Journal of Molecular Structure, 40 (1977) 1-11 @Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands MICROWAVE SPECTRUM, CONFORMATIONAL PREFERENCE, INTRAMOLECULAR HYDROGEN BOND, BARRIER TO INTERNAL ROTATlON, DIPOLE MOMENT, AND CENTRIFUGAL DISTORTION OF l-FLUORO-2-PROPANOL K.-M. MARSTOKK and HARALD MØLLENDAL Department of Chemistry, The University of Oslo, Blindern, Oslo 3 (Norway) (Received 31 January 1977) ABSTRACT The microwave spectra of 1-fluoro-2-propanol, CH3CH(OH)CH,F, and one deuterated species, CH,CH(OD)CH,F, have been investigated in the 18-30 GHz spectral region. Only one rotamer with an intramolecular hydrogen bond forme d between the fluorine atom and the hydroxyl group was assigned. This conformation is also characterized by having the C-F bond approximately anti to the methyl group. The FCCO dihedral angle is 59 :t 2° and the HOCC dihedral angle is 58 :t 3°. Further conformations, if they exist, are at least 0.75 kcal mol-' less stable. Five vibrationally excited states belonging to four different normal modes were assigned and their fundamental frequencies determined. The barrier to internal rotation of the methyl group was found to be 2796 :t 50 cal mol-' . The dipole moment is /la = 0.510:t 0.009 D, /lb = 1.496 :t 0.026 D, /le = 0.298 :t 0.014 D, and /ltot = 1.608 :t 0.030 D. Extensive centrifugal distortion analyses were carried out for the ground and the first excited state of the heavy-atom torsional mode and accurate values were determined for all quartic and two sextic coefficients. INTRODUCTION In mono-substituted propanols, where the hydroxyl group and a protonaccepting gro up are placed on neighbouring carbon atoms, two rotamers with intramolecular hydrogen bonds may exist. These two typical conformations are shown in Fig. 1 in the case of 1-fluoro-2-propanol. Form I has the methyl group approximately anti to the C-F bond, while conformer Il has the methyl group roughly in the gauche position. These rotamers are interchangeable by an approximately 1200 rotation about the CH(OH)-CH2F bond followed by an appropriate rotation about the C-O bond allowing the hydrogen bond to be formed. Further rotamers not stabilized by hydrogen bonding are of course possible, but are expected to be of considerably higher energies. For example, it has very recently been shown by Hagen and Hedberg [1] that the hydrogen-bonded conformation of the closely related niolecule 2-fluoroethanol is at least 2.7 kcal mol-1 more stable than any non-hydrogen-bonded anti form. The high stability of 2 H H H H ',OH H H HO ,CH3 , , , , F" I .... "F" IL Fig. 1. The two possible intramolecularly hydrogen-bonded conformations of l-fluoro-2propanol viewed aiong the CH,F-CH(OH)CH3 bond. Dots indicate possible nonbonded stabilizing interactions. It is seen that rotamer Il might be expected to be stabilized not only by hydrogen bonding, but by dipole-dipole interaction between the methyl group and the C-F bond as well. this rotamer has be en corro borated by microwave [2] and IR [3] spectroscopic studies of the gaseous state and IR [3] and proton magnetic resonance work [4] on condensed phases. Besides intramolecular hydrogen bonding, rotamer Il might be expected to be additionally stabilized by attraction between the methyl group and the fluorine atom. This interaction might be of the dipole type. In fact, Hirota [5] found that the corresponding conformation of the closely related n-propyl fluoride is 0.4 7 :!: 0.31 kcal morI more stable than the anti form. The latter, of course, corresponds to rotamer I of Fig. 1. Since n-propyl fluoride and 1-fluoro-2-propanol are so similar, it was expected that conformer Il would be preferred. However, the microwave spectrum clearly reveals that this is not the case. Contrary to expectation, rotamer I is found to be at least 0.75 kcal morI more stable than form Il. EXPERIMENT AL The title compound was synthesized using the procedure of Bergmann and Cohen [6]. The sample was purified by gas chromatography before use. The deuterated species was made by admitting a small amount of heavy water to the cell already containing the 1-fluoro-2-propanol. The microwave spectrum was studied using a conventional Stark modulated spectrometer. The cell was cooled with small portions of dry ice, and the temperature is estimated to have been roughly -40°C. The 18-30 GHz spectral region was examined. 