Journal of MOLECULAR STRUCTURE ELSEVIER Journal of Molecular Structure 445 (1998) 161- 178 The conformers of chloromethyl dimethyl fluorosilane studied by vibrational spectroscopy and ab initio methods’ Valdemaras Aleksa2,“, Peter Klaeboe”‘*, Claus J. Nielsen”, Gamil A. Guirgisb “Department ofChemistq Universir): ofOslo, P.O. Box 1033, 0315 Oslo. Norway ‘Bayer Corporation, Bushy Park Plant, Research and Development Department, Charleston, SC 29423-8088, Received 29 August 1997: accepted 7 October USA 1997 Abstract Chloromethyl dimethyl fluorosilane (CH2CI-(CH3)2SiF) was synthesized and investigated by vibrational spectroscopy and by ab initio quantum chemical methods. Raman spectra of the liquid were obtained at seven temperatures between 295 and 174 K, and spectra of the amorphous and crystalline solids were recorded. The infrared spectra of the vapour, of the amorphous and crystalline states were obtained between 4000 and 50 cm-‘. The compound was mixed with argon and nitrogen and the vapour mixture was deposited on a Csl window at 5 and at 15 K, the infrared spectra were recorded in the range 4000-400 cm-’ before and after annealing. The spectra reveal that the compound exists as anti and gauche conformers in the vapour, liquid, in the unannealed matrices and in the amorphous solid. Six cases were observed when infrared and Raman bands present in the fluid phases vanished after crystallization. Raman temperature studies in the liquid gave A coniH = 0.2 + 0. I5 kJ mol-‘. The gauche conformer was the low energy conformer and the only one present in the crystal. The IR bands vanishing in the argon and nitrogen matrix spectra after annealing to ca. 28-34 K, suggested that the anti conformer had a lower energy than the gauche in both matrices. The conformational barrier was estimated to be ca. 7 kJ mol-‘. Ab initio calculations at the HF/3-2 lG*, HF/6-3 1G*, HF/6-3 1 I G* and MP2/6-3 1G* levels of approximation gave optimized geometries, IR and Raman intensities and vibrational frequencies for the anti and gauche conformers. After scaling, a reasonably good agreement between the experimental and calculated wavenumbers for the anti and gauche conformers was obtained. 0 1998 Elsevier Science B.V. Keywords: Ab initio calculations; Conformations; Halosilanes; 1. Introduction In our laboratories, a series of halomethyl dimethyl halosilanes, CH2X-(CH3)2SiY (X = Cl, Br; Y = H, F, * Corresponding author. ’ In memory of Professor Otto Bastiansen; a good friend. an excellent scientist, teacher and university rector. ’ Permanent address: Department of General Physics and Spectroscopy, Vilnius University, Vilnius 2734, Lithuania. 0022-2860/98/$19.00 0 1998 Elsevier PII SOO22-2860(97)00422-5 Science Vibrational spectra Cl) are currently being investigated by vibrational methods. We are interested in spectroscopic comparing the thermodynamic and spectroscopic results for this series of halosilanes and the differences caused by the various halogen substituents. It is of particular interest to elucidate the differences in bond’ mg between the carbon and silicon atoms by comparing the vibrational spectra and the conformational equilibria in halogenated molecules with C-C, Si-C B.V. All rights reserved 162 V. Aleksa et al.Nournal c?fMolecular Structure 445 ( 1998) 161- I78 and Si-Si central bonds. Various saturated organic compounds containing one [l-3], two [4-61 or three [7] silicon atoms with conformational equilibria have previously been investigated in different laboratories and several molecules with Si-Si bonds without conformers have been studied [8,9]. Two studies of vinyl silanes with conformational equilibria have been published [ 10,l l] and we have recently reported results from spectroscopic studies of four halomethyl dimethyl halosilanes [12-151. Chloromethyl dimethyl fluorosilane, CH&l(CHj)#iF (CDFS), was synthesized and the infrared and Raman spectra were investigated. Raman spectra of the liquid were recorded and polarization ratios were obtained. Spectra of the liquid were recorded at different temperatures, some of them far below the melting point since CDFS, like other related molecules, exhibit large super cooling. Raman spectra of CDFS as a crystal were observed using different cooling techniques. The vapour, amorphous and crystalline samples of CDFS were recorded in the middle and far infrared regions. An infrared matrix isolation technique was employed to obtain spectra of the compound trapped in argon and nitrogen matrices. With this technique, neighbouring bands of different conformers, which overlap in spectra of the vapour and liquid, can frequently be separated, due to the narrow band widths observed in the matrix spectra. Also, by appropriate annealing of the matrices in the temperature range 25-38 K, the conformational barriers can often be estimated in the matrices. The conformational energies, the structure, the force constants and the Raman and infrared intensities were calculated by ab initio quantum chemical methods. Two staggered conformations of CDFS are expected and they are illustrated in Fig. 1. 2. Experimental 2.1. Sample preparation The sample of CDFS was prepared by reaction of chloromethyl dimethyl chlorosilane [ 161 with freshly sublimed antimony trifluoride at room temperature for 1 h. The compound was distilled in a low temperature, low pressure fractionation column and the purity was checked by mass spectrometry. No apparent impurities were observed in the vibrational spectra. 