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Analysis of the ν6(A″2) band of cyclopropane-d6 recorded under high resolution
JOURNAL
OF
MOLECULAR
SPECTROSCOPY
81,
494-506 (1980)
Analysis of the z+(A;) Band of Cyclopropane-d, Recorded under High Resolution1,2 A. H. NIELSEN, S. J. DAUNT, AND G. W. HALSEY Molecular
Spectroscopy Laboratory, University of Tennessee,
Department of Physics and Astronomy. Knoxville, Tennessee 37916
The parallel band u6(A!J of C3Ds near 2336 cm-’ has been studied with high resolution (Av = 0.020-0.024 cm-‘) in the infrared. The band has been analyzed using standard techniques and the following parameters have been determined: B” = 0.461388(20) cm-i, 0; = 3.83(17) x lo-’ cm-‘, v0 = 2336.764(2) cm-‘, aS = (B” - B’) = 8.823(12) x 10m4cm-‘, pJ = (0; - DJ) = 0, and a“ = (c” - C’) = 4.5(5) x 10m4cm-‘. 1. INTRODUCTION
In the past 10 years or more much experimental work on the infrared and Raman spectra of the cyclopropanes C,H, (I -13) and CBD, (1, 3, 6, 13-1.5) has appeared in the literature. There have also been several normal coordinate analyses (I, 16-20), ab initio force field studies (21,22), and absolute band intensity studies (23-25) reported. The present paper deals solely with the infrared spectrum of the v6(A;) parallel band of C,D, located at 2336.764 cm-‘. This band has been ascribed to the in-phase CD, antisymmetric stretching vibration. There have been only two previous investigations of this band (1, 14), both at medium resolution. This paper presents the results of the first high-resolution measurement of a CBD, vibration-rotation band. The band has been analyzed using standard methods and values of B”, Dy, CUB= (B” - B’), B’, v,,, pJ = (Dy - D;), and c& have been obtained. Comparison of these new results with previous work and a discussion of these results is given herein. 2. EXPERIMENTAL
DETAILS
All observations were made with the University of Tennessee Smeter Littrowtype vacuum infrared spectrometric system (26) equipped with an 8 x 16 in. (20 x 40 cm) Bausch and Lomb echelle grating blazed at 65” and ruled with 316 lines/cm. The grating was double-passed and used in the thirteenth order for the reported measurements. To keep the energy peaked, the 9 x 18 cm equilateral LiF prism in a Wadsworth-Littrow mounting (27) used for order sorting continuously tracked the grating as it scanned the spectrum. Both the grating and prism drives ’ This research was supported by the Planetary Atmospheres Program of the National Aeronautics and Space Administration (Grant NGL-43-001-006). ’ A preliminary report of this work was presented at the Ohio State University Molecular Spectroscopy Symposium, 1979, Paper ME5. 0022-2852/80/060494-13$02.00/O Copyright All rights
8
1980 by Academic
of reproduction
Press,
Inc.
in any form reserved.
494
THE y6 BAND OF C,D,
495
operated under computer control and all data were digitally recorded at - 1 x 10T3 cm-l intervals. The detector was a Santa Barbara Research Corporation InSb photovoltaic detector operating at 77 K. The source was a carbon rod furnace operating at 2600°C (28). The C3D, was obtained from Merck, Sharpe and Dohme and was the same sample as that used in an earlier Raman study (23). The only impurities observed were small amounts of CO, and C3D,H. A l-m stainless-steel cell with KBr windows situated inside the vacuum tank was filled by means of a gas-handling system external to the spectrometer. All observations were made at room temperature (22°C). The C3D, band extends from about 2290 to 2370 cm-’ (Fig. 1) and therefore overlaps a portion of the CO, fundamental v3 at 2350 cm-‘. This fact makes it convenient to use the CO* lines (29) for calibration of the C3D, lines. The small impurity of CO, in the sample gave rise to easily visible lines, denoted by circles in Figs. 1 and 2. Two complete scans were made across the band at a pressure of 0.3 Torr of the C3D, with the small impurity of COz, and one run was made at a pressure of 1.8 Torr of the C3D6 augmented by an added pressure of 0.2 Torr of pure 12C1602 obtained from Matheson Gas Products. The calibration lines were fitted to a thirdorder polynomial with a standard deviation of 1.3 x lop3 cm-‘. The spectral resolution of the spectrometer (FWHM of single lines) varied from 0.020 at 2290 cm-l to 0.024 at 2375 cm-‘. The line position measurements from the different scans were reproducible to about 1 x 10m3cm-‘. 3. ANALYSIS
The complete band is shown in Fig. 1 with the J “lines” from P(38) to R(38) labeled. With the resolution available the assignment was straightforward, in
FIG.1.Survey scan of the v6(A;) parallel band of cyclopropane-d,. The experimental conditions are described in the text. The lines denoted by circles are due to an impurity of CO, in the sample.
