPSSh level. Three internal coordinates characterizing the H and Si···Si motion were frozen, whereas all other internal coordinates were allowed to relax. The starting points for the constrained optimizations were obtained by a corresponding distortion of the symmetric stationary point (transition state). The internal coordinate values at the grid points were chosen in such a way to include all the stationary point geometries. In total, several hundred constrained optimizations were performed for each complex under study. The choice of the coordinates for constructing the PES was dictated by the following considerations. The X coordinate describes the deviation of the hydride from the midpoint of the two silicons along the Si···Si vector. The Y coordinate, which corresponds to the Rh−H stretching vibration, indicates the hydride motion perpendicular to the Si···Si vector. The Si···Si distance is taken as the Z coordinate (see Figure 6). Zero values (0,0,0) of the X, Y, and Z coordinates

fragment in the bis(silyl) hydride complexes formally resembles the N···H···N moiety in proton sponge cations with a strong hydrogen bond, a detailed study on which we have published recently.48 In the latter, depending on the barrier, the proton can be localized near one of the nitrogens or delocalized between both, very much like in the complexes under study the hydride can be localized near one silyl or delocalized between both. The main difference between these two classes is that the Rh−H bond has no correspondence in proton sponge cations. The model complexes for our study (see Figures 4 and 5) were chosen in anticipation that the hydrogen transfer barriers in them could be quite different, and hence, they might exhibit diverse dynamic behavior. In some cases, halogen substituents were placed on silyl in order to cause an IHI effect that could affect the PES. Niobium complexes with SiMe2X ligands were demonstrated10,11,24,25,49 to exhibit IHI. Note that a related H···Si···H double interaction was first found in an iron complex50 and later in a tungsten51 and a ruthenium complex,52 although some indication of an H···Si···H motif in a ruthenium complex had been presented before.19

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COMPUTATIONAL METHODS

Since we are interested in the intrinsic structure and dynamics of the complexes under study, i.e., not affected by solvent or crystalline environment, all calculations were done as if the system were in the gas phase. DFT Calculations. All geometry optimizations were performed using Gaussian 0953 and Turbomole 5.1054 program packages. The PBEPBE,55 B3LYP,56−58 M06L,59 M062X,60 BP86,56,61 and TPSSh62 functionals were employed. B3LYP was chosen since it is a generally accepted standard and often affords quite good metal−ligand bond distances and energies.59,63 The PBEPBE functional was included owing to its good performance for Si···H···Si bridges, which we observed in our previous works.33,64,65 BP86 was chosen since it performs well for metal−ligand bonds.63 The meta-GGA functional M06L and the hybrid meta-GGA functional TPSSh were utilized because they reportedly provide very good metal−ligand bond energies.59,60,63,66 The PBEPBE and TPSSh functionals were used in conjunction with the “resolution-of-identity” (RI) procedure.67 In addition, MP268 calculations were carried out as well, also using the RI approximation.69 As long as various density functionals possibly yield qualitatively different pictures for organometallic complexes, calculation of highC


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maximum-wave function path, which is defined as a curve in the XYZ space along which ρ(X,Y,Z) is a maximum with respect to any lateral displacement.48 Physically, it corresponds to the most probable pathway of hydride transfer. It is instructive to compare it with the minimum energy path on the PES. A possible deviation between both curves manifests quantum effects, notably the tunneling. For systems with delocalized hydride behavior, we also use the spatial extent X̅ of the wave function along the X coordinate to characterize the degree of delocalization:

Figure 6. Coordinate system used in this work (see text for details).

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correspond to the symmetric stationary point. A similar coordinate system was used successfully in our previous study of proton sponge cations.48 Upon being generated point by point, the PES was represented by a polynomial expression, which is very advantageous for solving the vibrational Schrödinger equation. While hydrogen motion within the molecular plane and its coupling with the Si···Si vibration are taken into account quantum-mechanically, their coupling with other vibrational modes is accounted for in a simplified way only. These considerations show the scope and limitations of our approach. More details about PES construction and fitting are available in the Supporting Information. Wave Function Analysis. Due to a low mass of the proton, hydride can sometimes behave as a quantum particle, surmounting a small barrier easier that it would in the classical case. In the case of hydride motion in a shallow potential, it is also advantageous to describe the hydride position on quantum-mechanical terms using the probability density ρ(X,Y,Z) of finding the hydride in the vicinity of the point with internal coordinates X,Y,Z. In the classical limit, the maxima of the probability density should be located near the potential energy minima, with ρ(X,Y,Z) compactly distributed in the vicinity of the PES minimum. However, when quantum effects are more pronounced, ρ(X,Y,Z) will be more delocalized, and ρ maxima do not need to coincide with the PES minima. Thus, comparing the PES with the ρ distribution, we can conclude on the presence or absence of quantum effects in the hydride motion. The probability density ρ(X,Y,Z) = |Ψ(X,Y,Z)|2 is related to the vibrational wave function Ψ(X,Y,Z), which is in turn obtained as a solution of the vibrational Schrödinger equation in the corresponding PES. In this work, the vibrational Schrödinger equation was solved variationally in a basis of distributed Gaussian functions87 using a Fortran code written by the authors. In order to get a better representation of hydrogen motion in the complexes under study, we consider the two-dimensional probability density in the coordinates X, Z defined as follows: ρ(X , Z) =

