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Correlation among the Gas-Phase, Solution, and Solid-Phase Geometrical and NMR Parameters of Dative Bonds in the Pentacoordinate Silicon Compounds. 1‑Substituted Silatranes Elena F. Belogolova and Valery F. Sidorkin* A. E. Favorsky Irkutsk Institute of Chemistry, Siberian Branch of the Russian Academy of Sciences, Favorsky, 1, Irkutsk 664033, Russian Federation S Supporting Information *

ABSTRACT: Silatranes XSi(OCH2CH2)3N exhibit a good linear relationship between their experimental and calculated (IGLO and GIAO) values of the NMR chemical shifts of 15N, δN, and the lengths of dative bonds Si←N, dSiN, determined in the gas phase (ED, CCSD), solutions (COSMO PBE0, B3PW91), and crystals (X-ray). An aggregate of the obtained data provides strong evidence that the gas-phase value of dSiN in MeSi(OCH2CH2)3N should be greater by ∼0.05 Å than that determined in the electron diffraction (ED) experiment (2.45 Å). Given this condition, a long-standing contradiction between the data of the structural (X-ray, ED) and NMR 15N experiments for the molecules of 1-methyl- and 1-fluorosilatrane regarding the sensitivity of their coordination contact Si←N to the medium effect is resolved.

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Å.2a,b It seemed tempting, using only the δN values measured in solution and assuming the validity of eq 1 in any medium, to perform the estimations of the experimentally unavailable solution values of dSiN and, consequently, the reactivity6 of silatranes with this equation. However, in realizing this idea,1d a contradiction arose between the data of structural (X-ray, ED) and NMR 15N experiments. Indeed, the interval of δN change upon the variation of solvent for MeSi(OCH2CH2)3N exceeds 3−4 times that for FSi(OCH2CH2)3N.1d According to eq 1, this suggests that the relatively weak coordination contact Si←N in 1methylsilatrane (judging by dSiN(X-ray) values)1d,2a,b is more sensitive to external factors as compared with the more strong Si←N contact in 1-fluorosilatrane, that is, in the limiting case of transition from the solid to gas phase, the ΔdSiNsolid−gas = dSiNgas − dSiNsolid value for MeSi(OCH2CH2)3N should exceed that for FSi(OCH2CH2)3N. However, this quite reasonable conclusion is not supported by X-ray and ED results,1d,2a,b which point to approximate equality: ΔdSiNsolid−gas(MeSi(OCH2CH2)3N) ≈ ΔdSiNsolid−gas(FSi(OCH2CH2)3N) ≈ 0.28 Å. To date, no plausible explanation for this unexpected fact has been advanced in the literature. Therefore, the question of applicability of eq 1 in practice remains open. So, the necessity arose to support theoretically or reject the hypothesis that the dependence of eq 1 is common

INTRODUCTION Silatranes XSi(YCH2CH2)3N, I (YO, NR, CH2, S), rather thoroughly studied by various physicochemical methods, are classic representatives of the class of organic derivatives of the pentacoordinate silicon atom.1 An attractive interaction between the nitrogen and silicon atoms in these compounds predetermines the peculiarity of their structure, unusual spectral characteristics, and reactivity, as well as a wide spectrum of biological activity. As a measure of strength of the dative Si←N bond in silatranes, in addition to its length (dSiN) and energetic and electronic characteristics, one may also use the values of isotropic 15N chemical shifts (δN) of the donor nitrogen atom.1a,d This is based on the fact that for the intramolecular complexes I, which contain the oxygen atoms in the equatorial plane (YO) − oxisilatranes by the Verkade terminology,1b a good linear relationship (R = 0.99) between the crystal values of dSiN and δN is observed upon variation of the substituent X (X = Me, CH3CH2, CH2CH, C6H5, ClCH2, ClCH2CH2CH2, CH3O, Cl, F):1a,d δ N = −252.41 − 47.07dSiN

(1) 1d

According to the data of IR and NMR spectroscopy and ED,2 X-ray,1d,3 and quantum chemistry4 methods, the coordination Si←N contact in silatranes turned out to be very sensitive not only to the internal factors, that is, to the X nature, but also to the external onesthe aggregate state of compounds and solvent polarity.5 For example, the transition of FSi(OCH2CH2)3N from the solid phase (X-ray) to the gas phase (ED) results in the increase of the Si···N distance by 0.28 © 2013 American Chemical Society

Received: April 10, 2013 Revised: May 21, 2013 Published: June 18, 2013 5365

dx.doi.org/10.1021/jp4035216 | J. Phys. Chem. A 2013, 117, 5365−5376

The Journal of Physical Chemistry A

Article

where σN (sol;sol) and σN (gas;gas) are, respectively, the values of the nitrogen nuclear shielding for molecules 1a−c in solution and in the gas phase, computed at their corresponding equilibrium solution and gas phase geometries. 20 The partitioning of ΔσN into the direct Δσpol N (polar contribution) and indirect Δσgeom (geometrical contribution) effects was N performed with the use of eqs 3 and 4.20

for crystals, gases, and solutions of silatranes XSi(OCH2CH2)3N at any substituent X. For solving the posed problem we invoke the molecules of 1hydro- (1a), methyl- (1b), and 1-fluorosilatranes (1c) that are key in series I as they are characterized by the most complete set of experimental values of δN and dSiN in different media.

(3)

ΔσNgeom = σN(sol; sol) − σN(sol; gas)

(4)

where σN(sol;gas) is the value of σN for molecules 1a−c in solution, computed at their equilibrium geometry in the gas phase. The direct effect is due to the perturbation of the solvent on the electronic wave function of the solute held at the geometry optimized in the gas phase, and the indirect one is due to the relaxation of this geometry under the influence of the solvent. The GIAO NMR shielding tensors of nitrogen in molecules 1a−c were partitioned into magnetic contributions from the various localized bonds and lone pairs present in the structures by employing the natural chemical shielding analysis (NCS)21 at the PBE0//6-311++G(2d,2p)//B3PW91/6-311G(d,p) level of theory. The Method2//Method1 notation implies that the calculation of property (energy or shielding) was performed with the Method2 for a structure optimized with Method1. The Orca22 program was employed for COSMO geometry optimization and IGLO chemical shift calculations. All remaining calculations were carried out with Gaussian 0923 program package. The degree of trigonal-bipyramidal (TBP) pentacoordination of the silicon atom in 1a−c was determined using eq 5,24 where θn are angles between axial and equatorial bonds at the silicon atom.

