Ab Initio and Density Functional Study

29 Si NMR Chemical Shifts of Siloxanes: Ab Initio and Density Functional Study Georgios Tsantes, Norbert Auner,* Thomas Müller* Institut für Anorganische Chemie, Johann Wolfgang Goethe-Universität Frankfurt a. M. D-60439 Frankfurt a. M., Germany Tel.: +49 69 798 29166 Fax: +49 69 798 29188 E-mail: tsantes@chemie.uni-frankfurt.de Keywords: 29 Si NMR, siloxanes, Computational Chemistry, NMR spectroscopy Since 1990 the ab initio calculation of NMR chemical shift parameters has been established as a reliable tool for structure elucidation of various types of compounds [1]. Based on a set of model disiloxanes, the predictive powers of various computational levels (HF, DFT, MP2) [2] for 29 Si NMR chemical shift calculations for linear, cyclic and cage-like polysiloxanes are compared. The dependence of the calculated NMR parameters on structural changes is discussed. Finally, the performance of our theoretical approach is tested using a series of 25 siloxanes and silanes. A survey of structural data for siloxanes [3] reveals that the scattering of the O-Si-O bond angle is comparatively small (105 114 ), but the spread of the Si-O-Si bond angle and of the Si O bond length is rather large (129 177 and 1.550 1.701 Å). Therefore, we investigated the effect of the flexibility of these structural parameters on the 29 Si NMR chemical shift. Disiloxane was choosen as a model compound for two reasons: it is the smallest molecule which has an Si O Si linkage; it is the major building block for siloxanes. The optimized molecular structure [4] of disiloxane at the B3LYP/6-31G(d) level of theory has an Si-O-Si angle of 153.3 and an Si O bond length of Å. The energy for linearization is as low as 1 kcal mol 1. This is in good qualitative agreement [5] with calculations at higher levels of theory which predict linearization barriers between 0.50 (MP2/6-311+G(3df)) and 1.36 kcal mol 1 (CCSD(T)/6-311G(2d)). Figure 1 shows the relative potential energy surface of disiloxane as calculated at the B3LYP/6-31G(d) level of theory. It is interesting to note the flat bottom of the surface, marked by light grey, which represents a potential energy well of only 2 kcal mol 1. A change of the Si-O-Si angle from 120 to 180 is covered by this energy range. Within the same energy band the 29 Si NMR shift decreases by 8 10 ppm (Fig. 2). The Si-O-Si bond angle and the Si O bond length were changed in 10 and in 0.03 Å steps, and after a partial optimization of the disiloxane structure at the B3LYP/6-31G(d) level of theory a subsequent NMR calculation (GIAO-MP2/A) [6, 7] was performed. The combined effect of both

29 Si NMR Chemical Shifts of Siloxanes: Ab Initio and Density Functional Study 335 structural parameters on the calculated 29 Si NMR shift is shown in Fig. 2. Associated with the increase of the Si-O-Si bond angle is a significant reduction of the Si O bond length. Both structural changes result in a high-field shift of δ 29 Si; δ 29 Si decreases by approximately 25 ppm in the range from 120 to 180 and 1.750 to 1.570 Å. This corresponds roughly to δ 4 ppm per 10 and 4 ppm per 0.05 Å. A similar picture results when the 29 Si NMR shift is calculated at different levels such as GIAO-HF/A, GIAO-B3LYP/A, or GIAO-MPW1PW91/A [6, 7], the only difference being in the absolute values. Fig. 1. H 3 Si-O-SiH 3 potential energy surface calculated at the B3LYP/6-31G(d) level of theory. Fig. 2. 29 Si NMR chemical shift from H 3 Si-O-SiH 3 calculated at the GIAO-MP2/A // B3LYP/6-31G(d) level of theory [6, 7].

