Dispersion-Energy-Driven Wagner–Meerwein Rearrangements in Oligosilanes

The installation of structural complex oligosilanes from linear starting materials by Lewis acid induced skeletal rearrangement reactions was studied under stable ion conditions. The produced cations were fully characterized by multinuclear NMR spectroscopy at low temperature, and the reaction course was studied by substitution experiments. The results of density functional theory calculations indicate the decisive role of attractive dispersion forces between neighboring trimethylsilyl groups for product formation in these rearrangement reactions. These attractive dispersion interactions control the course of Wagner–Meerwein rearrangements in oligosilanes, in contrast to the classical rearrangement in hydrocarbon systems, which are dominated by electronic substituent effects such as resonance and hyperconjugation.


Experimental Part
All manipulations of air-and moisture-sensitive compounds were carried out under an argon or nitrogen atmosphere using Schlenk techniques or a standard glove box (Braun Unilab). Glassware was dried in an oven at T = 120 °C and evacuated prior to use. The solvents tetrahydrofuran (THF), benzene and toluene were dried over sodium and distilled under a nitrogen atmosphere.
After removal of the solvent, the product 19 was obtained as colorless wax (

Cation Preparation
For the preparation of polysilanyl cations trityl tetrakis(pentafluorophenyl)borate was used. The NMR characterization data for the anion are given below and not repeated for each preparation reaction. Negligible differences compared to these data were found for the NMR chemical shifts or coupling constants of the anion depending on the solvent or temperature.
[B(C 6 Synthesis of hydrogen-bridged silyl borate 8[B(C 6 F 5 ) 4 ] from 2,5-dihydridohexasilane 5 92 mg (1 equiv., 0.10 mmol) of trityl tetrakis(pentafluorophenyl)borate was evacuated in the NMR tube and then cooled to T = -80 °C. A solution of 47 mg (1 equiv., 0.10 mmol) of 2,5dihydridohexasilane 5 [6] in chlorobenzene-d 5 (0.7 mL) was added to the cold trityl borate via a syringe. The addition was performed so slowly that the solution froze before it reached the trityl borate. The NMR tube was slowly allowed to warm until the solvent melted and the silane slowly reached the trityl borate. At that point, the NMR tube, which was wrapped in a gauze bandage soaked by T = -70 °C cold ethanol, was quickly shaken with a vortex mixer and then quickly transferred to the NMR spectrometer pre-cooled to T = -30 °C.

S-9
Trapping reaction of hydrogen-bridged silyl cation 8 [8] 0.1 mL (0.10 mmol, 1 M in toluene) of sodium triethylborohydride was added to the NMR sample of bis-silyl borate 8[B(C 6 F 5 ) 4 ] at T = -30 °C. The mixture was allowed to warm to room temperature and the NMR spectra were recorded. The NMR data are identical with reported literature data. [8]       S-13

Computational Details
General All quantum chemical calculations were carried out using the Gaussian09 package, Versions B01 and D01. [9] The molecular structure optimizations were performed using the M06-2X functional [10] along with the 6-311+G(d,p) basis set. Every stationary point was identified by a subsequent frequency calculation either as minimum (Number of imaginary frequencies (NIMAG): 0) or transition state (NIMAG: 1). Table S1     S-17

Calculations of the PES and Reaction Coordinates
The structure optimization of the non-hydrogen-bridged cations 6, 13, 15 and 16 revealed a strong tendency for these cations to form intramolecularly stabilized structures. As an example, structure optimizations for the polysilanyl cation 6 are documented here in more detail. Figure S12 shows the progress of the structure optimization at the M062X/6-311+G(d,p) level for a molecular arrangement which corresponds to anti-6. The data shown in Figure S12 indicates that there is no stationary point that resembles anti-6. Instead, cation 13 in its syn-conformation is formed during the structure optimization. In contrast, a stationary point was located for a molecular arrangement corresponding to syn-6 ( Figure S13)  Table S1).
Parts of the potential energy surface (PES) connecting cations 7, 8 and 14 were calculated for the isolated cations in the gas phase ( Figure S15). Figure S16 shows the PES determined for the cation/chlorobenzene complexes in the gas-phase. The results of calculations using the polarized continuum model (PCM) to mimic the influences of the solvent chlorobenzene on the structure optimizations of the cation/chlorobenzene complexes are summarized in Figure 5 in the main text.
All three PESs show the same signature for the relative energies of the supposed intermediates. The main difference occurs between the calculations for the free cations and the solvent complexes. As  Figure S16 and Figure 5). We started an intensive computational search for transition states on all three PES shown in Figures S15, S16 and 5, which was however not successful as we were not able to locate transitions states, which are relevant for the investigated rearrangement reactions. Only transition states belonging to methyl-or silyl group rotations were found as indicated by the inspection of the respective imaginary frequency. Therefore, we have to (calculated for the complex 6(PhCl)).
The PESs calculated for the Germanium containing cations and their chlorobenzene complexes are very similar in their signature and in their relative energies to the persila case (compare Figures S15/S17 and S16/S18). For the free cations in the gas phase ( Figure S17      S-23