3 RESULTS Microwave spectrum and assignment of the ground state Preliminary rotational constants were computed for rotamers I and Il by combining structural parameters taken from related compounds. Band moment calculations [7] indicated that rotamer I should have a dipole moment of about 1.6 D with a dominating component of roughly 1.4 D along the b-axis while the hypothetical conformation Il was predicted to have a dipole moment of about 1.4 D with the largest components of approximately 1.0 D along the b- and c-axes. The molecule was found to possess a fairly rich microwave spectrum dominated by Q-branch transitions. The strongest of these were rapidly assigned as being b-type belanging to the ground vibrational state of form I. After same searching, low J b-type R-branch lines were identified by their Stark effects and a full set of rotational constants could be determined. Additional transitions were then measured and inc1uded in a first order Watson [8] centrifugal distortion analysis employing Scf>rensen's program [9]. The improved spectroscopic constants thus obtained were used to predict the frequencies of further medium and high J/P- and R-branch b-type transitions which were subsequently measured and inc1uded in the least squares fitting procedure. In this manner about 230 transitions were assigned. The maximum value of J was 60. At these high values of J the rotational energies are sa large that quite weak transitions are observed. Searches for even higher J transitions were not successful presurnably because intensities were toa low to make definite assignments. As high J lines were assigned, it was found that the first order Watson centrifugal distortion formula was insufficient and sextic distortion coefficients had to be added. Only HJ and HJK could be determined. Inc1usion of additional sextic coefficients led to correlations close to the absolute value of 1 and only marginal improvement of the standard deviation of the fit. In addition to the b-type lines, several very weak low J R-brancha-type tran~itions were assigned. No c-type and no Q-branch a-type lines were found although their frequencies could be very well predicted. This can be explained by the faet that both Ila and Ile are quite small, 0.510 D and 0.298 D, respectively, thus producing insufficient intensities. Table llists 41 selected transitions* and Table 2 shows the speetroscopic constants derived from 205 transitions used in the least squares procedure. As shown in Table 2, very accurate values have thus been obtained not only for the rotational constants but for the centrifugal distortion constants as well. *The complete list of frequencies for the ground, the vibrationally excited states, and the deuterated speeies is available from the authors upon request, or from the Microwave Data Center, Molecular Spectroscopy Section, National Bureau of Standards, Washington D.C. 20234, U.S.A., where it has been deposited. 4 TABLE 1 Selected transition Transition a-type 20" --+30,3 21" --+3", 41,4 --+5 1,5 b- type 1,,0 --+2,,1 30,3 --+41,4 73,4 --+8,,7 104,6 --+113,9 16.,. --+ 177,,1 16.,9--+ 177,10 2614,12 --+2713,15 2614,13 --+2713,14 321.,14 --+3317,17 321.,15--+ 38'1,17 38Z1,I. 46,6,20 46'6,Z1 3317,16 --+39'0,'0 --+39'0,19 --+4715,13 --+47 15,n 5230,22 --+ 5329,25 5230,23 --+5329,'4 5833,25 --+5932". 5833,'6 --+5932,27 1611,S --+151,,4 1611,6 --+151,,3 2315,. --+22'6,7 23,5,9 --+22'6,6 30'9,11 --+29'0,10 30,9,12 --+29,0,9 4025,,5 --+39'6,14 4025,16 --+39'6,13 4730,'7 --+4631,'6 4730,1. --+4631,15 6037,13 -+ 593.,n 6037,,4 --+593.,Z1 70,7--+7.,6 3,,3 --+3,,2 7,,7 --+7,,6 5,,3 --+53" 5,,4 --+53,3 10". --+ 103,7 113,. -+ 114,7 153,12 --+154,1, a:!:0.10 MHz. for the ground vibrational state of CH3CH(OH)CH,F Observed frequencya (MHz) Obs.