The calculation of ²⁹Si NMR chemical shifts of tetracoordinated silicon compounds in the gas phase and in solution

Abstract

Aiming at the identification of an efficient computational protocol for the accurate NMR assessment of organosilanes in low-polarity organic solvents, ²⁹Si NMR chemical shifts of a selected set of such species relevant in organic synthesis have been calculated relative to tetramethylsilane (TMS, 1) using selected density functional and perturbation theory methods. Satisfactory results are obtained when using triple zeta quality basis sets such as IGLO-III. Solvent effects impact the calculated results through both, changes in substrate geometry as well as changes in the actual shieldings. Spin–orbit (SO) corrections are required for systems carrying more than one chlorine atom directly bonded to silicon. Best overall results are obtained using gas phase geometries optimized at MPW1K/6-31+G(d) level in combination with shielding calculations performed at MPW1K/IGLO-III level in the presence of the PCM continuum solvation model.

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Introduction

The measurement of ²⁹Si NMR chemical shifts is exceedingly helpful in elucidating the identity of silicon-containing molecular systems.^1–13 This is not only true for stable reactants and products of well-defined transformations, but also for silicon-based species generated as transient intermediates in the course of a reaction.¹⁴ In this latter case the combination of theoretically predicted and experimentally measured ²⁹Si NMR chemical shifts is particularly helpful, as was amply demonstrated in detailed studies of, for example, silylenes¹⁵ and disilenes.¹⁶ When attempting to follow the course of base-catalyzed silylation reactions of alcohols, which constitute an important protecting group strategy in organic synthesis,^17,18 we were confronted with the appearance of a number of silicon-based species with rather similar chemical shifts in the solution-phase ²⁹Si NMR spectra.¹⁹ With the goal of identifying a computational protocol for the accurate theoretical prediction of the respective chemical shifts in low-polarity organic solvents, we analyze here the performance of strategies based on DFT- and MP2-level calculations.^20–27 Our particular emphasis will be on the effects of geometry optimization, methods for actual shift calculations, the modeling of solvent effects, and the evaluation of relativistic effects.

Results and discussion

The effects of geometry optimization

We first investigated the influence of molecular structures optimized using several computationally efficient methods on the quality of ²⁹Si chemical shifts evaluated on these structures at MP2(FULL)/IGLO-III level. These calculations were performed using SiMe₃Cl (2) as a model system for silyl chloride reagents used in organic synthesis. Experimentally measured chemical shifts for this system are available in selected solvents at room temperature such as benzene with δ(²⁹Si, 2) = +30.21 ppm,²⁸ benzene-d₆ with δ(²⁹Si, 2) = +30.64 ppm,²⁹ toluene-d₈ with δ(²⁹Si, 2) = +30 ppm,³⁰ and CDCl₃ with δ(²⁹Si, 2) = +30.7 ppm.³¹ It thus appears that organic solvents of intermediate polarity have only a very limited influence on the ²⁹Si chemical shift in 2. Using microwave spectroscopy the gas phase Si–Cl bond distance in 2 has been determined in two separate studies as r(Si–Cl, 2) = 202.2 ± 5 pm³² and 203 pm.³³ In the solid state the Si–Cl bond distance has been determined to be of comparable length at r(Si–Cl, 2) = 209 pm,³⁴ 201.0 pm (0.23 GPa and 296 K),³⁵ and 208.6 pm (0.1 MPa and 157 K).³⁶

The marked dependence of computed chemical shifts on the molecular structure is illustrated in Fig. 1, which displays ²⁹Si chemical shifts calculated for SiMe₃Cl (2) at MP2(FULL)/IGLO-III level employing structures optimized at various levels of theory in combination with the 6-31+G(d) basis set (the results obtained from MP2(FULL)/IGLO-III geometry optimizations are included as a reference). ²⁹Si chemical shifts evaluated for various points along a relaxed scan (MPW1K/6-31+G(d) structures) of the Si–Cl distance in 2 from 200 to 300 pm (solid line in Fig. 1) show an almost linear dependence with larger Si–Cl distances leading to systematically higher chemical shifts. This trend is also visible in the δ(²⁹Si) data evaluated on molecular structures fully optimized with different methods in the gas phase (Fig. 1, solid circles): the shortest Si–Cl bond distances (about 208.5 pm) are obtained in MPW1K and MP2(FC) optimizations, while the other density functionals tested yield longer Si–Cl bonds reaching 211 pm obtained with the B3LYP hybrid functional. The shift values calculated for these gas phase geometries at MP2(FULL)/IGLO-III level vary by approx. 2 ppm from +29.7 to +32.0 ppm. As detailed further below, use of the PCM solvent model for structure optimization (Fig. 1, empty squares) leads to systematically longer Si–Cl bonds and, correspondingly, to systematically higher δ(²⁹Si) values, with larger deviations from experiment for the cases tested.