2.2. Raman spectral measurements The Raman spectra were obtained using a Dilor RTI-30 spectrometer (triple monochromator) and recorded digitally. An argon ion laser from Spectra Physics (model 2000) was employed using the 5 14.5 nm line with 90” excitation. Spectra of the liquid, of the amorphous solid and of the crystal were obtained at nine different temperatures between 295 and 174 K in a capillary tube of 2 mm inner diameter surrounded by a Dewar, cooled by gaseous nitrogen evaporated from a reservoir [ 171. From these spectra the enthalpy difference, A,,,rH, in the liquid between the conformers was calculated. All the halomethyl dimethyl halosilanes investigated, including CDFS, had unusually large undercooling and it was sometimes possible to study the liquid 50-60” below the freezing point. The crystallization occurred spontaneously around 155 K and an gauche Fig. 1. The anti and gauche conformers of chloromethyl dimethyl fluorosilane (CDFS). V. Aleksa Table et al.Nournal ofMoleculur Structure 445 (I 998) 161-I 78 163 1 Infrared and Raman Vapour spectral Ar matrix data a and assignments N2 matrix for chloromethyl Solid amorphous 2990 vvw 2992 vvw 2993 vvw 2982 w 2985 w 2985 w 2980 w 2982 m 2982 w 2916 m 2919 m 2978 m dimethyl fluorosilane Liquid ClyStal (CDFS) Solid amorphous crystal 85 K 85 K 2993~~ 2992 w,br,D 2998 w 2915 m 2973 m,br,D 2975 m 2969 m 2967 m Gauche Anti VlVZ VIV2 V) VI Vl vs VI v8 2957 VW 2950 w 2951~ 2952 m 2945 w 2941 VVWJ 2948 w 2940 w 2942 VWL 2944 w 2938 w 2942 w 2935 m,P 2943 m 2934 VW 2934 vvw 2928 w 2933 ml 2929 VW 2909 w 2909 w 2914 s,P 2920 m,br 2810 w 2915 vvw 2915 VW 2868 vvw 2875 VW 2872 vvw 2798 VW 2789 VW 2800 vvw 1475 vvw 1475 VW 1440 VW 1445 “VW 1460 VW 1455 w 1445 w 1446 VW 1435 w 1434 w 1435 1431 w 1432 14lOm 1415 m 1416 m 1405 m 1407 m 1408 m 1407 m 1406 w 1393 w 1395 w 1391 1398 m 1391 m 1388 m 1377 w 1434 VW 1414 w 1302 VW 1412 w 1356 w 1360 VW 1306 VW 1308 VW 1305 w 1300 w 1294 VW 1295 VW 1286 VW 1264 vs 1257 vs 1405 m,D 1408 m 1415 w 1402 w 1401 m 1391 VW 1389 w 1360~ 1359 VW 1260 w 1260 w 1251 w 1248 VW 1288 ww,D 1271 ml. 1268 vs,br 1263 vs 1259 vs 1183 m 1266 s 1265 w,P 1260 vs 1254 s 1184~ 1193 w 1199ww,D? 1192~~ 1186m 1180 w,D? 1183 w 1177m 1178mT 1181 m 1172m 1171 ml 1174 w 1184m 1185 w V. A1ek.w et til./Journul of Molecular Structure 445 (1998) 161-178 164 Table I (continued) VapOUI 1099 m AI matrix N2 matrix 5K 5K Solid crystal amorphous crystal 85 K 85 K 85 K 85 K 1112ml 1108 w 1091 wl? 1102w 1092 VW 978 YW IllOm 1109 w,D 1116 * I100 vw,D 1lOOw 1112w Anti “17 1 “17 986 VW 968 VW 949 w,br Gauche Solid amorphous 1097mT? 994 w,br Liquid 941 m 941 m 924 w 932 w 903 sl 903 vsl 891 s 885 m * 947 VW 912 w 900 s 896 VW 897 VW 895 VW “I8 * 876 “s ?? 888 VW 889 VW 852 s 854 m,D 852 yw * 832 w,D 834 VW 812m 81Om 816m “20 891 vs,br 886 “S 884 “S 893 s 878 ST 876 w 854 “s 854 “s 853 “S 834 “ST 835 “s 834 s VI8 859 s 854 “s 863 VW 853 w ! “19 “19 847 “S 845 “s 837 “S 814 s 810~1 812 sl 812 “s 825 s 817 s 1 * “20 779 WT 783 w,br 776 m 778 m 775 m 772 m 776 “VW 774 w 770 w “21 “21 752 m 753 m 754 m 755 w 754 VW 755 s,P 753 s 756 s “22 v22 748 “wl 145 wl 745 w 749 w 748 s,P 744 s 748 s v23 v23 698 wl 700 m 700 w 702 w,D 702 m 702 m v24 V24 687 s 681 s 681 s 683 m,D 682 m 681 m v25 v25 738 vwl 692 s 695 wL 690 mT 686 sf 687 s 682 m 684 sl I 676 wl V26 672 vwl 663 w 662 ml 662 m 660 m 660 m 654 VW 654 m 654 br 657 m,P 658 m 659 m 657 vwl 659 w,br 650 vwl 650 VW 630”“~ 614 VW *? V26 V. Aleksa et al./Journal Table I of Molecular Structure 445 (1998) 161-178 165 (continued) Interpretation Raman Vapour Ar matrix N2 matrix Solid Liquid Solid amorphous crystal 5K 5K 85 K 85 K 607 W 609 wt 609 w 606m * 607 vs,P 609 YS 602 w 601 vwL 600 vwl 598m 596 m 598 vs,P 598 vs 599 vvw 599 -NW Gauche amorphous crystal 85 K 85 K 573 vvw * Anti V27 596 vs V27 572 vvw 560 w,br * 532 w,br 397 VW 398 vw 398 VW 390 VW 389~~ 385 VW 385 VW 376 VW 376 w 328 s 328 s,br 376 w 331 s 326 s1 330 m,P 329 m 330 m 325 w ?? Vlll 284 ww 280 vs,br 286 s 286 s 279 s 276m*? 285 w,D 281 m 283 m * 267 w,P? 265 m * 246 VW 250 w 237 vw,P 239 m 250 m V30 213 m 213m 211 s,D 210 s,br 213 m %I %I 204 m,D? 203 w,sh 206 m VI2 v32 v33 v34 h3 V35 V35 266 s 203 VW 115 W 202 W 207 VW I77 w,br 184~~ 133m 134m v29 V28 v29 ho 182vw? 132 vw,P 13ow 135w v34 127~~ 94 m,br 105m 84 w 86 W 95 vw 78 w 70 W 64 w 56 m 80 w 61 m a Abbreviations: s, strong; m, medium; w, weak; v, very: br, broad; P, polarized; D, depolarized; and 1, signify bands which increase or decrease in intensities after annealing. 105w 88 VW lattice 74 VW lattice 64 m V36 v3b 43 m lattice 28 m lanice *, denotes vanishing bands; t V. Akksa 166 et ol.Nournal of Molecular anisotropic crystal containing only one conformer was obtained. Independently, the vapour of CDFS was condensed on a copper finger at 80 K. An amorphous phase was first formed and the spectra were quite similar to those of the liquid. After annealing to ca. 145 155 K and retooling to 80 K, a crystalline phase was obtained having much sharper Raman bands than those of the amorphous solid. 