198
J. Phys. Chem. 1980, 84, 198-202
Absolute Infrared Intensities of Methane. Dipole Moment Derivatives and Bond Charge Parameters J. H. G. Bode and W.
M. A. Smit"
Analytical Chemistry Laboratory, University of Utrecht, 3522 A D Utrecht, The Netherlands (Received May 22, 1979) Publication costs assisted by the Analytical Chemistry Laboratory
The absolute infrared intensities of methane and methane-d4 have been measured by using the WilsonWells-Penner-Weber method. The obtained intensity values are compared with all known absolute intensity data for methane and its deuterated derivatives. The observed differences are not easily interpretable due to the use of different measuring methods and the generally incomplete way in which the experimental conditions are reported. Using additional data from ab initio and CNDO calculations, we have analyzed the intensity data in terms of dipole moment derivatives and bond charge parameters. In order to check the quality of our experimental data we have predicted the absolute intensities for CH,D and CD3H from the calculated dipole moment derivative values. The predicted intensities are in very good agreement with the experimental values for these molecules.
Introduction The integrated intensities of the fundamental absorption bands of CH4,1-20CD4,',15 and partly deuterated methanes7J5921have been reported previously by several authors. The reported values cover a period of almost 40 years. The large scattering in the reported values, obtained by different experimental methods, mainly reflects the considerable systematic errors involved in the measurements of these quantities. In view of the improvement in resolution power and photometric accuracy of modern infrared spectrophotometers the more recent measurements might be expected to show a better mutual consistency. However, the results of Tanabe,14 Varanasi et al.,13J6and Saeki et al.15 show still differences of up to 10% for the v4 bending mode. In view of these differences it seems worthwhile to repeat the measurements once again in order to contribute to the improvement of the mutual consistency of the intensity values obtained from different laboratories. In the present paper we report the absolute IR intensities of the fundamental absorption bands of both CH4 and CD4. The intensities are interpreted in terms of dipole moment derivatives and bond charge parameter^.^^.^^ Due to the symmetry of the methane molecule there are only two (threefold degenerate) active vibrations and thus the number of bond charge parameters exceeds the number of experimental data. Therefore, in order to obtain a complete set of bond charge parameters involved in both active modes the experimental data have to be completed with some additional relations between these parameters. For that purpose ab initio and CNDO results have been used.
pressures were varied from 1 to 6 cmHg. The CD, intensities were measured with a Perkin-Elmer 180 spectrophotometer with the KRS-5 cell a t sample pressures ranging from 2 to 12 cmHg. The spectral slit width was better than 1.0 cm-l a t both bands. Cell filling and measurement of sample pressures were performed according to the procedure described by Overend et a1.26 Sample pressures were measured with an accuracy of k0.5mmHg by use of a mercury manometer. No detectable adsorption/desorption of sample gas in the cell could be observed, nor were there any leakages at high or low pressures. Care was taken so that no sample gas was left in the valves or plumbing outside the cell before the cell was pressurized with pure nitrogen (the KRS-5 cell up to 60 atm, the KBr cell up to 40 atm). At these pressures the rotational structure was sufficiently broadened, as appears from the Wilson-Wells and Beer's law plots (see Figures 1-3). Backgrounds were determined from spectra obtained by filling the cells only with nitrogen.
