J . Phys. Chem. 1985,89, 1309-1312
1309
Cotton-Mouton Effect, Magnetic Anisotropy, and Charge Distribution of Cyclopropane P. B. Lukins,l” D. R. Laver,” A. D. Buckingham,lband G. L. D. Ritchie*” School of Chemistry, University of Sydney, New South Wales 2006, Australia, and University Chemical Laboratory, Cambridge CB2 1 E W, United Kingdom (Received: August 28, 1984)
Measurements of the Cotton-Mouton effect of cyclopropane over a range of temperature (=260-400 K) and pressure (=50-600 Wa) are reported. An analysis of the temperature dependence shows that at normal temperatures the temperature-independent contribution, which arises from distortion of the electronic structure by the magnetic field, is not negligible in comparison with the temperaturedependent contribution from molecular orientation. A definitive value of the molecular magnetic anisotropy is obtained Ax/J T2= -19.2 f 1.9) and this, in combination with the known electric quadrupole moment and molecular geometry, enables other magnetic properties to be derived.
Introduction Considerable interest has been shown in the electric and magnetic properties, in particular the magnetic anisotropy and the degree of electron delocalization, of cyclopropane. The magnetic anisotropy describes the molecular charge distribution and its interaction with a magnetic field and is relevant to considerations of the molecular quadrupole moment, the anisotropy in the second moment of the electronic charge distribution, the diamagnetic and temperature-independent paramagnetic contributions to the magnetizability, and the molecular g valueU2The most recent, and apparently the most reliable, value of the magnetic anisotropy of cyclopropane was obtained from a pulsed Fourier-transform microwave Zeeman spectroscopic study of the cyclopropane-hydrogen chloride and cyclopropane-hydrogen cyanide complexes.’ Of course, cyclopropane itself could not be so examined, and the adequacy of the procedures used to decompose the observed properties of the complexes into those of the free molecules and the reliability of the results have yet to be established. Insofar as the magnetic anisotropy derived in this way was found to be seriously at variance with an earlier result from a single-temperature study of the Cotton-Mouton e f f e ~ t , ~ we were prompted to use the considerably improved equipment now available5 to investigate the latter effect over a wide range of pressure and temperature? We here report a definitive value for the magnetic anisotropy of cyclopropane and quantify the contribution which the magnetic hyperpolarizability makes to the Cotton-Mouton effect of this molecule.
where eq l a is a measure of the refractive index difference, n,, - n,, induced in the gas by the magnetic induction, B, and eq 1b is the theoretical relationship between the observed birefringence and fundamental molecular properties; A7 (= q)laB,)laB I / 3 t a a , 4 , . Aa (= azz- ax,),and Ax (= xZr- x,) are the anisotropies 111 the magnetic hyperpolarizability, the optical-frequency electric polarizability, and the magnetizability, respectively. From perturbation theory,2e*8the magnetizability of a diamagnetic molecule is
in which ri is the position vector describing the ith electron, and L is the electronic orbital angular momentum operator. The magnetic anisotropy of an axially symmetric molecule is therefore expressible in the form
Ax = Axd
+ 2)2]-1[(nn- n , ) B 2 ] B , o
= (N~po~/27oto)[A + ~(2/3kT)AaAx]
(4) a knowledge of these latter properties makes possible the separation of A x into diamagnetic and temperature-independent paramagnetic contributions. In addition, the connection between the molecular g value, which relates the rotational angular momentum to the magnetic moment, the magnetic anisotropy, and the quadrupole moment is, for an axially symmetric molecule
-
g z z ~ z z gxxzxx
= (-Mp/e)[(4m,/e)Ax + 01
(5)
where ,Z and Zxx are the moments of inertia. Obviously, individual values of g,, and gxx cannot be obtained from eq 5, but it is nevertheless of interest to use the free-molecule values of Ax and 0, from birefringence experiments, to define the quantity on the right-hand side of this equation, which can alternatively be estimated from the reported g value and the known molecular structure.