2.3. Infrared spectral measurements The spectra in the middle infrared region (MIR) were recorded on the following Fourier transform spectrometers: a Bruker model IFS-88 (4000-450 cm-‘), a Nicolet model 800 (4000-450 cm-‘) and a Perkin-Elmer model 2000 (4000-450 cm-‘), while the far infrared region (FIR) was covered by a Bruker IFS- 113~ vacuum spectrometer (600-50 cm-‘). Beamsplitters of Ge substrate on KBr were employed in the MIR, and beamsplitters with 3.5 and 12 p thickness of Mylar and of the metal mesh type were used in the FIR. The vapour was studied in cells with KBr (10 cm) and polyethylene windows (20 cm). The amorphous and crystalline solids were deposited on a CsI window in the MIR region and on a wedge Structure 445 (1998) 161-l 78 shaped window of silicon in the FIR region, both cryostats were cooled with liquid nitrogen. The sample was diluted with argon or nitrogen (1:500 and 1: 1000) and deposited on a CsI window at either 5 or 15 K of a Displex cryostat from APD (model HS-4) with a three stage cooling system. The spectra of the unannealed matrices were first recorded. Subsequently, the matrices were annealed to temperatures between 15 and 20 K to remove site effects. They were then annealed in steps of 3-5 K to a maximum of 34 K in argon and 32 K in nitrogen, in periods from 10 min to 1 h. Higher temperature measurements are not feasible since the inert gases then have too high a pressure in the cryostat and the matrices turn ‘soft’, followed by diffusion of the solute. After each annealing the window was retooled to 5 K and the spectra were recorded 3. Results and discussion 3.1. Raman spectral results The experimental results for CDFS from Raman and infrared spectra in different phases are collected in Table 1. Tr I I I 6000 x .z 2 2 E 4000 600 Wavenumber Fig. 2. Raman spectra (900-50 I cm-’ cm-‘) of CDFS as a liquid at 298 K and as a crystalline solid at 80 K. V. Aleksa et d./Journal of Molecular Structure 445 (1998) 161-I 167 78 very small intensity variations with temperature of certain bands relative to neighbouring bands were observed, and were interpreted as a displacement of the conformational equilibrium. The Raman bands which vanished upon crystallization belong to one conformer, and they were paired with other bands (often neighbours) which remained in the crystal. However, it is a priori quite uncertain whether these remaining bands are characteristic of only one conformer or whether they belong to overlapping bands of both conformers. In some cases the results of the force constant calculations strongly suggest that the remaining bands may be caused by one conformer only. To determine the conformational enthalpy difference from the variable temperature spectra the bands of the two possible conformers of CDFS should both have reasonably high intensities, they should also be situated on a flat background and not overlap other bands in the spectra. Moreover, they must be ‘pure’, meaning that their intensities should be due to one conformer only, with no contribution, neither from fundamentals nor from combination bands of the other conformer. For this reason, we have measured more than one pair of bands and carried out independent calculations of A,,,@ for each pair. Considerable discrepancies Raman spectra below 1500 cm-’ of the liquid and of the annealed crystalline solid at 80 K are compared in Fig. 2. Certain bands present in Raman spectra of the liquid and of the amorphous solid disappear in the spectrum of the crystal. These bands are equipped with asterisks in Table 1 and attributed to the second conformer which is absent in the crystal. The same bands also disappear in the infrared spectra of the crystalline CDFS. (By comparison with the calculated wavenumbers obtained from the ab initio calculations after appropriate scaling, it will be shown below that the vanishing bands pertain to the anti conformer. Accordingly, the bands present in the crystal should belong to the gauche rotamer.) The small number of vanishing Raman and infrared bands reveal that most of the fundamentals of one conformer overlap those of the other. This conclusion agrees with the earlier results obtained for saturated [l-3] and vinyl [ 10,l l] silanes with conformational equilibria. It is probably due to a low conformational barrier, a relatively weak interaction between the end groups and the long Si-C distance in these molecules compared to the C-C distance in ethanes. Raman spectra of the liquid were recorded at nine different temperatures between 295 and 174 K. Only 1.5 8 -I 1.0 Ei .g 2 0.5 0.0 -1 3200 3100 3000 Wavenumber Fig. 3. Infrared vapour spectrum of CDFS in the C-H stretching 2900 2800 I cm-’ region. Pressure, 45 Torr; path length, IO cm. V. Aleksa et al.Nournal 168 1600 of Molecular Structure 1200 1400 1000 Wavenumber Fig. 4. Infrared vapour spectrum (1600-500 I 800 600 /cm-’ cm-‘) of CDFS as a vapour. Path length, 10 cm; 9 Torr pressure. might occur between the A,,,,H values obtained from different pairs of bands, indicating either poor signal to noise ratio, overlapping bands or an ill-defined background. Eventually, one or both bands of the I 445 (1998) 161-178 I pair may be contaminated by the other conformer, meaning a superposition between a fundamental of one conformer and a fundamental, combination band or overtone belonging to the other conformer. I I I 1.0 8 El .i E OS 0.0 I I I I I I 600 500 400 300 200 100 Wavenumber I cm-’ Fig. 5. Far infrared spectum (630-50 cm-‘) of CDFS as a vapour. Path length, 20 cm; 45 Torr pressure. Curve A: beamsplitter, resolution. Curve B: beamsplitter, 12 p’; resolution, 4 cm-‘. 