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CALCULATIONAL DETAILS The structure of molecules 1a−c was studied using the resource-intensive high-level coupled-cluster singles and doubles (CCSD) approach in conjunction with the 6-31G(d) and 6-311G(d,p) basis sets and the MP2 method with the 6311G(2d,p), 6-311G(d,p), 6-311++G(d,p), and cc-pvTZ basis sets. In addition, we invoked three density functional methods with the 6-31G(d), 6-311G(d,p), and 6-311++G(d,p) basis sets: one-parameter hybrid-GGA exchange-correlation functional PBE0,7 hybrid GGA functional B3PW91,8 having recommended itself well for studying nonclassical structures,9 and new generation hybrid meta-GGA functional M06-2X.10 The correspondence of the DFT and MP2 optimized structures to the minima on the potential energy surface (PES) was confirmed by the positive eigenvalues of the corresponding Hessians. A solvent effect on the geometry of 1a−c was estimated in the framework of: (i) two continuum models (conductor-like screening model, COSMO,11 and conductor-like polarizable continuum model, C-PCM);12 (ii) the discrete solvation model (“supermolecular” (SM) or “claster” approach)13 with explicit inclusion of solvent molecules; (iii) the combined model SM + C-PCM. In the models (ii) and (iii) the energy of formation, ΔEc, for complexes of 1a−c with chloroform and methanol molecules was determined as the difference in the free energies of the complexes and their initial components taking into account the zero-point vibration energies (ZPE) and the basis set superposition error (BSSE).14 The Gibbs free energy of complexation, ΔGc, was estimated at 298.15 and 160 K. The ΔEc and ΔGc values were calculated at the B3PW91/6311G(d,p)//B3PW91/6-311G(d,p) and MP2/6-311++G(3df,3pd)//B3PW91/6-311G(d,p) (single point calculation) levels of theory. ZPE and thermal corrections to ΔEc were estimated with the B3PW91/6-311G(d,p) method. The 15N NMR chemical shifts (δN) of 1a−c were calculated using the GIAO (gauge including atomic orbital)15 and IGLO (individual gauge for localized molecular orbitals)16 approaches (HF, MP2, PBE0, B3LYP, B3PW91 methods with the 6-311+ +G(2d,p), 6-311++G(2d,2p), and IGLOIII17 basis sets) relative to ammonia [δN = σN(NH3) − σN(1), where σN is nitrogen shielding constant]. Further they were converted to the nitromethane scale [δN = (σN[NH3] − σN[1]) − 400.9] taking into account the 400.9 ppm difference between the δN values of liquid CH3NO2 and gaseous NH3.18 The indirect calculation of δN was dictated by the known problems of calculating the reasonable value of the nitrogen shielding in nitromethane.19 The solvent effect on σN was estimated in the framework of the continuum models C-PCM and COSMO as: ΔσN = σN(sol; sol) − σN(gas; gas)

ΔσNpol = σN(sol; gas) − σN(gas; gas)

3

ηa =

■

109.5 − 1/3 ∑n = 1 θn 109.5 − 90

× 100%

(5)

RESULTS AND DISCUSSION Length of the Coordination Si←N Contact and the Chemical Shift of Molecules 1a−c in the Gas Phase. In considering theoretically the question about the dependence δN = f(dSiN) in the series of silatranes I, the choice of the relevant methods for optimization of their geometry and calculation of the nitrogen chemical shift is of great importance. Making this choice based only on the literature data does not seem feasible. Indeed, all of the used methods HF,2c,25,26 MP2,2c,9a,26,27 DFT (B3LYP,2c,9a,26−28 PBE29), regardless of the basis set size, failed to reproduce with a good accuracy ∼0.01−0.03 Å the ED values of dSiN (available only for 1-hydro-, 1-methyl-, and 1fluorosilatranes) for all three molecules 1a−c. The reason for this may be a relatively “soft” character of the dependence of the total energies of I on the length of the coordination Si···N contact, particularly in the case of 1a and 1b.1d,4 For example, dSiN(B3LYP) and dSiN(HF) in 1b exceed dSiN(ED) at least by 0.1 Å and 0.2 Å, respectively. In contrast, the PBE/TZ2P method leads to the shortened (by 0.05−0.1 Å) Si···N distances as compared to the ED data.29 Quantitatively, the MP2 calculations of dSiN in 1a−c in the 6-311G(2d,d) basis set are most preferable.26 Nevertheless, at this theory level, too, for 1a the correspondence between the ED (2.406 Å)2c and calculated (2.327 Å)26 values of dSiN is not satisfactory.

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Table 1. Gas-Phase Experimental (ED) and Calculated Internuclear Distances SiN (dSiN, Å), X−Si (dXSi, Å), N−C (dNC, Å), and Bond Angle C−N−C (∠CNC, deg) in the Molecules of X-Substituted Silatranes 1a−c 1a

1b

1c

a

X

method

H

(ED)a CCSDb CCSD MP2 MP2 MP2 PBE0 PBE0 PBE0 B3PW91 B3PW91 B3PW91 M06-2X M06-2X (ED)c CCSDb CCSD MP2 MP2 MP2 MP2 PBE0 PBE0 PBE0 B3PW91 B3PW91 B3PW91 M06-2X M06-2X (ED)d CCSD CCSD MP2 MP2 MP2 MP2 PBE0 PBE0 PBE0 B3PW91 B3PW91 B3PW91 M06-2X M06-2X

Me

F

dSiN

basis set

2.406(27) 2.393 2.425 2.332 2.352 2.355 2.318 2.371 2.376 2.347 2.400 2.405 2.453 2.535 2.453(47) 2.515 2.525 2.420 2.441 2.458 2.371 2.461 2.502 2.520 2.501 2.533 2.558 2.686 2.700 2.324(14) 2.322 2.324 2.276 2.312 2.276 2.233 2.287 2.293 2.277 2.323 2.321 2.304 2.370 2.352