336 G. Tsantes, N. Auner, T. Müller The prediction of NMR chemical shifts depends crucially on the quality of the optimized structure and on the precision of the subsequent NMR calculation. Therefore various computational methods in combination with different basis sets were tested for their ability to predict the important geometrical parameters like the Si-O-Si angle and the Si O bond length. After a full geometry optimization, four theoretical levels were used to calculate the 29 Si NMR shift. Disiloxane, hexafluorodisiloxane, hexachlorodisiloxane and hexamethyldisiloxane were used as model compounds (Fig. 3). δ / ppm -30,0-31,0-32,0-33,0-34,0-35,0-36,0-37,0-38,0-39,0-40,0-41,0-42,0-43,0-44,0-45,0-46,0-47,0-48,0-49,0-50,0-51,0-52,0-53,0-54,0-55,0 HF/6-31G(d) 170.0 HF/6-31G(2d) 142.8 HF/6-311G(d) 180.0 HF/6-311+G(d) 179.9 HF/6-311+G(2d) 146.6 B3LYP/6-31G(d) 152.9 B3LYP/6-31G(2d) 141.9 B3LYP/6-311G(d) 179.6 B3LYP/6-311+G(d) 179.8 B3LYP/6-311+G(2d) 141.8 MP2/6-31G(d) 143.6 MP2/6-31G(2d) 136.1 MP2/6-311G(d) 155.2 MP2/6-311+G(d) 156.5 MP2/6-311+G(2d) 137.4 exp. H 3 Si Si-O-Si O SiH 3 ED Si-O: 1.634(2) Si-O-Si: 144.1(9) X-ray Si-O: 1.631(6) Si-O-Si: 142.2(3) GIAO-HF/A GIAO-B3LYP/A GIAO-MPW1PW91/A GIAO-MP2/A 1.626 1.633 1.620 1.623 1.622 1.650 1.639 1.643 1.659 1.660 1.643 1.651 Si-O Fig. 3. Effect of various levels of theory used to calculate geometrical parameters combined with subsequent 29 Si NMR chemical shift calculations on disiloxane [8]. When using HF theory for the geometry optimization the use of two sets of polarization functions is necessary to reproduce the Si-O-Si angle. Methods which include electron correlation (i.e. MP2- or DFT-based methods) do not require such extended basis sets. Based on the same geometry, GIAO-HF/A [6, 7] and GIAO-B3LYP/A [6, 7] methods result in very similar shifts, usually with a difference of only 1 2 ppm from each other. In the case of the 29 Si NMR shift of hexachlorodisiloxane, all combinations of theoretical levels used result in significantly greater errors in comparison to the other three disiloxanes. The exact prediction of the Si-O-Si angle is not sufficient for an accurate δ 29 Si NMR prediction. In the case of hexamethyldisiloxane the HF/6-31G(d) geometry optimization results in an Si-O-Si angle of approximately 180, in contrast to the experimentally derived

29 Si NMR Chemical Shifts of Siloxanes: Ab Initio and Density Functional Study 337 value of 148. Nevertheless the calculated GIAO-B3LYP/A [6, 7] 29 Si NMR chemical shift is in good agreement with the experimental shift due to the calculated Si O bond length of 1.636 Å (exp. 1.63 Å). This is in contrast to the MP2/6-31G(d) geometry, where the Si-O-Si bond angle is in agreement with the experimental value but the Si O bond length differs by 0.04 Å. As a consequence the subsequent GIAO-B3LYP/A [6, 7] 29 Si NMR chemical shift calculation results in a greater difference from the experimental value than the GIAO-B3LYP/A//HF/6-31G(d) level of theory. Finally, the predictive power of our theoretical approach was tested using a series of 25 siloxanes and silanes, including a silsesquioxane and a cyclotrisilthiane (Fig. 4). All the structures were fully optimized and characterized as minima on the potential energy surface and the 29 Si NMR chemical shifts were calculated. The GIAO-HF/A [6, 7] calculations agree slightly better with the experimental shifts than the GIAO-B3LYP/A [6, 7] level of theory. Both theoretical levels have difficulties in predicting correct δ 29 Si NMR chemical shifts of compounds containing Si Cl bonds, regardless of whether chlorodisiloxanes or chlorosilanes are involved. 60 40 20 GIAO-HF/A // B3LYP/6-31G(d) y = 0.995 * x + 3.650 R=0.989 60 GIAO-B3LYP/A // B3LYP/6-31G(d) 40 y = 1.089*x + 8.141 R = 0.982 20 calc. shift / ppm 0-20 -40-60 -80-100 -120-120 -100-80 -60-40 -20 0 20 40 exper. shift / ppm calc. shift / ppm 0-20 -40-60 -80-100 -120-140 -120-100 -80-60 -40-20 0 20 40 exper. shift / ppm Compound G exp. G HF/A G B3LYP/A Compound G exp. G HF/A G B3LYP/A H 3 Si-O-SiH 3 38.0 43.6 44.3 Me 3 Si-O-Si*HCl 2 39.8 29.7 32.7 F 3 Si-O-SiF 3 112.8 115.7 116.6 Cl 3 Si*-O-SiMe 3 48.5 36.1 34.4 Cl 3 Si-O-SiCl 3 45.5 32.1 30.3 Cl 3 Si-O-Si*Me 3 20.1 19.8 24.4 Me 3 Si-O-SiMe 3 7.3 5.4 7.8 (MeO) 3 Si-O-Si(OMe) 3 86.0 83.4 89.2 MeSiCl 3 12.7 26.1 39.6 OHMe 2 Si-O-SiMe 2 OH 12.6 12.1 10.7 Me 2 SiCl 2 32.0 38.1 51.9 F 3 Si-SiF 3 77.9 75.3 76.4 Me 3 SiCl 29.8 31.8 40.6 Cl 3 Si-SiCl 3 6.2 9.6 20.2 MeSiF 3 56.2 57.2 55.8 hexachlorocyclotrisiloxane 58.2 47.7 48.4 Me 2 SiF 2 4.4 1.9 7.5 hexamethylcyclotrisiloxane 9.2 6.7 6.5 Me 3 SiF 32.0 28.5 36.2 cyclotrisilthiane 20.9 9.8 3.9 Me 2 HSi-O-SiHMe 2 5.3 4.4 1.6 Me 3 Si-OH 14.9 15.3 20.0 PhH 2 Si-O-SiH 2 Ph 25.2 28.2 27.8 octasilsesquioxane 84.5 80.4 90.3 Me 3 Si*-O-SiHCl 2 18.1 24.4 19.3 all values in ppm Fig. 4. Calculated and experimentally derived 29 Si NMR chemical shifts from siloxanes, silanes, and one silthiane.

