1589
J. Phys. Chem. 1986, 90, 1589-1592 that it must be concluded that the small system size and periodic boundary conditions affect critical nucleus formation in an unphysical way. Thus far we have been unable to determine the exact nature of the effect of periodic boundary conditions on the nucleation process. In our previous paper we suggested that catastrophic growth occurs when the growing nucleus becomes large enough to feel the influence of its periodic image. The results of this study imply that the critical nucleus, which is normally formed well before the onset of catastrophic growth, must already interact with its image somehow. The best explanation of our observed results seems to be that even the smallest nuclei have a large sphere of influence because
of the diffuseness of the interface between solid and liquid. Although our results strictly apply only to the specific conditions of our simulations, they bring into serious question whether other studies that purport to observe homogeneous nucleation are free of artifacts. Thus, it is likely that simulations of even larger systems than 1300 particles will be necessary for a meaningful study of homogeneous nucleation in supercooled dense liquids, although we cannot say how large a system will be required.
Acknowledgment. This work was supported by the National Science Foundation through Grants C H E 81-07165 and C H E 84-10701 (H.C.A.) and through an N S F Graduate Fellowship (J.D.H).
Cross Sections for Fluorescence Quenching of Br,( BO,’) Gases As Studied by Laser Excited Fluorescence
by Collision with Foreign
Mamoru Kitamma,+ Kuniaki Nakagawa,t Kaoru Suzuki, Tamotsu Kondow, Kozo Kuchitsu,* Department of Chemistry, Faculty of Science, The University of Tokyo, Bunkyo- ku. Tokyo I 13, Japan
Toshiaki Munakata, and Takahiro Kasuya Institute of Physical and Chemical Research, Wako, Saitama 351 -01, Japan (Received: September 4, 1985)
Cross sections for Br2(B0,+-X0,+) fluorescence quenching were obtained by state-selecteddye laser excitation. A good correlation was observed between the cross sections by a number of quenchers and the dispersion-type parameters given by Thayer and Yardley. The symmetry of the repulsive state which contributes mainly to the collision-induced predissociation of Br2(B0,+) was estimated from the u’dependence of the cross sections to be O;(311), allowing an approximate potential curve for this state to be constructed.
1. Introduction Fluorescence quenching of Br,(BO,+-XO,+) by thermal collision is known to be due to the collision-induced predissociation of Br2(BOu+) Br2(B0,+) + Q 2Br(2P3,2) + Q (1)
-
where Q is the collision partner (quencher).] The fluorescence lifetime of Br2(B0,+) and the quenching cross section by collision with Br2(XOg+)(self-quenching) were first obtained by Capelle et al.2 using a pulsed dye laser with a resolution of 3-24 cm-I. The rovibrational level dependence of the collision-free lifetimes and self-quenching cross sections were subsequently measured systematically by Clyne and Heaven3 using a narrow-bandwidth dye laser. Clyne et aL4 also investigated theoretically the rovibrational level dependence of the collision-free fluorescence lifetime and reported that the dependence was mainly due to spontaneous predissociation of Br,(BO,+) into the lu(’II) repulsive state. As for the quenching of Br2(B0,+) fluorescence by collision with foreign gases, the following measurements have been carried out by two research groups. Bugrim et aL5 obtained the quenching cross sections of Br2(B0,+) by rare gases, oxygen, nitrogen, and carbon dioxide using a C W mercury lamp (546.1 nm in air) as an excitation source. The cross sections obtained were found to be correlated with a polarizability-dependent parameter derived by Selwyn and Steinfeld.6 Bugrim et aL5 concluded that the repulsive state which was responsible for the collision-induced predissociation of Br2(B0,+) was OUJ3II), but the basis of this conclusion was not mentioned clearly. The quenching cross ‘Present address: N T T Electrical Communications Laboratories, Morinosato Wakamiya, Atsugi, Kanagawa 243-01, Japan. *Present address: Department of Physics, Faculty of Science, Toyama University, Gofuku, Toyama 930, Japan.