(la) (lb)
(1) (a) School of Chemistry, University of Sydney. (b) University Chemical Laboratory, Cambridge. (2) (a) Flygare, W. H.; Shoemaker, R. L. Symp. Faraday Soc. 1969, No. 3,119-130. (b) Flygare, W. H.; Benson, R. C. Mol. Phys. 1971,20,225-250. (c) Ditchfield, R. In “MTPInternational Review of Science”; Buckingham, A. D., Ed.;Butterworths: London, 1972; Phys. Chem. Ser. 1, Vol. 2, Chapter 4, pp 91-157. (d) Appleman, B. R.; Dailey, B. P. Adv. Magn. Reson. 1974, 7,231-320. (e) Flygare, W. H. Chem. Rev. 1974, 74,653-687. ( f ) Sutter, D. H.; Flygare, W. H . Top. Curr. Chem. 1976, 63, 89-186. (3) Aldrich, P.D.; Kukolich, S. G.; Campbell, E. J.; Read, W. G. J . Am. Chem. SOC.1983,105, 5569-5576. (4) Buckingham, A. D.; Richard, W. H.; Whiffen, D. H . Trons. Faraday
Units The theory of the Cotton-Mouton effect’ gave the molar Cotton-Mouton constant of an axially symmetric, diamagnetic molecule as
SOC.1%7,63, 1057-1064.
-
( 5 ) Lukins, P . B.; Buckingham, A. D.; Ritchie, G. L. D. J. Phys. Chem. 1984.88, 2414-2418. (6) We are indebted to a referee of ref 5 , who encouraged us to undertake
(7) Buckingham, A. D.; Pople, J. A. Proc. Phys. Soc., London, Sect. B 1956,69, 1133-1138. ( 8 ) Buckingham, A. D.; Cordle, J. H. Mol. Phys. 1974.28, 1037-1047.
the present study.
0022-365418512089-1309%01 .SO10 0 1985 American Chemical Societv , , I
(3)
and since Axd can be written in terms of the molecular geometry and the electric quadrupole moment, 0, as
Theory Relevant theory was described in the recent study5 of the temperature dependence of the Cotton-Mouton effects of benzene, 1,3,5-trifluorobenzene, and hexafluorobenzene; symbols and other details not explicitly mentioned here are as in the earlier report. For a system of noninteracting, diamagnetic, and axially symmetric molecules, the molar Cotton-Mouton constant, ,C, is, in SI units (see below)’ ,C = 2nV,p2[3(n2
+ AxP
-
1310 The Journal of Physical Chemistry, Vol. 89, No. 7, 1985 TABLE I: Cotton-Mouton Effect of Cyclopropane at 632.8 m T/K 103T I /K-I no. of Dress. 2.473 10 404.3 16 364.1 2.746 5 343.2 2.914 7 319.0 3.135 16 305.4 3.274 21 295.5 3.384 12 280.1 3.570 3.826 7 261.4
Lukins et al.
D/Wa
no. of meas
106B/m3mol-'
50-160 100-300 125-400 117-350 1 19-600 136-599 105-327 140-155
63 72 35 52 80 110 60 39
-199 -250 -281 -333 -368 -398 -466 -566
lo2' ,C/m5
A-2 mol-I
0.695 f 0.045 0.764 f 0.045 0.738 f 0.050 0.849 f 0.025 0.884 f 0.017 0.939 f 0.015 1.021f 0.039 1.080f 0.030
in which the primed quantities are expressed in cgs units. In order to convert to SI units, each of the primed quantities is transformed into SI units, indicated by unprimed symbols H' = (40apo)'/2H
(7)
A d = ( 106/4aeo)Aa
(8)
Ax' = (106/4a)Ax
(9)
AT' = 105(co/4a)2A~
(10)
so that eq 1 becomes
,C = 2nV,[3(n2 + 2)2]-'[(n,, - n,)H-Z]Hlo
+
= ( N A / ~ ~ O C O ) [ A T(2po/3kT)A~uAx] J
(lla) (llb)
In addition, it is convenient to define the magnetic susceptibility and the magnetic hyperpolarizability in terms of the magnetic induction, B, rather than the magnetic field strength, H, as x*aB = - ( a 2 w a B , aBBh-0 = wo-'xag v*a&yb
= (a2*a,5'/aBy
aBb)B=O
= pO-21?a,9.y6
(12) (13)
from which eq 1, with asterisked quantities implied, follows. The conversion factors for ,C, Aa, Ax, and ATJcan be written as (,C'/cm3
G-2 mol-') = (106/4~)2(,C/m5 A-z mol-') = 0.6333 X 10'O(,C/mS A-2 mol-') (14)
