The microwave spectrum and OH internal rotation

The microwave spectrum and OH internal rotation dynamics of gauche-2,2,2-trifluoroethanol Li-Hong Xu, G. T. Fraser, F. J. Lovas, and R. D. Suenram Molecular Physics Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899

C. W. Gillies and H. E. Warner Department of Chemistry, Rensselaer Polytechnic Institute, Troy, New York 12180

J. Z. Gillies Department of Chemistry, Siena College, Loudonville, New York 12211

~Received 24 July 1995; accepted 6 September 1995! The microwave spectra of CF3CH2OH and CF3CH2OD have been investigated from 5 to 26 GHz with a pulsed-nozzle Fourier-transform microwave spectrometer and from 26 to 42 GHz with an electric resonance optothermal spectrometer. Tunneling of the OH proton between the two isoenergetic gauche conformations splits the observed transitions into two tunneling components. An effective rotation-tunneling Hamiltonian is used to fit the a- and b-type pure rotational and c-type torsional-rotational transitions for both isotopomers to better than 5 and 13 kHz for the OH and OD forms, respectively. The tunneling splittings determined from the fits for the OH and OD isotopomers are 5868.6952~16! and 208.5037~42! MHz, respectively. A structural analysis using the moments of inertia of the OH and OD isotopomers determines that the hydroxyl hydrogen is directed toward the fluorine with a F•••H separation of 2.561~1! Å and a dihedral angle of f~CCOH!568.97~6!°. The observed tunneling splittings are fit to a double-minimum potential, giving gauche–gauche tunneling barriers of 763 and 720 cm21 and OH torsional fundamental frequencies of 364 and 271 cm21 for CF3CH2OH and CF3CH2OD, respectively. The uncertainties shown in parentheses throughout the paper are one standard deviation. © 1995 American Institute of Physics.

I. INTRODUCTION

Rotational isomerism and internal rotation of the OH group have been studied in a number of simple alcohols, including ethanol, propargyl alcohol, isopropanol, and fluoromethanol.1–7 The gauche configuration has been observed for all four alcohols mentioned above. Trans conformers have also been identified for ethanol and isopropanol. In the case of ethanol, the gauche conformer is 41 cm21 higher in energy than the trans form.2 The reverse is found for isopropanol where the energy difference, DE ~trans-gauche!, is 175 cm21.6 Since the gauche conformer exists in two isoenergetic forms, tunneling of the hydroxyl proton through the barrier splits the rotational transitions into two tunneling components. In the case of gauche propargyl alcohol, for example, two sets of a- and b-type pure rotational transitions are observed, one set for the symmetric tunneling state and the other set for the antisymmetric tunneling state. In addition, c-type rotation-tunneling transitions are observed between the symmetric and antisymmetric tunneling states. Measurements of the c-type transitions allow direct determination of the tunneling splitting. The gauche– gauche tunneling splitting varies dramatically in the four alcohols noted above. Ethanol has a tunneling splitting of 96.7 GHz,2 propargyl alcohol, 644 GHz,4 isopropanol, 46.8 GHz,6 and fluoromethanol, 1.8 GHz.7 In the case of ethanol and isopropanol, the observed tunneling splittings have been combined with far-infrared torsional transition frequencies to obtain the potential functions for internal rotation of the hydroxyl group.2,6 Microwave studies of the 2-haloethanols, including