0022-3654/86/2090-1589$01.50/0
sections of Br,(BO,+) by foreign gases were also measured by Clyne et al.’>*by laser excited fluorescence, but they provided no detailed discussion on the mechanism of the quenching. In our previous study? the dependences of the quenching cross sections on the properties of the quenchers and on the vibrational levels of I,(BO,+) were obtained in the collision-induced predissociation of I,(BO,+)
The symmetry of the repulsive state was discussed on the basis of the formulation given by Thayer and Yardley.Io Its potential energy curve was estimated from the dependence of the quenching cross sections on the vibrational levels. This method was extended in the present study to an analysis of collision-induced predissociation of Br,(BO,+). The quenching cross sections of Br2(BOu+,u’=14) by a variety of quenchers were obtained in order to clarify the intermolecular interaction between (1) Herzberg, G. “Spectra of Diatomic Molecules”; Van Nostrand: New York, 1950; Chapter VII. (2) Capelle, G.; Sakurai, K.; Broida, H . P. J . Chem. Phys. 1971,54. 1728. (3) Cline, M. A. A.; Heaven, M. C. J . Chem. SOC.,.Faraday Trans. 2 1978. 74. 1992. (4) Ciyne, M. A. A.; Heaven, M. C.; Tellinghuisen, J. J . Chem. Phys. 1982. 76. 5341. Bugrim, E. D.; Makrenko, S. N.; Tsikora, I. L. Opr. Specfrosc. 1975, 39, 15. ( 6 ) Selwyn, J. E.; Steinfeld, J. I. Chem. Phys. Left. 1969, 4, 217. (7) Clyne, M. A. A.; Heaven, M. C.; Martinetz, E. J . Chem. SOC.,Faraday Trans. 2 1980, 76, 405. ( 8 ) Clyne, M. A. A,; Heaven, M. C.; Davis, S. J. J . Chem SOC.,Faraday Trans. 2 1980, 76, 961. (9) Nakagawa, K.; Kitamura, M.; Suzuki, K.; Kondow, T.; Kuchitsu, K.; Munakata, T.; Kasuya, T. Chem. Phys., submitted for publication. (10) Thayer, C. A,; Yardley, J. T. J . Chem. Phys 1972, 57, 3992.
6)
0 1986 American Chemical Society
1590
The Journal of Physical Chemistry, Vol. 90, No. 8, 1986
Kitamura et al.
TABLE I: Observed Cross Sections for the Quenching of Br2(B0,+.b’ = 14)
quencher nitrogen
oxygen argon krypton ethane dichloromethane methyl bromide 1 , l (gem)-dichloroethylene cis-dichloroethylene trans-dichloroethylene chloroform benzene dibromomethane carbon tetrachloride bromoform
uQ/A2
14 f 3 18 f 3 19f2 28 f 3 43 f 3
55 f 5
55 f 4 59 f 5 60 f 7 60 f 5 60 f 5 62 f 6 66 f 8 67 f 6 84 f 10
RCIA 4.07’ 3.940
3.97“ 4.03‘ 4.440 4.61‘ 4.1 I 4.99
*
4.99 4.99 4.95“ 4.860 4.89’ 5.17’
5.W
“Calculated by using the uLJvalue taken from ref 17. *Calculated by using the estimated RQvalue from the molecular geometry and the van der Waals radii of component atoms (see section 3.1). Br2(B0,+) and the quencher. The effect of the dipole moment of the quencher was examined, because it was shown to provide important information about the symmetry of the repulsive state; for instance, our recent studies have shown that the dipole moment of the quencher has no influence in the case of 12(B0,+)9where the influence is small but significant in the case of ICI(BO+).” The dependence of the cross sections on the vibrational levels of Br2(B0,+) by both polar and nonpolar quenchers was further examined by rovibrational state-selected excitation of bromine to the BO,’ state. The symmetry and the potential energy curve of the repulsive state which causes the collision-induced predissociation of Br2(B0,+) were estimated. The present study consists of low-resolution and high-resolution measurements. In the former the quenching cross sections of Br2(BOUf,u’=14) by a number of quenchers at 583.8-nm excitation was obtained. In the latter the dependence of the cross sections on the vibrational levels of Br,(BO,+) was investigated.
1 0.5
0
p /Torr Q Figure 1. Typical examples of the Stern-Volmer plot: (a) l.l(gem)dichloroethylene, (b) cis-dichloroethylene, (c) trans-dichloroethylene.