-calc. frequency (MHz) 18559.95 20100.36 29138.40 0.01 -0.05 -0.03 -0.06 -0.15 -0.26 0.00 0.00 0.00 28453.99 26767.54 18344.59 29612.59 29551.29 29641.41 28351.62 28351.62 23252.83 23252.83 29559.43 29559.43 26670.27 26670.27 21735.17 21735.17 28077.99 28077.99 22258.97 22258.97 20646.34 20646.34 18994.63 18994.63 19750.73 19750.73 29108.65 29108.65 21113.20 21113.20 22362.54 18775.63 28402.94 25105.25 27842.10 20620.48 30003.4 7 28016.92 0.07 -0.02 0.01 0.05 -0.06 0.06 -0.03 -0.04 0.03 0.03 -0.10 -0.10 0.06 0.06 -0.02 -0.02 -0.09 -0.09 0.08 0.08 0.13 0.13 -0.07 -0.07 -0.08 -0.08 0.11 0.11 -0.14 -0.14 0.03 0.03 0.08 -0.02 0.10 0.03 0.00 -0.07 -0.18 -0.28 1.03 1.87 5.93 5.80 28.84 28.84 56.14 56.14 92.09 92.09 165.87 165.87 242.4 7 242.4 7 331.97 331.97 -7.20 -7.20 -21.50 -21.50 -47.45 -47.45 -111.74 -111.74 -181. 70 -181. 70 -372.13 -372.13 -1.32 -0.33 -1.74 -1.02 -1.22 -3.48 -5.70 -10.25 0.00 0.00 0.00 6.00 0.01 0.01 0.11 0.11 0.23 0.23 0.56 0.56 1.23 1.23 1.92 1.92 3.51 3.51 0.01 0.01 0.02 0.02 0.03 0.03 0.03 0.03 0.24 0.24 -0.41 -0.41 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Centrifugal Total (MHz) distortion Sextic (MHz) BLE 2 ctroscopic 'ational constants and CH3CH(OD)CH2F Grounda First excited torsiona ,ber of transitions .1Hz) 205 0.077 MHz) MHz) MHz) kHz) 8570.5576 :!:0.0043 3566.4735 :!:0.0017 2742.4504 :!:0.0021 0.7646 :!:0.0061 6.416 :!:0.058 1.640 :!:0.020 0.1747 :!:0.0038 3.56 :!:0.11 0.001079 :!:0.000051 -0.0209 :!:0.0011 , (kHz) (kHz) tHz) kHz) Hz) (Hz) state for CH3CH(OH)CH2F Second lo west bending modea Ground b 25 0.244 21 0.136 24 0.087 8592.314:!: 0.051 3561.633:!: 0.020 2733.601:!: 0.019 d 8.08 :!:0.88 -11.5:!: 6.0 0.228 :!:0.052 2.96 :!:1.05 d d 8519.227:!: 0.040 3560.406:!: 0.018 2737.034:!: 0.018 d 7.17 :!:0.47 0.8:!: 3.5 0.264 :!:0.030 2.82:!: 0.59 d d 8158.248 :!:0.016 3566.051 :!:0.013 2698.411 :!:0.012 0.59 :!:0.25 7.32:!: 0.42 0.15:!: 2.24 0.182 :!:0.020 3.38 :!:0.42 d d Lowest modea 117 0.062 Second excited heavy-atom torsiona 31 0.151 8525.0492 :!:0.0056 3561.8778 :!:0.0020 2739.9096 :!:0.0024 0.7825 :!:0.0072 6.326 :!:0.064 1.158:!: 0.025 0.1714 :!:0.0059 3.51 :!:0.12 0.00147 :!:0.00019 -0.0144 :!:0.0037 8485.663 :!:0.029 3557.479 :!:0.011 2737.203 :!:0.012 0.85:!: 0.11 6.25:!: 0.39 1.3 :!:2.6 0.197 :!:0.024 2.80 :!:0.48 d d :ertainties represent one standard deviation. 13CH(OH)CH2F. bCH,CH(OD)CH2F. CStandard heavy-atom deviation of the fit. dNot determined. bending Assumed to be zero. <:J1 6 The deuterated species, CH3CH(OD)CHzF, was studied mainly to obtain structural information on the intramolecular hydrogen bond. The assignment of its ground vibrational state microwave spectrum was made quite readily. In this case 24 transitions involving J less than 16 were measured. The resulting spectroscopic constants are displayed in Table 2. Vibrationally excited states The ground state lines were accompanied by a rich satellite spectrum presumably belonging to vibrationally excited states. Five of these were ultimately assigned to four different normal modes as shown in Tables 2 and 3. The strongest satellite spectrum was assigned to the first excited state of the heavy-atom torsional mode. Relative intens it y measurements [10] yielded 109 :t 10 cm-1 for its fundamental frequency. As shown in Table 2, about 120 transitions of b-type were assigned to this made yielding high-accuracy spectroscopic constants. The maximum value of J was 43 in this case and, as in the case of the ground state, the sextic coefficients HJ and HJK were determined. The sec ond eJ~cited state of this mode was also assigned, and the derived spectroscopic constants are collected in Table 2. The variation of the rotational constants upon excitation of the heavy-atom torsional mode is seen to be quite linear. It is therefore concluded that this mode is nearly harmonic [11]. Table 2 includes the spectroscopic constants of what is believed to be the lowest bending mode. The centrifugal distortion constants were not well characterized in this case and so few R-branch lines were measured