Fig. 1 Calculated δ(²⁹Si) values for SiMe₃Cl (2) (MP2: solid circles and PCM/MP2: empty symbols; IGLO-III basis set) using molecular structures optimized at various levels of theory using the 6-31+G(d) basis set. Dashed line: experimental value in CDCl₃; solid line: relaxed scan along the Si–Cl bond (gas phase, MPW1K structures). Empty circles: PCM/MP2 shifts on gas phase structures; empty squares: PCM/MP2 shifts on solution-phase geometries (all solvent calculations: CHCl₃, UAHF radii).

We further explored whether chemical shift predictions can be improved through the use of more sophisticated basis sets in gas phase geometry optimizations for selected Pople-style and correlation consistent (cc) basis sets (Table 1). Use of the systematically developed cc basis sets results in a systematic decrease of Si–Cl bond distances in the order cc-pVDZ, cc-pVTZ, and cc-pVQZ, irrespective of the theoretical method used. This directly impacts the ²⁹Si chemical shift calculations performed at MP2(FULL)/IGLO-III level, where shorter Si–Cl bonds are again observed to yield lower shift values. A comparable trend is not observed for Pople-style basis sets of double- and triple-zeta quality. Among all quantum mechanical methods the MP2(FC) level is most strongly affected by these variations. Taking the MP2(FC)/cc-pVQZ structure as reference, the best agreement is observed at the MPW1K/6-31+G(d) level, which was therefore chosen for all subsequent geometry optimizations.

Table 1 Influence of basis set choice on the gas phase geometry optimized with various methods and the gas phase ²⁹Si chemical shift of 2 (evaluated at MP2(FULL)/IGLO-III level)

Basis set	PBE1PBE		MPW1K		M06-2X		MP2(FC)
	r(Si–Cl) (pm)	δ(^29Si) (ppm)	r(Si–Cl) (pm)	δ(^29Si) (ppm)	r(Si–Cl) (pm)	δ(^29Si) (ppm)	r(Si–Cl) (pm)	δ(^29Si) (ppm)
6-31+G(d)	209.5	+30.84	208.3	+30.32	209.4	+31.02	208.5	+29.70
6-31+G(2d,p)	209.6	+31.81	208.5	+31.37	209.5	+31.90	210.2	+32.60
6-31++G(2d,p)	209.6	+31.82	208.5	+31.38	209.5	+31.92	210.3	+32.63
6-31++G(2df,p)	208.9	+30.90	207.8	+30.43	211.4	+34.14	208.5	+30.44
6-311++G(2d,p)	209.4	+31.82	208.3	+31.31	209.3	+31.90	209.9	+32.30
cc-pVDZ	211.2	+32.98	210.2	+32.63	211.1	+33.16	210.7	+31.83
cc-pVTZ	209.1	+31.23	208.1	+30.81	209.1	+31.39	208.6	+30.79
cc-pVQZ	208.5	+30.77	207.6	+30.36	208.5	+30.92	207.8	+30.24

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Theoretical methods for chemical shift calculations