496
NIELSEN,
DAUNT, AND HALSEY TABLE I
Observed” and Calculatedb Wavenumbers J
in cm-’ for the v~(A~) Band of Cyclopropane-d, R(J)
P(J) talc.
%S.
&
(3alc.
LX?&
0
k-)
his-
2337.6888
2338.6054 tf) 2339.5203 (d’
2338.6081
-2.7
2339.5255
-5.2
-4.8
2340.4405
2340.4412
-0.7
2333.0662
-4.5
2341.3537
2341.3551
-1.4
2332.1338
2332.1364
-2.6
2342.2650
2342.2671
-2.1
6
2331.2019
2331.2050
-3.1
2343.1763
2343.1773
-1.0
7
2330.2719
2330.2718
0.1
2344.0863
2344.0857
0.6
8
2329.3369
2329.3369
0.0
2344.9941
2344.9923
1.8
9
2328.4000
2328.4004
-0.4
2345.8974
2345.8970
0.4
10
2327.4638
2327.4621
1.7
2346.8004
2346.7999
0.5
11
2326.5223
2326.5222
0.1
2347.7027
2347.7009
1.8
12
2325.5819
2325.5806
1.3
2348.6012
2348.6000
1.2
13
2324.6394
2324.6374
2.0
2349.4987
2349.4972
1.5
14
2323.6948
2323.6926
2.2
2350.3939
2350.3926
1.3
15
2322.7465
2322.7461
0.4
2351.2860
2351.2860
0.0
16
2321.7991
2321.7979
1.2
2352.1762
2352.1775
-1.3
17
2320.8487
2320.8482
0.5
2353.0661
2353.0671
-1.0
18
2319.8973
2319.8968
0.5
2353.9557
2353.9548
0.9
19
2318.9453
2318.9439
1.4
2354.8412
2354.8405
0.7
20
2317.9900
2317.9894
0.6
2355.7253
2355.7242
1.1
1
2335~8522(c)
2335.8450
7.2
2
2334.9263(c)
2334.9205
5.8
3
2333.9894(d)
2333.9942
4
2333.0617(d)
5
(a) Allvalues areaverages ofthn?esepamte-uremn Cc) and (f).
tsexcepttkeemrkedwith
(b) CTa&&db?ii values using the equaticn " = 2336.7678+0.9219006C&w8.822x10-4m2-1.55678 k)cmlyIl7zmmdinhight?rpressuresran. in fittings. (d) these lines wxe k?) mtlmaswed.
EadlybleMedwithC-branchesandnotinclukd
given weights of 0 in the regression analysis by wighting routine &I
zalmstarrpletelyotscured by P(14) of co2.