Results and Discussion Absolute Intensities. The integrated intensities have
been determined by using the Wilson-Wells-PennerWeber The intensity values obtained from the Beer's law plots are listed in Table I together with the literature values. Our intensity values belong to the lower ones obtained with the Wilson-Wells-Penner-Weber method. However, recent results from high-resolution line intensity measurements16'20seem to support the lower values. Complete sets of CHI and CD4intensity data have been reported by Heicklen7 and Saeki et al.15 Our values for v3 of both CH, and CD4do not differ significantly from those of Saeki et al. The differences between our values Experimental Section and those of Heicklen for v3 are somewhat larger. However, the v4 values of Heicklen are in close agreement with our The CH4 sample was obtained from Matheson Gas values whereas the differences between our v4 values and Products, Belgium, and the CD4sample from Merck Sharp those of Saeki et al. are more pronounced. The intensities and Dohme, Canada Ltd. The samples had a specified of the CHI absorption bands recently reported by Varanasi purity of better than 99% and were used without further et, aI.I3J6 were obtained from high-resolution measurements purification. The meausurements of the CH4 intensities (spectral slit width 0.1-0.3 cm-I). The intensity for v4 is were carried out with a Perkin-Elmer Model 421 grating spectrophotometer equipped as described p r e v i ~ u s l y . * ~ ~ ~in~good agreement with our value. For v3 the difference is larger although not outside the error limits (see Table The spectral slit width was 1.9 cm-I a t 3000 cm-' and 1.0 cm-I a t 1300 cm-l. Stainless steel cells were used, one with I). The experimental errors in the intensity values as given KRS-5 windows (effective pathlength 5.15 cm, pressure by us are standard deviations, resulting from a leastlimitation 80 atm) and one with KBr windows (effective squares procedure in which errors in the observed band pathlength 8.915 cm, pressure limitation 40 atm). Sample 0022-3654/80/2084-0 198$01 .OO/O
0 1980 American Chemical Society
The Journal of Physical Chemistry, Vol. 84, No. 2, 1980
Absolute IR Intensities of Methane
TABLE I: Absolute Intensities (Ai, km/mol) for t h e Infrared Absorption Bands of CB, and CD,
-
m
e ref t
h
o
d
a
A5
I
0
20
60
40 p
(atm)
Figure 1. Influen'ce of broadening pressure on the measured absolute intensities of CH,,. Sample pressure 3.4 cmHg.
-
A4 _ _ _ _ _ I _
_ l l l l _ l _ l _ l
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
lg9
DISP
ww ww ww MISC ww
WWPW MISC CCBM MISC MISC GCBM GC MISC WWPW
16 17 18 19 20 this work
GC HRTL HRGS HRTL HRTL WWPW
7 15
WWPW WWPW
this work
WWPW
CH, 72.6 67.2 80.3
33.2 33.7 35.2
30.8 73.4 69.7 71.6 65.0 83.0
i i i i
1.1 2.1 10.7 3.3
64.7 69.9
i i
3.2 3.5
35.5 33.3 41.4
i ?-
i
0.8 1.0 6.2
36.3
68.0 i 2.0 (64.2)b 64.3 62.8
i
33.5 36.0 i 1.0 (30.7)b 32.5 i 1.8
0.7
65 5 i- 0.9
25.3 i 1 . 5 28.3 i 0.8 31.8 I 0.6
CD4 33.1 i 1.0 30.1 i 1.0 (28.9)b 28.8 i 1.4
19.0 i 0.6 19.8 i 0.4 (18.7)b 18.4 i 0.5
a DISP = dispersion; WW = Wilson--U7ells;WWPW = Wilson-Wells-Penner-Weber; GC = curve-of-growth; GCBM = curve-of-growth, band model; HRGS = high-resolution grating spectrometer; HRTL = high-resolution tunaCalculated ble laser; MISC = miscellaneous methods. value; see text.
Flgure 2. Beer's law plots for the integrated intensities of CH4.
I _ _
1
0002
I _ _
0004
pt ( m atm)
*
0006
Flgure 3. Beer's law plots for the integrated intensities of CD,.
