Rayleigh Scattering Depolarization Ratio and Molecular Polarizability Anisotropy for Gases BY MARTIN P. BOGAARD,t A. DAVID BUCKiNGHAM,* RAYMOND K. PIERENS$ AND ALLAN H. WHITE$ University Chemical Laboratory, Lensfield Road, Cambridge CB2 1 EW Received 14th June, 1978 The depolarization ratio for Rayleigh scattering by 39 molecular species are reported for A = 488.0, 514.5 and 632.8 nm. The literature has been critically surveyed for refractivities which are used in conjunction with the observed depolarization ratios to yield the anisotropy of the molecular polariz- ability of the molecules. Results are given for C02, OCS, CS2, C2H6, C3Hs, isobutane, cyclo- propane, C2H4, allene, C2H2, methylacetylene, dimethylacetylene, spiropentane, cyclohexane, CHC13, CF2CI2, CH3Br, CH31, t-butylchloride, t-butylbromide, ethylene oxide, (CH3)2O, (CH3)2S, H2S, S02, Nz, N20 and CO.C6Ht5, C~HSF, 1,3,5-CsH3F3, C6F6, CH,CN, (CH,)ZCO, CH3F, CHZF2, CHF3, CH3C1, CHZC12, The anisotropy of the electric dipole polarizability is a molecular property which, in addition to its intrinsic interest,l is needed in the evaluation of molecular quadru- pole moments,2 magnetizability anisotropies 3* and molecular hyperpolariz- abilities 1* from measurements of the birefringence induced in gases by electric or magnetic fields. It is also relevant to the evaluation of long-range intermolecular forces. The frequency dependence of the polarizability anisotropy can be used6* ' to deduce orientationally dependent intermolecular forces. The molecular polarizability anisotropy can be determined from measurements of the depolarization ratio of Rayleigh scattered light.Although the advent of laser light sources has made such measurements at well defined wavelengths a relatively easy procedure, the literature contains only a few results. *-l This paper reports measurements, generally for three wavelengths, of the de- polarization ratio of Rayleigh light scattered by a number of gases. The measure- ments have been made over a number of years on molecules which have been of interest here. The results are combined with refractive-index data to yield the anisotropy in the molecular polarizability. EXPERIMENTAL APPARATUS AND PROCEDURE The optical system is very similar to that described by Bridge and Buckingham except that the scattering cell is outside the laser cavity.For measurements at 632.8 nm a 50 mW He+Ne laser was used ; all other measurements were made with an argon ion laser. Both lasers have a beam divergence of < 1 mrad and this introduces negligible errors in the determination of the depolarization ratio. A Glan-Thompson prism sets the plane of j- Present address : $ Present address : S Present address : Australia. 6009, Australia. School of Chemistry, University of New South Wales, Sydney, N.S.W. 2033, School of Chemistry, University of Sydney, N.S.W. 2006, Australia. Department of Chemistry, University of Western Australia, Nedlands, W.A. 3008BOGAARD, BUCKINGHAM, PIERENS AND WHITE 3009 polarization of the approximately vertically polarized laser beam at 90+0.02" to the scattering plane, The silica scattering cell has the entrance and exit windows for the laser beam set at the Brewster angle.It has a blackened horn opposite the viewing window. The cell is connected to a vacuum line through a Millipore filter of 0.10p.m pore size; provision is made for measuring the gas pressure in the cell. After traversing the scattering cell the laser beam falls onto either a monitoring photocell or a light trap. The solid angle over which scattered light is collected is defined by two circular stops; one immediately outside the viewing window of the cell and one in front of the photo- multiplier. The aperture of these stops is chosen to minimise " geometrical errors " ;' the maximum divergence of light accepted by the detector is < 3". The degree of polarization of the scattered light is determined with a second