3.5 p; 2 cm-’ V. Aleksa et al.Nournal of Molecular Structure 700 750 cm-‘) of amorphous 1 (-) I I I 600 500 400 600 /cm-’ and crystalline .) solids of CDFS at 80 K (. I cm-‘) of amorphous 200 300 Wavenumber Fig. 7. Far infrared spectra (630-50 169 I78 independent of temperature. In spite of careful spectral deconvolution and measuring the band areas with advanced computer programs, the calculations based upon band areas were invariably erratic and showed The intensities of each band pair were fitted to the equation In K = AconfHIRT + constant, where K is the ratio in peak heights or integrated areas between anti and gauche bands, and it is assumed that A,,,,H is 0.0 16/- 650 Wavenumber Fig. 6. Infrared spectra (800-500 445 (I 998) (-) I 100 /cm-’ and crystalline (. .) solids of CDFS at 80 K V. Aleksa 170 et al.Nourtd of’Molecular results An infrared vapour spectrum of CDFS in the C-H stretching region (3150-2750 cm-‘) is presented in Fig. 3 while a spectrum in the 1600-500 cm-’ region is given in Fig. 4. A vapour spectrum in the FIR region 650-50 cm-’ at the full pressure of 45 Tot-r appears in Fig. 5. As is apparent from these figures, practically no rotational fine structure was observed except for I 445 (I 998) 161- 178 the bands at 2946, 1177 and 687 cm-’ which all seemed to have ill defined C-type contours. The infrared spectra of the amorphous and crystalline solids at 80 K are presented in the regions 800-500 cm-’ (Fig. 6) and 600-50 cm-’ (Fig. 7). A few infrared bands present in spectra of the amorphous solid vanished in the spectra of the crystal after annealing: 1092, 876, 834,606,266 and possibly 276 cm-‘. They are generally the same bands as those disappearing in the Raman spectra of the crystal (see above). These bands are enhanced in the Raman spectra with higher temperatures and therefore belong to the high energy conformer of the liquid. In the infrared spectra of CDFS in matrices at 5 K the bands are sharp and contain much information. Spectra were recorded of argon and in nitrogen matrices with solute to matrix ratios of 1:500 and 1: 1000 and deposited both at 5 and 15 K. The quality of the infrared spectra of CDFS isolated in matrices is generally better when deposited at 15 K; however, in the case of very low conformational barriers, the 5 K deposition temperature is advantageous to prevent instantaneous conformational conversion. Infrared spectra of CDFS in unannealed matrices and in matrices annealed to 32 K in nitrogen deposited at large deviations in the van’t Hoff plots. Therefore, only peak height measurements were employed in the final quantitative calculations. All together six band pairs were included in the van’t Hoff plots 288/264*, 606*/598, 883*/812, 884*/854 and 1109/l lOO* cm-‘, in which the band equipped with asterisks vanished in the crystal. The bands at 606*/598 cm-’ were both very intense in Raman and assigned to the C-Cl stretching modes of the two conformers. The A,,,‘H(anti - gauche) values calculated from the various band pairs gave remarkably constant values, 0.16, 0.18, 0.22, 0.24 and 0.18 kJ mall’, respectively, leading to a average value of A,,,‘H = 0.2 2 0.1 kJ mall’ with gauche apparently being the low energy conformer (see below). 3.2. Infrared spectral Structure I I 800 Wavenumber 600 I cm-’ Fig. 8. Infrared spectra (I 350-600 cm-‘) of CDFS in a nitrogen matrix (I : 1000) deposited and recorded at 5 K: unannealed (-) (- -) to 33 K. and annealed V. Aleksa et al./Journul ofMolecular Structure I I 1200 1000 800 Fig. 9. Infrared spectra (1350-600cm-‘) of CDFS in an argon matrix annealed to 35 K (. .). cm-‘). Corre5 K are given in Fig. 8 (1000-600 sponding spectra in argon matrices, deposited at 15 K and annealed to 34 K are shown in Fig. 9 (1300-600 cm-‘). Supposedly, the conformational equilibrium of the vapour phase is maintained when the gas mixture is quickly frozen on the CsI window at 5 or 15 K, provided that the barrier to conformational equilibrium is high enough to prevent conversion. Very small spectral changes occurred both in the argon and nitrogen matrices when the samples were X s Hj T Y Fig. IO. Internal coordinates 16 I- I78 I Wavenumber HZ 445 (1998) of CDFS. 171 600 I cm-’ ( I : 1000) deposited at 15 K and recorded at 5 K: unannealed (---_) and annealed to temperatures below 20 K, indicating negligible site effects. This is in contradiction to the related molecule bromomethyl dimethyl fluorosilane [ 12,131, in which large site effects were observed. At higher annealing temperatures (20-34 K) changes were observed both in the argon and nitrogen matrix spectra which were correlated with conformational changes in CDFS. It is highly significant that the bands vanishing in the matrix spectra after annealing did not disappear on crystallization, but were present in the infrared and Raman spectra of the crystals. These bands remained in the crystal and belonged to the low energy conformer in the liquid. Accordingly, opposite conformers were more stable in the liquid and in the matrices, exactly as observed for bromomethyl dimethyl fluorosilane [ 131. It can be clearly seen in both matrices that the bands at 1112, 903, 812 and 600 cm-’ (nitrogen matrix) vanish or are reduced in intensity after annealing. As is apparent from Fig. 9, the band at 1 112 cm-’ was reduced in intensity compared to that at 1102 cm-’ in nitrogen matrices after annealing. The bands around 903 and 812 cm-’ nearly vanished in both matrices after annealing compared to those at 172 V. Aleksa et al./fournal of‘Molecular 884 and 835 cm-’ (Figs. 8 and 9). Another example is the band at 600 cm-’ diminishing in intensity compared to that at 609 cm-‘. Therefore, it can be coneluded that the high energy conformer in the liquid (anti) is the low energy conformer in both matrices. Table 2 Calculated and observed fundamentals a “<al‘ Vib. no. (cm-‘) for the anti conformer h Y,,lc scaled IIR int. c IR int. d Structure 445 (1998) 161-I 78 Accordingly, the conformational stabilities in the liquid state and in the argon and nitrogen matrices are opposite, as observed for bromomethyl dimethyl fluorosilane [ 131. As discussed below, the conformer present in the crystal, which is also the low energy of chloromethyl dimethyl Ruorosilane (CDFS) Dep. Y,,b\. fIK IR PED ’ m m m w w w w w VW m,D m.D _ S22( 100) SO(49), S8(30), S7(20) SS(SO), S8(37), S7( 12) S25(55), S24(45) S7(67), S8(32) S24(55), S25(45) S6(99) S23(99) Sl9(78) Sl8(81), Sl9(12) S33(89) S34(89) Sl3(86) S15(95) S30(94) S 