areas as well as in the sample pressures were taken into account.29 Thle integration intervals that we have used for the measuremcmt of the band areas are as follows: for CHI, 3200-2850,1400-1200; for CD4,2400-2100,1150-850. The
number of measurements for each band can be seen from Figures 2 and 3. Since no information was available on the experimental conditions and error treatment used for the intensities reported by IIeicklen7 nothing can be said about the differences between the v3 intensity values of Heicklen and our values. The error limits reported by Varanasi et al.13J6 stem from the standard deviation of the individual line intensities. However, the origin of the reported standard deviations is not discussed. Moreover, it is not clear how the errors in the total band intensities are obtained from the standard deviations of the individual lines. Although the results of the curve-of-growth method for CH4 are in good agreement with our values, the differences betwleen both results are difficult to discuss especially viewing the above remarks about the error treatment. The errors reported by Saeki et al. include both errors in sample pressure and band area. However, the number of measurements and the integration intervals are not given by these authors. This makes it difficult to gain insight in the possible origin of the differences betwieen their and our values. It is very interesting to note, however, that the calculated values for the v3 and v4 intensitie~of CH4 and CD4 reported by Saeki et al. are in close agreement with our observed values (see Table I, values in parentheses). T h e calculated values, obtained with intensity parameters derived from the integrated intensities of CH4, CD4,CH3D, CD3H, and CH2D2,I5may be considered to be better than the observed values since the experimental errors have been averaged over the isotopic series. The internal consistency of the measurements may be checked by applying the F-sum rule, first derived by Crt~wford.~~ Since methane has no permanent moment the
The Journal of Physical Chemistry, Vol. 84, No.
200
2, 1980
Bode and Smit
TABLE 11: F-Sum Rulea Results for the Observed Absolute Infrared Intensities of CH,and CD,
ref 7 ref 1 5 this work a
2.610 2.745 2.481
f
A, S , = l/,(Ar, t Ar, t Ar, + Ar,) , A a Z 3- A & , , E S,, = 1 2 ~ 1 ' Z ( 2 A-~ ,A, o ~ , ,- A o ~ , 2AQ3,) A
2.486 * 0.062 2.508 i 0.043 2.346 c 0.056
0.061
I0.060
i.
TABLE 111: Symmetry Coordinates, Geometry Parameters, and Force Constantsa
0.035
S z b = 1/,(A0113- A & , , - A o ~ , ,
F,
+ A&,,)
+
A
S,, = l/,(Ar, - Ar, - Ar, t Ar4) S,,= l/,(-Ar, + Ar, - Ar, t Ar,)
s3,= '/,(Ar, +
Reference 30.
Ar, - Ar, - Ar,) S,, = ~ - " ' ( A G ,-~ A Q , , ) A s,, = 2 - 1 ' z ( A ~ -, , A a , , ) A s,, = 2 - 1 ' 2 ( A ~ -3 qA",,) A geometry parameters : rCH = 1.093 A , 01 = 109.471" (tetrahedral) force constants lmdvn A - l l : F , = 5.482, F,, = 0.581, F,3= 5.383, F,, = 0.547, F,,= -0.225 \
'A
"
(' J. L. Duncan and I. M. Mills, Spectrochim. Acta, 20, 523 (1964).
H3
Flgure 4. Definition of the internal coordinates, bond vectors, and Cartesian axes for methane.
quantity leading to A. i
viwi
TABLE IV: Dipole Moment Derivatives for CH, and CD, sign combination('
(ap /aQi)* is an isotopic i n ~ a r i a n t , ~ ~ ? ~ '
a ~ lax 8 3 x 9
~0.7344
i0.4848
t0.5113
20.3867
+0.6544
t0.5092
t0.3417
+0.3568
aw,/as,,,
-0.7502
-0.7387
a P x I a g,x ,
t0.3818
+0.3690
D
= i
Norgi -(ap/aQJ2 3c2ui2
ir-l
a Pxl a 4x = isotopic invariant
t +