(Aa'/cm3) = (lo6/4ac0)(Aa/C m2 V-') = 0.8988 X 1016(Aa/C m2 V-I) (15) (Ax'/erg G-2) = (lO6/4a)(Ax/m3) = (lO-')(Ax/J T2) (16) (Av'/cm3 G-2) = (1024?reo)-'(A~/Cm2 V-I T2) = 0.8988 X l O * ( A ~ / Cmz V-' T2 ) (17) It should also be noted that the molar Cotton-Mouton constant introduced by Konig: and used by others,'OJ1differs by a factor of 9 from eq 1; and that ATJas defined by Hiittner and collaborators" differs by a factor of 5 from that in the present study. Experimental Section The apparatus was as recently d e ~ c r i b e dexcept ,~ that an alternative gas-handling system, which incorporates a Budenberg super test gauge (accuracy f l P a ) was employed. In addition, the accessible temperature range was extended by using a stream of air passed through dry ice to cool the cell; the precision of measurements a t the lower end of the range was limited by the available vapor pressure, while at the upper end the diminution of the effect became a serious constraint. It may be noted here that at 300 K the molar Cotton-Mouton constant of cyclopropane is approximately 50 times smaller than that of benzene, and KBnig, H. Ann. Phys. (Leiprig) 1938, 31, 289-314. (10)Le Fkre, R. J. W.; Williams, P.H.; Eckert. J. M. Ausr. J . Chem.
(9)
1965, 18, 1133-1152.
(11) Kling, H.; Geschka, H.; Hiittner, W. Chem. Phys. Lett. 1983, 96, 631-635.
3.0
3.5
4.0
103~-1/~-1
Figure 1. Temperature dependence of the vapor-state Cotton-Mouton effect of cyclopropane.
reliable determination of the temperature dependence of the effect in the former was beyond the capability of apparatus previously in u ~ e . ~ , ' ~ A mass spectrometric analysis gave the purity of the sample of cyclopropane as >99.9%; the main impurity was air. Measurements of the magnetic field induced birefringence at 632.8 nm were made a t eight temperatures (=261-404 K) and, a t each temperature, over a range of pressure (up to =600 kPa). From an operational point of view, eq la, the definition of the molar Cotton-Mouton constant, can be written as
,C = [po2hn/3(nz + 2)2aJB2 d1](4/Vm-l)
(18)
in which 4 = (2a1/h)(nl - nl) is the phase retardation in light of wavelength h after traversal of the pathlength, I ; Vm-l,the reciprocal of the molar volume, is proportional to the gas density; and s B 2 d l = 3.289 f 0.045 T2 m.5 The crux of the experiment is therefore the determination, at each temperature, of the slope of a plot of 4 against V,-*. Recorded density virial coefficient^'^ were used to calculate values of V,-' from the observed pressures; second Cotton-Mouton virial coefficients were not discernible. The results are summarised in Table I, where the uncertainties shown are based on the standard deviations derived from the least-squares fitting of straight lines to the density dependence data, together with appropriate allowance for systematic errors. It is of interest to compare the two previously reported single-temperature molar Cotton-Mouton constants (quoted here as 102',C/m5 A-2 mol-') with the values (shown in parentheses) which can be interpolated from the data in Table I. From obs e r v a t i o n ~of~the effect at 546.1 nm and 20 OC. a value of 1.83 (12) Bogaard, M.P.;Buckingham, A. D.; Corfield, M. G.; Dunmur, D. A.; White, A. H. Chem. Phys. Lett. 1972, 12, 558-559. (13) Dymond, J. H.;Smith, E. B. "The Virial Coefficients of Pure Gases and Mixtures"; Clarendon Press: Oxford, 1980.