338 G. Tsantes, N. Auner, T. Müller Acknowledgments: This work was supported by Dow Corning Corporation and SBC GmbH. References [1] a) Helgaker, M. Jaszunski, K. Ruud, Chem. Rev. 1999, 99, 293; b) J. R. Cheeseman, M. J. Frisch, G. W. Trucks, T. A. Keith, J. Chem. Phys. 1996, 104, 5497. [2] For an introduction in the applied methods and basis sets, see: a) W. J. Hehre, L. Radom, P. v. R. Schleyer, J. A. Pople, Ab initio Molecular Orbital Theory, Wiley: New York, 1986; b) J. B. Foresman, Æ. Frisch, Exploring Chemistry with Electronic Structure Methods, 2nd edn., Gaussian Inc.: Pittsburgh, 1996. [3] M. Kaftory et al., The Structural Chemistry of Organosilicon Compounds, in Chemistry of Organic Silicon Compounds, Z. Rappoport, Y. Apeloig, Eds., John Wiley: New York., 1998, Vol. 2, Part 1. [4] All calculations were performed with Gaussian 98 (Revision A.9), M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, V. G. Zakrzewski, J. A. Montgomery, R. E. Stratmann, J. C. Burant, S. Dapprich, J. M. Millam, A. D. Daniels, K. N. Kudin, M. C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G. A. Petersson, P. Y. Ayala, Q. Cui, K. Morokuma, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. Cioslowski, J. V. Ortiz, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P. M. W. Gill, B. G. Johnson, W. Chen, M. W. Wong, J. L. Andres, M. Head- Gordon, E. S. Replogle, J. A. Pople, Gaussian, Inc., Pittsburgh PA, 1998. [5] G. I. Csonka, J. Reffy, Chem. Phys. Lett. 1994, 229, 191. [6] A: Si: 6-311+G(2df), all other elements 6-31G(d). [7] K. Wolinski, J. F. Hilton, P. Pulay, J. Am. Chem. Soc. 1990, 112, 8251. [8] a) Identical calculations were done also for hexafluorodisiloxane, hexachlorodisiloxane, and hexamethyldisiloxane; b) For experimental data about siloxanes: W.S. Sheldrick, Structural Chemistry of Organic Silicon Compounds, in The Chemistry of Organic Silicon Compounds, S. Patai, Z. Rappoport, Eds., Wiley: New York, 1989, Vol. 1, Chap. 3, p. 242.