14(92) S28(94) Sl6(38), S3(34), S17(10) S17(43), Sl6(22), S2(10) S31(25), S29(34), S21(22) S3(5l), S16(18), S17(16) S32(74) S2(37), SS4(35), S l7( 13) S21(52), S31(43) S29(47), S28( 14), S31( 14) S32(13) S4(44), S2(23) Sl(69), Sl2(11), S3(10) S9(32), Sl2(27), Sl7(16), S13(12) S26(62), S27(12). S31(lO) SlO(48). Sl l(20) S 11(40), S 10( 18) S9( 16). Sl6(15) S27(58), S26( 19) S20(81) S36(92) Sl2(40), S13(20), Sll(l1) S35(87), S36( IO) A” A’ A’ A” A’ A” A’ A” A’ A’ A” A” A’ A’ A” A’ A” A’ A’ A” A’ A” A’ A” A” 3304 3248 3246 3245 3239 3237 3174 3173 1600 1595 1588 1586 1581 1452 1447 I345 1235 967 948 918 852 842 812 755 734 2974 2923 2921 2920 2915 2914 2857 2856 1440 1436 1429 1427 1423 1307 1302 1210 1111 870 853 826 767 758 730 680 661 6 41 2 5 29 7 3 8 9 8 2 0. I 17 28 56 9 2 151 I60 140 41 17 3 8 0.1 78 125 86 31 136 37 232 3 1 10 2 15 15 2 0.2 2 6 0.5 0.7 0.04 1 2 11 3 2 0.75 0.3 1 0.38 0.75 0.74 0.75 0.01 0.75 0.61 0.75 0.75 0.75 0.75 0.03 0.75 0.3 1 0.75 0.58 0.30 0.75 0.65 0.75 0.54 0.75 0.75 2973 2973 2969 2935 2935 2935 2914 2914 1446 1434 1408 1405 1391 1265 1251 1174 1100 888 854 832 776 755 748 702 683 S A’ A’ A’ 720 628 300 648 565 300 69 4 II 9 22 0.7 0.7 I 0.01 0.74 657 607 285 m w s w,D A” A’ A’ 291 275 211 291 275 211 20 20 0.06 1 I .4 1.3 0.75 0.59 0.58 285 267 211 s s m w,D W,P s,D A” A’ A” A’ A” 205 153 143 128 68 205 153 143 128 68 0.9 0.5 0.1 5 4 0.4 0.06 0.03 0.5 2 0.75 0.41 0.75 0.73 0.75 204 132 132 95 80 w w w m w m,D vw,P VW,P VW,P m,P m,P m,P s,P SF w m m w m,D “S w.P “S m VW vw,D “S VW “S m,D VS W,D m m w m s,P s,P ’ Calculated at the HF level employing the 6-31 I G* basis set. h Scaled ab initio values with factors of 0.9 for stretches and bends and 1.O for frequencies ’ Calculated infrared intensities (km mol-‘) d Calculated Raman cross sections (A” mot-‘). e Contributions of less than 10% are omitted. VW w,D m,D m.P V&P W below 300 cm _I V. Aleksu et al./Joumul conformer in the liquid and in the amorphous solid, is believed to be gauche. Therefore the anti conformer has the lower energy in the two matrices. The lowest annealing temperature at which the equilibrium of the solute molecule is displaced from the high to the low energy conformation was used for estimating the conformational barrier. For both matrices this temperature was ca. 28 K. From the curves given by Barnes [ 181 the conformational barrier was therefore be estimated to be 7-8 kJ mol-‘. Table 3 Calculated Vib. no. and observed fundamentals 173 of Molecular Structure 445 (199X) 161-178 (cm-‘) for the gauche conformer Secondary effects due to matrix viscosity or matrixsolute interactions might influence the barrier height, but the estimated value is supposedly valid for the isolated molecules in the vapour phase. In Table 1 the infrared and Raman bands vanishing in the crystalline solids are signified by asterisks, but the infrared bands in argon and nitrogen matrices are fitted with arrows pointing upwards or downwards, respectively, if the bands increase or decrease in intensity after annealing. of chloromethyl dimethyl fluorosilane (CDFS) ’ Y,,lc U’crlc scaled IIR int. IR int. Dep. Y”tl\. IIR IR PED 3291 3255 3239 2962 2930 2915 7 II 24 71 73 128 0.72 0.74 0.69 2973 2973 2969 m m m m,D 3236 3234 323 I 3173 3168 1601 1593 1589 1586 1577 1451 1446 1353 I249 983 951 883 855 835 822 758 750 694 624 348 289 241 215 203 157 146 126 63 2913 2910 2908 2856 285 I 1441 1434 1430 1427 1419 1306 1301 1218 II24 885 856 795 770 751 740 682 675 625 561 314 289 241 215 203 157 146 126 56 21 31 3 7 6 I5 3 2 2 I3 30 52 I2 0.9 I85 141 122 27 II 2 23 6 33 5 39 23 I I 0.2 0.1 0.07 0.9 3 77 121 23 160 70 2 I4 7 I2 8 3 0.2 0.9 7 0.2 I 0.4 1 2 I9 I 6 3 22 3 I 1 2 0.4 0.03 0.04 0.2 0.8 0.18 0.53 0.65 0.01 0.00 0.73 0.75 0.75 0.75 0.72 0.04 0.35 0.5 I 0.75 0.55 0.47 0.7 I 0.75 0.7 I 0.42 0.75 0.72 0.48 0.05 0.50 0.70 0.36 0.65 0.72 0.55 0.74 0.75 0.74 2935 2935 2935 2914 2914 1446 1434 1408 I405 1391 1265 1251 1180 1109 896 854 812 776 755 748 702 683 657 598 330 285 237 211 204 132 132 95 80 w w w w w VW m,P S22(99) S7(49), S24(48) S24(33). S7(31), SE(l8). S5(14) S5(74), S7( I I ). S24( I I) SE(77). S5( IO) S25(89) S6(70). S23(27) S23(7 1). S6(28) S19(85) Sl8(82), S19(10) S34(49), S33(43) S33(41), S34(46) S13(84). S33(1 I) s I S(94) S30(93) S l4(92) S28(95) S 17(22), S3(42), S l6( 12) Sl6(51), Sl7(20). S2(14) S31(35),S21(32) S3(53), Sl7(25), Sl6( 14) S32(80) S4(50). S2(23) S29(52), S28( 12) S21(44), S31(43) S2(37), S4(21), Sl(l6) Sl(48). Sl2(16). S4(13) SO(23). S 10(20), S26( IO)? S26(39), S I O(23) S9(67), Sl7(14) S27(21), S26(25), Sl2(15) Sll(52), SlO(21) S20(82) S36(90) S I2(42), S27(24), S I3( 19) S35(83) a See footnotes to Table 2. m m w “S “S m m s “S s m m w m s m w s s VW m w w w m w m.D m.P m,P S,P S,P VW m,D W,P w,D w,D VW m,D m VW LP S,P W.D m.D m.P VS,P m,P w,D VW.P s,D m,D vw,P vw,P vw,P VW 174 V. Aleksa et al./Journul C$ Molecular 3.3. Quantum chemical calculations Quantum chemical calculations were performed using the GAUSSIAN-94 program [19]. Several levels of approximations were employed: HF/3-2 1G*, HF/6-3 1G*, HF/6-3 1 lG*, MP2/6-3 I G* and MP2/ 6-31 lG*. The minima on the potential surface were found by relaxing the geometry. The geometrical parameters calculated at the HF/6-3 1 lG* level are very similar to those of bromomethyl dimethyl fluorosilane [ 131 and they have not been presented for the sake of brevity. The calculations of conformational energies of anti and gauche CDFS all favour anti as the low energy Table 4 Symmetry A’ A” coordinates 1 2 3 4 5 6 7 8 9 IO II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 for chloromethyl dimethyl fluorosilane Si-C symmetric stretch Si-C antisymmetric stretch Si-F stretch C-Cl