Glan-Thompson prism mounted in a graduated circle fitted with a micrometer-controlled tangent drive ; this enables the orienta- tion of the prism to be set with an accuracy better than 10'.The entrance face of the prism is set accurately perpendicular to the scattered light direction. Both this prism and the prism in the laser beam have an extinction ratio better than An EM1 9558B photo- multiplier is used to measure the scattered light intensity ; the dependence of its sensitivity on polarization direction was checked and found to be negligible. Two methods of measurement have been used: an analogue method and a photon- counting method. No systematic variation in the depolarization ratio was found for those substances investigated with both methods.For the analogue method the laser beam incident on the cell is intensity-modulated with a chopper. A lock-in amplifier with a differential input is used as a null detector; it detects the balance between the signal derived from the photomultiplier and that derived from a photocell which monitors the laser beam after it has passed through the cell. The latter signal is accurately attenuated by a factor F with a voltage divider until balance is achieved ; F-l is proportional to the scattering cross-section of the gas in the scattering cell. Measurements are made for the scattered light polarized parallel and perpendicular to the scattering plane. These measurements are then corrected by subtracting the corresponding values obtained with an evacuated cell and their ratio then yields the depolarization ratio.The voltage divider is constructed from two decade boxes and has sufficient resolution and accuracy to yield depolarization ratios accurate to one part in lo5. The photon-counting method uses an SSR 1120 amplifier/discriminator and SSR 11 10 counter. The laser intensity is suffciently stable over a period of minutes to make continuous monitoring of the laser intensity unnecessary. After traversing the cell the laser beam is caught in a light trap. Depohrization ratios are obtained as the ratio of the counts measured, in a chosen time interval, for the horizontal and vertical components of the light scattered by the gas-filled cell less the relevant counts measured for the evacuated cell.Care is taken to keep the count rate below 5 x lo5 s-l to avoid " pile-up " errors due to the dead-time (10 ns) of the discriminator. The compounds used were commercial samples. Liquids were degassed by several freeze-pump-thaw cycles and by trap-tetrap distillation. The cell was filled by passing the vapour above the degassed liquid through the 0.1 pm filter ; care was taken that the vapour pressure in the cell did not exceed one-half the room temperature saturation vapour pressure. Gases were taken directly from commercial cylinders and passed through the filter. Clean- ing procedures for the cell have been described previously.' The effect of impurities on the observed depolarization ratio, P&s, can be appreciable. If a and b refer to the species and impurity respectively where R = dbat/d,a: and p, a and d are respectively the depolarization ratio, mean polar- izability and number density.The species for which Ap is found to be significant will now be listed; the important impurities, with the upper limit of concentration (mole fraction) as stated by the supplier, are shown in parenthesis : ethane (ethylene 3 %), methylacetylene (dimethyl ether 1.2 %, allene 0.5 %), fluoromethane (dimethyl ether < 1 % by g.l.c.), rifluoromethane (nitrogen 1 %), dimethyl ether (carbon dioxide 0.25 %, methanol 0.5 %),molecule carbon dioxide carbonyl sulphide carbon disulphide ethane propane isobutane cyclopropane ethylene allene acetylene methylacetylene dimethylacetylene spiropentane cyclohexane benzene fluorobenzene 1,3,5-trifluorobenzene hexafluorobenzene acetonitrile acetone TABLE 1 .