6-31G(d) 6-311G(d,p) 6-311G(d,p) 6-311G(2d,p) 6-311++G(d,p) 6-31G(d) 6-311G(d,p) 6-311++G(d,p) 6-31G(d) 6-311G(d,p) 6-311++G(d,p) 6-31G(d) 6-311G(d,p) 6-31G(d) 6-311G(d,p) 6-311G(d,p) 6-311G(2d,p) 6-311++G(d,p) cc-pVTZ 6-31G(d) 6-311G(d,p) 6-311++G(d,p) 6-31G(d) 6-311G(d,p) 6-311++G(d,p) 6-31G(d) 6-311G(d,p) 6-31G(d) 6-311G(d,p) 6-311G(d,p) 6-311G(2d,p) 6-311++G(d,p) cc-pVTZ 6-31G(d) 6-311G(d,p) 6-311++G(d,p) 6-31G(d) 6-311G(d,p) 6-311++G(d,p) 6-31G(d) 6-311G(d,p)

dXSi

dNC

∠CNC

1.478 1.465 1.466 1.467 1.466 1.478 1.475 1.474 1.477 1.474 1.473 1.470 1.465 1.853 1.864 1.857 1.857 1.859 1.857 1.863 1.863 1.854 1.853 1.866 1.857 1.856 1.854 1.847 1.568(6) 1.612 1.605 1.611 1.600 1.616 1.606 1.604 1.609 1.614 1.607 1.612 1.616 1.599 1.605

1.443(7) 1.464 1.461 1.463 1.459 1.463 1.459 1.456 1.456 1.461 1.459 1.459 1.457 1.454 1.458(6) 1.459 1.457 1.458 1.455 1.458 1.456 1.452 1.450 1.450 1.454 1.452 1.452 1.447 1.448 1.481(8) 1.468 1.466 1.466 1.461 1.467 1.463 1.461 1.460 1.461 1.464 1.463 1.464 1.461 1.462

113.2(17) 115.6 115.9 115.1 115.5 115.2 115.4 115.8 115.8 115.7 116.1 116.1 116.5 117.1 114.7(13) 116.6 116.8 115.8 116.2 116.0 115.4 116.5 116.9 117.0 116.9 117.1 117.3 118.6 118.6 115.0(3) 115.1 115.2 114.8 115.3 114.8 114.5 115.3 115.3 115.2 115.6 115.6 115.4 115.9 115.7

Reference 2c. bOur data from ref 27b. cReference 2a. dReference 2b.

than by ∼0.03 Å and 4°, respectively (see Table 1 and Tables S1−S2 in the Supporting Information). The exceptions are the bond distances at the silicon atom (dSiN, dSiF) and the OCC bond angle. The Si−F bond in 1c is systematically underestimated by 0.03−0.04 Å with all considered methods, and the calculated OCC angle in all structures is 4−8° less than the experimental one. A considerable discrepancy in the performance of the MP2 method in the 6-311G(2d,p) basis set and that in the correlation-consistent cc-pVTZ basis is surprising. For example, in the former the ED value dSiN in molecule 1c is reproduced with an accuracy to ∼0.01 Å, whereas in cc-pVTZ it is markedly lower, ∼0.09 Å!

No quantum chemical estimations of δN for molecules 1a−c have been performed in the literature.30 At the relatively low GIAO-HF//HF level of theory with the 3-21G, 6-31G, and 631G(d) basis sets only the nitrogen shielding constants σN have been calculated for silatranes I (X = H, Me, F, Cl).30a−c The experimental (ED) and calculated (with methods chosen by us) values of some structural parameters of molecules 1a−c are given in Table 1. The extended range of these parameters is presented in Tables S1 and S2 in the Supporting Information. The most of the bond lengths and bond angles for molecules 1a−c calculated at different theory levels agree closely with each other and deviate from the experimental data not more 5367



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Figure 1. Selected experimental (ED) and B3PW91/6-311G(d,p) (italics) and CCSD/6-311G(d,p) (bold) calculated bond distances (Å) for silatranes 1a−c.

Figure 2. B3PW91/6-311G(d,p) optimized geometries and energies of complexation (kcal/mol) of complexes 1a·CHCl3, 1a·2CHCl3, and 1c·CHCl3 in the SM model (MP2/6-311++G(3df,3pd)//B3PW91/6-311G(d,p) values of ΔEc and ΔGc are given in parentheses).

value of the nitrogen chemical shift δN in this molecule with the experimentally found1d (unfortunately, only for 1-methylsilatrane) one. Indeed, the calculated GIAO MP2/6-311++G(2d,p)//CCSD/6-31G(d) and GIAO MP2/6-311++G(2d,p)// CCSD/6-311G(d,p) values of δN for 1b (−370.7 and −370.4 ppm, respectively) virtually coincide with δN(exp) = −370.7 ppm. In contrast, with the MP2/6-311G(2d,p) geometry of 1b, that supports dSiN (ED) very well (Table 1), a marked discrepancy ∼2 ppm (see Table 3) between the GIAO MP2/6311++G(2d,p) value of δN and δN(exp) is observed. Note that the inclusion of diffusion functions for heavy and light atoms in the basis sets of the B3PW91 and PBE0 methods resulted (see Table 1) in insignificant change of dSiN (∼0.007 Å) in the case of 1-hydrosilatrane and in increasing by ∼0.03 Å the discrepancy between the calculated and ED values of dSiN in the case of 1-fluorosilatrane. At the MP2 level of theory the transition from the 6-311G(d,p) to the 6-311++G(d,p) basis set has no effect on dSiN in 1c and improves an agreement of this distance with the ED data for 1a by 0.02 Å. Solvent Effect on the Geometry and Nitrogen Chemical Shift of Molecules 1a−c. A study of the solvent effect on the geometry of silatranes 1a−c at the CCSD level of theory with the use of generally available programs is not feasible now. So, for this purpose we applied the B3PW91/6311G(d,p) and PBE0/6-311G(d,p) methods. As stated above,

It should be emphasized that the precision for determining the ED internuclear Si···N distance in the molecule of 1methylsilatrane 1b is considerably less than in 1-hydro- 1a and 1-fluorosilatrane 1c, because the SiN vibration amplitude has not been optimized during the least-squares refinement of the ED data for 1b,2a as opposed to that for 1a and 1c. So, a key moment in choosing the reliable method for the calculation of the geometry of I is first of all the reproduction of the ED values of the coordination Si←N contact length in structures 1a and 1c with a reasonable accuracy ∼0.01−0.03 Å.31 Only three methods dealt successfully (Figure 1, Table 1) with this task: CCSD with the 6-31G(d) and 6-311G(d,p) basis sets, B3PW91/6-311G(d,p), and PBE0/6-311G(d,p). However, for molecule MeSi(OCH2CH2)3N the dSiN(CCSD), dSiN(B3PW91), and dSiN(PBE0) values therewith exceed dSiN(ED) by 0.05 and more angstroms. Such a large difference in the dSiN values in this case with regard to the aforesaid may be reasonably explained by the reason that the value dSiN ∼2.50 Å predicted by the CCSD, B3PW91, and PBE0 methods for 1b is more accurate than the conventional dSiN (ED) ∼ 2.45 Å2a (it is pertinent to emphasize that when analyzing the ED data for 1b the authors of ref 2a also did not exclude the possibility of the location for the Si←N distance under the peak at around 2.5 Å). The necessity of the dSiN(ED) correction in the case of 1b is further witnessed by the comparison of the calculated gas phase 5368