FCH2CH2OH,8 ClCH2CH2OH,9 and BrCH2CH2OH,9 have shown that the most stable conformations are gauche, allowing a close approach of the hydroxyl hydrogen with the halogen. The O–H and C–X bonds are nearly parallel and the H•••X nonbonded distance is close to the sum of the van der Waals radii. In the gauche configuration, the O–H and C–X bond dipole moments are nearly antiparallel, giving a favorable dipole–dipole interaction.9 Since internal rotation of the hydroxyl group about the C–O bond in these alcohols does not give isoenergetic gauche forms, tunneling is not possible in the 2-haloethanols. Presumably, an analogous interaction in 2,2,2-trifluoroethanol, CF3CH2OH, should stabilize the gauche conformer and in this case internal rotation of the hydroxyl group would give isoenergetic gauche forms, making tunneling possible. The structures of the trans and gauche conformers of CF3CH2OH are illustrated in Fig. 1. Although there was no high resolution microwave study of 2,2,2-trifluoroethanol, Durig and Larsen derived a potential function for internal rotation of the hydroxy group based upon low-resolution far-infrared measurements of the torsional fundamentals of the OH and OD isotopomers, and their potential is shown in Fig. 1.10 In the present paper, we report microwave assignments of the two tunneling states of gauche CF3CH2OH and CF3CH2OD. The analyses of the rotational spectra provide direct determinations of the tunneling splittings for the two isotopomers. A partial molecular structure is derived from the rotational constants of the two isotopomers after correcting for the effects of tunneling. The observed tunneling splittings are fit to a double-minimum potential and a gauche–

J.Downloaded¬22¬Sep¬2009¬to¬129.6.168.96.¬Redistribution¬subject¬to¬AIP¬license¬or¬copyright;¬see¬http://jcp.aip.org/jcp/copyright.jsp Chem. Phys. 103 (22), 8 December 1995 0021-9606/95/103(22)/9541/8/$6.00 © 1995 American Institute of Physics 9541

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Xu et al.: Microwave spectrum and OH internal rotation

FIG. 1. The gauche and trans conformations of 2,2,2-trifluoroethanol illustrated with the torsional potential of Durig and Larsen ~Ref. 10! obtained from the low-resolution far-infrared spectrum of CF3CH2OH.

gauche barrier is obtained which differs significantly from the barrier determined in the far-infrared study.10 II. EXPERIMENT

The rotational spectrum of 2,2,2-trifluoroethanol was measured from 5 to 26 GHz with pulsed-nozzle Fourier transform microwave spectrometers at Rensselaer ~Ref. 11! and at NIST ~Refs. 12 and 13! operating with the gas pulse directed along the cavity axis.14 Gas mixtures of 1% by volume of CF3CH2OH were used in argon or 80%Ne/20%He, with the sensitivity approximately a factor of two higher in the Ne/He mixture. Saturated D2O inlet lines were used with CF3CH2OH to obtain the spectra of CF3CH2OD. Additional microwave measurements were made between 26 and 42 GHz using an electric-resonance optother-

FIG. 2. Electric resonance optothermal spectrum of 2,2,2-trifluoroethanol showing the b-type K 2158-7 Q-branch series for the symmetric (s) and antisymmetric (a) tunneling states. The spectrum was acquired in approximately 275 s.

FIG. 3. Electric resonance optothermal spectrum of 2,2,2-trifluoroethanol showing the b-type K 2153-2 Q-branch series for the symmetric (s) and antisymmetric (a) tunneling states.

mal spectrometer15 by seeding CF3CH2OH in helium. A sample EROS spectrum of the two K 2158 –7, Q-branch series is shown in Fig. 2. In the absence of tunneling, the Q-branch transitions for the symmetric and antisymmetric states become degenerate. The EROS transitions were not included in the final analysis because the measurement precision is approximately 50 times worse than in the Fouriertransform microwave measurements. A. Spectroscopic analysis

tion

Initial microwave searches were guided by a low resoluStark and optoacoustic microwave study of

FIG. 4. The low J rotational energy levels of the symmetric (s) and antisymmetric (a) tunneling states of gauche CF3CH2OH. The vertical lines show pure rotational a- and b-type transitions while the c-type torsionalrotational transitions connect rotational levels from the symmetric and antisymmetric states.

J. Chem. Phys., Vol. 103, No. 22, 8 December 1995 Downloaded¬22¬Sep¬2009¬to¬129.6.168.96.¬Redistribution¬subject¬to¬AIP¬license¬or¬copyright;¬see¬http://jcp.aip.org/jcp/copyright.jsp


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TABLE I. Observed microwave transitions for gauche CF3CH2OH in MHz. Experimental uncertainties ~1s! on the frequencies are estimated to be less than 0.004 MHz. s and a refer to the symmetric and antisymmetric tunneling states associated with tunneling of the OH proton between the two isoenergetic gauche configurations. s a a s a s a a s a a s a a s s a a s a a s a a s s a s a s s a a s s a s s a a a a a a a s a a s a a