Chemical shift calculations at MP2(FULL)/IGLO-III level are quite challenging for larger molecular systems and an effort has therefore been made to identify more economical approaches. Table 2 displays ²⁹Si shift values for SiMe₃Cl (2) computed with selected combinations of methods and basis sets based on the MPW1K/6-31+G(d)-optimized geometry. Compared to the experimental value of δ(²⁹Si, 2) = +30.7 ppm³¹ largest deviations are found for the 6-311++G(2d,2p)²⁶ basis set, while the def2-TZVP,^37,38 cc-pVTZ,³⁹ and IGLO-III⁴⁰ triple zeta basis sets yield generally better results. The quadruple zeta pcS-3 basis set specifically developed for NMR calculations⁴¹ performs as well as IGLO-III, but its use is computationally significantly more demanding. We note that second-order perturbation theory in its canonical (MP2) or local (LMP2) variants perform best, closely followed by the HCTH407⁴² and MPW1K²⁰ hybrid functionals. Interestingly, the DF-LMP2/IGLO-III⁴³ calculations closely reproduce the much more costly MP2(FULL)/IGLO-III calculations, which we chose as reference method for ²⁹Si chemical shift calculations. The worst performer found here is clearly the M06-2X⁴⁴ functional, which responds more sensitively to the individual basis set design than any other method listed in Table 2. The deviations of MPW1K and HCTH407 are comparable to those of the MP2 methods and the performance of these two methods is better than that of the other DFT methods tested here.

Table 2 Calculated δ(²⁹Si) chemical shifts for 2 using different theoretical methods and basis sets^a

Method^b	6-311++G(2d,2p)	Def2-TZVP	cc-pVDZ	cc-pVTZ	cc-pVQZ	pcS-3	IGLO-III
a Geometries optimized with MPW1K/6-31+G(d). b Method used for NMR chemical shift calculations.
HCTH407	+35.00	+32.37	+32.63	+32.91	+26.37	+31.94	+31.40
B3LYP	+36.37	+34.29	+34.13	+34.14	+27.60	+33.44	+32.94
B3PW91	+36.84	+34.92	+35.31	+34.64	+28.78	+34.15	+33.66
PBE1PBE	+36.56	+34.68	+35.35	+34.83	+29.37	+33.93	+33.31
MPW1K	+34.83	+33.06	+33.89	+33.59	+28.09	+32.44	+31.88
M06-2X	+42.67	+38.10	+38.85	+31.00	+36.82	+35.64	+37.24
DF-LMP2	+33.05	+31.47	+31.36	+33.09	+29.55	+30.25	+28.40
MP2(FULL)	+33.65	+31.92	+30.71	+32.54	+28.59	+31.31	+30.32

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Solvent effects

The experimental reference shift data for SiMe₃Cl (2) has been determined in apolar organic solvents such as CDCl₃ or benzene. As a first straightforward approach to account for solvent effects we performed shift calculations in combination with the polarizable continuum model (PCM) for chloroform at PCM/MP2(FULL)/IGLO-III level based on the MPW1K/6-31+G(d) gas-phase geometry, which leads to downfield shifts of the ²⁹Si signal in SiMe₃Cl (2) by 1.5–2.0 ppm relative to the gas phase value (+30.32 ppm), depending on the particular PCM variant employed (Table 3). An additional downfield shift of the same magnitude is obtained upon inclusion of the polarizable continuum also for geometry optimization at PCM/MPW1K/6-31+G(d) level owing to the elongated Si–Cl bond present in the optimized structure (Table 3). From a glance at the data compiled in Table 3 it is apparent that the particular choice of the atomic radii used to construct the solute cavity in the PCM calculations has only a minute influence on structures and chemical shifts.

Table 3 Influence of continuum solvation models on ²⁹Si chemical shift calculations (PCM/MP2(FULL)/IGLO-III) for SiMe₃Cl (2)

	Gas-phase structure^a		Solution-phase structure^b
	r(Si–Cl) (pm)	δ(^29Si) (ppm)	r(Si–Cl) (pm)	δ(^29Si) (ppm)
a Optimized at MPW1K/6-31+G(d) level. b Optimized in CDCl3 with different solvation models at MPW1K/6-31+G(d) level.
PCM(UFF)	208.4	+31.80	210.19	+34.34
PCM(UAHF)	208.4	+32.15	210.40	+35.00
PCM(UAKS)	208.4	+32.15	210.40	+35.00
SMD	208.4	+32.28	210.48	+35.22

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A more detailed picture is presented in Fig. 1 above, where the PCM/MP2(FULL)/IGLO-III shift data using the gas-phase geometries (empty circles) and the solution-phase geometries (empty squares) for selected hybrid DFT methods are shown. Taking the MPW1K/6-31+G(d) gas phase geometries as an example, we can see that the PCM(UAHF)/MP2(FULL)/IGLO-III shifts are 1.7 ppm larger as compared to the gas phase MP2(FULL)/IGLO-III shifts. This is also found for all other methods used for geometry optimization. Reoptimizing the geometry of SiMe₃Cl (2) in the presence of the PCM reaction field leads to elongation of the Si–Cl bond, which at PCM/MPW1K/6-31+G(d) level reaches up to 210.4 pm. This geometrical change is accompanied by a downfield shift in the ²⁹Si resonance to +35.0 ppm. This is found in a very similar manner also for all other methods used for geometry optimization and we may thus conclude that the PCM continuum solvation model impacts ²⁹Si shift calculations in a significant way through changes in the molecular structure.