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Table 2. Internuclear Distances SiN (dSiN, Å), X−Si (dXSi, Å), Si−O (dSiO, Å), Bond Angle O−Si−O (∠OSiO, deg), Degree of Pentacoordination of the Silicon Atom (ηa, %) in the Gas Phase, Solutions, and Crystals for Silatranes XSi(OCH2CH2)3Na X

medium

method

dSiN, Å

dXSi, Å

dSiO, Å

H

gas gas CHCl3 CHCl3 CHCl3 CHCl3 DMSO DMSO DMSO DMSO solidb gas gas CHCl3 CHCl3 CHCl3 CHCl3 DMSO DMSO DMSO DMSO solidc gas gas CHCl3 CHCl3 CHCl3 CHCl3 DMSO DMSO DMSO DMSO solidd

B3PW91 PBE0 C-PCM B3PW91 C-PCM PBE0 COSMO B3PW91 COSMO PBE0 C-PCM B3PW91 C-PCM PBE0 COSMO B3PW91 COSMO PBE0 X-ray B3PW91 PBE0 C-PCM B3PW91 C-PCM PBE0 COSMO B3PW91 COSMO PBE0 C-PCM B3PW91 C-PCM PBE0 COSMO B3PW91 COSMO PBE0 X-ray B3PW91 PBE0 C-PCM B3PW91 C-PCM PBE0 COSMO B3PW91 COSMO PBE0 C-PCM B3PW91 C-PCM PBE0 COSMO B3PW91 COSMO PBE0 X-ray

2.400 2.371 2.209 2.191 2.199 2.181 2.165 2.151 2.133 2.124 2.088 2.533 2.502 2.320 2.292 2.315 2.285 2.266 2.243 2.239 2.221 2.160 2.321 2.293 2.150 2.134 2.141 2.128 2.114 2.100 2.091 2.078 2.042(1)

1.474 1.475 1.486 1.487 1.485 1.486 1.491 1.492 1.493 1.494 1.38 1.857 1.854 1.872 1.869 1.871 1.869 1.878 1.875 1.879 1.875 1.880 1.612 1.609 1.637 1.633 1.637 1.633 1.645 1.641 1.649 1.645 1.622(1)

1.677 1.675 1.687 1.685 1.689 1.686 1.690 1.687 1.693 1.689 1.659(4) 1.676 1.673 1.688 1.686 1.689 1.687 1.691 1.689 1.694 1.691 1.679 1.666 1.664 1.674 1.672 1.675 1.673 1.676 1.673 1.678 1.675 1.645(2)

Me

F

a

∠OSiO, deg

ηa, %

116.6 116.8 118.4 118.5 118.5 118.6 118.8 118.8 119.0 119.0

45 46 63 64 64 64 68 68 70 71

114.8 115.1 117.2 117.4 117.3 117.5 117.8 117.9 118.0 118.1 118.6 117.6 117.8 119.1 119.1 119.1 119.2 119.3 119.4 119.5 119.5 119.5(5)

32 33 51 52 51 53 56 57 58 59 65 54 55 72 72 72 73 76 76 78 79 79

All calculations were performed with the 6-311G(d,p) basis set. bReference 3. cReference 33.34 dReference 35.

Figure 3. Interrelation (“ideal” is given by the solid line) of the calculated, δNsol(calc), and experimental, δNsol(exp), values of the nitrogen chemical shifts for silatranes 1a−c in the chloroform (□), methanol (○), and dimethyl sulfoxide (△) solvents. The calculations of δNsol were performed: (a) in the C-PCM GIAO PBE0/6-311++G(2d,2p)//B3PW91/6-311G(d,p) approximation; (b) in the COSMO IGLO PBE0/IGLOIII//PBE0/6311G(d,p) approximation.

proposed32 that they may form H-complexes with the proton− donor solvents. Indeed, the interaction of 1a−c with chloroform (see examples in Figure 2 and Figures S1 and S2 in the Supporting Information) and methanol (see Figure S3 in the Supporting Information) leads to the formation of the

they provide (Table 1) an agreement with the dSiN (CCSD) values for all three structures 1a−c with acceptable accuracy. Irrespective of the X substituent nature, silatranes XSi(OCH2CH2)3N possess at least three accessible basic centers (oxygen atoms). As a consequence, it has been repeatedly 5369



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Table 3. Calculated (δNcalc, ppm) and Experimental (δNexp, ppm) Nitrogen Chemical Shifts of the Molecules of Silatranes XSi(OCH2CH2)3N in the Gas Phase, Solutions, and Crystalsa X

medium

model

δNcalc

H H H H H H H H H H H H H H H Me Me Me Me Me Me Me Me Me Me Me Me Me Me Me Me Me Me F F F F F F F F F F F F F F F F

gas gas gas gas gas gas CHCl3 CHCl3 CHCl3 CHCl3 DMSO DMSO DMSO DMSO solid gas gas gas gas gas gas gas gas CHCl3 CHCl3 CHCl3 CHCl3 CHCl3 DMSO DMSO DMSO DMSO solid gas gas gas gas gas gas CHCl3 CHCl3 CHCl3 CHCl3 DMSO DMSO DMSO DMSO DMSO solid

GIAO MP2/6-311++G(2d,p)//CCSD/6-31G(d) GIAO MP2/6-311++G(2d,p)//CCSD/6-311G(d,p) GIAO PBE0/6-311++G(2d,2p)//B3PW91 IGLO PBE0/IGLOIII//B3PW91 GIAO PBE0/6-311++G(2d,2p)//PBE0 IGLO PBE0/IGLOIII//PBE0 C-PCM GIAO PBE0/6-311++G(2d,2p)//B3PW91 COSMO IGLO PBE0/IGLOIII//B3PW91 C-PCM GIAO PBE0/6-311++G(2d,2p)//PBE0 COSMO IGLO PBE0/IGLOIII//PBE0 C-PCM GIAO PBE0/6-311++G(2d,2p)//B3PW91 COSMO IGLO PBE0/IGLOIII//B3PW91 C-PCM GIAO PBE0/6-311++G(2d,2p)//PBE0 COSMO IGLO PBE0/IGLOIII//PBE0