101 101 321 321 220 220 322 423 423 717 524 524 625 616 211 625 726 515 111 111 414 202 202 313 313 413 312 312 212 212 202 202 211 211 330 936 220 221 423 322 221 220 321 422 523 312 624 212 212 725 110

-

s a a s a s a a s s a s a s a s a s s a s s a a s a a s a s s a a s s a a a s s s s s s s a s a s s s

000 000 312 312 211 211 313 414 414 707 515 515 616 606 101 616 717 505 000 000 404 111 111 220 220 321 221 221 111 111 101 101 110 110 321 927 110 111 413 312 211 212 313 414 515 202 616 101 101 717 000

5625.773 5627.398 7465.901 7490.388 7494.855 7499.885 7637.398 7708.451 7742.871 7786.911 7794.030 7853.845 7892.759 7920.599 7925.188 7984.195 8003.360 8042.741 8116.819 8116.852 8150.377 9860.183 8765.088 9223.005 9247.024 9254.340 9395.928 9415.494 11 202.750 11 220.658 11 251.239 11 254.538 11 260.885 11 276.497 12 499.883 12 508.222 12 906.072 12 934.455 13 225.202 13 295.752 13 349.318 13 433.354 13 464.240 13 506.925 13 562.656 13 584.867 13 633.015 13 692.198 13 711.712 13 719.733 14 015.092

2,2,2-trifluoroethanol.16 Subbands which fit the relation, n5(2A2B2C)(K 21 1 21 ), were assigned to a b-type Q-branch series of the nearly prolate gauche rotamer.16 Figure 3 shows one of these Q-branch series observed with the EROS spectrometer. These data correctly predicted the location of the K 2151-0, b-type Q-branch transitions in the 7.3– 8.0 GHz region measured in the present Fourier-transform experiments. However, there were far more lines observed than predicted by our structural model and it was not possible to obtain a Q-branch spectral assignment. The structural model also predicted a-type, J51-0, 2-1, and 3-2 tran-

s s a s a a s s a a s a a s s s s s a s a a s a a s s s a a s s a s a s a s s s a a s s a a s s a s s

404 303 303 515 202 414 414 514 413 312 625 524 523 624 524 523 551 550 313 313 322 321 303 303 312 322 321 312 212 211 321 322 221 221 220 220 313 413 313 404 404 414 414 404 404 413 422 422 322 423 322

-

a s a a s a s a a s a a a a s s a a a s a a s a a s s s s s a a a s a s a a s s a a s s a a s a a a s

312 212 212 423 110 321 321 422 322 220 533 431 432 532 431 432 541 542 212 212 221 220 202 202 211 221 220 211 110 111 211 212 110 110 111 111 202 303 202 313 313 313 313 303 303 312 321 312 211 313 211

14 086.608 14 415.618 14 443.516 14 546.271 14 605.839 14 771.096 14 782.701 14 958.662 15 054.648 15 245.360 15 533.502 15 549.293 15 557.538 15 600.455 15 668.254 15 703.823 16 735.249 16 735.249 16 805.548 16 830.697 16 860.643 16 861.591 16 876.094 16 881.186 16 890.546 16 900.262 16 904.718 16 914.211 17 043.506 17 159.152 18 549.903 18 631.970 18 755.511 18 775.208 18 785.293 18 804.335 19 243.216 19 254.965 19 291.178 20 084.953 20 145.059 22 409.671 22 440.400 22 500.035 22 507.093 22 519.367 22 541.656 24 201.009 24 355.265 24 357.607 24 398.986

sitions for the gauche conformer in the region of 5.6, 11.2, and 16.9 GHz, respectively. All of these transitions up to K52 were split into two components due to tunneling of the OH proton between the two isoenergetic gauche configurations. Stark effect measurements were used to obtain initial assignments of the lines. Detailed assignments of the observed spectra were obtained by combination differences of three or four transitions summing to less than 10 kHz. Figure 4 illustrates a few of the K 2150,1 rotational energy levels of both states. Pure rotational a- and b- type transitions are observed within the symmetric and antisymmetric tunneling