2. Experimental Methods and Results 2.1. Low-Resolution Measurement. A nitrogen laser-pumped dye laser was used in this measurement. The Br2(B0,+-XOg+) fluorescence following the dye laser excitation was detected by a photomultiplier (RCA 7265). Undispersed fluorescence excitation spectra and fluorescence decay curves were recorded by using a boxcar integrator. The fluorescence decay curves were obtained by scanning the boxcar aperture over the waveform of the fluorescence decay. The excitation laser wavelength was fixed a t 583.8 nm a t the head of the 14-2 band of the Br2(B0,+-XOg+) transition. Since a fluorescence excitation spectrum12 showed that this band was free from blending with other bands, it was possible to excite the u’ = 14 state with a purity of better than 95% with 3-cm-’ resolution. The quenching cross sections of Br2(B0,+,u’= 14) by 15 quenchers are listed in Table I. The fluorescence cell was made of Pyrex glass with three optical windows made of fused quartz, and fluorescence from Br2(BOUf)was detected a t right angles to the excitation beam. A sharp-cutoff filter was installed between the fluorescence cell and the photomultiplier in order to eliminate the scattered laser light. The pressure of the fluorescence cell was measured with a capacitance manometer. A sample of bromine of natural isotopic abundance was used. The partial pressure of bromine was maintained a t 100 mtorr throughout the measurement. Bromine and quenchers, except for nitrogen, oxygen, and argon, were purified by vacuum distillation before use. Fluorescence decay curves were recorded as a function of the pressure of the quencher (0-500 mtorr) mixed with bromine. The ( I 1 ) Kitamura, M.; Kondow, T.; Kuchitsu, K : Munakata, T ; Kasuya. T Chem. Phys. L e f t . 1985, 118. 130 (1 2 ) Kitamura, M. Ph D Thesis. University of Tokyo, 1984.
01 0
I
1
I
10
20
30 VI
Figure 2. Observed u’ dependence of the quenching cross sections for Br2(BO,’).
quenching rate constants of Br,(BO,+,u’= 14) were obtained from the Stern-Volmer plot. The quenching cross section was calculated as (m/8akT)’i2 times the rate constant, where m is the reduced mass, k is the Boltzmann constant, and T is the ambient temperature. Typical examples of the Stern-Volmer plot are shown in Figure 1. No deviation from a straight line in the plot was observed for all the quenchers studied; this indicates that collisional vibrational relaxation plays no significant role in the present case. The slope of the plot was found to be independent of the partial pressure of bromine within the range of 50-200 mtorr. The errors listed in Table I were estimated in the manner described in our previous work;9 about 60% of the uncertainties originated from the reproducibility of the fluorescence lifetimes measured in different runs. The cross sections obtained for c’= 14 are about 30% smaller than those reported by Bugrim et aL5 for u‘ = 19 in the case of Ar, Kr, and O,,where their cross sections are divided by a for the sake of consistency. The agreement is worse in the case of N2,where our cross section is -0.4 times that reported by Bugrim et aL5 The discrepancy cannot be explained by the difference in the vibrational states studied, since the cross sections for c’ = 14 should be larger than those for u’ = 19 (see section 2.2 and Figure 2). The origin of this discrepancy remains unknown.
Fluorescence Quenching of Br,(BO,+)
2.2. High-Resolution Measurement. The apparatus used in this measurement was almost the same as that described previ0us1y.~ A Nd:YAG laser-pumped dye laser was used for an excitation source. An intracavity etalon was installed so that a resolution of 0.08 cm-I was achieved. Fluorescence excitation spectra between 520 and 580 nm were measured simultaneously by use of gated integrators. The Br2(B0,+-XOg+) fluorescence was detected by a photomultiplier (RCA 7265). A small portion of the laser light was introduced to another fluorescence cell filled with a saturated pressure of iodine, whose fluorescence was detected with a photodiode. The absolute wavenumber of the laser was monitored by using the 12(B0,+-XOg+) spectrum with reference to the atlas of iodine visible absorption spectra.I3 Fluorescence decay curves were recorded with a transient digitizer and accumulated in a microcomputer so as to attain a signal-to-noise ratio of about 20. The collision-free lifetime of the fluorescence from Br,(BO,+,u’= ll,J’= 12), estimated to be 0.90 f 0.05 ps, agreed with that reported in the l i t e r a t ~ r e . ~The quenching cross sections by argon, oxygen, and dichloromethane for the vibrational levels between u’ = 6 