See eq 1for the meaning of the symbols. Note that Ai has t o be divided by uiwi and not by vi2 or by w? as has been mistakenly done by several a ~ t h o r s . ~ ~ ~ ~ * - ~ ~ The F-sum values given in Table I1 show a reasonable consistency for the CH4 and CD4 intensities although the differences are outside the error limits in all three cases. This indicates the presence of systematic experimental errors and/or methodical errors (limited validity of harmonic oscillator-linear dipole approximation). The F-sum result for the calculated intensities of CHI and CD4 given by Saeki et al.,15 viz. CHI, 2.406; CD4, 2.377 cm3 mol-', proves the quality of these values and shows a pleasing correspondence with the F-sum result for our observed values. Dipole Moment Derivatives. In the harmonic-oscillator linear-dipole approximation the relation connecting the absolute intensity Ai and the derivative of the molecular dipole moment with respect to the normal coordinate Qi reads35 Ai = (N0rgi/3c2)(vi/ui) ( a ~ / QJ2 a
(1)
where No is Avogadro's number, g, is the degeneracy, c is the velocity of light, and vi and oi are the observed and harmonic frequencies, respectively. The elements apLE/aQ, (5 = x , y, z ) of the polar tensor PQare easily obtained from the Ai values by taking into account the symmetry of the methane molecule. The dipole moment derivatives with respect to the symmetry coordinates are obtained from Ps = PQLs-'
(2)
where Ls-l is the matrix relating normal and symmetry coordinates, Q = LS-lS. The symmetry coordinates are related to the internal coordinates by S = UR, with the internal coordinates defined in Figure 4. The symmetry coordinates, geometry parameters and force constants are given in Table 111. The a p/aSi values are given in Table IV for all possible sign combinations of the ap/aQi quantities. Comparison of the a p/aSi values for CH4and CD4 leads to the (+,-) or (-,+) sign combinations for the a p /
amu"" 9
D A - ' amu'"' wXlaS~,, D A-
a P x / asp,
7
D A-
-t
D
D A(' - - combination: change signs of ap/aS values for combination: similar for + - combination.
I
+
TABLE V: Theoretical Dipole Moment Derivatives for Methane
CNDOIS
INDO ab initio
38 39 36 this work 36 this work 37' 37b 36'
' Calculation 3 in ref 37. STO 4-31G basis set.
-0.63 -0.629 -0.635 -0.624 -0,805 -0.803 -0,908 - 0.977 -1.015
t0.45 t0.240 t0.240 t0.235 t0.006 t0.006 +0.518 t 0.329 +0.481
Calculation 1 5 in ref 37.
aQi's. In view of the ab initio calculated ap/aSi value^^^,^^ listed in Table V the (-,+) sign combination has to be chosen. Other authors arrived a t the same sign choice by using similar a r g u m e n t ~ . l ~Although , ~ ~ - ~ ~ the differences between the dipole moment derivatives calculated by quantum mechanical methods (CNDO/2, INDO, ab initio) are quite large, they all show the same signs. As usual, the ab initio and CNDO/2 results are superior to the INDO results. The work of Meyer and P ~ l a clearly y ~ ~ demonstrates the basis-set sensitivity of the calculated values of the dipole moment derivatives and the limited success to predict reliable values for these quantitives by ab initio methods. Bond Charge Parameters. The observed absolute intensities can be interpreted in terms of bond charge parameters, viz., effective bond charges and bond charge
The Journal of Physical Chemistry, Vol. 84, No. 2, 1980 201
Absolute IR Intensities of Methane
TABLE VI: Ebnd Charge Parameters for CH, and CD, in Terms of Symtnetry Coordinates and Internal Coordinates In Terms of Symmetry Coordinates ~~
q, D
a-l
( a q / a r ) - (aq/ar)', D A-2 ( a q l a a ) - (aq/aai)', D A - ~
ab initio"
exptl*
0.278 -0.975
0.278 -0.844 0.014
--
0.093
In Terms of Internal Coordinates
-
~ - . _ _ _ _
CHdC q, D A - * (aq/3r!,
0.27 8 -0.792
CD,'
D A-
0.009
(asiar);,
0.057 t
0.056 t
(aqiaaj, D 8(aq/aa)', D A-
0.278
0.278
- 0.783 t 0.033
D A-
mean values'
5
0.001 0.0083
i
0.0020 -0.0083
*
0.0020
- 0.788 i 0.024
0.056
0.002 0.0051 i 0.0056 .0.0051 0.0056
*
*
0.002 0.0067 f 0.0042 - 0.0067 i
Flgure 5. Dependence of bond charge parameters on q value. The vertical dotted line indicates the chosen q value, viz., q = 0.278 D A-' (see text).