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TABLE II. Observed microwave transitions for gauche CF3CH2OD in MHz. Experimental uncertainties ~1s! on the frequencies are estimated to be less than ;0.010 MHz and are limited by the complex observed line shapes resulting from unresolved or partially resolved deuterium nuclear quadrupole hyperfine structure. s and a refer to the symmetric and antisymmetric tunneling states associated with tunneling of the OD deuteron between the two isoenergetic gauche configurations. a a s s a s a a s a s a a s s a a a a a a a a s s a s a a s a s a s s a a

220 423 110 111 111 202 110 202 202 202 212 212 202 202 211 211 836 735 633 533 532 432 431 211 212 212 303 211 303 303 303 414 413 413 313 313 303

-

a a a s a a s a s s s a a s s a s s s s s s s a s a a s a s s s a s s a a

211 414 000 000 000 110 000 111 111 110 111 111 101 101 110 110 826 725 625 523 524 422 423 101 101 101 211 101 212 212 211 321 322 322 212 212 202

7571.986 7814.388 7817.712 8001.409 8002.359 8196.694 8235.164 8427.869 8430.402 8612.470 10 927.181 10 934.999 10 953.369 10 954.433 10 974.020 10 980.757 12 859.709 12 868.925 12 881.612 12 883.433 12 885.745 12 888.147 12 889.124 13 314.939 13 451.228 13 460.501 13 646.772 13 738.524 13 922.185 13 934.084 14 067.767 14 152.032 14 437.111 14 501.021 16 388.030 16 424.272 16 429.300

states and c-type torsional-rotational transitions connect the levels between the symmetric and antisymmetric states. The observed Fourier-transform microwave transitions for CF3CH2OH and CF3CH2OD are listed in Tables I and II. Transitions were only observed for the gauche conformer, consistent with the trans conformer being higher in energy.6 As mentioned earlier, transitions were measured for both the symmetric and antisymmetric tunneling states associated with the isoenergetic gauche configurations. The tunneling state selection rules for the a- and b-type transitions are symmetric–symmetric and antisymmetric–antisymmetric, while for the c-type transitions they are symmetricantisymmetric since the a and b axis components of the molecular dipole moment are symmetric functions of the tunneling coordinate while the c-axis component is an antisymmetric function of the tunneling coordinate. In Table I, we denote the symmetric tunneling state by s or ‘‘1,’’ and the antisymmetric tunneling state by a or ‘‘2.’’ No evidence was found for any splitting associated with the internal rotation of the CF3 top. The transition frequencies listed in Tables I and II were

s a s s s a a s a s a a s s a s a a s a s a s a s a a s a s s s a a a s s

303 321 322 321 312 312 221 221 220 220 220 221 312 313 313 404 312 404 404 404 515 414 414 404 404 423 422 422 413 413 321 322 322 321 322 414 413

-

s a s s s a a s a s s s a s a a s a s s s a s a s a a s a s a a a s s s a

202 220 221 220 211 211 110 110 111 111 110 111 202 202 202 312 202 313 313 312 422 313 313 303 303 322 321 321 312 312 211 212 211 211 212 303 303

16 430.882 16 431.155 16 432.491 16 432.758 16 438.808 16 473.460 18 552.637 18 553.573 18 576.999 18 578.491 18 761.608 18 786.391 18 800.314 18 884.824 18 931.375 19 079.744 19 257.547 19 402.251 19 452.462 19 533.291 19 548.968 21 742.274 21 848.059 21 904.324 21 906.405 21 908.119 21 908.774 21 910.898 21 966.449 22 074.345 23 796.756 23 866.458 24 002.784 24 218.742 24 290.097 24 302.003 24 445.336

fit to essentially experimental precision using the effective rotation-tunneling Hamiltonian of Quade and Lin,17 and others18,19 H5 @ A 1 J2a 1B 1 J2b1C 1 J2c # u 1 &^ 1 u 1 @ A 2 J2a 1B 2 J2b 1C 2 J2c 1 n tun# u 2 &^ 2 u 1 @ D ac ~ JaJc1JcJa! 1D bc ~ JbJc1JcJb!#@ u 1 &^ 2 u 1 u 2 &^ 1 u # .