and 34 were obtained. The fluorescence cell and the method of sample preparation were similar to those in the low-resolution measurement. The fluorescence excitation spectra of Br2(B0,+-XOg+) obtained in the high-resolution measurements were assigned with the aid of the molecular constants of the 79-79 and 81-81 isotopes.I4 The constants for the 79-81 isotope were calculated on the basis of the isotope shift. The Br2(B0,+-XOg+) spectra were congested because of the overlapping of the hot bands and bands of three isotopic species. The lines for the lifetime measurements were so selected that single vibrational levels were excited with a purity of better than 95%. The u’dependence of the quenching cross sections were obtained in the range of u’= 6 and 34; the rotational levels excited were always between J’= 11 and 18. The dependence of the cross sections of the excited rotational levels was found to be negligible between J’ = 10 and 20. The quenching cross sections for Br,(BO,+) are plotted against the excited vibrational levels in Figure 2. The u’dependences for the three quenchers shown in Figure 2 are very similar in shape, with a single maximum around u’ = 14. Errors in the cross sections were estimated as in the low-resolution measurement. 3. Discussion 3. I . Intermolecular Interaction between Br2(B0,+) and the Quencher. The formulation for the quenching process given by Thayer and YardleyIo was applied to the collision-induced predissociation of Br2(B0,+), as in our previous paperg for the 12(B0,+) quenching. According to this formulation, the cross section, uQ, can be represented as a sum of uQ1and uQII,which represent the dipole interaction and the dispersion-type interaction, respectively, as
Here m is the reduced mass, Fif is the Franck-Condon factor between the bound and repulsive states, pifis the dipole transition moment, hQ is the dipole moment of the quencher, R , is the hard-sphere collision radius, aifis the matrix element of the dispersion interaction, aQ is the polarizability of the quencher, and I is the ionization potential. Suffixes i and f denote the initial (bound) and final (repulsive) states of the excited molecule; M and Q denote the excited molecule and the quencher, respectively. As shown in Table I, the quenching cross sections for Br, (BO,+,u’= 14) by trans, cis, and gem isomers of dichloroethylene (!3) Gerstenkorn, S.; Luc, P. ”Atlas du Spectre d’Absorption de la Molecule d’Iode”; CNRS: Paris, 1978. (14) Barrow, R. F.; Clark, T. C.; Coxon, J. A,; Yee, K. K. J . Mol. Spectrosc. 1974, 5 1 , 428.
a:trans
CHBq
8 0 - b:cis ] C 2 H 2 C I 2 c:1,1
CCI 4
.CH
0
3 6 0b”
a, b.
-a0,
CH3Br
c
Br
CHC13 0
CH2CI2
C2H6
‘01-
I
I
0
Kr
N2
Figure 3. Correlation between the observed cross sections of Br2 (BO,+,u’= 14) and the dispersion-type parameter given by Thayer and YardleyIo (see eq 5 and 6 ) . The R, values used in this calculation are listed in Table I.
are nearly equal. These isomers have equal mass and very similar polarizabilities, ionization potentials, and molecular geometries, but they differ in their dipole moments: 0, 1.89, and 1.34 D for the trans, cis, and gem isomers, r e ~ p e c t i v e l y . ’ ~ .This ’ ~ suggests that the dipole moment of the quencher makes no important influence on the collision-induced predissociation of Br2(BO,’, u’=14). This conclusion is identical with that on the collisioninduced predissociation of 12(B0,+).9 Therefore, the observed cross sections can be described in terms I in eq 5. The observed cross sections listed in of the U ~ shown Table I are thus plotted in Figure 3 against the parameter X, given in eq 6, which depends on the properties of the quencher. The hard-sphere collision radius, R,, is estimated as R , = I/2(RQ RBr2i),where RBr2* is estimated to be 4.45 A from the internuclear distance of Br2(B0,+,u’=14) and the van der Waals radius of Br and RQis the hard-sphere collision radius of the quencher, which is assumed to be equal to the Lennard-Jones parameter, uLJ,when available]’ or estimated from the molecular geometry and the van der Waals radii of component atoms. The uncertainty in R , arising from that in RBr2*is systematic, and it causes the abscissa of Figure 3 to shift uniformly; hence it may not disturb the correlation between uQ and XQ. On the other hand, the uncertainty in R , originating from that in RQ, estimated to be -3%, causes an uncertainty of -30% in XQ. These uncertainties in XQ and the approximations made in deriving eq 3-6 make the present correlation no more than semiquantitative. Nevertheless, the observed correlation shown in Figure 3 can be interpreted as the predominant