∫ ρ(X , Y , Z)dY = ∫ |Ψ(X , Y , Z)|2 dY

X̅ =

⟨Ψ(X , Y , Z)|X2|Ψ(X , Y , Z)⟩

(2)

RESULTS AND DISCUSSION Performance of Density Functionals and MP2. All optimizations were performed employing the six different density functionals and the MP2 method. Using the resulting DFT and MP2 geometries, single-point CCSD calculations were carried out. Assuming that the structure with the lowest absolute CCSD energy is closer to the (unknown) CCSD minimum, we can conclude that the method yielding this structure is the best one. The calculations revealed that for complexes Cp1−Cp3, Tp1, and Tp2 the lowest coupled-cluster energies correspond to the TPSSh geometries. The performance of M06L and M062X is slightly poorer. However, for complexes Cp4−Cp10 the lowest CCSD energies are obtained for M06L geometries, while for Tp3 from the M062X geometry. The TPSSh functional for these complexes shows a slightly poorer but still acceptable performance (see Table 1). The CCSD energy difference between TPSSh and M06L geometries for complexes Cp7 and Cp10 is negligible. The structures obtained by all other methods yield far higher CCSD energies. The optimized Rh−Si and Si−H distances for the minimum structures are given in Tables 2 and 3 for the Cp complexes and in Table 4 for the Tp complexes. For complexes Cp1−Cp3 M06L underestimates both the Rh−Si bond length and the Si−H distances. On the other hand, TPSSh overestimates the Rh−Si bond length and Si−H distances in complexes Cp4−Cp10. The B3LYP functional yields an end-on (η1-) structure for Cp5 (Figure 7), which differs principally from that calculated by the other functionals and is high in CCSD energy. Thus, the B3LYP functional cannot be reliably used for this kind of complexes. All optimized Cp complexes are asymmetric (Figure 7), with one Si−H distance shorter (1.900−2.140 Å) than the other (1.981−2.196 Å). The values of both distances vary about 0.2 Å among the functionals. MP2 gives less asymmetric structures than other functionals. For all the Tp complexes, MP2, BP86, and PBEPBE give minima of Cs symmetry with two equivalent Si···H bonds. On the contrary, the M06L and M062X functionals afford highly

(1)

where Ψ is the three-dimensional vibrational wave function. The twodimensional ρ(X,Z) gives the probability of finding the molecule at the nuclear configuration (X,Z) at an arbitrary value of the coordinate Y. For systems with two wave function maxima, we also consider the

Table 1. Relative CCSD Energies (in kcal·mol−1) for Optimized Minima of Complexes Cp1−Tp3 with Respect to the CCSD Energy Computed at the TPSSh Geometry (for Cp1−Cp3, Tp1, Tp2), M06L Geometry (for Cp4−Cp10), and M062X Geometry (for Tp3)

PBEPBE M06L M062X B3LYP BP86 TPSSh MP2

Cp1

Cp2

Cp3

Cp4

Cp5

Cp6

Cp7

Cp8

Cp9

Cp10

Tp1

Tp2

Tp3

2.46 0.41 1.34 2.40 3.32 0 1.18

2.25 0.24 0.84 2.32 3.27 0 1.99

2.09 0.17 0.75 2.20 3.26 0 0.75

2.49 0 0.69 2.70 3.67 0.25 0.31

2.70 0 0.84 3.02 3.76 0.21 2.19

2.52 0 0.38 2.34 3.50 0.20 2.71

2.50 0 0.20 2.54 3.50 0.05 1.99

2.49 0 0.05 2.69 3.73 0.30 1.66

3.07 0 0.82 2.34 4.52 0.15 1.04

2.05 0 0.86 1.94 2.77 0.02 1.32

2.56 0.88 0.95 1.19 3.39 0 2.99

3.98 0.63 0.25 1.04 4.84 0 3.85

5.65 0.50 0 1.78 6.87 0.93 1.85

D


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Table 2. Rh−Si and Si−H Distances (in ångströms) and Mayer Bond Orders (MBO) for Complexes Cp1−Cp5 (minima) Optimized by Various Density Functionals and MP2a method complex

distance and MBO

PBEPBE

M06L

M062X

B3LYP

BP86

TPSSh

MP2

Cp1

Rh−Si1 Rh−Si2 Si1−H Si2−H MBO Si1−H MBO Si2−H Rh−Si1 Rh−Si2 Si1−H Si2−H MBO Si1−H MBO Si2−H Rh−Si1 Rh−Si2 Si1−H Si2−H MBO Si1−H MBO Si2−H Rh−Si1 Rh−Si2 Si1−H Si2−H MBO Si1−H MBO Si2−H Rh−Si1 Rh−Si2 Si1−H Si2−H MBO Si1−H MBO Si2−H

2.447 2.435 1.992 2.076 0.180 0.136 2.408 2.400 2.012 2.066 0.173 0.137 2.416 2.408 2.005 2.053 0.178 0.142 2.416 2.408 1.992 2.050 0.181 0.139 2.525 2.500 2.004 2.084 0.146 0.102