Electric and Magnetic Properties of Cyclopropane TABLE II: Analysis of the Temperature Dependence of the Cotton-Mouton Effect of Cyclopropane DroDertv intercept/ms A-2 mol-' slope/m5 A-2 K mol-' 1050AT/C m2 V-I T2 lO'OAa/C m2 V-l 1029Ax/J T2 105Ax/J T2mol-' 1 0 2 9 ~ 1/-2~ 1 0 2 9 J~1-2~ ~ io29xxx/~-1-2 io%/C m2 10"'e~,,Zn(z,2 - x?)/C m2 -1O4e(O1Ci(z: - x?)lO)/C m2 1 0 2 9 A ~ d /T2 J 1OZ9AxP/JT2 1046122/kgm2 10461xx/kgm2 1046(gz,Izz- gxxI,,)/kg m2
lo2'
X X
value
* *
-0.09 0.08 0.302 0.025 -20 20 -0.818 0.042b -19.2 f 1.9 -11.6 f 1.1 -65.1 1.3' -77.9 f 1.8 -58.7 f 1.5 5.9 f 1.6d -133.4e 139.3 -61.3 42.0 6.706 4.177f 0.39 f 0.05
(+230)" (-16.1 f 1.6)" (-9.7 f 1.0)" (-74.7 1.7)" (-59.8 f 1.7)" (3.5 f 1.3)" (1 36.2)" (-59.8)" (43.2)" (0.34 f 0.01)'
uValues from ref 3 in parentheses for comparison. bCalculated from data in ref 15 and 17; see text. 'Mean magnetizability, x = (2xxx + xz,)/3, from Barter, C.; Meisenheimer, R. G.; Stevenson, D. P. J. Phys. Chem. 1960, 64, 1312-1316. dRecalculated from data in ref 19 and revised value of polarizability anisotropy; see text. e Calculated from molecular geometry given in ref 20. /Calculated from rotational constants quoted in ref 3.
f 0.39 (present work, 632.8 nm, 20 OC, 0.94 f 0.02) was obtained, while a more recent remea~urement'~ at 632.8 nm and 23 OC gave 0.81 f 0.11 (present work, 632.8 nm, 23 OC, 0.93 0.02). The first of these is in error by nearly loo%, and the second by about 13%;in any case, the absence of information as to the temperature dependence made it impossible reliably to derive the magnetic anisotropy from these results.
*
Discussion From eq l b it can be seen that the molar Cotton-Mouton constant should exhibit a linear dependence on the reciprocal of the absolute temperature. Figure 1 shows a plot of ,C against TI,and Table I1 contains the intercept and slope of the weighted-fit least-squares straight line, together with a detailed analysis of the derived magnetic anisotropy and related properties of cyclopropane. The intercept at T I = 0 is only about one-twentieth as large as that found for benzene but, because the Cotton-Mouton constant of cyclopropane is only about one-fiftieth as large, the temperature-independendent contribution represented by the intercept is, in relative terms, very much more significant;it amounts to approximately -10 f 10% of the Cotton-Mouton constant at 298 K and cannot be ignored in the evaluation of the magnetic anisotropy. Analogous temperature-dependence studies of the Cotton-Mouton effects of ethane, ethene, and ethyne were recently reported" and it is of interest to compare the corresponding percentage contributions from, and also the values of, A7 (quoted here as 10S0A7/Cm2 V-' T2)for the four molecules: ethane, -25%, 25; ethene, -l%, -3; ethyne, -45%, 68; and cyclopropane, -lo%, -20. In all four cases the sign of the temperature-independent term, which originates in distortion of the electronic structure by the magnetic field, is opposite to that of the temperature-dependent contribution, which arises from molecular orientation. In consequence, the contribution from the magnetic hyperpolarizability has the effect of increasing the slope of the plot of ,C against T'and, thereby, the magnitude of the derived magnetic anisotropy beyond the values which would be obtained if this term were assumed to be zero. It is not yet possible to offer an explanation of this observation. In order to deduce the magnetic anisotropy, Ax, from the slope of the plot of ,C against TI,the corresponding polarizability anisotropy, Act, at 632.8 nm is required. The depolarization ratio of cyclopropane is very small, so that the anisotropy derived from (14) Corfield, M. G. Ph.D. Thesis, University of Bristol, 1969.