Effects of explicit solvation were subsequently explored for complexes of SiMe₃Cl (2) with one molecule of CHCl₃. A number of minima were identified in MPW1K/6-31+G(d) geometry optimizations (Fig. 2). The longest Si–Cl bond with 209.5 pm (and thus the largest downfield shifted ²⁹Si signal) is found for solute–solvent complex 2_3, in which the chlorine atom of SiMe₃Cl forms a hydrogen bond to chloroform (Table 4). In terms of gas phase free energies ΔG₂₉₈ structure 2_3 is not the most stable conformer, but is 7 kJ mol⁻¹ less stable than the best structure 2_1. Due to only weak interactions between the methyl groups of 2 and chlorine atoms of the solvent molecule, the Si–Cl distance in structure 2_1 is hardly different from that of 2 alone. After Boltzmann averaging, δ(²⁹Si) is only +0.18 ppm higher than the experimental result. In solution phase, the most stable structure is 2_3. The continuum solvation model increases the Si–Cl distance and also reduces the energy gap between different conformers. With the PCM solvent model δ(²⁹Si) values are 5 ppm higher than the experimental value. We thus have to conclude that, at least for model system 2, the gas phase predictions are significantly closer to the solution phase experiment as compared to solution-phase calculations based on a combined implicit–explicit solvent model.

Fig. 2 Structures of SiMe₃Cl (2) complexed to CHCl₃ obtained at MPW1K/6-31+G(d) level in the gas phase (dashed lines show shortest contacts between solvent and solute molecules).

Table 4 ²⁹Si chemical shifts for complexes 2_1–2_5 of SiMe₃Cl (2) with one chloroform molecule at MP2(FULL)/IGLO-III//MPW1K/6-31+G(d) level (bond distances are in pm, free energies ΔG₂₉₈ are in kJ mol⁻¹ and chemical shifts are in ppm)

	Gas phase			Solution phase^a
	r(Si–Cl)	ΔG298	δ(^29Si)	r(Si–Cl)	ΔG298	δ(^29Si)
a Solvent effects calculated at PCM(UAHF)/MP2(FULL)/IGLO-III//MPW1K/6-31+G(d) level. b δ(^29Si) shift calculated as Boltzmann average, for detail see ESI.
2_1	208.6	0.00	+30.70	210.50	1.02	+35.09
2_2	208.6	0.99	+30.89	210.50	3.02	+35.43
2_3	209.5	7.01	+33.81	210.70	0.00	+36.24
2_4	208.5	7.44	+30.69	210.40	1.29	+35.16
2_5	208.7	7.91	+31.28	210.40	2.06	+35.06
Ave^b			+30.88			+35.52

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Spin–orbit corrections for chlorosilanes

²⁹Si Chemical shifts calculated at MPW1K/IGLO-III//MPW1K/6-31+G(d) level for the SiMe_4−xCl_x compounds show a systematic deviation between theoretically calculated and experimentally measured shift data (Fig. 3). That the deviations are systematic in nature can readily be seen from the good linear correlation between the actual deviation and the number of chlorine atoms (Fig. 3).¹⁵ The importance of heavy-atom-induced spin–orbit (SO) effects for nuclear magnetic shifts of group 14 element halides have been highlighted by several groups.^45–50 According to these earlier reports, the experimentally observed normal halogen dependence (NHD), i.e. the characteristic high-field shift of the nucleus bound directly to the halogen substituents with increasing atomic number of the halogen, is mainly a result of spin–orbit effects. In these studies it was found that shifts calculated with the inclusion of SO effects agree significantly better with the experiment than their non-relativistic counterparts.