2.425 2.410 1.942 2.016 0.197 0.140 2.387 2.377 1.972 2.022 0.185 0.143 2.394 2.387 1.946 1.998 0.196 0.146 2.399 2.389 1.934 1.981 0.209 0.142 2.509 2.469 1.906 2.060 0.200 0.102

2.385 2.366 1.934 2.021 0.183 0.124 2.352 2.340 1.949 2.013 0.183 0.132 2.356 2.344 1.941 2.003 0.188 0.136 2.362 2.348 1.931 1.987 0.197 0.135 2.469 2.423 1.903 2.060 0.187 0.092

2.467 2.440 1.949 2.105 0.202 0.129 2.420 2.411 1.998 2.067 0.178 0.142 2.429 2.419 1.988 2.058 0.185 0.146 2.429 2.419 1.976 2.053 0.190 0.142 2.953 2.449 1.615 2.610 0.460 0.010

2.454 2.441 1.994 2.085 0.188 0.144 2.414 2.406 2.017 2.072 0.18 0.145 2.423 2.415 2.011 2.059 0.185 0.15 2.423 2.414 1.998 2.057 0.187 0.146 2.010 2.099 2.01 2.099 0.151 0.107

2.436 2.421 1.98 2.089 0.171 0.117 2.394 2.386 2.000 2.069 0.166 0.124 2.399 2.392 1.994 2.063 0.169 0.127 2.401 2.393 1.976 2.060 0.171 0.121 2.523 2.477 1.928 2.136 0.161 0.075

2.427 2.419 2.066 2.121

Cp2

Cp3

Cp4

Cp5

a

2.376 2.374 2.072 2.117

2.388 2.386 2.047 2.097

2.384 2.382 2.019 2.064

2.490 2.478 2.072 2.125

Geometries that correspond to the lowest CCSD energy are in italics.

asymmetric structures for Tp2 and Tp3. B3LYP again yields an unrealistic η1-structure for complex Tp2. The TPSSh structures of all three Tp complexes are highly asymmetric, with essentially η1-silyl-η2-silane coordination and the two Rh−Si distances differing by about 0.04 and 0.19 Å for Tp1 and Tp2, respectively. The corresponding difference for Si−H distances is 0.29 and 0.74 Å. In the M062X structure for complex Tp3 the difference between two Rh−Si distances is 0.06 Å and that between two Si−H distances is 0.40 Å. Since, according to our tests, TPSSh turns out to have the best performance for Cp1−Cp3, Tp1, and Tp2, M062X for Tp3, and M06L for Cp4−Cp10, henceforward we will discuss the TPSSh, M062X, or M06L geometries, whichever gives the lowest CCSD energy. Minimum Structures. Figures 8 and 9 give the structures optimized by TPSSh or M06L, whichever gives the lowest CCSD energy. The Rh−Si distances in halogen-containing complexes Cp2−Cp4 are shorter than those in Cp1. The same is true for complexes Cp6−Cp8 when compared with Cp5. This contraction is due to the IHI, which appears in Cp2−Cp4 and Cp6−Cp8, where the halogen atom is in the trans-position to the hydride. When the substituents at the silicon atom pass from Cl to Br to I, the IHI gets stronger, and the Si1−H distances shorter. This occurs because corresponding interacting orbitals (σ(Si−X), σ*(Si−X), and σ(M−H)) are energetically closer to each other, thus facilitating the interaction.10

Complexes Cp1 and Cp5 have weak simultaneous interactions between hydrogen and silicon atoms, as indicated by the MBO. In the series of complexes Cp1, Cp10, and Cp9, having the SiMe3−, SiH3−, and SiF3− silyl ligands in the trans-position to the hydride, respectively, the Rh−Sitrans distances are 2.403, 2.366, and 2.279 Å, respectively. This trend can be explained in terms of Bent’s rule.88 Due to a high electronegativity of fluorine, the Si−F bond has more p character than the Si−H and Si−Me bonds. Hence, the lone pair in SiF3− has a higher s character, which leads to a shorter Rh−Si bond. Note that the Rh−H bond length in these three complexes hardly varies and is about 1.59 Å. A similar situation occurs for complexes Tp2 (with the SiH3− ligand) and Tp3 (with the SiF3− ligand): Tp3 has shorter Rh−Si distances (see Table 4). Transition States. The transition-state structures and hydrogen transfer barriers ΔE, defined as the energy difference between the transition state and the minimum, for the Cp and Tp complexes are represented in Table 5. All of them are symmetric with respect to the hydrogen position (see Figure 10). The TPSSh functional tends to underestimate the barriers (compared to CCSD) for complexes TSCp1−TSCp3, TSTp1, and TSTp2. However, for complex TSTp1 the difference between the TPSSh and CCSD barriers is as small as 0.05 kcal·mol−1. The M06L functional overestimates barriers for almost all complexes (TSCp4−TSCp9), except for TSCp10. In the case of TSTp3, CCSD yields a lower energy for the E