that I::.Jcould not be determined at all. Relative intens it y measurements yielded 151 :t 15 cm-l for this fundamental. Twenty-one lines of the first excited state of the presumed second lowest bending fundamental were assigned. The derived spectroscopic constants are listed in Table 2. The remarks made for the preceding mode with regard to the centrifugal distortion coefficients are valid in this case as well. TABLE 3 Molecular constants CH,CH(OH)CH,F Rotational constantsa A = 8555.31 :t 0.07 AA AE = 8555.13 :t = 8555.40:!: Direction for the first excited (MHz) B 0.05 BA 0.05 AE state of the methyl group torsional = 3563.57 :t 0.07 c = 2740.37 = 3563.71 :t 0.05 :!: 0.05 CA CE = 2740.49 = 2740.31 = 3563.50 :!: :!: :t cosines Aa = 0.8544 Ab = 0.4641 Ac = 0.2336 Barrier, reduced barrier, and moment of inertia of methyl top V, = 2796:!: 50 cal mol-' s = 78.78 la. = 3.20 uA' a Uncertainties of rotational constants represent one standard deviation. 0.06 0.04 0.04 mode of 7 Moreover, about 20 transitions attributable to the first excited state of the methyl group torsional mode were measured and will be discussed below in the section on barrier determination. Barrier to internat rotation of the methyt group Most of the Q-branch transitions belonging to the first excited state of the torsional mode of the methyl group display ed typical splittings due to tunnelling through the three-fold barrier. The splittings of the R-branch lines were generally less than in the case of the Q-branch transitions and could not be resolved. Both the A- as well as the E-species lines could be fitted reasonably well to Watson's first order centrifugal distortion formula using the same unresolved R-branch transition. The resulting rotational constants are given in Table 3. The centrifugal distortion constants obtained were so inaccurate that they are not quoted in this Table. The Q-branch lines of Table 4 were used to determine the rotational barrier since they display well-defined splittings. Our computer program described in ref. 12 was used to calculate the barrier. The direction cosines of the methyl group quoted in Table 3 were computed from the plausible molecular structure shown in Table 5. The moment of inertia of the methyl group about its symmetry axis was assumed to be 3.20 uA2. V3 was then varied to match the observed splittings exactly with the results shown in Table 4. The average barrier was found to be 2796 cal mol-I. The error limit is difficult to estimate, but :1:50 cal mori seems reasonable when taking into account possible systematic errors. A torsional frequency of 208 cm-I is calculated from the barrier. This alm ost coincides with 210:!: 15 cm-I determined by the relative intensity method. TABLE 4 Split Q-branch lines of the first excited to determine the rotational barrier Transitions Observed VA 9.,8 -> 9,,7 82,6 -> 83,s 92,7 -> 93,6 102,8 -> 103,7 112,9 -> 113,8 132,1, -> 133,,0 62,s -> 63,. 113,8 -> 11.,7 123,9 -> 12.,8 133,10 -> 13.,9 143,,1 -> 144,10 a 20888.70 21091.15 20422.44 20577.06 21753.02 27532.38 28545.65 29915.29 28195.60 27104.12 26956.78 state of the methyl frequencies vA (MHz) - VEb -0.50 -1.62 -1.53 -1.16 -0.98 -0.45 -1.90 -2.49 -2.13 -1.96 -1.49 MI-h' b+fIl (\ l\"T-J~ Barrier (cal mol-') 2800 2780 2761 2803 2784 2827 2755 2793 2816 2807 2835 Average a+fIl1; group torsional 2796 mode used 8 T ABLE 5 Plausible structural parametersa rotamer I of CH,CH(OH)CH2F Assumed struetural C-F C-O FH,C-CH(OH)-(HO)HC-CH, o-H C-H and observed parameters 1.379 A 1.427 A 1.533 A 1.520 A 0.990 A 1.093 A and calculated LFCC LCOH LCCC LCCH LHCH LHCO L FCCCdihedral Fitted struetural LFCOOdihedral LHOCCdihedral Kraitehman Observed: Calculated: Ao Bo Co constants of 109.50° 105.00° 112.00° 109.48° 109.48° 109.48° 180.00° parameters = 59 = 58 :t 2° from :t 30 from syn syn 's eoordinates for the hydroxyl lal Ibl 0.1464 A 1. 