Fig. 3 Comparison between experimentally measured and theoretically calculated shift values at MPW1K/IGLO-III//MPW1K/6-31+G(d) level for alkylchlorosilanes SiMe_4−xCl_x with x = 1–4. SO corrections are obtained from ZORA-SO-PBE0/TZ2P single-point calculations. Geometries are obtained at MPW1K/6-31+G(d) level in gas phase.

We evaluated contributions of relativistic spin–orbit effects to the nuclear magnetic shielding constants for the series of SiMe_4−xCl_x compounds employing the two-component zeroth-order regular approximation (ZORA)^51,52 formalism, as implemented in ADF. The SO correction per chloro-substituent increases monotonously from approximately −2 ppm (SiMe₃Cl) to −3 ppm for SiMe₂Cl₂, −4 ppm for SiMeCl₃, and −5 ppm for SiCl₄. In line with the discussion of Kaupp et al. on SO-induced heavy-atom effects on NMR chemical shifts,⁴⁷ this trend can readily be explained based on the analogy to the Fermi-contact mechanism of spin–spin coupling. The increasing involvement of valence silicon s-type orbitals in the bonding orbitals to the chloro-substituents results in larger SO contributions in the series from SiMe₃Cl to SiCl₄.⁵³ Aside from the chlorine count there is only a rather limited influence of other silicon substituents on the magnitude of the SO corrections. A SO correction of around −2 ± 0.5 ppm per chlorine substituent will thus be typical for different chloromonosilanes (see also Table 5). For systems with more than one conformer, Boltzmann-weighted SO corrections are close to the SO-correction for the most stable conformer.⁵⁴

Table 5 The ²⁹Si NMR chemical shifts of selected chemical species

	System	δ exp (ppm)	δ ^gascal ^b (ppm)	δ ^gas+socal ^c (ppm)	δ ^sp+socal ^d (ppm)	δ ^opt+socal ^e (ppm)
a Experimentally measured δexp(^29Si) values for all systems. The solvent is given in parenthesis. b δ ^gascal(^29Si) chemical shift in gas phase using gas phase structure at MPW1K/IGLO-III//MPW1K/6-31+G(d) level. c δ ^gas+socal(^29Si) gas phase chemical shift with added Boltzmann-weighted SO corrections. SO corrections are obtained at ZORA-SO-PBE0/TZ2P level in gas phase. d δ ^sp+socal(^29Si) chemical shifts are calculated with PCM(UAHF)/MPW1K/IGLO-III(+ZORA-SO)//MPW1K/6-31+G(d). Boltzmann-averaged SO corrections are calculated at ZORA-SO-PBE0/TZ2P in gas phase based on gas phase structures. e δ ^opt+socal(^29Si) chemical shifts are calculated with PCM(UAHF)/MPW1K/IGLO-III//PCM/UAHF-MPW1K/6-31+G(d) level and corrected with Boltzmann-weighted SO corrections at ZORA-SO-PBE0/TZ2P level based on gas phase geometries. For more detailed information on the SO corrections see ESI.
2		+30.70 (CDCl3)^31	+31.92	+29.82	+31.90	+34.90
3		−18.50 (CDCl3)^15	+2.49	−18.11	−18.05	−18.13
4		−1.57 (CDCl3)	−5.39	−5.19	−3.01	−1.15
5		+8.40 (C6D6)^55	+8.97	+8.57	+8.18	+10.41
6		+9.91 (CDCl3)	+11.59	+10.79	+11.21	+12.78
7		+12.70 (CDCl3)	+26.04	+14.04	+15.30	+16.53
8		+12.86 (CDCl3)	+16.12	+14.42	+14.73	+15.22
9		+15.54 (CDCl3)	+17.07	+16.37	+16.88	+18.16
10		+15.80 (CDCl3)	+17.40	+16.60	+17.28	+18.51
11		+17.08 (CDCl3)	+16.41	+16.01	+17.13	+19.06
12		+18.42 (CDCl3)	+21.10	+20.40	+20.68	+21.01
13		+20.34 (CDCl3)	+19.48	+19.08	+19.09	+20.10
14		+20.39 (CDCl3)	+17.69	+17.09	+17.84	+18.70
15		+20.58 (CDCl3)	+21.46	+20.66	+20.95	+18.51
16		+26.69 (CDCl3)	+22.95	+22.55	+23.36	+24.16
17		+32.00 (CDCl3)^3	+38.81	+32.81	+35.13	+37.66
18		+32.16 (CDCl3)	+35.70	+35.30	+36.18	+34.47
19		+33.25 (CDCl3)	+38.44	+37.94	+36.40	+37.00
20		+35.89 (CDCl3)	+36.81	+35.31	+37.13	+39.80
21		+36.09 (CDCl3)	+37.78	+35.78	+37.62	+39.98
22		+43.71 (CDCl3)	+44.50	+44.00	+46.55	+51.65
23		+45.21 (CDCl3)	+51.41	+50.81	+49.83	+49.12
24		+45.96 (CDCl3)	+43.30	+42.70	+43.68	+48.94

