Hydrogen Tunneling in Catalytic Hydrolysis and Alcoholysis of Silanes

Abstract An unprecedented quantum tunneling effect has been observed in catalytic Si−H bond activations at room temperature. The cationic hydrido‐silyl‐iridium(III) complex, {Ir[SiMe(o‐C6H4SMe)2](H)(PPh3)(THF)}[BArF 4], has proven to be a highly efficient catalyst for the hydrolysis and the alcoholysis of organosilanes. When triethylsilane was used as a substrate, the system revealed the largest kinetic isotopic effect (KIESi−H/Si−D=346±4) ever reported for this type of reaction. This unexpectedly high KIE, measured at room temperature, together with the calculated Arrhenius preexponential factor ratio (AH/AD=0.0004) and difference in the observed activation energy [(E aD −E aH )=34.07 kJ mol−1] are consistent with the participation of quantum tunneling in the catalytic process. DFT calculations have been used to unravel the reaction pathway and identify the rate‐determining step. Aditionally, isotopic effects were considered by different methods, and tunneling effects have been calculated to be crucial in the process.


Catalytic experiments
A closed reaction vessel equipped with a pressure transducer (Manonthemoon kinetic kit X102) [2] was immersed in a thermostated ethylene glycol/water bath and charged with the catalyst (1, 4.2 mg, 0.0025 mmol; 2, 1.9 mg, 0.0025 mmol; and [Ir(cod)Cl]2, 0.85 mg, 0.00125 mmol) in 1 mL of distilled THF and H2O or alcohol (2.5 mmol). Once the pressure of the system was stabilized, the silane (0.25 mmol) was added, which was considered initial reaction time. The solution was left stirring until the pressure stabilized again, which was indicative that the reaction ended. Then, the reaction mixture was filtered through a small silica pad eluting with pentane to remove the catalyst, and the solvent was removed under vacuum. The residue was analyzed by 1 H NMR in CDCl3. The quantity of gas evolved was calculated from the measured pressure inside the reaction vessel following the ideal gases law equation (reactor volume 13.2 mL).

Topographic maps of silanes
Steric maps were evaluated with the SambVca 2.0 package.The radius of the sphere around the centre atom was set to: 3.5 Å or 5 Å, distance from the centre of the sphere: 2.26 Å, mesh spacing: 0.1 Å, H atoms omitted and atom radii: Bondi radii scaled by 1.17, as recommended by Cavallo. [3] Figure S8. Topographic maps and percent buried volume for Et3SiH, Me2PhSiH, MePh2SiH and Ph3SiH.

Catalytic studies
Hydrolysis of silanes using 1 Figure S9. Reaction profiles (equivalents of H2 vs time) and first-order plots for the hydrolysis of different silanes using 1 (1 mol %) as precatalyst at 25 ºC.

Theoretical Procedures
All calculations were carried out within the Density Functional Theory (DFT), [4,5] using the Gaussian16 program package. [6] In order to determine the reaction mechanism, the following procedure was followed.
First, geometry optimizations were performed by using the M06 exchange-correlation functional, [7] combined with the 6-31+G(d,p) basis set for the non-metal atoms, [8,9] and the ECP60MDF Sttutgart-Cologne relativistic core potentials along with the aug-cc-pVDZ-PP basis set for Ir, [10] taking into account solvent effect (THF) by means of the integral equation formalism of the polarized continuum model (IEFPCM). [11] After the geometry optimizations, harmonic vibrational frequencies were obtained by analytical differentiation of gradients, at the same level of theory, to identify whether the characterized structures were true minima. Such frequencies were then used to evaluate the zero-point vibrational energy (ZPVE) and the thermal (T = 298 K) vibrational corrections to the Gibbs free energy (G corr ). Then, single-point calculations using the 6-311++G(2df,2p) basis set [12] for non-metal atoms and same ECP combined with aug-cc-pVTZ-PP basis set for Ir, [10] were performed on the optimized structures to refine the electronic energy (Eelec). In this vein, the Gibbs free energies (G sol ) of each species in solution were calculated as follows: equation (1) Finally, these free energy values were used to calculate the DG values of the reaction mechanism. This reaction mechanism is depicted in Figure 7 of the manuscript, and the corresponding species are depicted in Figure S25. Figure S25. Representation of the calculated geometries corresponding to the intermediates and transition states involved in the mechanism represented in Figure 7 of the manuscript.