stretch CH: symmetric stretch CH 1symmetric stretch CH, antisymmetric stretch CH1 antisymmetric stretch Symmetric C-Si-C bend Antisymmetric C-Si-C bend Antisymmetric C-Si-C bend Si-C-F bend CH2 scissor CH2 rock CH2 symmetric deformation CH2 antisymmetric deformation CH2 antisymmetric deformation CH, antisymmetric deformation CH? antisymmetric deformation CH, torsion Si-C antisymmetric stretch CHZ antisymmetric stretch CH? symmetric stretch CH? antisymmetric stretch CH? antisymmetric stretch C-Si-F deformation C-Si-C deformation CH2 twist CH 2 rock CH 1symmetric deformation CH i antisymmetric deformation CHj antisymmetric deformation CH, antisymmetric deformation CH2 antisymmetric deformation CH #Zl torsion CHx torsion Structurr 445 (I 998) 16/L I78 conformer in agreement with the results [20] for the other CH2X-(CH3)$5iY molecules studied. The conformational energy difference predicted by the HF/6-3 11 G* calculations, employed for comparing the CH2X-(CH3)$iY series of molecules [20], was 4.6 kJ mol-‘. This energy difference did not change substantially when using second order Moller-Plesset perturbation. 3.4. Normal coordinate calculations Analytical HF force constants were derived for each of the two conformers in CDFS, using the 6-31 lG* basis set. The calculated ab initio force constants were (CDFS) S, =3-“?(R, &=6-“‘(2R, +Rz+R,) -R?-R3) s, =s S, = T Ss=2m”z(.s,+s8) S,=6m’l”(d, +d2+d3+dz,+d5+dG) S,=12+(2d,-d,-d,+2d,-d,-de) S,=$(d>-d?+ds-de) S,=6-“2(X,+177+Xj-~,-~2-~j) S,,=6-“‘(2Z, --Ez-E3) S,, =6-“‘(2+, -@y$) .S,,=Q ~,,=~(Yl+Y?+4+~2) .~,4=;(Y,+Y?-e,-ez Sls=l2~‘!?(P,+P2+P3--01,--012--013+Pq+P5+Ph-Q14-015-01h) S,,=W’iZ(2P, -Pz-P3+2P4-Ps-P6) &,=f(fi,-&+0,-L&) s,8=12~‘~~(201,-01~-oIj+201~-01s-01~) Sw=~(olz-%+~S-%) szo=2~“*(7*+Q) S,, =2m”2(Rz-R3) S,,=2-“*(s,-s,) &=6-“*(d, +dz+d,-d,-d,-d,) S>1=12-‘i2(2d, -d2-d3-2d4+ds+dh) S>s=t(d2-d-(-ds+de) SZh=2-“*(E2-E3) S,,=6-“+-@3) Szx=f(~l-~*-~,+~2) &9=f(Yl-Y*+h-b) s,“=l2-“*(p,+P2+P3-a,-~~-a~--P~-P5-P6+(Y~+(Ys+01~) S,,=12-‘12(2P,--P?-P3-2P4+Ps+Pb) &*=f(P*-P3-Ps+&) s,,=12~“~(201,--01*--01~-2~~+01s+01~) s,,=~(oI?--(y~--oIs+oL~) &5 =71 s36=2-“*(72-73) V. Aleksa et al./Journal of Molecular transformed from Cartesian to symmetry coordinates, derived from a set of valence coordinates. The ab initio calculated wavenumbers are invariably larger than the experimental values. In order to make a complete assignment of the observed infrared and Raman bands, a normal coordinate analysis with scaled force constants was carried out. Various scaling factors to the different types of motions were tested in an iteration procedure. However, reasonably good agreement between the experimental and calculated wavenumbers was achieved by using scaling factors of 0.9 for the stretching and bending modes above, and 1.0 for the modes below 400 cm-‘. The infrared intensities, Raman scattering cross-sections and Raman polarization ratios were calculated and these data are listed in Tables 2 and 3. The potential energy distributions (PEDs) given in Tables 2 and 3 are expressed in terms of the symmetry coordinates. The normalized symmetry coordinates have been constructed from a set of valence coordinates which are given in Table 4. Only PED terms greater than 10% have been included in Tables 2 and 3. The C-H, C-Cl and Si-F stretching modes are reasonably well localized, but the CH3 rock, C-C stretches and the skeletal deformations are highly mixed. Obviously, the vibrational modes for the anti conformer, separated into symmetry species A’ and A”, are more localized than those of the gauche conformer in which all the modes belong to the same species. 4. Discussion 4. I. Conformations It can be seen from Table 1 that the vibrational bands at 1100, 888, 834, 609 and 265 cm-’ (Raman bands of the liquid) vanish during crystallization both in the infrared and Raman spectra. In addition, the Raman bands at 947, 560 and 325 cm-’ with no IR counterparts seem to disappear and the IR band at 279 cm-’ possibly vanishes in the crystal. These bands not only disappear in the crystal, they are also enhanced in the IR spectra of the argon and nitrogen matrices after annealing. Finally, they increase in intensity with temperature as observed in the Raman spectra of the liquid. Structure 445 (1998) 161-l 78 175 As discussed for bromomethyl dimethyl fluorosilane [13], neither the infrared vapour contours, Raman polarization data nor the ab initio calculated energies could answer the following question: do the bands vanishing in the crystal spectra belong to the anti or the gauche conformer? While the calculated energies for the anti and gauche rotamers, derived from the ab initio calculations have large uncertainties, the force constants and the wavenumbers after appropriate scaling usually give a good agreement with those of the observed fundamentals. Within the group frequency regions for the CH3 and CH2 stretching and deformation vibrations, the calculated wavenumbers for the anti and gauche fundamentals overlap completely (Tables 2 and 3). Below 1200 cm-’ there are eight instances in which the anti and gauche fundamentals are separated more than 10 cm-‘. Frequently, the observed anti/gauche band pairs were situated approximately at these frequencies. The following observed band pairs from Raman spectra of the liquid, 1109/1100*, 896/888*, 832*/ 812, 607’1598 and 267*/237 cm-’ (the bands with asterisks vanished in the infrared and/or Raman spectra), were correlated with the scaled, calculated wavenumbers of the anti and gauche conformers, respectively (Tables 2 and 3). It was found merely from the direction of the shifts that in all instances the bands with asterisks were preferably fitted with anti and the remaining bands with gauche. The experimental and calculated shifts were also in reasonable agreement for these band pairs. An exception is the band pair 285/279*, tentatively assigned to Vet, in which 285 cm-’ supposedly coincides with v2x of the anti conformer, and 279 cm-’ was observed only in the infrared spectra. For this uncertain band pair, the 279” cm-’ band was correlated with the anti conformer, and the 285 cm-’ band with the gauche. However, the calculated wavenumbers were separated only by 2 cm-’ making this band pair very uncertain as a conformational probe. Thus, we feel that there are compelling reasons to assign the vanishing bands to the anti conformer, meaning that the gauche conformer remains in the crystal and is also the low energy conformer in the liquid. Some additional arguments support this conclusion. 