−365.7 −366.3 −363.9 −364.9 −363.4 −364.5 −355.0 −355.9 −355.7 −356.2 −353.4 −353.1 −354.0 −353.9

GIAO MP2/6-311++G(2d,p)//CCSD/6-31G(d) GIAO MP2/6-311++G(2d,p)//CCSD/6-311G(d,p) GIAO MP2/6-311++G(2d,p)//MP2/6-311G(2d,p) GIAO MP2/6-311++G(2d,p)//B3PW91 GIAO PBE0/6-311++G(2d,2p)//B3PW91 IGLO PBE0/IGLOIII//B3PW91 GIAO PBE0/6-311++G(2d,2p)//PBE0 IGLO PBE0/IGLOIII//PBE0 C-PCM GIAO MP2/6-311++G(2d,p)//B3PW91 C-PCM GIAO PBE0/6-311++G(2d,2p)//B3PW91 COSMO IGLO PBE0/IGLOIII//B3PW91 C-PCM GIAO PBE0/6-311++G(2d,2p)//PBE0 COSMO IGLO PBE0/IGLOIII//PBE0 C-PCM GIAO PBE0/6-311++G(2d,2p)//B3PW91 COSMO IGLO PBE0/IGLOIII//B3PW91 C-PCM GIAO PBE0/6-311++G(2d,2p)//PBE0 COSMO IGLO PBE0/IGLOIII//PBE0

−370.7 −370.4 −372.3 −374.0 −370.2 −371.2 −369.7 −370.7 −364.5 −359.9 −361.0 −359.9 −360.6 −357.6 −357.5 −357.8 −357.8

GIAO MP2/6-311++G(2d,p)//CCSD/6-31G(d) GIAO MP2/6-311++G(2d,p)//CCSD/6-311G(d,p) GIAO PBE0/6-311++G(2d,2p)//B3PW91 IGLO PBE0/IGLOIII//B3PW91 GIAO PBE0/6-311++G(2d,2p)//PBE0 IGLO PBE0/IGLOIII//PBE0 C-PCM GIAO PBE0/6-311++G(2d,2p)//B3PW91 COSMO IGLO PBE0/IGLOIII//B3PW91 C-PCM GIAO PBE0/6-311++G(2d,2p)//PBE0 COSMO IGLO PBE0/IGLOIII//PBE0 C-PCM GIAO MP2/6-311++G(2d,2p)//B3PW91 C-PCM GIAO PBE0/6-311++G(2d,2p)//B3PW91 COSMO IGLO PBE0/IGLOIII//B3PW91 C-PCM GIAO PBE0/6-311++G(2d,2p)//PBE0 COSMO IGLO PBE0/IGLOIII//PBE0

−359.2 −358.9 −356.4 −357.6 −356.3 −357.4 −349.0 −349.8 −349.7 −350.6 −354.9 −347.8 −348.1 −348.6 −349.0

δNexp

−354.4 −354.4 −354.4 −354.4 −353.0 −353.0 −353.0 −353.0 −351.6 −370.7 −370.7 −370.7 −370.7 −370.7 −370.7 −370.7 −370.7 −359.4 −359.4 −359.4 −359.4 −359.4 −356.4 −356.4 −356.4 −356.4 −355.6

−349.3 −349.3 −349.3 −349.3 −348.4 −348.4 −348.4 −348.4 −348.4 −348.3

a

B3PW91 and PBE0 geometry optimizations were performed with the 6-311G(d,p) basis set. The experimental values of the nitrogen chemical shifts are taken from refs 1d, 39, and 40.

associates of 1:1 and 1:2 composition, which are stabilized by the hydrogen bonds O···H−C or O···H−O, and, in the case of 1c, by the bifurcated (three-center) F···H···O bond. This is evidenced from the essential exceeding of the sum of the van der Waals radii for O(F) and H (∼2.7 Å) over the length of the O···H and F···H contacts.

The energy of formation for solvates (1a−c)·CHCl3 and (1a−c)·CH3OH (Figure 2 and Figures S1−S3 in the Supporting Information) is relatively small in absolute magnitude and depends only slightly on the nature of the X substituent at the silicon atom. When both acidic and polar properties of the considered solvents are taken into account, a weakening of the interaction 5370



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the following analysis of the sensitivity of the structure of 1a−c to the medium effect. As could be expected,1d in any phase state of 1a−c (see Tables 1 and 2), judging by the dSiN values, the Si←N bonding in these structures is strengthened with increasing the electronegativity of the substituent X (Me < H < F):

between 1a-c and chloroform and methanol is observed (see Figure 2 and Figures S1−S3 in the Supporting Information). For example, if in the gas phase (SM model) the |ΔEc | value for 1a·CHCl3 amounts to, according to the MP2/6-311+ +G(3df,3pd) single point calculations, 5.4 kcal/mol, then in the hybrid model (SM + C-PCM) it decreases to 4.7 kcal/mol. Based on the dSiN values (see Table 2, Figure 2 and Figure S1) it may be concluded that the Si←N coordination in molecules 1a−c is essentially enhanced upon the inclusion of them in the associates with H-acids. Judging by the positive ΔGc values, the complexes of 1a−c with CHCl3 and CH3OH in any composition are not stable (Figure 2).36 However, according to the MP2/6-311++G(3df,3pd) single point calculations, they may exist at low temperatures (Figure 2). It should be noted that at T = 160 K the formation of the complex of the diacetylenic silatrane (CH3)3Si−CC−CC−Si(OCH2CH2)3 with chloroform has been established (X-ray).37 Thus, a realistic description of the structure of 1a−c in solutions at room temperature is apparently possible in the framework of the nonspecific solvation models.38 This is evidenced by close to ideal linear correlation (Figure 3) between the solution experimental, δNsol(exp), and calculated, δNsol(calc), nitrogen chemical shifts of 1a−c. It may be obtained (Table 3 and Table S3 in the Supporting Information) if B3PW91/6-311G(d,p) as well as PBE0/6-311G(d,p) geometries of 1a−c found with the continuum C-PCM and COSMO models (Figure 3 and Figure S4 in the Supporting Information) are used when calculating δNsol in the GIAO and IGLO approximations. The quality of correlation between δNsol(exp) and δNsol(calc) is markedly affected (see Table 3 and Table S4 in the Supporting Information) by the choice of method for obtaining the wave function for δNsol(calc). The best results are attained with the GIAO PBE0, B3PW91, and IGLO PBE0/IGLOIII functions. The difference in the GIAO DFT values of δNsol(calc) for the 6-311++G(2d,p) and 6-311++G(2d,2p) basis sets therewith does not exceed 0.7 ppm (see Table 3 and Table S3 in the Supporting Information). The performance of the GIAO and IGLO B3LYP calculation schemes is slightly below. Note that for 1-methylsilatrane in the gas phase the δNgas(GIAO MP2/6-311++G(2d,p)//B3PW91/6-311G(d,p)) value deviates from δNgas(exp) = −370.7 ppm by 3.3 ppm, and in the chloroform solvent δNsol(C-PCM GIAO MP2/6311++G(2d,p)//B3PW91/6-311G(d,p)) exceeds in absolute magnitude δNsol(exp) = −359.4 ppm by 5.1 ppm. The transition of the highly polar (dipole moment is greater than 4.5 D) molecules 1a−c from the gas phase to solution (regardless of the continuum model used) of any polarity and further to the solid state (Tables 1 and 2) affected mostly structural parameters of the coordination XSiO3N center (especially, dSiN).41 Therewith, a consequent shortening of the dative Si←N contact is observed (Table 2 and Table S5 in the Supporting Information): dSiN gas > dSiN sol > dSiN solid