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Table 3. Rh−Si and Si−H Distances (in ångströms) and Mayer Bond Orders (MBO) for Complexes Cp6−Cp10 (minima) Optimized by Various Density Functionals and MP2a method complex

distance and MBO

PBEPBE

M06L

M062X

B3LYP

BP86

TPSSh

MP2

Cp6

Rh−Si1 Rh−Si2 Si1−H Si2−H MBO Si1−H MBO Si2−H Rh−Si1 Rh−Si2 Si1−H Si2−H MBO Si1−H MBO Si2−H Rh−Si1 Rh−Si2 Si1−H Si2−H MBO Si1−H MBO Si2−H Rh−Si1 Rh−Si2 Si1−H Si2−H MBO Si1−H MBO Si2−H Rh−Si1 Rh−Si2 Si1−H Si2−H MBO Si1−H MBO Si2−H

2.478 2.462 2.022 2.060 0.141 0.112 2.486 2.467 1.990 2.068 0.153 0.112 2.486 2.467 1.974 2.068 0.164 0.112 2.466 2.455 2.056 2.145 0.152 0.114 2.438 2.427 2.081 2.158 0.157 0.117

2.458 2.435 1.936 2.024 0.184 0.120 2.471 2.444 1.912 2.024 0.196 0.118 2.475 2.446 1.900 2.023 0.201 0.115 2.466 2.432 1.994 2.083 0.182 0.117 2.418 2.406 2.006 2.110 0.190 0.121

2.419 2.396 1.945 2.010 0.168 0.115 2.426 2.400 1.930 2.009 0.175 0.114 2.432 2.401 1.913 2.009 0.181 0.112 2.409 2.394 2.005 2.082 0.161 0.107 2.377 2.367 2.017 2.076 0.166 0.120

2.500 2.468 1.970 2.097 0.167 0.109 2.514 2.474 1.938 2.116 0.179 0.104 2.517 2.476 1.924 2.116 0.188 0.100 2.483 2.466 2.028 2.154 0.163 0.112 2.450 2.437 2.059 2.165 0.167 0.116

2.484 2.469 2.032 2.070 0.146 0.119 2.492 2.474 2.001 2.078 0.157 0.119 2.495 2.474 1.981 2.080 0.169 0.117 2.473 2.464 2.065 2.137 0.157 0.125 2.445 2.433 2.085 2.165 0.164 0.124

2.462 2.445 1.997 2.060 0.139 0.101 2.471 2.450 1.975 2.067 0.147 0.100 2.472 2.450 1.956 2.069 0.157 0.097 2.455 2.439 2.029 2.156 0.149 0.096 2.425 2.412 2.063 2.160 0.151 0.103

2.430 2.424 2.066 2.109

Cp7

Cp8

Cp9

Cp10

a

2.447 2.442 2.059 2.104

2.443 2.439 2.035 2.079

2.443 2.438 2.118 2.184

2.419 2.416 2.140 2.196


Table 4. Rh−Si and Si−H Distances (in ångströms) and Mayer Bond Orders (MBO) for Complexes Tp1−Tp3 (minima) Optimized by Various Density Functionals and MP2a method complex

distance and MBO

PBEPBE

M06L

M062X

B3LYP

BP86

TPSSh

MP2

Tp1

Rh−Si1 Rh−Si2 Si1−H Si2−H MBO Si1−H MBO Si2−H Rh−Si1 Rh−Si2 Si1−H Si2−H MBO Si1−H MBO Si2−H Rh−Si1 Rh−Si2 Si1−H Si2−H MBO Si1−H MBO Si2−H

2.407 2.407 1.973 1.973 0.178 0.178 2.444 2.444 2.008 2.008 0.151 0.151 2.368 2.368 2.043 2.043 0.100 0.100

2.393 2.393 1.934 1.934 0.189 0.189 2.545 2.396 1.692 2.380 0.366 0.035 2.382 2.331 1.813 2.263 0.272 0.025

2.359 2.359 1.934 1.934 0.172 0.172 2.523 2.346 1.714 2.299 0.335 0.036 2.344 2.281 1.850 2.254 0.207 0.027

2.499 2.389 1.723 2.264 0.348 0.073 2.731 2.398 1.613 2.539 0.457 0.021 2.451 2.350 1.743 2.332 0.289 0.024

2.412 2.412 1.982 1.982 0.183 0.183 2.450 2.450 2.013 2.013 0.156 0.156 2.375 2.375 2.049 2.049 0.104 0.104

2.426 2.384 1.827 2.117 0.247 0.102 2.581 2.392 1.672 2.414 0.362 0.021 2.401 2.337 1.782 2.324 0.245 0.017

2.372 2.372 2.118 2.118

Tp2

Tp3

a

2.432 2.432 2.085 2.085

2.353 2.353 2.089 2.089


F


Organometallics

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Interestingly, the harmonic imaginary frequency for the TSCp1−TSCp10 transition states does not directly correspond to the hydrogen motion, but to the concerted internal rotation of the Cp and the silyl ligands. Nonetheless, IRC calculations indicate that this imaginary frequency corresponds to the hydride transfer between the silicons. In TSTp1−TSTp3 the imaginary frequency corresponds directly to the hydride transfer. As shown in Table 5, ΔE varies between 0 and 3.4 kcal·mol−1. The Cp complexes mainly tend to exhibit higher barriers than the Tp complexes. For the low-barrier complexes (Cp9−Cp10, Tp1−Tp3) a lower ΔE is achieved for the complexes with a shorter Si···Si distance. However, for the entire set of complexes under study (Cp1−Cp10, Tp1−Tp3) no simple correlation between interatomic distances and the hydrogen transfer barriers can be found. Since the hydride in the complexes with low barriers is expected to exhibit some kind of quantum behavior, it is tempting to study in depth the hydride dynamics in them. We have chosen complexes Cp9, Tp1, Tp2, and Tp3, since they represent a good variety of hydrogen transfer barriers.