interaction causing the collision-induced predissociation of Br2(BOu+,u’=14) being of the dispersion type. 3.2. Symmetry of the Repulsive State. The discussion in section 3.1 indicates, according to eq 3 and 4, that uQ1= 0 and uQ = ad1for Br2(B0,+,u’=14), and that p,f 0 and aif# 0. The matrix elements plfand alfcontain (ilrlf) and (ilrlk) (klrlf), respectively, where li), Ik), If) are the kets of the initial, intermediate, and final states of the excited molecule, respectively, and the Therefore, the symmetry of symmetry of the initial state is 0.’, the repulsive (final) state which is mainly involved in the collision-induced predissociation a t u’ = 14 is likely to be ungerade. This conclusion is analogous to that reached in the collision-induced predissociation of 12(B0,+).9 As illustrated in Figure 2, the u’dependences of the quenching cross sections by polar and ncnpolar quenchers are very similar in shape. This implies that the above argument in regard to the
+
(15) Howe, J. A,; Flygare, W. H. J . Chem. Phys. 1962, 36, 650. (16) Myott, A. A,; Hobbs, M. E.; Gross, R. M. J . A m . Chem. SOC.1941, 63, 659. (17) Hirschfelder, J. 0.;Curtiss, C. F.; Bird, R. B. “Molecular Theory of Gases and Liquids”; Wiley: New York, 1954.
1592 The Journal of Physical Chemistry, Vol. 90, No. 8, 1986
2.5
3.0
3.5
io
20
30 VI
Figure 4. (a) Approximate potential energy curves for Br, near the BO,’ state. The broken curves VI and V2 correspond to the potentials given by eq 7 and 8, respectively. The potential V, appears to be an approximate representation of the repulsive state responsible for the collisional quenching of Br2(BOUt).See section 3.3. (b) Calculated c’dependence of the Franck-Condon factors between the BO,’ state and the repulsive states illustrated in (a).
symmetry of the repulsive state can be extended to 6 5 II’5 34. 3.3. Potential Energy Curve of the Repulsive State. The observed cross section is shown to be nearly equal to the uQ1’ given in eq 5 . The coefficients of uQrlwhich depend on the vibrational level are Fif,R,, and lM.However, the factor which mainly determines the oscillations in the v’dependence of the cross section ~ change in I , for v ’ = 6-34 is Fiffor the following r e a ~ o n .The causes a smooth variation of only up to 5% in uqll. The v‘dependence of the only semiempirical parameter, R,, is more extensive because uQIIis proportional to RF9, but this dependence is expected to be monotonical in the range of the vibrational states of the present concern: The internuclear distance increases -20% from v’ = 6 to 34. If the van der Waals radius of Br,(BO,’) is assumed to be proportional to the internuclear distance, R, increases by -lo%, resulting in a decrease in uQI1by 50-60%. Nevertheless, the c’dependence of R, does not influence the overall oscillations of the u’dependence of uQI1. Therefore, the characteristic feature of the observed v’dependence, which is ascribed to that of the Franck-Condon factor, can be used to obtain semiquantitative information on the potential energy curve of the repulsive state. Among the many repulsive states which are expected to be located near the potential curve of the BO: state,I8 only the l,(’n) has been investigated experimentally. This state has been shown to be the final state of the spontaneous predissociation of Br, (BO,+).4 The e’dependence of the Franck-Condon factors between BO,’ and l u ( l I I ) was obtained by Clyne et al.;4 it is shown in Figure 4b by a solid curve. It has two maxima at e‘ = 5 and 10, a minimum a t 1’’ = 7, and tends to nearly zero a t e‘> 25. To the contrary, the observed c’dependence has a single maximum around u’ = 14, no minimum between E’= 6 and 34, and the cross sections for e ’ > 25 are as large as about 2 / 3 of that for L” = 14. These discrepancies show that a repulsive state other than l,(’II) makes a substantial contribution to the collision-induced predissociation of Br2(BOut). According to Mulliken,I8 the O;(311), Al,(311) and A’2,(3n) states are located in the vicinity of the BO,’ state. Therefore, these states are the candidates of the repulsive states for the collisioninduced predissociation. The Franck-Condon factors between the BO,’ and A1,(311) states were calculated by Clyne and coworkers4 to be about 3 orders of magnitude smaller than those between the BO,’ and l,(’II) states. The Franck-Condon factors between the BO,’ and A’2u(311) states are expected to be even smaller, because the inner repulsive wall of the A’2J3n) potential curve, whose location mainly determines the magnitude of the (18) Mulliken, R. S. J . Chem. Phys. 1934, 46, 549; 1940, 5 7 , 500.