Evaluation of the Effect of Dispersion Interaction
In general, the effect of dispersion interactions is already taken into account by using the M06-2X functional. To our experience this functional provides optimized molecular structures that are close to those obtained from experimental methods. These theoretical structures are also a good basis for reliable NMR calculations. For a quantitative evaluation of the size of the dispersion energy contribution to the relative stability of the investigated cations molecular structure optimizations with the standard B3LYP functional were performed. [12] The obtained structures and energies were then compared to results from B3LYP/D3 calculations, which uses Grimme's D3 dispersion correction. [13,14] The evaluation of the energetic effects is given in the main text. For a comparison of structural data, see Table S3 in which we compiled data of hydrogen-bridged cation 8 obtained with the different methods. In general, the interatomic distances computed with the different methods are very similar. The exception here is the molecular structure computed with the standard B3LYP functional that predicts the longest Si -Si bonds from all methods tested here. Of particular interest is the fact that the central Si2 -Si3 bond is calculated with the standard B3LYP to be 244 pm which is 3 pm longer than predicted by the dispersion corrected B3LYP/D3 and 6 pm longer than calculated using the M06-2X method (Table S3). Clearly, this is also a structural indication for the attractive dispersion interactions operating in the hydrogen-bridged cation 8.

Substituent Effects on the Stability of Molecules with Cationic Si -H -Si -Bridges
The effect of silyl groups on the thermodynamic stability of carbocations is well documented and in particular, the so-called -silyl effect is significant for the stability of carbocations. [15,16] Therefore, we probed the effect of trimethylsilyl substitution on the stability of hydrogen-bridged silyl cations by calculating the reaction energy of isodesmic reactions S1 and S2. Equation S1 evaluates the -effect of four trimethylsilyl groups (as in cation 7) and equation S2 probes the -effect of four trimethylsilyl groups as in cation 8, in both cases compared to substituent effect of methyl groups. Finally, the isodesmic reaction S3 compares the effect of the substituents on the relative stability of the isomeric cations 7 and 8. The results obtained using different density functionals are summarized in Table S4   Table S4. Calculated reaction energies for equation S1-3. S1 -effect [kJ mol -1 (Table S4, eq S1).
More interesting is the small size of the -effect. According to eq. S2 cation 8 is stabilized by only -24 kJ mol -1 compared to the permethylated cation 21. The relative small size of the effect compared to those calculated for carbocations can be attributed (i) to the long Si + -Si  bonds, which severely hampers the orbital overlap required for hyperconjugation, and, (ii) to the conformation of S-25 the cyclic cation 8, which prevents an optimal alignment of the Si  -SiMe 3 bonds for hyperconjugation in respect of the LUMO of the cation (see Figure S19 for the molecular structure and the depiction of the LUMO). The LUMO of the molecule is in essence an antisymmetric combination of unoccupied 3p(Si) atomic orbitals directed to the bridging H-Atom. The -effect of the four trimethylsilyl groups in cation 7 is larger than the -effect of these substituents in cation 8.
Consequently, the net result of both stabilizing electronic substituent effects is a destabilization of cation 8 compared to cation 7 by 13 kJ mol -1 . This result contradicts the direct comparison of the calculated absolute energies of the two isomeric cations, which predicts cation 8 to be more stable than cation 7 by -31 kJ mol -1 . Furthermore, the higher thermodynamic stability of cation 8 versus cation 7 is in agreement with the experiment. Obviously, the more favorable attractive dispersion forces between the vicinal trimethylsilyl groups in cation 8 overrule the unfavorable balance of the electronic substituent effects. This fact points to the decisive role that attractive dispersion forces play in these systems.
Calculations using the dispersion corrected B3LYP/D3 functional result in nearly identical results (see Table S4). In contrast, the standard B3LYP functional predicts a smaller -effect but larger -effect. In consequence, calculations based on the standard B3LYP functional predict a net stabilization of cation 8 compared to cation 7 by the electronic substituent effects. A clear analysis of the influence of dispersion on the reaction energies of the isodesmic reaction S1-3 is however not straightforward.
Dispersion energy contributions are also important for silanes and the effects are even greater than calculated for the cations. For example, the energy difference calculated for the silanes 5 and 9 at B3LYP is -3 kJ mol -1 in favor of silane 5, while the dispersion corrected B3LYP/D3 method favors silane 9 by -36 kJ mol -1 . Therefore, the effect of the dispersion energy for the silanes 5 and 9 is -39 kJ mol -1 in favor of silane 9. The same calculations reveals an additional stabilization of cation 8 compared to cation 7 by only -11 kJ mol -1 . This imbalance makes an easy breakdown of the isodesmic reactions S1-S3 in terms for the electronic substituent effects and dispersion energy effects not straightforward and only the net effects of the trimethylsilyl substituents (dispersion + electronic) are evaluated. S-26