0.0042
and ps oyerlap densities were divided into a part on carbon and a part on hydrogen in such a way that the resukting bond charge parameters reproduced exactly the ap/aS values given by Meyer and Pulay for the same calculation. The bond charge value obtained in this way (see Table VI) has been used to solve the bond charge equations. 'The resulting reorganization parameter values are given in Table VI. The values derived from the ab initio results are collected in the same table. From the bond charge equations the following relations between q k and the reorganization parameters are eouily obtained:
" Calculated from Table IX of ref 37. Note that S, in ref 37 is defined with the opposite sign. Calculated from e q 8, Dispersions are obtained from the experimental errors in the intensities only.
*
reorgarni~ations.~~*~~ The bond charge parameters are related to the PQ polar tensor t h r o ~ g h ~ ~ , ~ ~
P, = [&q,
+ aAA]oLs
(3)
where t,he matrices within the brackets are defined in ref 22 and 23. The effective bond charges q k have to satisfy the conditionz2 (4) where p is the permanent molecular dipole moment, & t h e effective moment of the kth bond, sq the sign of q k , q k the effective bond charge of the kth bond, rk the bond length, and ek a unit bond direction vector (see Figure 4). The bond dipole moment & points from the negatively charged end of the band to the positively charged end. The sign of q k is taken as positive when the adopted bond direction vector 'ek has the same direction as &, otherwise the sign is negative. Obviously, for CHI and CD4 symmetry requires p = 1;kll.k = 0 and thus eq 4 gives neither information about the magnitude of the effective bond charges nor about the direction of Irk. The number of different bond charge reorganization parameters is reduced to four by symmetry considerations, viz., aqk/ark, a q k / a r / (k f l ) , aqk/aakl( k # I ) , and a q k / a q m (k # 1 # m), which will hereafter be denoted as (aq/ar), (aqlar)', ( a q / a a)', and (aq/aa),respectively. Moreover, a close inspection of the displacements resulting from a unit change in an internal coordinate asi given by the A matrix in terms of the redundant set internal coordinatesz4reveals (see Appendix) ( a q / a a) = - ( a q / a a)'
(5)
leaving only three independent bond charge reorganization parameters. The bond charge parameters in terms of symmetry coordinates are q, [(aq/ar) - (aq/ar)'], and [ ( a q / a a ) - (aq/aa)'].In view of eq 5 the last parameter reduces to 2(aq/aa). Since only two intensity data are available, one additional relation is needed to solve the bond charge equations in terms of symmetry coordinates. The ab initio results of Meyer and P ~ l a have y ~ ~been used t o obtain a value for the bond charge q. The population analysis and charge shifts during vibration given by Meyer and Pulay for their calculation 3 on methane have been used to derive a value for q in the following way. The ss
for CH4 [ ( a q l a r )- (aq/ar)'] = -0.9150qk -- 0.5944 ( d q / a a ) = -0.3536qk + 0.1069
(6)
for CD4 [(aqlar) - (aq/ar)'] = -0.9148qk - 0.5853 ( a q / a a ) = -0.3535qk + 0.1034
(7)
Averaging eq 6 and 7 over both isotopes (CH4/CD4)leads to
[ ( a q l a r ) - (aq/ar)'] = -0.9149qk - 0.5899 (aq/d a) = -0.3536qk + 0.1052
(8)
The relations of eq 8 are graphically depicted in Figure 5 , clearly showing the sensitivity of the reorganization parameter values to the value of q k . In order to arrive a t the individual bond charge parameters one more additional relation is needed. Because of the lack of ab initio data we have used rather arbitrarily the following result, obtained from our CNDO calculations: (aqlar)' = -0.072(aq/ar) This leads to the final bond charge parameter values listed in Table VI. The close correspondence between the parameter values for CHI and CD4 reflects once more the consistency of the observed intensities. As a further check on the quality of our parameters obtained from the lCH4 and CD4intensities the absolute intensities for the isotopic series CH4, CD4, CH3D, and CD3H have been calculi3ted by using the mean parameter values of Table VI. The results are shown in Table VI1 together with the corresponding observed and predicted values of Saeki et al.15 and the observed values of Hiller and Straley.21 Comparing the experimental values for CH3D and CDBHof both H[iller and Straley and Saeki et al. with our predicted values, we found a very satisfactory correspondence. Also the values
202
The Journal of Physical Chemistry, Vol. 84, No. 2, 1980
TABLE VII: Observed a n d Predicted I n t e n s i t i e s for CH,, , CD,, CH,D, a n d CBD, (units, k m / m o l ) calcd int
obsd int oa
_-__ _ _ CH, CD, CH,D
ref
21
15
this work
ref 15
this
64.2 30.8 28.9 18.7 48.0
work 65.5 30.6 29.4 18.9 48.3
6.1.