~1!

Here, u1& and u2& are J50 tunneling wave functions for the symmetric and antisymmetric tunneling states, respectively, A, B, and C are rotational constants, ntun is the J50 tunneling splitting, and D ac and D bc are off-diagonal rotational constant terms. The (a,b,c) axis system is defined so that the a,b plane contains the heavy atoms and the c axis is normal to this plane. Matrix elements of H were evaluated using a symmetrized product basis of tunneling wave functions, u1& and u2&, and prolate symmetric rotor wave functions, u JKM & . The Hamiltonian allows the A, B, and C rotational constants to differ between the symmetric and antisymmetric



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TABLE III. Spectroscopic constants for gauche CF3CH2OH and CF3CH2OD in MHz. For CF3CH2OH, DJ , DJK , and DK , and for CF3CH2OD, B1C, B2C, A, DJ , DJK , and DK , are constrained to be the same for the two tunneling states. Uncertainties are one standard deviation from the least-squares fit. CF3CH2OH Antisymmetric B1C B2C A DJ DJK DK D bc D ac ntun sa

CF3CH2OD Symmetric

Antisymmetric

5626.224 61~44! 5626.239 26~41! 29.1011~11! 29.1512~11! 5318.272 99~36! 5318.282 22~52! 0.000 4991~67! 0.000 499 1~67! 0.003 633~13! 0.003 633~13! 20.002 717~33! 20.002 717~33! 4.930 96~72! 62.609 56~55! 5868.6952~16! 0.0048

Symmetric

5480.3619~49! 5480.3619~49! 21.4188~47! 21.4188~47! 5272.3513~62! 5272.3513~62! 0.000 536~31! 0.000536~31! 0.003 874~16! 0.003874~16! 20.004 69~71! 20.00469~71! 9.818 70~43! 90.740~66! 208.5037~43! 0.013

a

Standard deviation of the least-squares fit.

tunneling states. Because the off-diagonal rotational constant terms, D ac and D bc , do not vanish as the barrier becomes large, the A, B, and C rotational constants do not converge to the rotational constants of the gauche configuration in the high tunneling barrier limit. For a structural elucidation from a gauche reference configuration, the A, B, and C rotational constants need to be corrected for the D ac and D bc terms to determine rotational constants A g , B g , and C g for the gauche minimum. In addition to the D ac and D bc terms, symmetry allows the presence of interactions off-diagonal in the tunneling state of the form 22Q a Ja@ u 1 &^ 2 u 1 u 2 &^ 1 u #

~2!

22Q b Jb@ u 1 &^ 2 u 1 u 2 &^ 1 u #

~3!

and

where Q a and Q b are Coriolis-type constants. The high quality of the fit discussed below using only the D ac and D bc off-diagonal terms indicates that the Q a and Q b Coriolis terms are small. Kakar and Quade2 similarly found for gauche ethanol that the D i j terms were more important than the Q i terms. The spectroscopic constants determined from the least squares fit of the transitions of Tables I and II to H are listed in Table III. The standard deviations of the fits of 5 and 13 kHz for the OH and OD isotopomer are close to the estimated experimental uncertainties of 5 and 10 kHz, respectively. The larger uncertainty for the deuterated species comes from the unresolved or partially resolved deuterium hyperfine structure which makes it difficult to locate the line centers precisely. We have also made extensive measurements of the microwave spectrum of the OH isotopomer in the EROS spectrometer. These transitions were not included in the fit since they are well predicted by the more precise FTMW predictions. For instance, the observed J59–20 lines of the K 2158 –7 b-type Q-branch series are predicted typically within 75 kHz of observation. For the normal isotopomer we fit a different set of rotational constants for the two states. The smaller tunneling splittings observed for the OD species give essentially the