The Journal of Physical Chemistry, Vol. 89, No. 7, 1985 1311 conventional mea~urements'~ of the intensity of Rayleigh scattered light is likely to be an overestimate, because of inclusion of the strongly depolarized vibrational Raman spectrum. Fortunately, the Raman spectroscopic method,I6 which circumvents this difficulty, has recently been applied to cyclopropane, and a reliable value of the depolarization ratio at 488.0 nm is available." If it is assumed that the dispersion in the corresponding polarizability anisotropy is the same as that in values derived from the reported Rayleigh depolarization ratios, the anisotropy at 632.8 nm, shown in Table 11, emerges as approximately 12% lower than from the direct measurements. The magnetic anisotropy so determined is also shown in Table 11. As noted above, the previously published single-temperaturemeasurement of the Cotton-Mouton effect and the derived magnetic anisotropy of cyclopropane were seriously in error; in consequence, the estimate of the magnetic hyperpolarizability anisotropy obtained indirectly, by difference, by Aldrich and collaborators3 is grossly in error in respect of both sign and magnitude. Our value of the magnetic anisotropy of cyclopropane, which can be considered as definitive, is about 15% higher than results deduced in the study of the cyclopropanehydrogen chloride and cyclopropane-hydrogen cyanide comp1exes.j Such a comparison provides a valuable test of the adequacy of the procedures used to decompose the observed properties of the complexes into those of the free molecules, and of the reliability of the results so obtained. Earlier experimental values of the magnetic anisotropy of cyclopropane, in particular the range of unreliable estimates from considerations of NMR shielding and the McConnell equation, have already been d i s c ~ s s e d and , ~ no further comment is required here. Because of the inherent difficulties, no attempt has been made in the present study to interpret the observed magnetic anisotropy of cyclopropane in terms of local and nonlocal contributions and the magnetic criterion of aromaticity.2e~f~'8 However, we note that the magnetic anisotropy now reported is entirely consistent with values (quoted here as 10sAx/J Tzmol-') for other threemembered ring systems:2c cyclopropenone, -1 7.8; cyclopropene, -1 7.0; methylenecyclopropane, -16.6; 1-methylcyclopropene, -15.2; cyclopropane, -1 1.6; aziridine, -10.6; and oxirane, -9.4. A knowledge of the electric quadrupole momentIg and the geometryZoof cyclopropane makes possible the separation, through eq 3 and 4, of the magnetic anisotropy into the oppositely signed diamagnetic and temperature-independent paramagnetic contributions. Note that the quadrupole moment in Table I1 is a slightly revised value, derived from the previously reported measurements of field-gradient induced birefringen~e'~ and the polarizability anisotropy discussed above. In addition, the same information allows an estimate to be made, through eq 5 , of the quantity gJz2 - gxxIxx,which can be evaluated directly from the results of the microwave spectroscopic study. It may also be noted, in relation to the quadrupole moment of cyclopropane, that the experimental results (quoted here as lO'%/C m2) from singletemperature birefringence measurements (5.9 1.6) and from the cyclopropane complexes (3.5 f 1.3) are significantly smaller than the value predicted by ab initio molecular orbital theory (8.4) .21
*
Summary The present study of the temperature dependence of the Cotton-Mouton effect of cyclopropane has served to reinforce the conclusion, originally drawn by Kling, Geschka, and Huttner" from a similar examination of ethane, ethene, and ethyne, that (15) Bogaard, M. P.; Buckingham, A. D.; Pierens, R. K.;White, A. H. J . Chem. Soc., Faraday Trans. 1 1978, 74, 3008-3015. (16) Murphy, W. F. J . Chem. Phys. 1977,67, 5877-5882. (17) Monan, M.; Bribes, J.-L.; Gaufr$s, R. J. Raman Specrrosc. 1982, 12, 190-193. (18) (a) Schmalz, T. G.; Norris, C. L.; Flygare, W. H. J. Am. Chem. Soc. 1973,95,7961-7967. (b) Schmalz, T. G.; Gierke, T. D.; Beak, P.; Flygare, W. H. Tetrahedron Lett. 1974, 2885-2888. (19) Buckingham, A. D.; Graham, C.; Williams, J. H. Mol. Phys. 1983, 49, 703-710. (20) Butcher, R. J.; Jones, W. J. J . Mol. Specrrosc. 1973, 47, 64-83. (21) Amos, R. D.; Williams, J. H. Chem. Phys. Lett. 1981, 84, 104-106.