Figure 7. Optimized minimum structure of Cp5 obtained using the B3LYP and M06L density functionals. Non-hydride hydrogens are omitted for clarity. Distances are given in ångströms.

transition state than for the minimum, leaving open the question of whether there are two minima or the PES is a single-well one. It should be noted that the TPSSh barrier for TSTp3 is 0.25 kcal·mol−1, the same value as the CCSD barrier obtained from TPSSh geometry (not given in Table 5).

Figure 8. Optimized minimum structures of Cp1−Cp8 obtained by TPSSh (Cp1−Cp3) and M06L (Cp4−Cp8) density functionals. Non-hydride hydrogens are omitted for clarity. Distances are given in ångströms. G


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Figure 9. Optimized minimum structures of Tp1−Tp3, Cp9, and Cp10 obtained by TPSSh (Tp1, Tp2), M06L (Cp9, Cp10), and M062X (Tp3) density functionals. Non-hydride hydrogens are omitted for clarity. Distances are given in ångströms.

higher the barrier, the larger the frequency: ν(Hx)(Tp1) < ν(Hx)(Tp3) < ν(Hx)(Tp2). Since harmonic ν(Hx) reflects the local PES curvature at the minimum, a higher barrier is associated with a higher local curvature. However, complex Cp9 has a higher barrier than Tp3, but exhibits a lower frequency. This is due to the fact that in complex Cp9 the hydrogen motion is coupled to internal rotation of Cp and silyl ligands, as explained above. When the barrier is low, the entire potential energy surface is quite shallow, and the resulting large-amplitude vibrations require an anharmonic treatment, since the harmonic frequency, which reflects the local curvature at the minimum, has little to do with the real vibrations. Keeping this in mind, we solved numerically the three-dimensional vibrational Schrödinger equation to obtain the anharmonic frequencies. The results are given in the penultimate column of Table 6. In the case of complex Tp1 (double-well potential with a low barrier), the anharmonic ν(Hx) frequency is more than 2.5 times lower than the harmonic one. For complex Tp2 (doublewell potential and a large barrier) there is a tunneling splitting of 34 cm−1, which originates from the double-well nature of the potential. For this reason, for complex Tp2 two anharmonic frequency values are given in Table 6, both of which are lower than the harmonic frequency. Complex Tp3 exhibits a significant difference between harmonic and anharmonic frequencies. In this case the barrier is substantial, and the potential curvature at the minima is increased, as is the harmonic frequency. At the same time, the anharmonic hydrogen motion is still delocalized (vide inf ra) and determined

Table 5. Rh−Si, Si−Si, and Si−H Distances (in ångströms) and Hydride Transfer Barriers ΔE (in kcal·mol−1) for TSCp1−TSCp10 and TSTp1−TSTp3 at TPSSh, M06L, or M062X, and CCSD (single points at TPSSh, M06L, or M062X geometries, whichever gives the lowest CCSD energy) Levels TPSSh or M06L

CCSD

complex

Rh−Si

Si−Si

Si−H

ΔE

ΔE

TSCp1 TSCp2 TSCp3 TSCp4 TSCp5 TSCp6 TSCp7 TSCp8 TSCp9 TSCp10 TSTp1 TSTp2 TSTp3

2.436 2.396 2.401 2.396 2.499 2.450 2.462 2.464 2.437 2.412 2.398 2.434 2.309

4.035 4.066 4.063 3.986 3.904 4.035 4.037 4.024 4.031 3.945 3.906 3.976 3.876

2.030 2.065 2.060 2.014 1.955 2.029 2.029 2.022 2.053 2.055 1.965 2.003 2.022

2.85 2.17 2.05 3.71 3.85 3.29 3.56 3.97 1.81 0.88 0.03 1.13 0.16

3.07 2.45 2.44 3.13 3.36 2.34 2.78 3.24 1.08 0.95 0.08 1.45 −0.08

Vibrational Frequencies. First, harmonic frequencies were computed by the Gaussian program using analytical energy second derivatives (Table 6, column 4). The harmonic frequency ν(Hx) along the Si−Si vector varies widely. ν(Hx) is much larger for Tp2 than for Tp1 and Tp3. These frequencies are in line with the hydrogen transfer barrier: the H


Organometallics

Article

Figure 10. Transition-state structures of Cp1 (obtained by TPSSh), Cp10 (obtained by M06L), and Tp2 (obtained by TPSSh). Non-hydride hydrogens are omitted for clarity. Distances are given in ångströms.