same A, B, and C rotational constants for the symmetric and antisymmetric states. Likewise, in gauche ethanol the symmetric and antisymmetric state rotational constants are more similar for the OD isotopomer than for the OH isotopomer.2 For the OH and OD isotopomer fits of 2,2,2-trifluoroethanol, the centrifugal distortion constants were constrained to be the same for the symmetric and antisymmetric tunneling states. Ignoring centrifugal distortion effects we calculate A g 55319.9 MHz, B g 52828.5 MHz, and C g 52796.3 MHz for CF3CH2OH and A g 55275.6 MHz, B g 52754.3 MHz, and C g 52722.8 MHz for CF3CH2OD by rotating the inertial axis system to remove the off-diagonal terms. The tunneling splittings determined for the OH and OD isotopomers are 5868.6952~16! and 208.5037~43! MHz, respectively. In gauche ethanol the tunneling splittings are significantly larger, 96 739 MHz for the OH isotopomer and 17 097 MHz for the OD isotopomer.2 B. Molecular structure

The spectroscopic data discussed above show that the lowest energy form of 2,2,2-trifluoroethanol has a gauche configuration. There is insufficient isotopic rotational constant data to determine a complete structure for 2,2,2trifluoroethanol. However, it is possible to use moments of inertia calculated from the rotational constants, A g , B g , and C g for CF3CH2OH and CF3CH2OD to estimate the dihedral angles, f~HOCC! and f~FCCO!, and several structural parameters involving the CF3 group. Iterative least-squares fits of the six moments of inertia to four or five structural parameters require fixing the remaining independent distances and angles. We found it necessary to fit parameters associated with the CF3 group in order to obtain overall standard deviations that approached the experimental uncertainties in the rotational constants. Table IV lists the structures determined from the three best fits. The assumed values of the structural parameters were obtained from the known geometries of CF3CH3 ~Ref. 20! and CH3CH2OH ~Ref. 1!. In addition, the barrier to internal rotation of the CF3 group was assumed to be high so that the three fluorine atoms are not all equivalent. This is reasonable because no CF3 internal-rotation splitting



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TABLE IV. Molecular structures of 2,2,2-trifluoroethanol from iterative fits of CF3CH2OH and CF3CH2OD moments of inertia. The moments of inertia used in the iterative fits were obtained from the A g , B g , and C g values of CF3CH2OH and CF3CH2OD; see text.

TABLE V. Comparison of Kraitchman and calculated hydroxyl hydrogen atom coordinates ~Å! of 2,2,2-trifluoroethanol. Kraitchmana

Parametera r~C–C! r~C–O! r~O–H! r~C–H! r~C–F1,2! r~C–F3! u~COH! u~CCO! u~F1,2CC! u~F3CC! f~F1CCO! f~F2CCO! f~F3CCO! f~CCOH! s~uÅ2!c

Fit I b

1.490 1.430b 0.960b 1.100b 1.3432~2! 1.3432~2! 105.4b 112.3b 111.871~5! 110.440~4! 60.23~1! 299.77~1! 180.0b 68.97~6! 0.002

Fit II b

1.490 1.430b 0.960b 1.100b 1.344~1! 1.340b 105.4b 112.3b 112.1~1! 110.5~1! 60.0b 300.0b 180.0b 68.7~5! 0.021

Calculated @f~CCOH!568.9°#b

Calculated @f~CCOH!5120°#c

2.102 0.626 20.677

2.567 20.222 20.716

Fit III 1.490b 1.430b 0.960b 1.100b 1.349~4! 1.327~11! 105.4b 112.3b 112.6~4! 110.7~2! 60.0b 300.0b 180.0b 69.0~5! 0.020

a

All distances are in Å and angles are in degrees. All fitted parameters have uncertainties in parentheses reported as one standard deviation of the fit. Held constant in the least squares fit; see text. c Overall standard deviation of the fit. b