1b < 1a < 1c

(7)

For the hypervalent silicon compounds with a TBP configuration of bonds at SiV, the inverse character of the mutual influence between two axial bonds is theoretically substantiated and experimentally demonstrated.1d,4b,42 With regard to silatranes this implies that in the three-center fourelectron (3c−4e) axial X−Si←N fragment the shortening, for whatever reason, of the Si←N bond should be accompanied by the weakening of the X−Si bond. On that ground we could expect, in view of eq 6, that dSiX gas < dSiX sol < dSiX solid

(8)

Indeed (Table 2), for 1b and 1c we have: dSiCgas < dSiCsolid; dSiFgas < dSiFsolid. These inequalities hold (see Tables 1 and 2) with the use of both the ED and calculated values of dSiCgas and dSiFgas. In the case of 1-hydrosilatrane 1a the comparison of dSiHgas and dSiHsolid is not possible due to the lack of the ED data on dSi−H and the difficulties of determining this bond distance with the X-ray analysis. In the framework of the applied continuum models the solution phase values of dSi−F in 1c exceed the solid phase ones, that is, contrary to eq 8, dSiFsol > dSiFsolid. One of the reasons for that appears to be associated, as noted above (see Table 1), with a substantial underestimation in the calculations (at any of the used levels of theory) of the Si−F bonding in 1c. In contrast, in the case of 1-methylsilatrane 1b (Table 2), in accordance with eq 8, dSiCsol < dSiCsolid. The sensitivity of the nitrogen chemical shift, δN, and the length of the dative Si←N contact, dSiN, in the intramolecular complexes 1a−c to their transition from solution to the solid state and from the weakly polar solvents CHCl3 and CH3OH to the highly polar DMSO (i.e., the absolute values of the changes in δN and dSiN upon the variation of the external surroundings: ΔδN = |δNmedium1 − δNmedium2|; |ΔdSiN = dSiNmedium1 − dSiNmedium2 |) increases consistently (Table S6 in the Supporting Information) as follows: ΔδN; ΔdSiN: 1c(X = F) < 1a(X = H) < 1b(X = Me)

(9)

In this case for the estimation of ΔδN and ΔdSiN one can use both the available calculated (δ N sol ; d SiN sol ) and the experimental (δNsol; δN solid; dSiNsolid) values of δN and dSiN (Tables 2 and 3). In contrast, for the transitions with the involvement of the isolated states of 1a−c (gas phase → solution or gas phase → solid state) the inequalities (9) hold true on condition that only CCSD, B3PW91, or PBE0 gas phase values of dSiN (≥2.5 Å) should be used for the estimation of ΔdSiNgas‑sol, that is, |dSiNgas − dSiNsol|, and ΔdSiNgas−solid, in 1-methylsilatrane 1b. Indeed, if based in the calculations of ΔdSiNgas−solid for molecule 1b on its ED value dSiNgas = 2.453 Å we come to the inconsistent order of ΔδNgas−solid and ΔdSiNgas−solid change in the series of 1a−c:

(6)

as well as an increase of the degree of trigonal-bipyramidal pentacoordination of silicon: ηa(gas) < ηa(solution) < ηa(crystal). It is important to note a good agreement between the solution phase geometrical parameters of 1a−c calculated with the PBE0 and B3PW91 methods. A maximum difference in the bond lengths for them is 0.02 Å. Therefore, the use of either of these two methods leads to fully consistent results of

ΔδNgas−solid: 1c(10.9 ppm) < 1a(14.1 ppm) < 1b(15.1 ppm) 5371

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ΔdSiNgas−solid: ̊ > 1b(0.29 A) ̊ ≈ 1c(0.28 A) ̊ 1a(0.35 A)