Table 6. Fundamental Frequencies (in cm−1) Obtained by Harmonic Analysis, by Solving the Three-Dimensional Vibrational Schrödinger Equation (denoted 3D), and by Solving the One-Dimensional Schrödinger Equation for the One-Dimensional Part of the Potential without Taking into Account the Coupling (1D)a anharmonic frequency complex

vibration

μH

harmonic frequency

1D

3D

ΔE

Tp1

ν(Hx) ν(Hy) ν(Si−Si) ν(Hx) ν(Hy) ν(Si−Si) ν(Hx) ν(Hy) ν(Si−Si) ν(Hx) ν(Hy) ν(Si−Si)

1.6550 1.0182 6.9318 2.2555 1.0161 5.1533 2.8485 1.0165 13.5978 2.2001 1.0160 4.5382

789 2122 341 1244 1968 137 914 2122 416 571 2149 65

358 2032 315 95 2032 337 153 2102 240 666 2136 333

288 1964 310 473, 749b 1792 287 118 2029 232 537 2081 350

0.03

Tp2

Tp3

Cp9

1.13

0.25

0.64

ν(Hx) and ν(Hy) are hydrogen vibrational frequencies; ν(Si−Si) is the frequency of silicon−silicon vibrations. μH is the reduced mass obtained from the harmonic analysis (in atomic mass units = dalton). ΔE is the hydride transfer barrier (in kcal·mol−1) at the TPSSh level. bTwo values due to tunneling splitting; see text. a

corresponds to a direct hydrogen transfer without assistance of the Si−Si motion, while when the coupling is present, the hydrogen transfer mainly occurs by way of Si−Si contraction. Wave Function Analysis. The most straightforward information regarding the hydrogen motion in the bis(silyl) hydride complexes under study is provided by the vibrational wave function Ψ(X,Y,Z). On a two-dimensional plot, it can be represented in the form of two-dimensional probability density ρ(X,Z) defined by eq 1. Figure 11 shows ρ(X,Z) along with the PES contour plots. The minimum-energy path on the PES and maximum wave function path (for Tp2 and Tp3) are also shown in Figure 11. For complex Tp1, having a double-well potential with an extremely low barrier (ΔE = 0.03 kcal·mol−1), the ground-state vibrational wave function has a single maximum corresponding to a symmetric structure, shifted by 0.156 Å away from the PES minimum. Consequently, the hydrogen is delocalized between two silicon atoms and the highest likelihood of finding it is in the symmetric configuration. The tiny barrier does not affect the hydrogen motion. The spatial extent (see eq 2) along the X coordinate, which is the average deviation of the hydrogen from the symmetric point, is ±0.185 Å. For complex Tp2, with a double-well potential and a relatively large barrier (ΔE = 1.13 kcal·mol−1), the vibrational wave function has two well-separated maxima, which are shifted

by the global potential width. For complex Cp9, harmonic and anharmonic frequencies are very similar. The frequencies for vibrations along the Y axis, which corresponds to the Rh−H stretching, can be compared with experimental IR spectra. For the Rh−H stretching vibrations (ν(Hy) in Table 6), the anharmonic frequencies are close to the harmonic ones and are within the region typical of experimental frequencies (1951−2090 cm−1),5,45,89−92 except for Tp2, where ν(Hy) is a bit lower. This gives us certainty that approximations incorporated in our computational models are reasonable. For the Si−Si vibrations, ν(Si−Si) in Table 6, the anharmonic values significantly deviate from the harmonic ones. The difference is most pronounced for complex Cp9, 65 cm−1 (harmonic) vs 350 cm−1 (anharmonic), and caused by coupling of hydrogen transfer with internal rotation of the Cp and SiMe3 groups. The frequencies obtained by solving the one-dimensional Schrödinger eq (1D) without taking into account the coupling between the X, Y, and Z coordinates are referred to in Table 6 as uncoupled frequencies. In the case of Tp1, Tp3, and Cp9, the coupled (3D) and uncoupled (1D) results are quite close, indicating the lack of coupling between hydrogen transfer and Si−Si vibrations. For Tp2, however, the difference between 1D and 3D parts is quite large, manifesting the coupling between X and Z coordinates. In mechanistic terms, the lack of coupling I


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Figure 11. PES and probability density contour plots for complexes Tp1−Tp3 and Cp9 in the coordinates X−Z. The coordinates are shifted with respect to the symmetric configuration. The shift is given by the formulas X = Xi − Xe, Z = Zi − Ze, where Xe and Ze are the respective values in the symmetric equilibrium configuration; Xi and Zi are the current values of these coordinates. The levels of ground-state probability density, with values from 0.1ρmax to 0.9ρmax, are given by the black dotted lines. Yellow dots show the minima of the PES. The minimum-energy path is given by the dark blue line, and the maximum wave function path between two maxima of the probability density is represented by the light blue curve.