-DEPOLARIZATION RATIOS, POLARIZABILJTXES AND POLARIZ ABILITY ANISOTROPIES 488.0 4.12 k0.02 4.00 f0.02 7.69 f0.03 0.190 kO.003 0.214 k0.003 0.153 50.003 0.1675 2 0.002 4.225 kO.03 1.266 20.005 1.897 50.005 2.29 kO.01 2.82 kO.01 0.322 kO.OO1 0.165 k0.003 1.98 kO.01 2.11 k0.02 2.27 kO.05 2.46 kO.02 loop0 at Alnm : lO40a/C2 m2 J-* at I/nm : a 514.5 4.085 kO.02 3.95 k0.02 7.56 k0.03 0.188 k0.004 0.208 kO.006 0.1495 5 0.002 0.162 kO.002 4.17 k0.03 1.889 k0.005 2.27 kO.01 2.79 k0.01 0.315 rt0.002 0.163 k0.003 1.96 kO.01 2.09 kO.02 2.24 k0.05 2.44 kO.02 I .2475 2 0.005 632.8 488.0 4.05 k0.02 2.965 3.88 20.05 5.86 7.18 k0.07 10.06 0.166 kO.OO1 5.07 0.195 k0.007 7.165 0.137 kO.010 9.219 0.1425 f 0.002 6.38 1.207 k0.002 4.78 4.00 k0.10 7.08 1.851 kO.004d 3.96 2.25 kO.02 6.49 - 8.32 - 8.96 0.136 k0.003 12.4 1.89 kO.01 11.87 2.006 20.006 11.65 - 11.6 - 11.87 1.725 3.0.05 1.715 f0.05 1.64 k0.05 5.04 0.603 20.006 0.5965f0.004 0.530 k0.005 7.24 514.5 2.957 5.85 9.96 5.06 7.147 9.186 6.35 4.76 7.03 3.94 6.45 8.29 8.93 12.3 11.79 11.58 11.5 11.82 5.02 7.22 632.8 2.933 5.79 9.65 5.01 7.075 9.087 6.28 4.70 6.91 3.88 6.35 8.19 - 12.2 11.56 11.37 11.3 11.65 4.96 7.14 lO4O(ct11 --crl)/C2lm* J-* at Ilnm : 488.0 514.5 632.8 2.398 2.381 2.350 4.67 4.63 4.53 11.40 11.18 10.53 0.858 0.851 0.791 (1.29) (1.26) (1.21) -1.40 -1.38 -1.30 - 1.01 1 - 0.991 - 0.91 8 (2.103) (2.077) (2.014) 5.80 5.72 5.50 2.140 2.129 2.072 3.86 3.82 3.75 5.52 5.47 - - 1.973 1.946 -1.95 -1.93 -1.74 -6.56 -6.48 -6.23 (6.65) (6.58) (6.32) - -6.87 -6.78 -7.33 -7.27 - 2.59 2.57 2.49 (2.19) (2.17) (2.02)TABLE 1 (cont ) .-DEPOLARIZ ATION RATIOS, POLARIZABILITIES AND POLARIZABILITY ANISOTROPIES molecule loop0 at A / n m : 488.0 514.5 lO4Oa/C2 m2 J-1 at I/nm : a lO40(all -al)/C2m* J - 1 at I/nm: a s * 632.8 488.0 514.5 632.8 b 488.0 514.5 632.8 fluoromet hane - - 0.094 k0.002 2.937 2.929 2.904 [3], 2 - - 0.345 difluoromethane 0.118 k O .0 0 4 0.117 fO.004 0.095 k0.003 3.07 3.06 3.04 c (0.409) (0.406) (0.363) trifluoromethane 0.071 kO.01 0.072 fO.01 0.050 50.004 3.145 3.139 3.119 [3] -0.32 -0.32 -0.27 chloromethane 0.787 k0.006 0.779 k0.008 0.755 fO.009 5.12 5.10 5.04 [3], 2 1.768 1,751 1.705 dichloromethane 1.164 k0.005 1.151 k0.005 1.081 k0.003 7.40 7.37 7.26 121 (3.117) (3.084) (2.947) t richlorome t hane 0.691 k0.003 0.689 kO.004 0.652 k0.005d 9.61 9.58 9.47 [3, 281 -3.109 -3.094 -2.974 dichlorodifluoromethane - - 0.687 f0.005 7.54 7.52 7.49 C - - (2.41 5) 2.327 2.308 2.253 bromomethane 0,890 k0.006 0.885 k0.005 0.865 kO.01 6.33 6.30 6.22 [31 3.091 3.062 2.946 iodomethane 0.849 k0.003 0.842 f0.003 0.809 k0.004 8.61 8.57 8.41 ~31 t-but ylchloride 0.156 k0.003 0.152 k0.004 0.129 k0.004 11.5 11.5 11.3 T 1.75 1.73 1.58 t-butylbromide 0.345 kO.004 0.342 20.005 0.329 k0.007 12.9 12.9 12.7 T 2.94 2.93 2.82 ethylene oxide 0.340 k0.004 0.336 k0.004 0.295 kO.01 4.97 4.96 4.91 [31 (1.126) (1.117) (1.034) dimethyl ether 0.375 20.002 0.371 k0.002 0.35 kO.01 5.87 5.85 5.81 [3, 461 (1.397) (1.384) (1.33) dimethyl sulphide 0.509 f0.004 0.506 k0.004 - 8.56 8.51 8.40 T (2.37) (2.35) - hydrogen sulphide 0.0625 k 0.004 0.061 k 0.005 0.044 & 0.003 4.290 4.267 4.199 [27, 40, 561 (0.42) (0.41) (0.34) sulphur dioxide 1.86 kO.01 1.85 fO.01 1.79 k0.01d 4.411 4.389 4.326 [40] (2.359) (2.341) (2.269) - 0.783 nitrogen - - 1.042 k0.006 1.984 1.979 1.967 [6, 491 - nitrous oxide 6.115 k0.02 6.08 k0.02 5.95 f0.04 3.365 3.354 3.318 [5, 14, 601 3.362 3.341 3.267 carbon monoxide 0.521 k0.007 0.519 k0.007 0.480 k0.005d 2.231 2.223 2.200 [37] 0.626 0.622 0.592 a For comparison with literature data in c.g.s.units : 1 e.s.u. (or cm3) = 1.1 12 64 x 10-l6 C2 m2 J-I. References [ ] are selected from Landolt- Bornstein, T refers to liquid data from Timmermans, CSee refractivities in the experimental section. dTaken from Bridge and Buckingham.e Values in brackets are 1040 X 3 4 K] /C2 m2 J-'.3012 MOLECULAR POLARIZABILITY ANISOTROPY FOR GASES hydrogen sulphide (propylene 0.3 %, propane 0.1 %), carbon monoxide (nitrogen 1 %, carbon dioxide 0.9 %). To avoid obscuring the variation of the depolarization ratio with wavelength, the uncertainty shown in table 1 does not include the effect of impurities ; how- ever, Ap fbllows readily from relation (1). REFRACTIVITIES The vaIues of a, the mean molecular polarizability, reported in table 1 have been ob- tained by a critical evaluation of literature data. The mean molecular polarizability a is related to the refractive index n by where Vm is the molar volume, N is Avogadro’s number and co is the permittivity of a vacuum (4x80 = 1.112 65x 10-l’ C V-l m-l = 1 e.s.u.).For gases at low densities n % 1 and (2) reduces to a = (2c0 Vm/N)(n- 1). (3) Most of the mean polarizabilities in table 1 have been obtained from gas-phase refractivities quoted in Landolt-Bornstein l2 (the original literature references, quoted here in square brackets, are given in Landolt-Bornstein ; because of errors in this reference, the original literature was consulted in most cases). Usually the refractivity is reported in a manner which allows for deviations from the ideal gas laws ; where such corrections were not made Vm was calculated using virial coefficients tabulated by Dymond and Smith.13 The quanti- ties n2,60, ni5760 and nd are defined by Landolt-Bornstein ;12 modern values l3 of the virial coefficients of hydrogen yield (nf,760- 1) = 1.000 61 (nd- 1).The following relations obtain : a/C2m2J-l = 6.5910~ (nE760- 1) = 7.1942~ (r~:,57~~-1). Theresultsin table 1 have been selected on the basis of consistency between authors. For some of the compounds studied gas-phase refractivities are not available and in these cases a was calculated from liquid data with the aid of eqn (2). Where a can be calcu- lated from both gas and liquid data agreement is usually within 1 %. Except where noted below values of the refractive index and density of liquids were taken from the com- pilation of Timmermans ;14 these a values are referenced in table 1 as T. The polarizability entry for some compounds, referenced (c) in table 1, needs individual mention.They are, in order : carbon disulphide: Lowrey’s corrections for non-ideal gas behaviour are too large (this was noted by Alms et al.),1° modern values of the virial co- efficients l3 yield the result in table 1 ; dimethylacetylene: based on liquid data,” dispersion assumed to be the same as for methylacetylene ; spiropentane: based on liquid data,16 dispersion assumed to be the same as for cyclopropane ; lY3,5-trifluorobenzene: based on liquid data,l dispersion estimated from results for benzene and hexailuorobenzene ; hexa- Jluorobenzene: based on liquid data ;l difluoromethane: estimated as the average for methane [5, 16, 431 and tetrafluoromethane [5] ; dichlorodifluoromethane: estimated as the average of tetrachioromethane [3, 451 and tetrafluoromethane [5].RESULTS AND DISCUSSION The results of our determinations of the depolarization ratio po, for incident light linearly polarised perpendicular to the scattering plane, are summarised in table 1 together with the mean molecular polarizabilities extracted from the literature. The error estimates attached to the po values are a combination of the reproducibility of results obtained within a series of measurements performed on a given day and those series done at widely separated intervals during which the apparatus was dismantled and reassembled. The error estimate includes, therefore, the uncertainty due to unavoidable differences in alignment. For those species where the presence of impurities leads to a significant uncertainty in po, the error limit may need to be increased accordingly (see experimental section).Table 2 compares the present results with other recent determinations usingBOGAARD, BUCKINGHAM, PIERENS A N D WHITE 301 3 laser light sources ; it shows that results from the principal investigators rarely differ by > 4 %. This figure is an order of magnitude larger than the precision usually