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²⁹Si chemical shifts for larger molecular systems

²⁹Si chemical shifts for a larger group of “typical” systems are collected in Table 5 and graphically shown in Fig. 4. Already the calculation of gas phase ²⁹Si chemical shifts at MPW1K/IGLO-III//MPW1K/6-31+G(d) level provides a rather accurate agreement with experimental results obtained in low polarity organic solvents with R² = 0.872 and MD = 2.54 ppm (panel (a) in Fig. 4). The largest deviations occur for systems containing more than one chlorine atom directly attached to silicon, and inclusion of SO-corrections evaluated at ZORA-SO-PBE0/TZ2P single point level improves correlation with experiment significantly for the entire dataset to R² = 0.978 and MD = 0.18 ppm (compare panel (a) and (b) in Fig. 4). Best theoretical predictions are then obtained through shielding calculations in the presence of the PCM continuum solvation model with gas phase structures and including the SO corrections. It is remarkable to see that the correlation for this approach based on gas phase structures (R² = 0.984, MD = 0.97 ppm) is even slightly better as compared to the approach based on solution-phase structures with R² = 0.983 and MD = 2.34 ppm (compare panel (c) and (d) in Fig. 4). Performing the actual shielding calculations with different functionals such as HCTH407 or with the local DF-LMP2 method lead to no further systematic improvement (see ESI† for details).

Fig. 4 Theoretically calculated vs. experimentally measured ²⁹Si chemical shifts for the data set collected in Table 5. (a) δ(²⁹Si) calculated at MPW1K/IGLO-III//MPW1K/6-31+G(d) level. (b) δ(²⁹Si) calculated at MPW1K/IGLO-III(+ZORA-SO)//MPW1K/6-31+G(d). (c) δ(²⁹Si) calculated at PCM(UAHF)/MPW1K/IGLO-III(+ZORA-SO)//MPW1K/6-31+G(d) level using gas phase structures. (d) δ(²⁹Si) calculated at PCM(UAHF)/MPW1K/IGLO-III(+ZORA-SO)//PCM(UAHF)MPW1K/6-31+G(d) level using solution phase structures.

Chemical shifts for ion pairs

Chemical shift calculations for the ion pair intermediates 18, 19, 23, and 24 included in Table 5 are somewhat less accurate as compared to all other systems at the MPW1K/IGLO-III(+ZORA-SO)//MPW1K/6-31+G(d) level. This may, in part, be due to significantly larger solvent effects for these polar species as well as their rather large conformational flexibility. How the latter actually impacts chemical shift calculations is illustrated in detail in Fig. 5 for silylpyridinium ion pair 19, whose experimentally measured ²⁹Si chemical shift amounts to +33.25 ppm in chloroform. For ion pairs, which have more than one conformer, chemical shifts are evaluated by Boltzmann averaging over individual conformers based on their relative free energies. When using gas-phase free energies the structures with the largest molecular dipole moment make the smallest contribution to the Boltzmann average due to their high relative energies (Table 6). In solution, however, these structures lead to the largest solvation energies: the dipole moment of conformer 19_1 is comparatively low at 10.30 D (MPW1K/6-31+G(d) level) and thus has the smallest solvation energy of −81.50 kJ mol⁻¹ (gas-phase geometry). Conformers 19_4 and 19_5 have slightly larger dipole moments and also slightly larger solvation energies around −96 kJ mol⁻¹. Conformer 19_6 has the largest dipole moment at 23.93 D, leading to a rather large solvation energy of −131.50 kJ mol⁻¹ (gas phase geometry) or −162.72 kJ mol⁻¹ (solution phase geometry). As a consequence of these variations in solvation energies, relative free energies in solution (ΔG^opt) are significantly smaller as compared to the gas phase. Despite these large changes in relative energies, the actual ion pair structure shows rather little change in gas-phase vs. solution-phase geometry optimization as exemplified for the Si–N bond distance (Table 6). This can also be stated for the electronic character of these ion pairs as characterized by the triflate ion charge, which assumes values between −0.94 and −0.96 for the best conformers 19_1 and 19_2 in gas-phase as well as in solution (Table 6).