from the PES minima by some 0.05 Å. The maximum wave function path does not exactly coincide with the minimum energy path, the former being less bent. Therefore, the coupling between the H motion (X coordinate) and Si−Si motion (Z coordinate) is significant, but tunneling is also considerable in this system. It can be seen from the minimum value of probability density on the maximum wave function path, which is 24% of the value at the maximum. This indicates that the hydrogen is well localized in the areas of the potential minima. For complex Tp3 (a double-well potential and a low barrier of 0.25 kcal·mol−1), the vibrational wave function has two weakly pronounced maxima separated by 0.133 Å from the respective PES minima, lying rather close to the TS. The maximum wave function path in this case is virtually a straight line that lies very close to the minimum energy path, which is also scarcely bent. This shows that in this case no Si−Si motion is necessary to effect the hydrogen transfer. The minimum value of the probability density on the maximum wave function path is 98% of its value at the maximum. Thus, the predominant transfer mechanism is the tunneling. The hydrogen motion is delocalized and the spatial extent X̅ = ±0.214 Å is larger than that of Tp1, showing a larger degree of delocalizaiton. We conclude that Tp3 is an intermediate case between one- and two-maxima wave functions.

For complex Cp9 (a double-well potential and an intermediate barrier of 0.64 kcal·mol−1) the vibrational wave function has a single maximum corresponding to a symmetric structure, similarly to complex Tp1. This maximum is located 0.283 Å from the PES minimum. Despite a far larger barrier than in complex Tp1, the hydrogen is delocalized, with a peak of probability density in the symmetric configuration. This can be accounted for by proximity of the two minima on the PES, which are separated by just 0.28 Å. It can be rationalized in terms of tunneling, which is known to depend exponentially on barrier width, as illustrated by a relatively small wave function spatial extent of ±0.116 Å. J(Si−H) Coupling Constants. We have demonstrated that in certain cases the hydride can be delocalized between two silyls and hence be prone to large-amplitude vibrations along the X coordinate. This means that the hydride may spend a substantial amount of time far away from the energy minimum. On the other hand, J(Si−H) depends strongly and nonlinearly on the Si−H internuclear separation. Hence, the vibrational motion of the hydride may influence the observed (i.e., averaged) Si−H spin−spin coupling constants. It is worth checking whether the effect of these vibrations on J(Si−H) is important. The rigorous way of doing this would be to compute the integral J


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Article

Table 7. Averaged Spin−Spin Coupling Constants ⟨J⟩ (in hertz) Obtained Taking into Account Vibrational Motion and Static Spin−Spin Coupling Constants in the Corresponding Minima Jmin Jmin Tp1 Tp2 Tp3 Cp9

⟨J ⟩ =

Javeraged

J(Si1−H)

J(Si2−H)

JTS

⟨J(Si1−H)⟩

⟨J(Si2−H)⟩

⟨J⟩

−55.01 −73.64 −136.28 −17.87

−13.11 +2.09 −15.47 −8.32

−30.86 −25.06 −66.04 −11.81

−54.29 −76.18 −123.93 −19.35

−16.42 +0.89 −29.44 −8.66

−35.32 −37.66 −76.67 −13.96

∭ |Ψ(X , Y , Z)|2 J(X , Y , Z)dX dY dZ

where ⟨J⟩ is the average spin−spin coupling constant, J(X,Y,Z) is the spin−spin coupling constant corresponding to a particular geometrical configuration (X,Y,Z), and Ψ(X,Y,Z) is the ground-state vibrational wave function. At a finite temperature, excited-state vibrational wave functions would be needed as well. Since such a computation would involve a prior calculation of J(Si−H) at very many molecular configurations, it is replaced by a finite summation over a limited number N of configurations according to eq 4 (N = 60 for Tp1 and Tp2; N = 80 for Tp3, Cp9)): N

⟨J ⟩ =

∑m = 1 |Ψ(X m , Ym , Zm)|2 J(X m , Ym , Zm) N

∑m = 1 |Ψ(X m , Ym , Zm)|2

■

CONCLUSIONS This work demonstrates that rhodium bis(silyl) hydride complexes tend to form an asymmetric arrangement of silyl and hydride ligands with two different Si···H distances. Nevertheless, in many cases the hydride ligand simultaneously interacts with both silyls. The hydride can be transferred from one silyl to the other, with energy barriers varying from 0 to 4 kcal·mol−1. Various density functionals and the MP2 method yield substantially different geometries of the bis(silyl) hydride complexes. Hence, care must be exercised when choosing a method for production calculations. In some cases the M06L and M062X functionals underestimate the Si−H distances, while TPSSh sometimes tends to overestimate them. MP2, B3LYP, and BP86 overestimate them in nearly all cases, whereas B3LYP in some cases incorrectly yields a η1-silyl-η2silane coordination. By comparison with the single-point CCSD results we conclude that the TPSSh and M06L functionals usually perform better than the other methods. For the complexes under study, the hydrogen transfer barrier varies between 0 and 3.4 kcal·mol−1. The Cp complexes typically have higher barriers than the Tp complexes. Among the complexes with a relatively low barrier (0−1.5 kcal·mol−1), somewhat smaller values are found for complexes with a shorter Si···Si distance. However, for the entire set of Cp and Tp complexes, the hydrogen transfer barrier does not obviously correlate with geometry parameters. To study the hydrogen dynamics in the Si···H···Si fragment, four complexes with relatively low hydrogen transfer barriers were selected. The three-dimensional PESs were constructed and the vibrational Schrödinger equation was solved in the resulting potentials. The PES turns out to be highly anharmonic for all these complexes, as demonstrated by much lower anharmonic vibrational frequencies compared to those computed within the harmonic approximation. Based on the analysis of the ground-state vibrational wave functions in these systems, a classification of the complexes according to the character of the hydrogen motion can be proposed. A single-maximum vibrational wave function, corresponding to hydrogen delocalization between both silyls, is found in complexes with a single-well potential or with a very low barrier such as TpRh(SiH3)2(SiMe3)(H) (ΔE = 0.03 kcal·mol−1). The delocalized hydride behavior can occur also in the case of a significant barrier, if both minima and the transition states are located on the PES in close proximity to each other, as is the case for the complex CpRh(SiMe3)2(SiF3)(H) (ΔE = 0.64 kcal·mol−1). On the contrary, in the systems with a relatively high barrier, such as TpRh(SiH3)2(PMe3)(H)+ (ΔE = 1.13 kcal·mol−1), the hydride behaves as a classical particle, as manifested by a wave function with two well-separated maxima localized near the