5.4
6.8
31.4
29.8
28.0
15.8 20.2
16.9 1 6 . 1 19.3 21.6
6.6 14.7
7.0 7.2 1 6 . 3 15.0
redundancy relation is also reflected by the A ma-trjx on internal coordinate basis, obtained fromz4A = mlBUGsl U, where Gs denotes the G matrix on symmetry coordinate basis. Thus eq 5 should perhaps more correctly be written as
_ _ _ _ _ _ _ _ _ I
u3 u, u3 v.,
3019 1311 2260 998
u,
49.2 2970 3017 2200 6.3 1307 1471 29.3 1161 I 2992 15.7 2 1 4 3 1 21.0 2251 1291 6.7 IOo3 15.3 1036
u, u2
u3 u. u6
C13,H
-
ref
Bode and Smit
u, u2
u, u,
v6
t
f
1
68.0 36.0 30.1 19.8 49.3
65.5 31.8 28.8 18.4
a D. L. Gray and A. G. Robiette, Mol. Phys.. 3 7 , 1903 (1979).
predicted by Saeki e t al. are in good agreement with our calculated values.
Acknowledgment. The authors thank Drs. A. J. Kaper and Mr. T. Visser for their valuable contribution to the intensity measurements. The authors are indebted to Dr. G. Restelli for a preprint of ref 20. Appendix Whereas the symmetry coordinates (see Table 11) represent physically possible distortions, the internal angle bending coordinates Aalm certainly do not. Indeed it is impossible to change one particular angIe without changing at least one of the other angles due to the redundancy relation Aa12 + Aay13 + Aa.14 + La23 + 4 ~ ~ + 2 4Aa34 0 lnternal angle bending coordinates which represent physically possible distortions should therefore consist of linear combinat,ions of the six angle bending coordinates Aalm. Such internal coordinates which correspond to the adopted symmetry coordinates are most easily found from R = 6s where U is defined by S = UR. Thus the rectangular (3N - 6)(3N- 5) IJ matrix transforms from the redundant set of 3R! - 5 R coordinates to the 3N - 6 independent S coordinate^.^^ This leads to the following internal angle bending coordinates: R(aiz) = 5/6Aau -
+ La14 + A"23
)'~(AQI~
f Aa24
+
and similar expressions for the remaining ones. This form of the internal bending coordinates which satisfies the
a q k / a R ( a l m ) = - a q d a R ( a d = -aqk/aR(ak,)
where k # I , k # m, 1 f vi. When the above given form of the coordinates R(q,) is kept in mind the relation between the reorganization parameters as given by eq 5 can be easily verified.