J. Phys. Chem. 1985,89, 1312-1314
1312
for weakly anisotropic molecules the magnetic hyperpolarizability can contribute significantly to the observed effect. In all four molecules the distortion and orientation contributions have been found to be opposite in sign, so that if the former were assumed to be zero the magnitude of the derived magnetic anisotropy would be underestimated. A reliable value of the magnetic anisotropy of cyclopropane has been obtained, and this is found to be larger than that deduced indirectly from a microwave Zeeman spectroscopic study of cyclopropane-hydrogen chloride and cyclo-
propanehydrogen cyanide complexes? In addition, several other electric and magnetic properties, which provide insight into the molecular charge distribution, have been considered. Acknowledgment. The award of a University of Sydney Special Project Research Scholarship (to P.B.L.) and financial support from the Australian Research Grants Scheme (to G.L.D.R.) are gratefully acknowledged. Registry No. Cyclopropane, 75-19-4.
Cotton-Mouton Effect and Anlsotropic Polarlzabillty of Fluorobenzene P. B. Lukins and G. L. D. Ritchie* School of Chemistry, University of Sydney, New South Wales 2006, Australia (Received: August 28, 1984)
Measurements of the vapor-state Cotton-Mouton effect of fluorobenzene are combined with the known magnetizability, mean polarizability, and Rayleigh depolarization ratio to obtain the elements of the anisotropic electric dipole polarizability (10%,/C m2 V-l etc., x direction coincident with C, axis, z direction perpendicular to molecular plane) of this molecule as 14.4 f 0.7, 13.8 f 0.7, and 7.26 f 0.15 at 441.6 nm and as 13.5 0.7, 13.5 f 0.7, and 7.15 f 0.15 at 632.8 nm.
*
Introduction Although the mean optical-frequency electric dipole polarizability of a molecule is readily accessible through refractive-index measurements, the diagonal elements of the anisotropic polarizability are, in general, much less easily 0btained.l To date, the main sources of information with respect to the anisotopy have been measurements of depolarization ratios for Rayleigh scattered laser light: the temperature dependence of the electrooptical Kerr effect,3 and, most recently, rotational Raman intensities! In the case of an axially symmetric molecule (i.e., a, = ayy # a,,) a complete specification of the polarizability is provided by the refractive index and, for example, the depolarization ratio; for molecules of lower symmetry (i.e., axx# ayy # a,,),values of three properties which yield independent equations in the three polarizabilities are required. We wish to demonstrate here, with (1) Bogaard, M. P.; Orr, B. J. In "MTPInternational Review of Science"; Buckingham, A. D., Ed.; Butterworths: London, 1975; Phys. Chem. Ser. 2, Vol. 2, pp 149-194. (2) (a) Bridge, N. J.; Buckingham, A. D. Proc. R . SOC.London, Ser. A 1966,295, 334-349. (b) Rowell, R. L.;Aval, G. M.; Barrett, J. J. J. Chem. Phys. 1971,54, 1960-1964. (c) Alms, G. R.; Burnham, A. K.; Flygare, W. H. J . Chem. Phys. 1975,63,3321-3326. (d) Panachev, F. I.; Korableva, E. Yu,; Shakhpronov, M. I. Russ. J . Phys. Chem. 1976,50,1130. (e) Bogaard, M. P.; Buckingham, A. D.; Pierens, R. K.; White, A. H. J . Chem. Soc., Faraday Trans. 