Kitamura et al. Franck-Condon factor, lies further away from that of the BO,’ potential than that of the Al,(311) potential. Therefore, contributions from the Al,(311) and A’2u(3n) states are estimated to be only minor, if any. The remaining candiate is the 0,J311) state. The potential energy curve of this state was estimated only roughly by Gibbs and Ogryzroi9to be a weakly bound state lying very close to the inner wall of the potenial of the BO,’ state, but detailed knowledge of this state has remained unknown. Therefore, a model calculation of the Franck-Condon factors was made in order to explain the observed o’dependence of the cross sections (Figure 3); the procedure is similar to that described for the collision-induced predissociation of I,( BO,’) .9 Two trial potentials were used: a repulsive Vl(r) and a weakly bound V2(r). The e’ dependences of the Franck-Condon factors are calculated by using Cooley‘s method.20,2’ The model potentials are represented as V,(r) = Al(r/ao)-BI V , ( r ) = -A#
-k B,r-‘*
(7)
(8)
where r is the internuclear distance, A , , B , , A,, and B2 are adjustable parameters, and a. is the Bohr radius. When the parameters are adjusted to be A , = 4.45 X lo’, cm-’ and B , = 14.0 for VI (eq 7) and A , = 8.5 X IO5 cm-’ A6 and B2 = 2.4 X lo8 cm-’ AI2 for V2 (eq S), both model potentials give broad curves which have a maximum around u ’ = 14 in the range of L” = 6 and 34, in qualitative agreement with the present experimental results. The potential energy curves and the calculated Franck-Condon factors are illustrated in Figure 4 by broken lines. In the case of V2,there is a strong correlation between the A , and B2 parameters. In spite of this parameter correlation, the above-mentioned feature of the potential function can specify the potential energy curve to less than 10% uncertainty in the range of 2.3 A 5 r 5 2.5 A. In contrast, the correlation between the A , and B , parameter in the case of VI is much weaker; the errors in A , and B, are thus estimated to be f0.10 X 10l2cm-’ and fO.l, respectively. The Fifcurve derived from V , ( r )has another sharp maximum a t v’= 2, where the peak is about 4 times as large as that a t e’= 14; this characteristic feature appears when a repulsive potential crosses at an attractive limb of the B-state potential. On the other hand, the Fifcurve based on V,(r) has a single maximum between E’= 0 and 34 and the value a t e’ = 2 is only about 20% of that at c‘ = 14. Therefore, the cross section for the e’ = 2 level has to be compared with that for v’= 14 in order to decide which model potential is closer to the real repulsive potential in question. The rate constant for the quenching by argon for e‘ = 2 was found by Clyne and co-workers’ to be about 1 order of magnitude smaller than that for e’ = 14.* Therefore, V2(r)seems to be favored, and the repulsive state responsible for the collision-induced predissociation of Br2(B0,’) is likely to be a weakly bound state located very close to the BO,+ potential. The present estimation of the potential curve is consistent with .’~ the existing rough estimates of the 0,J3n) p ~ t e n t i a l . ’ ~ In summary, the O;(3n) state with a potential curve analogous to the Vz(r)shown in Figure 4a is probably the repulsive state which is mainly associated with the collision-induced predissociation of Br2(B0,’). Registry No. Br,, 7726-95-6; N,,1721-37-9; 0,. 1782-44-7; Ar, 7440-37- 1; Kr, 7439-90-9; C2H,, 74-84-0; CH2CI,, 75-09-2; CH,Br, 74-83-9; 1 , 1-C,H2C12,75-35-4; cis-C2H2C12,156-59-2; trans-C2H2C12, 156-60-5; CHCI,. 67-66-3; CH2Br2,74-95-3; CCI,, 56-23-5; CHBr,, 75-25-2; benzene, 71-43-2. (19) Gibbs, D. B.; Ogryzro, E. A. Can. J . Chem. 1965, 43, 1905 (20) Cooky, J. W. Math. Compuration 1961, 15, 313. (21) Cashion, J. K. J . Chem. Phys. 1963, 39, 1872.