attained in the measurement; it is, however, comparable to the 3 % variation in po found by some workers on realignment of the apparatus. The treatment of Bridge and Buckingham shows that the effects of divergence of the incident laser light beam and the angular aperture of the scattered light detector should result in errors < 0.1 % even for CHF3. Slight misalignment of the polarizing prism in the incident beam gives negligible errors.Strain birefringence in the optical windows used is typically rad which results in a negligible error (< 0.1 %) from the window which passes the incident beam. A similar strain birefringence in the window which passes the scattered light yields an absolute error of about 4 x in p o ; this is important only for those species with small depolarization ratios. Particularly significant are the results for COz, OCS, CS2 and N20. These species are readily obtained in a high state of purity and are highly anisotropic, strong scatterers for which strain birefringence and stray light effects are small. Yet the present results differ from those reported by Burnham and co-workers lo* l9 by up to 5 %. Pressure- dependent background scattering may account for these differences but the effects of such scattering are difficult to establish and eliminate with certainty.A slight change (< 1 %) of po with decreasing gas pressure was detected for allene, bromo- methane, chloromethane and isobutane and is mentioned without comment. For these compounds the entries in table 1 are averages for a pressure range 0.1-1 atm. In conclusion, it seems best to assume that the accuracy of depolarization ratios is no better than NN + 3 %. Nonetheless, for a set of po values taken from a given investigator the precision is considerably better than this and the variation of po TABLE 2.-LITERATURE VALUES OF DEPOLARIZATION RATIOS (1oopo) FOR 488.0 AND 632.8 nm. The numbers in parentheses are experimental uncertainties in the last quoted figure.N2 N2O so2 co co2 cs2 ocs CH3CH3 CH, CH2CH3 H2C=CH2 HC=CH CHSCdH C6H6 CH3F CHzF2 CHF3 CH3CI CHC13 CH3Br CH31 CH3CN ref. (10) ref. (19) 1.07 (2) - 6.28 (3) - 1.99 (2) - 4.18 (4) 4.00 ( 5 ) 7.98 (2) - 4.20 (2) - - 0.20 (1) - - - - - - 1.87 (1) - 2.12 (1) 2.10 (5) 1.99 (2) - - 0.10 (1) - - - - 0.78 (1) 0.76 (1) - 0.85 (1) 0.80 (1) 1.68 (2) 1.65 (2) 0.685 (10) - - 488.0 nm others a 1.08 5.5 - 3.8 I - 0.52 0.82 - 1.90 (3)b - - I - - - - this work 6.12 (2) 1.86 (1) 0.52 (3) 4.12 (2) 7.69 (3) 4.00 (2) 0.190 (3) 0.214 (3) 1.266 (5) 1.897 (5) 2.29 (1) 1.98 (1) 0.118 (4) 0.07 (1) 0.787 (6) 0.691 (3) 0.890 (6) 0.849 (3) - 1.535 (3)b 1.73 (5) 632.8 nm ref. (8) this work 1.018 (5) 1.042 (6) 5.96 (2) 5.95 (4) 1.79 (1) 0.480 (5) - 4.03 (1) 4.05 (2) - 7.18 (7) - 3.88 (5) 0.198 (1) 0.166 (1) - 0.195 (7) 1.210 (5) 1.207 (2) 1.851 (4) - 2.25 (2) 1.90 (1) 1.89 (1) - 0.094 (2) 0.179 (5) 0.095 (3) 0.050 (5) 0.050 (4) 0.766 (4) 0.755 (9) 0.652 (5) - - 0.865 (1) - 1.64 (5) - 0.809 (4) (1 Unless otherwise indicated these results are taken from ref.(9) or G. M. Aval, R. L. Rowel1 and J. J. Barrett, J. Chern. Phys., 1972, 57, 3104. From ref. (11).3014 MOLECULAR POLARIZABILITY ANISOTROPY FOR GASES with wavelength is significant. For the dispersion of po the present results are in good agreement with those reported earlier.1° For a gas consisting of randomly oriented molecules in the absence of electronic angular momentum and magnetic fields, the depolarization of Rayleigh scattered light is determined by K the anisotropy of the polarizability tensor aSr : For incident light vertically polarized to the scattering plane, the depolarization ratio p o for Rayleigh scattering at 90" to the incident beam is given by the classical relation The limits of applicability of this expression have been discussed in some detail by Bridge and Buckingham who conclude that for other than the lightest molecules eqn (5) remains valid provided the whole of the rotational Raman spectrum is in- cluded in the measurement of p o ; however, vibrational Raman scattering must be excluded.Observations on the isotropic molecules SF6 and CC14 suggest that the contribution to po from vibrational Raman scattering is of order 2 x This contribution may be significant therefore for all molecules with p o < A recent determination 2o of the depolarization ratio at 514.5 nm for CHF3 explicitly excludes the vibrational Raman contribution and yields po = (2.67 & 0.32) x The result reported here is (7.2 & 1 .O) x K 2 = (3as,as, - %!?a,,)/2~ssa,,.