Calculation of the theoretical Kinetic Isotope Effect by means of Eyring and Bigeleisen-Mayer approaches, including Wigner and Bell Inverse Parabola tunneling corrections
The theoretical Kinetic Isotope Effect (KIE), without the consideration of tunneling effects, is calculated as the ratio between the calculated reaction rate constant for H and D: In order to calculate these reaction rate constants, Transition State Theory is applied. In this vein, Substituting these expressions in the expression we obtain the following: Other method to calculate Kinetic Isotope Effects is the Bigeleisen-Mayer method. [13,14] This method is more sophisticated than the Eyring one, but no tunneling corrections are included. Hence, Wigner tunneling correction [15][16][17] and the Bell Inverse Parabola [18] correction have been considered as well. Both Wigner and Bell's methods are one dimensional approaches for tunneling.
In Wigner approach, tunnel corrections are considered very simply as a function of the imaginary frequency of the reaction coordinate at the TS structure.
According to the calculated imaginary frequency for H (-589 cm -1 ), and D (-428 cm -1 ) in TS1, the correction factor would take the following values for and .
Hence, considering Wigner tunneling correction and the calculated imaginary frequencies for H and D, the corrected KIE would be increased by a factor of , which is not enough to explain the large observed experimental KIE values.
In the Bell's approach, the shape of the PES at the TS is approached as an inverse parabola. It is a bit more sophisticated than Wigner's approach, but large errors are associated to these methods for H transfer. Nevertheless, they may be used as indicative of tunneling when they increase the calculated Bigeleisen KIE value. [19] We have calculated the KIE values according to these 3 methods, namely, Bigeleisen-Mayer, Wigner and Bell as implemented in the p-quiver program. [20] and are collected in Table   S2 along with the Eyring KIE value.

Calculation of the KIE considering quantum tunneling by means of the WBK method
In order to calculate the Potential Energy Surfaces for H/D transfer tunneling, we focused on the imaginary frequency of the TS1 structure. Its value is calculated to be -589 cm -1 for H transfer.
Visualization of this normal mode shows the H transfer from HSi(Et)3 to Ir catalyst, as expected for this H/D transfer process. IRC calculations [21,22] Figure S26) and three for D (at 9.21 kJ/mol, 27.62 kJ/mol and 46.04 kJ/mol, red dashed lines in Figure S26). We are aware that this harmonic approach is accurate near C0, while the accuracy decreases near TS1 due to the anharmonicity of the PES. Nevertheless, from a qualitative point of view this approach is sufficient to take into account the tunneling effects from excited vibrational levels. Hence, in order to calculate the tunneling transmission coefficient for H and D, the probability of tunneling from all available energy levels should be considered, along with the population of each level.
According to the Wentzel-Kramers-Brillouin (WKB) semiclassical approach, [23] the probability of tunneling from each level can be calculated by the next expression being V(x) the calculated one-dimensional PES and E the energy associated to the vibrational level. The population of each vibrational level (PBi) can be calculated according to Boltzmann distribution function for a given temperature. The calculated values are collected in Table S3. Having into account these values, the transmission probability ( ) is calculated by averaging the tunneling probability from each energy level taking into account its population.
Notice that in this formulation the value of ranges from 0 to 1, and its physical meaning is to provide the probability of tunneling per event. Hence, in order to obtain the effect of tunneling in the rate constant, one should multiply this probability by the number of events occurring during a second, i.e. the vibrational frequency. So, the tunneling rate (k tun ) would be obtained as the product of and the frequency the vibration takes place: In this vein, in order to move from C0 to C1 in the reaction mechanism, H/D have two paths. One, moving above the barrier (Eyring or Bigeleisen), and the other by moving through tunneling. Hence, the reaction rate constant would be the sum of both events.
If the tunneling effect is negligible, then the rate constant is governed by the barrier height, but as tunneling importance increases its influence in the rate constant is more important. Taking  In Table S4 we provide all these results, calculated according to the procedure described above. and total theoretical KIE (KIE theo ), at different temperatures (K) are given.   As can be observed from the values given in Table S6, the behavior of the with temperature is correctly described by the . This behavior comes from the fact that increases with the temperature more than , once higher vibrational levels become available for D. As a consequence, the KIE decreases.