(OCH2CH2)3N caused by their transition from the gas phase to solution or from the weakly polar to highly polar solvent (Tables 2, 3).45 The partitioning of the shielding constant σN of the intramolecular complexes 1a−c in the gas phase and in the CCl4, CHCl3, THF, CH2Cl2, CH3OH, CH3CN, DMSO, and H2O solvents (C-PCM model, see Tables S8−S10 in the Supporting Information) into magnetic contributions from the various bonds and lone pairs allowed us to establish the following. The NCS nitrogen atomic orbital 1s(N) makes a largest contribution to σN (see Tables S8−S10 in the Supporting Information), determining its diamagnetic character. This contribution does not depend on the X nature and medium effects and is equal to 240 ppm. The next greater contribution to σN is σSiN/Lp(N). It comes from the Si←N bond orbital (in the NBO analysis it is localized for the structures with dSiN < 2.3 Å) or from the nitrogen lone pair (dSiN > 2.3 Å) interacting with the antibonding orbital σ*SiX of the SiX bond.46 The value of contributions from the N−C bond orbitals (3σNC), taken as a sum over three bonds, is comparable with the contribution from σSiN/Lp(N), however its change with the variation of the polarity of surroundings goes in opposite to σN direction. The contributions from the remaining NBO localized orbitals to σN of structures 1a−c are relatively small and vary insignificantly with the change of dSiN (see Tables S6−S8 in the Supporting Information). As illustrated in Figure 5, the variation of the length of the dative Si←N bond in molecules 1a−c under the influence of the medium results in a consistent change in the shielding constant σN and the contribution to it from the localized orbital of the Si←N bond or the nitrogen lone pair σSiN/Lp(N). So, the downfield shift of the 15N resonance of silatranes XSi(OCH2CH2)3N upon the strengthening of their dative Si←N bond is due to the corresponding decrease in the contribution σSiN/LP(N) to δN. Correlation between the Nitrogen Chemical Shift and the Length of the Coordinate Si←N Bond for Silatranes in the Gas Phase, Solutions, and Crystals. As noted in the Introduction, there is a good linear relationship (eq 1) between the crystal values of d SiN and δ N in silatranes XSi(OCH2CH2)3N. It turned out that the gas phase and solution points (dSiN, δN) presented in Tables 1−3, that characterize molecules 1a−c, are grouped well (Figure 6) along the correlation line of eq 1. Their maximum deviation from it does not exceed 1.7 ppm. Note, that, in accordance with the aforesaid, the (dSiN(CCSD), δN(exp)) point for 1b (denoted by number 1) essentially lies on the line of eq 1, whereas the (dSiN(ED), δN(exp)) point (denoted by number 2) deviates markedly from it. Thus, the relationship of eq 1 is common for the crystals, solutions, and isolated molecules of the intramolecular complexes XSi(OCH2CH2)3N at any substituent X.

(11)

ΔδNgas−solid

The values in the parentheses were obtained using experimental solid phase1d and calculated GIAO MP2/6-311+ +G(2d,p)//CCSD/6-31G(d) gas phase δN of compounds 1a− c (Table 3). There are no strong reasons to believe that we should deal with two (eqs 10 and 11), rather than one (eq 9), dependences of ΔdSiNgas−solid on the X substituent nature upon the variation of the external surroundings of silatranes XSi(OCH2CH2)3N. Therefore, in light of the foregoing (see the previous part) one can conclude: the reason for the discrepancy (noted in the Introduction) between the sensitivity of molecules 1a−c to external factors, which was determined from the results of structural (X-ray, ED) experiments, on the one hand, and that determined from the NMR 15N experiments, on the other hand, is a ED value of dSiN for 1b. According to the CCSD, B3PW91, and PBE0 calculations, it is underestimated by ∼0.05 Å. From the inequality chain of eq 9, in view of eq 7, it follows that the weaker the Si←N coordination in the initial silatrane, then the greater the sensitivity of not only its geometrical (dSiN), but also its magnetic (δN)1d characteristics to the medium effect.43 This raises the question: Why do the corresponding differences ΔδN and ΔdSiN vary consistently in 1a−c under the change of their aggregate state or the solvent polarity? To answer the posed question, we have analyzed, with the example of transition of the hypervalent structures 1a−c from the gas phase to the DMSO solution, the relationship between the polar ΔσNpol (eq 3) and geometrical Δσgeom (eq 4) N contributions to the total solvent effect ΔσN (eq 2), that is, ΔδN. It turned out that the change in the nitrogen chemical shift, ΔδN, induced by medium is mainly governed, in compliance with eq 9, by the geometrical contribution Δσgeom N (Figure 4 and Table S7 in the Supporting Information) rather than the polar one Δσpol N , as is peculiar to the covalent molecules.20,44 The direct (eq 3) and indirect (eq 4) medium effects act on ΔσN in opposite directions. A tendency to the downfield shift of δN is observed upon strengthening the Si←N interaction in silatranes XSi-

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CONCLUSIONS Ab initio (CCSD, MP2) and DFT (B3PW91, PBE0, M06-2X) methods were applied to study the structure of the hypervalent molecules of 1-hydro- (1a), 1-methyl- (1b), and 1-fluorosilatrane (1c) in the gas phase and a series of solvents. Only three of them succeeded in reproducing the ED values of the length of the coordination Si←N contact (dSiN) in species 1a and 1c with a reasonable accuracy (∼0.01−0.03 Å). A realistic description of the structure of silatranes XSi(OCH2CH2)3N in solutions at room temperature is possible in the framework of the nonspecific solvation models COSMO and C-PCM. This

Figure 4. Geometrical (geom) and polar (pol) contributions to the (total) solvent effect (DMSO solvent) on the nitrogen nuclear shielding (ΔσN) for the hypervalent structures 1a−c. The calculations geom were performed at the GIAO C-PCM PBE0/6of Δσpol N and ΔσN 311++G(2d,2p)//C-PCM-B3PW91/6-311G(d,p) level of theory. 5372



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Figure 5. Dependence of the nitrogen isotropic nuclear shielding (σN) and the contributions to it from σSiN/Lp(N) and 3σCN on the Si←N bond length in the molecules of 1-hydro- (1a), 1-methyl- (1b), and 1-fluorosilatrane (1c) in the gas phase and eight solvents. The σN value was taken without the constant contribution to it from the 1s nitrogen orbital.

theoretically supported. Practically, this allows to use, with confidence, the eq 1 for the estimation of the strength of the coordinate Si←N bonding, and therefore, the reactivity of silatranes in solutions by the value of their measured nitrogen chemical shift.

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ASSOCIATED CONTENT

S Supporting Information *

Figures S1−S3 with structures and energetics of complex formation for the intermolecular complexes of 1a−c with one and two CHCl3 molecules, as well as one CH3OH molecule, Figure S4 with correlation between calculated and experimental values of nitrogen chemical shifts for 1a−c in three solvents, Tables S1 and S2 with the extended range of calculated structural parameters for 1a−c, Table S3−S5 with experimental and calculated values of nitrogen chemical shifts and Si←N bond lengths of 1a−c in solutions, Table S6 with calculated and experimental intervals of change in the Si←N bond length and nitrogen chemical shift of 1a−c under the influence of the medium, Table S7 with calculated total, direct, and indirect effects of the DMSO solvent on 15N magnetic shielding in 1a− c, Tables S8−S10 with NCS orbital contributions to the isotropic nitrogen magnetic shielding for 1a−c in the gas phase and several solutions. This material is available free of charge via the Internet at http://pubs.acs.org.