(3)

(4)

Owing to this approximation, our results should be regarded as semiquantitative. The results and their comparison with “static” J(Si1−H) and J(Si2−H) values in the minima and the transition states are represented in Table 7. Two versions of averaged J are given: the first one corresponds to the local vibration around a minimum (⟨J(Si1−H)⟩ and ⟨J(Si2−H)⟩); the second, denoted ⟨J⟩, to the delocalized motion or fluctional behavior. The latter one is essentially an arithmetic mean of the former. For complexes Tp1, and Cp9, both J(Si1−H) and J(Si2−H) are negative, thus corroborating the existence of the double Si···H···Si interaction. The same is true even for complex Tp3, where the Si2···H separation is more than 2.3 Å and the Mayer bond order is nearly vanishing. However, for complex Tp2, J(Si2−H) is slightly positive, meaning that the lack of the direct interaction for the Si···H separation of 2.41 Å is very large in this case. For complexes Tp1, Tp2, and Cp9, there is no large difference between spin−spin coupling constant Jmin in the minimum and corresponding averaged values ⟨J(Si1−H)⟩ and ⟨J(Si2−H)⟩. However, for complex Tp3 taking the vibrations into account results in a nearly double value of J(Si2−H). This is accounted for by the fact that the vibrational wave function is quite large both near the minima and near the transition state. This increases the probability of finding the hydride at Si2···H distances smaller than the equilibrium one, leading to a higher ⟨J(Si2−H)⟩. Interestingly, the spin−spin coupling constant in the transition state JTS is quite different from the averaged value ⟨J⟩ (given in the rightmost column of Table 7) even for the complexes with a delocalized vibrational wave function. On the other hand, ⟨J⟩ turns out to be quite close to the arithmetic mean of the local spin−spin coupling constants J(Si1−H) and J(Si2−H) in minima. This provides a justification of the common procedure of computing coupling constants for fluctional molecules as a weighted average of the values calculated in PES minima. K


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PES minima. The hydrogen transfer is coupled with Si−Si motion in this case. An intermediate situation between localized and delocalized hydride behavior is also possible, when the vibrational wave function has two weakly pronounced maxima. In this case there is virtually no coupling between the H and Si−Si motion, with tunneling accounting for a large part of the hydrogen transfer. The maximum wave function path is a straight line, showing that the hydrogen transfer is independent from the Si−Si distance contraction. The example is the complex TpRh(SiF3)2(PMe3)(H)+ (ΔE = 0.25 kcal·mol−1). In the complexes TpRh(SiH 3 ) 2 (SiMe 3 )(H), TpRh(SiF3)2(PMe3)(H)+, and CpRh(SiMe3)2(SiF3)(H) both spin− spin coupling constants J(Si1−H) and J(Si2−H) are negative, which is indicative of direct simultaneous Si···H···Si interactions. Conversely, J(Si 2 −H) for complex TpRh(SiH3)2(PMe3)(H)+ is slightly positive, indicating the absence of a Si2···H interaction. The vibrationally averaged spin−spin coupling constants are quite close to the arithmetic mean of J(Si1−H) and J(Si2−H), which justifies the widely used procedure of calculating ⟨J⟩ by averaging the corresponding values in the minima.

■

ASSOCIATED CONTENT

S Supporting Information *

Jacobi coordinates for triatomic system, linear least-squares method for three-dimensional case, weights used for fitting, polynomial coefficients for Tp1, Tp2, Tp3, and Cp9, and derivation of the Hamiltonian matrix elements are available. Tables of atomic coordinates for minima and transition states of complexes Cp1−Tp3 are also included. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +34-972-418362. Fax: +34-972-418356. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to Professor G. I. Nikonov of Brock University, Canada, for a stimulating discussion. Financial support from the Spanish Ministerio de Ciencia e Innovación (grant CTQ201123156/BQU) and the European Fund for Regional Development (grant UNGI08-4E-003) is gratefully appreciated. Y.H. thanks the Universitat de Girona for a graduate fellowship.

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REFERENCES

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Hydride Complexes - American Chemical Society

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