1. In bromomethyl dimethyl fluorosilane [ 131, in which the vibrational spectra and conformations 176 V. Aleksa et d./Jnurnd of Molecuhr are strikingly similar to those of CDFS, the experimentally determined band pairs and the results of the calculations also revealed that the gauche conformer was present in the crystals similar to the conclusion for CDFS. 2. We expect the anti conformer to be the more stable conformer not only in the vapour but probably in the matrices as well, considering the low enthalpy difference between the conformers in the liquid (0.2 kJ mall’). The bond moments of C-Cl and Si-F are much larger than those of the other bonds in CDFS. It is therefore expected that the anti conformer with opposite C-Cl and Si-F bonds should have a much smaller dipole moment than gauche in which these bonds make approximately a tetrahedral angle. In numerous conformational systems a stabilization of the polar conformer in polar solvents and in the liquid compared to the vapour have been reported [2 11. This observation also agrees with the dielectric theory first proposed by Onsager [22]. Therefore, while anti is the low energy conformer in the matrices and, presumably, in the vapour, the stabilization of the polar gauche molecules in the liquid leads to gauche being the low energy conformer in the liquid. Again, the findings in bromomethyl dimethyl fluorosilane [ 133 are in complete agreement with the present results. In the related molecules in this series, however, i.e. chloromethyl dimethyl chlorosilane [ 141 and bromomethyl dimethyl chlorosilane [ 1.51,the low energy conformer in the liquid and in the matrices was anti in both cases. Thus, the size, electronegativity and polarization of the halogens apparently play an important role for the relative conformational stability. In the two related molecules, bromomethyl dimethyl silane (CH2Br-(CH&SiH) and dichloromethyl methyl difluorosilane (CHC12-CH$iF& interesting phase transitions were observed in the crystals. Still unpublished results from our laboratories reveal that for both molecules two different crystals were formed after annealing, each crystal contained a separate conformer for these compounds, making it possible to obtain very complete spectra of each conformer. Surprisingly, the results for the deuterated molecule CH2Br-(CH&SiD was not as clear cut as for the parent compound, possibly because Structure 445 (1998) 161-178 of small impurities of the latter, lowering the melting and transition points. 4.2. Spectral assignments The assignments of the infrared and Raman spectra of CDFS to the anti and gauche conformers appear in Tables l-3. For the sake of similarity, the fundamentals of both the anti and gauche conformers have been numbered consecutively, instead of the conventional numbering of the modes in the anti conformer belonging to species A’ before those of A”‘. We expect eight C-H stretching fundamentals, VI-v& of each conformer due to eight hydrogens belonging to the CH3 and CHZ groups in CDFS. Some of these are accidentally degenerate and, moreover, the fundamentals of the anti conformer completely overlap those of gauche as expected for these group frequencies. The vI-vx modes were assigned to infrared and Raman bands between 2973 and 2914 cm-’ (wavenumbers from Raman spectra of the liquid when available) while the weak or very weak bands above or below this region are supposedly combination bands or overtones. Similar to the C-H stretching region the ab initio calculations suggest that the CH3 deformation and the CH2 scissoring and wagging modes should overlap considerably. Thus, the scaled wavenumbers suggest (Tables 2 and 3) that five fundamentals (v~---v,~) for both the anti and gauche conformers should be situated between 1440 and 1400 cm-‘, while four fundamentals (Y IJ-~ ,,) were expected between 1350 and 1100 cm-‘. We have assigned v~--v~~ for the two conformers to bands present both in the infrared and Raman spectra at 1446, 1434, 1408, 1405 and 1391, 1265 and 1251 cm-’ (R aman values), respectively. Most of these bands were medium or weak in intensity both in the infrared and Raman spectra, an exception being the very strong infrared bands at 1263 and 1259 cm-’ in the argon matrix, assigned to ~14 and vls. It appears from the infrared matrix spectra that vi6 might be separated into a gauche and an anti fundamental at 1178 and 117 1 cm-‘, respectively. The v i6 mode consisted of an anti and a gauche pair at 1100 and 1109 cm-‘, concluded from the vanishing bands during crystallization and supported by the calculations. The band pair at 896 and 888 cm-’ V. Aieksa et al.Noun~al of Molecular gave rise to very weak bands in the Raman spectra, but intense infrared bands in the amorphous state at 903 and 884 cm-‘. They were attributed to the anti and gauche fundamentals Y,a in