7338 A 0.2856 A 1.7338 A Hydrogen bond parameters H. . . F 2.351 A LC-F,OHb 5.72° Rotational rotational eonstants Observed 8570.5576 3566.4 735 2742.4504 O...F LOH. . . F hydrogen atom lei Imaginary 0.1142 A 2.783 A 105.43° (MHz) aSee text; bangle between Calculated 8550.02 3552.66 2731.63 C-F and o-H Difference 0.24% 0.39% 0.39% bonds. The anti form of ethanol has the CH3CH(OH)-fragment in common with, and the hydroxyl gro up conformation similar to, that of 1-fluoro-2-propanol. In anti ethanol the rotational barrier is 3329 :t 25 cal mol-I [13]. The barrier is thus aremarkable 533 cal mol-I less than in anti ethanol. However, the barrier is dose to 2.69 kcal mori which Hirota [5] determined for anti n-propyl fluoride. In another related molecule, 1-amino-2-propanol [14], the rotational barrier was found as 3173 :t 100 cal mol-I, which is doser to the ethanol case than to the title compound. The fluorine atom thus has a large effect on the bar rier height in the two propane derivatives. We find this noteworthy since the fluorine is not bonded to the atom to which the methyl group is attached. Searches for further conformations The assignments made as described above indude a total of about 450 transitions for the parent species and encompass all strong and practically all medium intensity lines of the spectrum. A large fraction of the weak transitions was also accounted for. 9 In an attempt to assign further rotamers careful Stark effect studies were made among the remaining weak lines, but no Stark splitting could be resolved. A restricted version of van Eijck's assignment procedure [15] was then employed. In particular, thousands of possibilities were teste d for transitions that might belong to the expected relatively strong b- and c-type Q-branch of the hypothetical rotamer Il. However, these efforts were unsuccessful. It is felt that additional rotamers would have been discovered if their individual concentrations had exceeded 10-15% of the total. Rotamer I is thus conservatively estimated to be at least 0.75 kcal mol-l more stable than any other conformation of the molecule. Structure Only six moments of inertia were determined for conformation I shown in Fig. 2. Consequently, a full molecular structure cannot be determined. Instead, we restricted ourselves to fitting the dihedral angles FCCO and HOCC with the rest of the structural parameters selected from related molecules as indicated in Table 5. The FCCO dihedral angle was fitted by minimizing the sum of the absolute values of the per cent differences between the observed and calculated rotational constants. In this manner a dihedral FCCO angle of 59 :!: 2° from the syn position was found. The HOCC dihedral angle was found by the following procedure. The principal axes coordinates of the hydroxyl hydrogen were first calculated by Kraitchman's equations [16] as lal = 0.1464 Å, Ibl = 1.7338 Å, and with the c-coordinate found to be imaginary . The a-axis coordinate is so small that no reliable value for the dihedral angle can be found by fitting to this parameter. Fortunately, the b-coordinate is large and the HOCC dihedral angle was then determined by fitting this angle until the b-coordinate was Fig. 2. Model of conformation I of l-fluoro-2-propanol. 10 reproduced exactly. This yielded 58 :t 3° from the sy n position for this angle. In 2-fluoroethanol the FCCO dihedral angle has be en determined as 62°12' :t 1° by microwave spectroscopy [2] and as 64.6 :t 1.1° byelectron diffraction [1], while the HOCC dihedral angle was found to be 55°33' :t 3° [2]. These values are thus dose to their counterparts in 1-fluoro-2-propanol. Table 5 als o summarizes important parameters characterizing the intramolecular hydrogen bond. The OH. . . F distance is seen to be about 2.35 Å which is 0.2 Å shorter than the sum of the van der Waals' radii of fluorine and hydrogen [17]. The C-F and O-H bonds are approximately 6° from bein g parallel. This would lead to a very favourable electrostatic interaction if the popular molecular model which assumes that localized bond dipoles exist within molecules were correct [2, 18]. Moreover , the hydrogen bond is very far from being linear with the O-H, . . F angle of about 105°. This, of course, implies that