of the transitions was observed at the 4 kHz resolution. The fits assume that the CCO plane bisects the FCF angle formed by the two fluorine atoms, F 1 and F 2 , which are located gauche with respect to the hydroxyl hydrogen. With this structure the third unique fluorine, F 3 , falls in the CCO plane and staggers the methylene hydrogens as shown in Fig. 5. The following parameters were determined in fit I: f~CCOH!, f~F1,2CCO!, r~C–F!, u~F1,2CC!, and u~F3CC!, where the C–F1,2 and C–F3 bond distances were assumed to be equal and f~F1CCO!53602f~F2CCO!. As shown in Table IV, this fit gives f~CCOH!568.97~6!° and f~F1CCO!560.23~1!°. The overall standard deviation is 0.002 uÅ2, with the largest correlation coefficient equal to 0.94. In fit II, f~CCOH!, r~C–F1,2!, u~F1,2CC!, and u~F3CC! were varied and f~F1CCO! is fixed at 60° to give an overall standard deviation of 0.021 uÅ2. The four structural parameters were not highly correlated with the magnitude of the largest off-diagonal element being 0.90 between r~C–F1,2! and u~F1,2CC!. In fit III, f~CCOH!, u~F1,2CC!, u~F3CC!,

aH bH cH

2.103 0.612 0.684

a

Determined from A g , B g , and C g for CF3CH2OH and CF3CH2OD employing Kraitchman equations ~Ref. 21!. b Calculated from the structure listed in Table IV for fit. I. c Calculated from the structure listed in Table IV for fit I substituting f~CCOH!5120° corresponding to a trans–gauche conformation.

r~C–F1,2!, and r~C–F3! are varied in the fit to give a standard deviation of 0.020 uÅ2. However, the resulting CF3 parameters are highly correlated, with three of the off-diagonal correlation matrix elements exceeding 0.99. As shown in Table IV, fit III gives values for f~CCOH!, r~C–F1,2!, u~F1,2CC!, and u~F3CC! which do not differ significantly from fit II. The sensitivity of f~CCOH! and f~F1CCO! to the assumed structural parameters was determined in several calculations. If the values of r~O–H!, u~COH!, and u~CCO! found for 2-chloroethanol8 are used in place of the values listed in Table IV for these parameters, the standard deviations of the three fits increase significantly ~by a factor of 10 for fit I and a factor of 2–3 for fits II and III! but f~CCOH! and f~F1CCO! are still 68° and 60°, respectively. When r~C–C! is fixed at 1.50 Å in fit I, the standard deviation remains at 0.002 uÅ2 and f~CCOH! and f~F1CCO! do not change significantly. However, r~C–F1,2!5r~C–F3! shorten to 1.339 Å and the angles u~F1,2CC! and u~F3CC! decrease to 111.4° and 110.0°, respectively. Kraitchman’s equations21 were used to calculate the hydroxyl hydrogen coordinates in the principal axis system of the normal isotopomer from the rotational constants, A g , B g , and C g for CF3CH2OH and CF3CH2OD. Table V compares these r s coordinates of the hydroxyl hydrogen with r 0 coordinates calculated from the structure listed in Table IV for fit I. The agreement is good and provides support for the assumptions made for the fixed parameters in fit I. A third calculation of the hydroxyl hydrogen coordinates was done by using the structural parameters of fit I, but changing the value of f~CCOH! to 120°. This conformation has a trans– gauche orientation of the hydroxyl hydrogen and there is poor agreement of the results of this calculation with the r s coordinates in Table V. C. Tunneling potential

The observed tunneling splittings were fit to a doubleminima potential, H ir5Fp2 1V ~ a ! ,

FIG. 5. The observed gauche conformer of 2,2,2-trifluoroethanol showing the two dihedral angles, f~CCOH!568.9° and f~F1CCO!560.2°, and the F•••H nonbonded distance of 2.56 Å.

~4!

where F is the effective rotational constant for internal rotation about the C–O bond, a is the internal rotation angle with a5180° corresponding to the trans conformation, and p is the conjugate momentum of a. The F values were assumed to be independent of a, since Durig and Larsen10 find



FIG. 6. Model potential for the OH proton tunneling between the two isoenergetic gauche configurations. Also shown are a few eigenvalues of the potential.

that a constant F value is a good approximation, with the angular dependent terms contributing on the order of only 1–2% to F. For the OH isotopomer we use F520.6949 cm21 and for the OD isotopomer we use F511.1034 cm21, as taken from Durig and Larsen.10 For V~a! we consider a quartic potential of the form, V ~ a ! 5V b @~ a / a e ! 4 22 ~ a / a e ! 2 #

~5!

for 2180°