1 1978, 74, 3008-3015. (f) Baas, F.;van den Hout, K. D. Physica A (Amsterdam) 1979,95, 597-601. (g) Haverkort, J. E. M.; Baas, F.; Beenakker, J. J. M. Chem. Phys. 1983, 79, 105-109. (3) (a) Buckingham, A. D.; Orr, B. J. Trans. Faraday SOC.1969, 65, 673-681. (b) Buckingham, A. D.; Orr, B. J. hoc. R. Soc. London, Ser. A 1968,305,259-269. (c) Buckingham, A. D.; Bogaard, M. P.; Dunmur, D. A.; Hobbs, C. P.; Orr, B. J. Trans. Faraday SOC.1970.66, 1548-1553. (d) Bogaard, M. P.; Buckingham, A. D.; Ritchie, G. L. D. Mol. Phys. 1970,18, 575-576. (e) Buckingham, A. D.; Sutter, H. J. Chem. Phys. 1976, 64, 364-369. (0Burnham, A. K.; Buxton, L. W.; Flygare, W. H. J. Chem. Phys. 1977,67,4990-4995. (g) Bogaard, M. P.; Orr, B. J.; Buckingham, A. D.; Ritchie, G. L.D. J. Chem. Soc.,Faraday Trans. 2 1978.74, 1573-1578. (h) Bogaard, M. P.; Buckingham, A. D.; Ritchie, G. L.D. J. Chem. Soc., Faraday Trans. 2 1981, 77, 1547-1551. (i) Bogaard, M. P.; Buckingham, A. D.; Ritchie G. L. D. Chem. Phys. Lett. 1982, 90, 183-187. (4) (a) Murphy, W. F. J . Chem. Phys. 1977,67,5877-5882. (b) Murphy, W. F. J . RamanSpectrosc. 1981, 1 1 , 339-345. (c) Monan, M.; Bribes, J.-L.; Gaufres, R. C. R . Hebd. Seances Acad. Sci., Ser. B 1980,290,521-524. (d) Monan, M.; Bribes, J.-L.; Gaufrb, R. J. Raman Spectrosc. 1982,12, 190-193. (e) Monan, M.; Bribes, J.-L.; Gaufres, R. J. Chim. Phys. Phys.-Chim. Biol. 1981, 78,781-786. (0 Monan, M.; Bribes, J.-L.; Gaufrh, R. J . Mol. Struct. 1982, 79, 83-86. 0022-3654185 12089-131 2%01.50/0 , I
,
~
fluorobenzene as an example, that observations of the magnetooptical Cotton-Mouton effect: in conjunction with the refractive index and Rayleigh depolarization ratio of the vapor, can provide a valuable route to the anisotropic polarizabilities of species in the latter category. Such a method has previously been used to obtain the apparent polarizabilities of many molecules in the dilutesolution state: but its rigorous application to free molecules has been hampered by the paucity of experimental data conceming the temperature dependence of the Cotton-Mouton effect. However, the renewed interest in this effect.'-* and the availability from microwave Zeeman spectroscopic studies of reliable anisotropic magnetizabilities for a wide range of molecules9 greatly enhance the applicability and usefulness of the procedure described here.
Theory Application of a uniform magnetic field to a gas induces anisotropy in the refractive index, and birefringence is observable if plane-polarized light is passed through the gas in a perpendicular direction. The low-density molar Cotton-Mouton constant is defined as
(5) (a) Buckingham, A. D.; Pople, J. A. Proc. Phys. SOC.,London, Sect. B 1956,69, 1133-1 138. (b) Buckingham, A. D.; Prichard, W. H.; Whiffen, D. H.J. Chem. SOC.,Chem. Commun. 1965, 51. (c) Buckingham, A. D.; Prichard, W. H.; Whiffen, D. H. Trans. Faraday Soc. 1%7,63, 1057-1064. (d)Bogaard, M. P.; Buckingham, A. D.; Corfield, M. G.; Dunmur, D. A,; White, A. H. Chem. Phys. Lett. 1972, 12, 558-559. (6) (a) Cheng, C. L.; Murthy, D. S.N.; Ritchie, G. L. D. Aust. J. Chem. 1972, 25, 1301-1305. (b) Calvert, R. L.;Ritchie, G. L. D. J . Chem. SOC., Furaday Trans. 2 1980, 76, 1249-1253. (c) Dennis, G. R.; Gentle, I. R.; Ritchie, G. L. D. J. Chem. SOC.,Faraday Trans. 2 1983, 79, 529-538. (d) Dennis, G. R.;,Gentle, I. R.;, Ritchie, G. L. D.;, Andrieu, C. G. J . Chem. Soc., Faraday Trans. 2 1983, 79, 539-545. (7) (a) Geachka, H.; Pferrer, S.;HBussler, H.; Htittner, W. Ber. Bunsenges. Phys. Chem. 1982, 86, 790-795. (b) Kling, H.; Dreier, E.; HUttner, W. J . Chem. Phys. 1983, 78,43094314, (c) Kling, H.; Geschka, H.; Hfittner, W. Chem. Phys. Lett. 1983.96, 631-635. (8) Lukins, P. B.; Buckingham, A. D.; Ritchie, G. L. D. J . Phys. Chem. 1984,88, 2414-2418. (9) (a) Flygare, W. H.; Benson, R. C. Mol. Phys. 1971,20,225-250. (b) Sutter, D. H.; Flygare, W. H. Top. Curr. Chem. 1976, 63, 89-186.
0 1985 American Chemical Society