Fig. 5 Relative free energies and chemical shifts of individual conformers of ion pair system 19 at different theory levels.

Table 6 Relative free energies, structural and charge parameters, and ²⁹Si chemical shifts for individual conformational isomers of ion pair 19. Charge parameters have been obtained from the NBO analysis⁵⁶

Level for free energy calculation		19_1	19_2	19_3	19_4	19_5	19_6
MPW1K/6-31+G(d)//MPW1K/6-31+G(d)	μ (Debye)	10.30	17.27	17.36	13.16	14.39	23.93
	ΔG (kJ mol^−1)	0.00	0.67	4.01	11.81	13.35	52.89
	r(Si–N) (pm)	184.3	184.9	184.9	184.7	182.9	190.1
	q(OTf)	−0.96	−0.94	−0.94	−0.95	−0.96	−0.95
	δ(^29Si) (ppm)	+39.24	+37.63	+37.64	+39.77	+33.49	+53.36
PCM/UAHF/MPW1K/6-31+G(d)//MPW1K/6-31+G(d)	ΔG^spsolv (kJ mol^−1)	−81.5	−97.65	−97.86	−95.60	−96.86	−131.50
	ΔG (kJ mol^−1)	15.54	0.00	3.13	13.20	13.47	18.23
	r(Si–N) (pm)	184.3	184.9	184.9	184.7	182.9	190.1
	q(OTf)	−0.96	−0.95	−0.95	−0.96	−0.97	−0.96
	δ(^29Si) (ppm)	+38.41	+36.90	+36.89	+38.33	+34.21	+48.90
PCM/UAHF/MPW1K-6-31+G(d)//PCM/UAHF/MPW1K-6-31+G(d)	ΔG^optsolv (kJ mol^−1)	−125.81	−119.41	−119.79	−133.05	−141.04	−162.72
	ΔG (kJ mol^−1)	4.31	0.00	0.29	5.10	2.69	14.51
	r(Si–N) (pm)	184.4	184.5	184.4	184.5	184.2	186.0
	q(OTf)	−0.98	−0.97	−0.97	−0.99	−0.99	−0.98
	δ(^29Si) (ppm)	+37.61	+37.72	+37.59	+38.13	+36.25	+41.64
MPW1K-D2/6-31+G(d)//MPW1K-D2/6-31+G(d)	ΔG (kJ mol^−1)	0.00	16.54	16.76	9.91	15.39	42.78
	r(Si–N) (pm)	183.0	183.5	183.2	183.2	181.6	213.8
	q(OTf)	−0.95	−0.94	−0.94	−0.95	−0.95	−0.78
	δ(^29Si) (ppm)	+37.69	+37.59	+37.99	+38.73	+32.88	−32.24

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The largest effects are observed for ion pair 19_6, whose structure also depends significantly on the chosen level of theory in the gas phase: geometry optimization at MPW1K/6-31+G(d) level leads to the structure shown as “19_6” in Fig. 5, which can be characterized as a true ion pair with a comparatively long (387 pm) distance between silicon atom and triflate counter ion. Reoptimization with the same functional and added dispersion corrections (MPW1K-D2/6-31+G(d)) leads to a structure best described as pentacoordinated silicon intermediate (termed 19_6′) with a much shorter Si–O(triflate) distance of 194 pm and a largely changed ²⁹Si chemical shift of −32.24 ppm.⁵⁷ More importantly, the very different chemical shift for pentacoordinate structure 19_6′ clearly supports the assignment of the experimentally detected ion pair species as systems with tetracoordinate silicon atoms. The “collapse” of the ion pair structure to a pentacoordinated intermediate upon geometry optimization at MPW1K-D2/6-31+G(d) level has only been observed for conformer 19_6 and not for any of the other (low-energy) conformers.