Figure 6. Position of the gas-phase and solution points (dSiN, δN) corresponding to molecules 1a−c with respect to the correlation line eq 1, that was found for the experimental values of dSiN and δN (solid squares) of silatranes XSi(OCH2CH2)3N in their crystals. For the gas phase the calculated points (dSiN(CCSD), δN(GIAO MP2//CCSD)) are denoted by open cycles, the points 1 (dSiN(CCSD), δN(exp)) and 2 (dSiN(ED), δN(exp)) are shown with solid cycles. The open squares are correspond to the calculated solution phase (dSiN(COSMO PBE0// PBE0), δN(IGLO COSMO PBE0//PBE0)) points.

is evidenced by close to ideal linear correlation between the solution experimental and calculated nitrogen chemical shifts of 1a−c. The reason for the discrepancy between the estimations of sensitivity of the geometry and magnetic properties of molecules 1a−c to the change in their aggregate state and solvent polarity, performed, on the one hand, from the results of structural (X-ray, ED) experiments, and, on the other hand, from the NMR 15N experiments is a ED value of dSiN for 1methylsilatrane, being equal to 2.45 Å. According to the CCSD, B3PW91, and PBE0 calculations, it is underestimated by ∼0.05 Å. In the intramolecular complexes XSi(OCH2CH2)3N the change in the nitrogen chemical shift, ΔδN, induced by medium is mainly governed by the geometrical contribution, rather than the polar one, as is peculiar to the covalent molecules. According to the NCS analysis data, the downfield shift of the 15N resonance of silatranes XSi(OCH2CH2)3N, that is observed with the strengthening of their dative Si←N bond under the influence of the medium, is due to the decrease in the contribution from the localized orbital of the Si←N bond (dSiN < 2.3 Å) or the nitrogen lone pair (dSiN > 2.3 Å) to δN. The hypothesis of the independence of the linear relationship (eq 1) between the length of the dative Si←N contact and the nitrogen chemical shift in the hypervalent structures XSi(OCH2CH2)3N from the substituent X and medium effects was

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +7-3952-424871. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

This article is dedicated to the memory of Professor V. A. Pestunovich, untimely deceased, who made an important contribution to the physical chemistry of silatranes. Financial support of our work by the International Association for the Promotion of Cooperation with Scientists from the New Independent States of the Former Soviet Union (INTAS) and Russian Foundation for Basic Research (RFBR) is gratefully acknowledged (Grants INTAS 03-51-4164 and RFBR 99-0333032). We are grateful to Irkutsk Supercomputer Center of SB RAS (http://hpc.icc.ru/) for providing computational resources of the computational cluster “Blackford” to perform calculations with Orca program. 5373



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(40) Kupche, E. L.; Lukevits, E. Correlation between 29Si-15N SpinSpin Coupling Constants and the 15N-NMR Chemical Shifts in Silatranes. Khim. Geterotsikl. Soed. 1989, 701−703; Chem. Heterocycl. Compd. (Engl. Transl.) 1989, 25, 586−588. (41) As a rule, the difference between the gas phase and liquid (solid) phase bond lengths and values of bond angles α for the bonds and angles that do not belong to the silicon polyhedron of 1a−c is rather small, for example: Δdgas‑sol = dgas − dsol < 0.02 Å; Δαgas‑sol = αgas − αsol < 3°. (42) (a) Sidorkin, V. F.; Pestunovich, V. A.; Voronkov, M. G. The Physical Chemistry of Silatranes. Usp. Khim. 1980, 49, 789−813; Russ. Chem. Rev. (Engl. Transl.) 1980, 49, 414−427. (b) Sidorkin, V. F.; Belogolova, E. F.; Pestunovich, V. A. Ab Initio Study of Medium Effects on the Geometries of the Compounds of Trigonal-Bipyramidal Silicon with Coordination Center ClSiC 3 O. J. Mol. Struct.: THEOCHEM 2001, 538, 59−65. (c) Belogolova, E. F.; Sidorkin, V. F. Ab Initio and DFT Study of the Structure of Pentacoordinated Silicon Compounds: Si-Substituted (O−Si)dimethyl(Nacetylacetamidomethyl)silanes. J. Mol. Struct.: THEOCHEM 2004, 668, 139−145. (d) Sidorkin, V. F.; Doronina, E. P. Cage Silaphosphanes with a P→Si Dative Bond. Organometallics 2009, 28, 5305−5315. (e) Doronina, E. P.; Sidorkin, V. F.; Lazareva, N. F. (PO→Si) Chelates of Silylmethyl Derivatives of Phosphoric Acids R2P(O)ZCH2SiMe3‑nHaln (n = 1−3; Z = O, NMe, CH2, S). Organometallics 2010, 29, 3327−3340. (f) Belogolova, E. F.; Doronina, E. P.; Belogolov, M. A.; Sidorkin, V. F. The Use of the Structural Correlation Method for the Estimation of the Quality of Ab Initio and DFT Predictions of Geometry Parameters of Related Compounds in the Gas Phase and in Solutions. An Example of (O− Si)chelates with ClSiC3O Coordination Center. J. Mol. Struct.: THEOCHEM 2010, 950, 72−78. (43) In general case, the dependence of the sensitivity of the geometry of pentacoordinate silicon compounds to the medium effect seems to be nonlinear (dome-shaped). See ref 42c and: (a) Kost, D.; Kalikhman, I. Hypervalent Silicon Compounds. In The Chemistry of Organic Silicon Compounds; Rappoport, Z., Apeloig, Y., Eds.; Wiley: Chichester, U.K., 1998; Vol. 2, pp 1339−1445. (b) Belogolova, E. F.; Sidorkin, V. F. Geometry of Intramolecular Silicon Complexes: an Ab Initio Estimation of the Sensitivity to the Effect of Medium: (Aroyloxymethyl)trifluorosilanes. Izv. Akad. Nauk, Ser. Khim. 2003, 1392−1396; Russ. Chem. Bull., Int. Ed. 2003, 52, 1472−1476. (44) Cremer, D.; Olsson, L.; Reichel, F.; Kraka, E. Calculations of NMR Chemical Shift - the Third Dimension of Quantum Chemistry. Isr. J. Chem. 1993, 33, 369−385. (45) The tendency to the downfield shift of δN in the molecules of silatranes on going from the weakly to highly polar solvent has been mentioned earlier. See ref 1d. (46) The energy of the Lp(N), σ*SiX interaction calculated using second-order perturbation theory falls in the range of 4−10 kcal/mol.

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