conditions for covalent bonding are rather unfavourable. The great stability [1-4] enjoyed by the hydrogen-bonded conformations in this sort of molecule thus seems perhaps to be largelya result of favourable electrostatic conditions rather than covalent forces in the hydrogen bond formation. Dipole moment Stark coefficients of the 62.5 -7 63,4 and 91,8 -7 9L,7transitions were used to determine the dipole moment. A DC voltage was applied between the Stark septum and the cell with the modulating square wave voltage superimposed. The DC voltage was calibrated employing the OCS 1 -7 2 transition with /locs = 0.71521 D [19]. The second order coefficients are given in Table 6. A least-squares fit utilizing a diagonal weight matrix was performed. The weights were chosen as the inverse squares of the experimental standard deviations of the coefficients appearing in Table 6. The results were /la "=0.510 :t 0.09 D, /lb = 1.496 :t 0.026 D, and /lc = 0.298 :t 0.014 D with a total dipole moment of 1.608 :t 0.030 D. As expected, this is only slightly larger than that of 2-fluoroethanol. (1.51:t 0.02 D [2]). DISCUSSION Not unexpectedly, an intramolecular hydrogen bond was found to be present in the most stable conformation of the molecule. However, the reason why rotamer I is preferred to the hypothetical form Il is difficult to find, as this is a situation opposite to that of n-propyl fluoride [5]. Steric repulsion between the fluorine atom and the nearest of the methyl group hydrogen atoms is hardly the cause, since there is little reason for believing that there could be rather large geometrical differences between gauche n-propyl fluoride and the hypothetical rotamer Il of 1-fluoro-2propanol. In fact, we think that the present example once more shows how complicated barrier forces may be and how limited simple mo dels of ten 11 T ABLE 6 Stark coefficients and dipole moment Transition of CH3CH(OH)CH2F fl v/E 2 (MHzV-2 cm2)'10. Obs. = 0.510 -19.70 IMI = 7 IMI = 8 IMI = 9 9.,8 -->92,7 Ila 4.38 :t 0.04 -9.50:t 0.09 IMI = 3 IMI = 5 IMI = 6 62,5 --> 63,4 :t Calc. :t 0.20 4.21 :t 0.04 5.56 :t 0.05 7.01 :t 0.07 4.376 -9.623 -19.249 4.507 5.335 6.812 0.009 D, Ilb = 1.496 :t 0.026 D, Ile = 0.298 :t 0.014 D, Iltot = 1.608 :t 0.030 D Uncertainties represent one standard deviation. are for.making predictions. Clearly, the popular model which assumes that potential functions are transferable [20] between related molecules would have failed in this case although it may be quite successful for other examples. ACKNOWLEDGEMENTS The authors are grateful to Cand. Mag. Arne MØller and his supervisor Cand. Real. Leiv Kr. Sydnes for synthesis and to Miss Gerd Teien for gas chromatography of the sample used in this work. REFERENCES 1 K. Hagen and K Hedberg, J. Am. Chem. Soc., 95 (1973) 8263. 2 K. S. Buckton and R. G. Azrak, J. Chem. Phys., 52 (1970) 5652. 3 P. Buckley, P. A. Giguere and D. Yamamoto, Can. J. Chem., 46 (1968) 2917. 4 K G. R. Pachler and P. L. Wessels, J. Mol. Struct., 6 (1970) 471. 5 E. Hirota, J. Chem. Phys., 37 (1962) 283. 6 E. D. Bergmann and S. Cohen, J. Chem. Soc., (1958) 2259. 7 C. P. Smyth, Dielectric Behavior and Structure, McGraw-Hill, New York, 1955, p. 244. 8 J. KG. Watson, J. Chem. Phys., 46 (1967) 1935. 9 G. O. Sørensen, J. Mol. Spectrosc., 22 (1967) 325. 10 A. S. Esbitt and E. B. Wilson, Jr., Rev. Sci. Instrum., 34 (1963) 901. 11 D. R. Herschbach and V. W. Laurie, J. Chem. Phys., 40 (1964) 3142. 12 K-M. Marstokk and H. Møllendal, J. Mol. Struct., 32 (1976) 191. 13 J. P. Culot, Fourth Austin Symposium on Gas Phase Molecular Structure, 1972, paper T8. 14 K-M. Marstokkand H. Møllendal, J. Mol. Struct., 35 (1976) 57. 15 B. P. van Eijck, J. Mol. Spectrosc., 38 (1971) 149. 16 J. Kraitchman, Am. J. Phys., 21 (1953) 17. 17 L. Pauling, The Nature of the Chemical Bond, Cornell University Press, Ithaca, New York, 1960, p. 260. 18 R. G. Azrak and E. B. Wilson, Jr., J. Chem. Phys., 52 (1970) 5299. 19 J. S. Muenter, J. Chem. Phys., 48 (1968) 4544. 20 O. L. Stiefvater and E. B. Wilson, Jr., J. Chem. Phys., 50 (1969) 5385.