Conclusions

Calculated ²⁹Si chemical shifts of (chloro)organosilanes depend strongly on structural details of the respective systems. MPW1K/6-31+(d) gas phase optimizations give structures close enough to experiment for reliable NMR shielding calculations. Relativistic spin–orbit effects are large for chlorosilane systems and reliable shielding calculations thus require SO corrections for these systems. For non-halosilane systems the SO effects are rather small and ²⁹Si shift predictions are thus possible without any relativistic corrections. Solvent effects on ²⁹Si NMR chemical shifts are quite systematic, but only of moderate size, and reliable shift predictions can thus be made using gas phase geometries and, in many cases, also using gas phase shielding calculations. For the (chloro)organosilane compound family studied here MPW1K/IGLO-III(+ZORA-SO)//MPW1K/6-31+G(d) calculations are thus recommended for ²⁹Si NMR shift calculation.

Computational details

Chemical shifts of ²⁹Si containing species (δ(²⁹Si)) are calculated using eqn (1), where σ(²⁹Si_TMS) is the chemical shielding for the reference compound tetramethylsilane (Si(CH₃)₄, TMS, 1) and σ(²⁹Si) is the shielding of the ²⁹Si nucleus in the compound under investigation:

δ(²⁹Si) = σ(²⁹Si_TMS) − σ(²⁹Si) (1)

Shieldings are calculated using the Gauge-Independent Atomic Orbital (GIAO) method.⁵⁸ Shielding values of chemicals are calculated with Gaussian 09, revision C.01⁵⁹ and MOLPRO, Version 2012.1.^60,61

The relativistic spin–orbit corrections to the nuclear magnetic shielding constants for ²⁹Si were calculated with the two-component zeroth-order regular approximation (ZORA)^51,52 using the Amsterdam Density Functional (ADF 2013.01) code.⁶² The hybrid functional PBE0^63–65 in combination with the Slater-type basis set TZ2P⁶⁶ optimized for relativistic ZORA calculations is used for these single point calculations at MPW1K/6-31+G(d) gas phase structures. The spin–orbit correction is calculated as δ(²⁹Si)_ZORA–δ(²⁹Si)_{non-relativistic} and then Boltzmann-averaged for compounds with more than one conformer. For more details on different functionals and basis sets see the ESI.†

Experimental details

All commercial chemicals were of reagent grade and were used as received unless otherwise noted. The substances tert-butyl-dimethylsilyl cyanide (4), tert-butyldiphenylsilyl chloride (8), 1-(tert-butyldimethylsilyl)imidazole (11), N-tert-butyldimethylsilyl-N-methyltrifluoroacetamide (16), and triisopropylsilyl chloride (20), were purchased in the highest purity from Sigma Aldrich and measured in freshly distilled CDCl₃ over CaH₂. ¹H and ¹³C NMR spectra were recorded on Varian 300 or Varian INOVA 400 machines at room temperature. All ¹H chemical shifts are reported in ppm (δ) relative to CDCl₃ (+7.26); ¹³C chemical shifts are reported in ppm (δ) relative to CDCl₃ (+77.16). All other chemicals were purchased from commercial suppliers at the highest available grade, store over orange gel in an desiccator and used without any further purification.

General procedure 1

For all purchased substances this procedure was performed. In a pre-dried NMR tube 30 mg of the substance were dissolved in 0.6 mL of freshly distilled CDCl₃. The tube was closed with a cap and sealed with parafilm.

General procedure 2

For the ion pairs (18, 19, 23, 24) two stock solutions have been prepared in the concentration of 0.5 M in freshly distilled CDCl₃. Both solutions (Lewis base and TBSOTf) are mixed in a ratio 1 : 1 and therefore the concentration of the intermediates can be 0.25 M max. The tube was closed with a cap and sealed with parafilm.

General procedure 3 (silylation of alcohols)

One equivalent of alcohol and 1.2 equivalents of used silyl chloride were dissolved in 20 mL DCM and 1.2 equivalents triethylamine was added. After adding up to 30 mmol% of a catalyst DMAP the reaction mixture stirred at RT up to 7 d. The reaction mixture was washed with sat. aq. NH₄Cl solution, extracted three times with DCM (10 mL) and the combined organic phases dried over MgSO₄. The solvent was removed under reduced pressure and column chromatography was used to purify the product.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c4cp01736f

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