References and Notes (1) R. Rollefson and H. Havens, Phys. Rev., 57, 710 (1940). (2) A. M. Thorndike, J . Chem. Phys., 15, 868 (1947). (3) H. L. Welsh, P. E. Pashler, and A. F. Dunri, J . Chem. Phys., 19, 340 (1951). (4) H. L. Welsh and P. J. Sandiford, J . Chem. Phys., 20, 1646 (1952). (5) J. Vincent-Geisze, C. R. Acad. Sci. Paris, 236, 2049 (1953). (6) R. L. Armstrong and H. L. Welsh, Specfrochim. Acta, 16, 840 (1960). (7) J. Heicklen, Specfrochim. Acta, 17, 201 (1961). Only the v3 intensity of CH, was measuredby Heicklen. The other intensities were obtained from E. Ruf, Masters Thesis, University of Minnesota, 1959. (8) D. E. Burch and D. Williams, Appl. Opt., 1, 587 (1962). (9) E. Flnkman, A. Goldman, and U. P. Oppenheim, J . Opt. SOC.Am., 57, 1130 (1967). (10) T. F. Hunter, J. Chem. SOC.A , 374 (1967) (11) Ya. I. Gerlovin and I.N Brlova, Opt. Specfrosc., 23, 33 (1967). (12) A Goldman, E. Finkman, and U. P. Oppenheim, J . Opt. Soc. Am., 59, 1218 (1969). (13) P. Varanasi, L. A. Pugh, and B. R. P. Bangaru, J . Quant. Spectrosc. Radiat. Transfer, 14, 829 (1974). (14) K. Tanabe. J . Mol. Strucf.. 29. 319 (19751. (15j S. Saeki, M. Mizuno, and S. Kondo, Sdectrochim. Acta, Part A , 32, 41-13m m -,.1 < (16) F:K. KOand P. Varanasi, J . Quant. Specfrosc. Radiat. Transfer, 18, 145 (1977). (17) M. Dang-Nhu, A. S. Pine, and A. G.Robiette, J . Mol. Spectrosc., 77, 57 (1979). (18) R. A. Toth, L. H. Brown, and R. H. Hunt, J . Mol. Spectrosc., 67, 1 (1977). (19) K. Fox, M. J. Reisfeld, and,R. S. McDowell, J . Chem. Phys., in press. (20) G. Restelli, F. Cappeliani, and G. Melandrone, Chem. Phys. Left. submitted for publication. (21) R. E. Hiller, Jr., and J. W. Straley, J . Mol. Spectrosc., 5, 24 (1960). (22) A. J. v. Straten and W. M. A. Smit, J. Mol. Specfrosc.,62, 297 (1976). (23) A. J. v. Straten and W. M. A. Smit, J. Mol. Spectrosc., 65, 202 (1977). (24) A. J. v. Straten and W. M. A. Smit, J . Chem. Phys., 67, 970 (1977). (25) W. M. A. Smit, A. J. v. Straten, and T. Visser, J . Mol. Struct., 48, 177 (1978). (26) J. Overend, M. J. Younquist, E. C . Curtis, and B. L. Crawford, Jr., J . Chem. Phys., 30, 532 (1959). (27) E. B. Wilson and A. J. Wells, J , Chem. Phys., 14, 578 (1946). (28) S. S. Penner and D. T. Weber, J . Chem. Phys., 18, 807 (1951). (29) A. G. Worthing and J. Geffner, "Treatment of Experimental Data", Wlley, New York, 1947, Chapter Xi. (30) B. L. Crawford, Jr., J. Chem. Phys., 20, 977 (1952). (31) J. Overend in "infrared Spectroscopy and Molecular Structure", M. Dairies, Ed., Elsevier, Amsterdam, 1963, Chapter X. (32) D. F. Eggers, I. C. Hisatsune, and I. Van Alten, J , Phys. Chem., 59, 1124 (1955). (33) G. B. Mast and W. T. King. J . Phys. Chem., 80, 2004 (1976). (34) R. E. Bruns and B. de Barros Neto. J . Chem. Phys., 69, 3374 (1978). (35) B. Crawford, Jr., J . Chem. Phys., 29, 1042 (1958); I. M. Mills and D. ti. Whiffen, /bid., 30, 1619 (1959). (36) V. Galasso, private communication. (37) W. Meyer and P. Puiay, J . Chem. Phys., 56, 2109 (1972). (38) G. A. Segal and M. L. Klein. J . Chem. Phys., 47, 4236 (1967). (39) J. H. Newton and W. B. Person, J . Phys. Chem., 82, 226 (1978).