(4) po = 3rc2/(5+4rc2). (5) For molecules with a three-fold or higher axis of symmetry eqn (4) reduces to where all and al are respectively the polarizability components parallel and per- pendicular to the axis of symmetry and a = $apS is the mean polarizability. Applica- tion of eqn (5) and (6) together with the mean polarizability yields the values of (all -al) listed in table 1. The sign of (all -al) has been assigned using experience gained in the examination of the polarizabilities obtained from the Kerr effect in gases and dilute solutions.21 Molecules which belong to the point groups C2, and DZh have three unique polarizabilities axx, a,, and azz, where x, y and z are the principal axes of inertia, and a and K~ are insufficient to determine all three.For these molecules table 1 lists 13arc1. It has been shown 22* 2o that for these asym- metric tops relative intensities of features in the rotational Raman spectrum can yield the magnitude and sign of (axx-a,,,,)/(a-3azZ). Together with a and K : ~ this can yield all three polarizability components. These are available for ethylene 22 and water.2o In favourable circumstances the second-order Stark effect can also yield infor ma- tion on the polarizability anisotropy and, if the mean polarizability is known, all three polarizability components of C2, asymmetric tops can be determined.This has been done for ozone,23* 24 Polarizabilities obtained from the Stark effect are static polarizabilities ; these can be related to the electronic polarizability if the intensity and polarization of the infrared absorption bands are known. There is reasonable agreement O between electronic polarizabilities determined from the static values corrected by subtracting atomic polarizabilities and from the frequency dependence of the light scattering. K = (all -a1)/3a, (6) Two of us (R. K. P. and A. H. W.) acknowledge with gratitude the receipt of a Royal Society and Nuffield Foundation Commonwealth Bursary. M. P. Bogaard and B. J. Orr, Electric Dbole Polarizabilities of Atoms amd Molecules, in International Review of Science, Physical Chemistry, Series 2, ed.A. D. Buckingham (Butter- worth, London, 1975), vol. 2, p. 149.BOGAARD, BUCKINGHAM, PIERENS AND WHITE 301 5 A. D. Buckingham and R. L. Disch, Proc. Roy. SOC. A , 1963, 273, 275. A. D. Buckingham, W. H. Prichard and D. H. Whiffen, Trans. Faruday Soc., 1967,63,1057. M. P. Bogaard, A. D. Buckingham, M. G. Corfield, D. A. Dunmur and A. H. White, Chem. Phys. Letters, 1971, 12, 558. A. D. Buckingham and B. J. Orr, Trans. Faraday SOC., 1969, 65,673. G. A. Victor and A. Dalgarno, J. Chem. Phys., 1969,50,2535. ’ P. R. Certain and L. W. Bruch, Intermolecular Forces, in M.T.P. International Review of Science, Physical Chemistry, Series 1, ed. W. Byers Brown (Butterworth, London, 1972), vol. 1, p. 113. R. L. Rowell, G. M. Aval and J. J. Barrett, J. Chem. Phys., 1971, 54, 1960. * N. J. Bridge and A. D. Buckingham, Proc. Roy. SOC. 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Rossiter (John Wiley, New York, 1972), chap. VI, vol. 1, part 3C. 22 G. W. Hills and W. J. Jones, J.C.S. Faraday 11, 1975, 71, 812. 23 W. L. Meerts, S. Stolte and A. Dymanus, Chem. Phys., 1977, 19,467. 24 K. M. Mack and J. S. Muenter, J. Chem. Phys., 1977,645, 5278. l F. I. Panachev, E. Yu. Korableva and M. I. Shakhparonov, Rum. J. Phys. Chem., 1976,50,1130. (PAPER 8/1116)