excellent agreement with the calculations. The infrared and Raman bands around 854 cm-’ are attributed to overlapping anti and gauche bands of vt9, calculated to be a few wavenumbers apart. A band pair at 832 and 8 12 cm-’ are assigned to v20, supported by spectra of the crystal and by the varit Hoff plots. All the modes between v21 and vZ6 were assigned as coinciding anti and gauche bands although for uZi and u25 the calculations indicated a separation of 10 and 14 cm-‘, respectively, between the two conformers. It is quite uncertain if the anti and gauche bands of u26 coincide at 657 cm-’ or if an anti band is situated at 682 cm-’ in the infrared vapour spectrum, as suggested by the calculations. The two intense Raman bands at 607 and 598 cm-’ and their infrared counterparts form the band pair for anti and gauche conformers of the uz7 mode, mainly associated with CC1 stretch. In bromomethyl dimethyl fluorosilane [ 131 the corresponding C-Br stretches were situated at 576 and 561 cm-‘, and for both compounds they represented the most intense Raman bands in the spectra. For CDFS and for bromomethyl dimethyl fluorosilane [ 131 the ab initio calculations suggested that vzg of the gauche and anti conformers should be separate at 48 and 38 cm-‘, respectively. In the spectra of both compounds, however, no obvious interpretation of ~28 could be found, probably due to overlap of yZ9. In CDFS v2x was tentatively assigned to the bands at 330 (gauche) and 285 cm-’ (anti), the latter possibly overlapping ~29 (gauche) and with a very uncertain ~29 (anti) at 279 cm-‘. More certain are the anti and gauche modes of vjl) at 267 and 237 cm-‘, respectively, well supported by the calculations, whereas for bromomethyl dimethyl fluorosilane [13] the tentative assignment of vjo was contradicted by the calculations. The vibrational modes ~3~--u35 were tentatively attributed to overlapping anti and gauche bands between 220 and 100 cm-’ observed in the infrared and Raman spectra. Particularly uncertain are the methyl torsions, yX3 and yX4, tentatively attributed to the weak, broad band around 132 cm-‘. Finally, the CH2Cl torsional mode of both conformers, vj6, is Structure 445 (1998) 161-178 177 attributed to the infrared band around 70 cm-‘. The corresponding Raman band in the liquid at 80 cm-’ is clearly evident in the R(v) representation [23]. While the assignments of the anti and gauche conformers of CDFS are mainly based upon the changes in the infrared and Raman spectra on crystallization and the results of the force constant calculations, the intensity variations in the matrix spectra after annealing, including argon and nitrogen, support the conclusions. As is apparent from the arrows pointing upwards and downwards in Table 1, in a number of cases the anti bands increased and the gauche bands decreased in intensities after annealing. However, in other instances the intensity variations among the matrix bands were probably caused by site effects and could not be correlated with conformational equilibria. Acknowledgements The authors are grateful to Mrs. Anne Horn for valuable assistance. VS acknowledges a Norwegian Government Scholarship under the Cultural Exchange Programs. References [I] M.A. Qtaitat. J.R. Durig. Spectrochim. Acta 49A (1993) 2139. [2] MS. Afifi, G.A. Guirgis, T.A. Mohamed, W.A. Herrebout, J.R. Durig, J. Raman Spectrosc. 25 (1994) 159. [3] J.R. Durig, G.A. Guirgis, T.A. Mohamed, W.A. Herrebout, MS. Atifi, J. Mol. Struct. 319 (1994) 109. [4] K. Hassler, W. Koll, K. Schenzel, .I. Mol. Struct. 348 (1995) 353. [5] M. Ernst, K. Schenzel, A. Jahn and K. Hassler, J. Mol. Struct.. in press. [6] M. Ernst, K. Schenzel, K. Jahn, W. Koll and K. Haaaler, J. Raman Spectrosc. 28 (1998) 589. [7] K. Schenzel, K. Hassler, Spectrochim. Acta 52A (1996) 637. [8] D.C. McKean, A.L. McPhail, H.G.M. Edwards, I.R. Lewis, V. Mastyukov, J.E. Boggs, Spectrochim. Acta 49A (I 993) 1079. [9] D.C. McKean, H.G.M. Edwards, I.R. Lewis, W.F. Murphy, V. Mastyukov, J.E. Boggs, Spectrochim. Acta 5 IA (I 995) 2237. [IO] J.F. Sullivan, M.A. Qtaitat, J.R. Durig, J. Mol. Struct., (Theochem) 202 ( 1989) 159. [I I] J.R. Durig, J.F. Sullivan, M.A. Qtaitat, J. Mol. Struct. 243 (1991) 239. [I21 H.M. Jensen, P. Klaeboe, C.J. Nielsen, V. Aleksa, G.A. Guirgis and J. R. Durig, J. Mol. Struct. 4 I O-4 I 1 ( 1997) 489. 178 V. Aleksa et al./Journal of Molecular Structure 445 (1998) 161-I 78 [ 131 H.M. Jensen, G.A. Guirgis, P. Klaeboe, C.J. Nielsen and V. Aleksa, Acta Chem. Stand. 52 (1998) in press. [14] H.M. Jensen, P. Klaeboe, V. Aleksa, C.J. Nielsen and G.A. Guirgis, Acta Chem. Stand. 52 (1998), in press. [IS] G.A. Guirgis, A. Nilsen, P. Klaeboe, V. Aleksa, C.J. Nielsen, J.R. Durig, J. Mol. Struct. 410-41 I (1997) 477. [16] J. Speier, J. Am. Chem. Sot. 73 (1951) 826. [ 171 F.A. Miller, B.M. Hamey, Appl. Spectrosc. 24 (1970) 29 I. [18] A.J. Barnes, J. Mol. Struct. 113 (1984) 161. [19] GAUSSIAN 94, Revision D.2: M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M. W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheeseman, T. Keith, G.A. Petersson, J.A. Montgomery, K. Raghavachari, M.A. Al-Laham, V.G. Zakrzewski, J.V. Ortiz, [20] 1211 [22] [23] J.B. Foresman, J. Cioslowski, B.B. Stefanov, A. Nanayakkara, M. Challacombe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.P. Stewart, M. Head-Gordon, C. Gonzalez and J.A. Pople, Gaussian, Inc., Pittsburgh, PA, 1995. P. Klaeboe, J. Mol. Struct. 408-409 (1997) 81. R.J. Abraham, and E. Bretschneider, Internal Rotation in Molecules, in W.J. Orville-Thomas (Ed.), Wiley, London, 1974. L. Onsager, J. Am. Chem. Sot. 58 (1936) 1486. F. Nielsen, Annu. Rep. Progr. Chem., Sect. C, Phys. Chem. 90 (1993) 3.