(f)Qllyllx?amainhig~pfessurescan.
contrast to the earlier studies (1,14). The K structure of the .I manifolds was unresolved with the present resolution. The Q branch shaded off toward lower wavenumbers and is discussed in the following section. There also appear to be two secondary Q branches on the low wavenumber side of the main Q branch. These are assigned to Q branches of “hot” bands. Utilizing the formulation found in Gordy and Cook (30) for fractional populations it was found that -67% of the molecules are in the ground state at 300 K. The v14 state at 524.5 cm-’ (13) contains 10.9% of the molecules with other states progressively less: ~~~(717cm-‘, 4.3%), v,(614.5 cm-l, 3.5%), v,&386.5 cm-‘, 1.9%), ~~(800 cm-‘, 1.5%), ~~~(964.0 cm-‘, 1.3%), 2~,,(0.9%). The stronger “hot” band has been assigned to vg + v14 - ~14
THE ve BAND OF C,D, TABLE
I-Continued
P(J)
2 aa.
497
R(J)
Qlc.
a.
Qlc.
21
2317.0329
2317.0333 -0.4
2356.6064
2356.6061
0.3
22
2316.0740
2316.0756 -1.6
2357.4844
2357.4659
-1.5
23
2315.1168
2315.1163
0.5
2358.3615
2358.3637
-2.2
24
2314.1532
2314.1556 -2.4
2359.2385
2359.2396
-1.1
25
2313.1920
2313.1932 -1.2
2360.1124
2360.1135
-1.1
26
2312.2291
2312.2294 -0.3
2360.9852
2360.9854
-0.2
27
2311.2636
2311.2640 -0.4
2361.8575
2361.8552
2.3
28
2310.2946
2310.2971 -2.5
2362.7230
2362.7230
0.0
29
2309.3285
2309.3287 -0.2
2363.5672
2363.5888
-1.6 -1.0
30
2308.3565
2308.3588 -2.3
2364.4515
2364.4525
31
2307.38Zl(d) 2307.3875 -5.4
2365.3168
2365.3142
2.6
32
2306.4158
2306.4146
1.2
2366.1783(d)
2366.1739
4.4
33
2305.4422
2305.4403
1.9
2367.0341
2367.0314
2.7
34
2304.4672
2304.4645
2.7
2367.8t349(f)
2367.0869
-2.0
35
2303.4903
2303.4873
3.0
2368.7416
2360.7403
1.3
36
2302.5072
2302.5087 -1.5
2369.5916
2369.5915
0.1
37
2301.5301
2301.5286
2370.4360td)
2370.4407
-4.7
38
2300.5452
2300.5471 -1.9
1.5
A more detailed record of the R branch is shown in Fig. 2. It may be seen that from about R(15) onward the lines appeared to develop a “splitting” which was not interpretable with the standard K* model. This “splitting” was therefore attributed to some unidentified perturbation. The v6 band of C,H, studied with high resolution by McCubbin et al. (5) exhibited a similar but much more severe perturbation. As discussed by McCubbin et al. (5), this perturbation will not affect the fitting of the lines to the usual combination relations used for determination of the ground state constants. The same cannot be assumed true for the upper state difference and sum relations. The maxima of the J manifolds were used in the fittings and the K-dependent terms were considered as effective contributions to the J-dependent terms. From computer simulations of the manifolds it was found that the maxima occurred at K = 1, 2, or 3 as J went from 0 to 35. From J = 15 onward, where the “splitting” began to be apparent in the manifolds, the maxima remained at K = 3, which is well below the K value of the observed resonance. Since the value of DJK was later found to be fairly small, the contributions of K = 1 and 2 to J manifolds forJ < 15 were not considered significant. The remaining manifolds had their maxima at -K = 3 and therefore the fitting was done on lines that would have the effective assignment QPS(J) or QR3(J). These facts are believed to be responsible for the consistency of the separate analyses reported below. The molecular constants were obtained from the measured wavenumbers by means of the usual upper and lower state combination difference relations and the
498
NIELSEN,
DAUNT, AND HALSEY
FIG. 2. An expanded portion of the R branch of vs of CaDa. The upper trace shows the observed spectrum. The lower trace is a computer simulation with the constants in the last column of Table III. The CO, impurity lines are marked with circles. The lines of C3D6 show signs of a weak perturbation for K > 15, which shows up as a “splitting” of the manifolds here for J 2 19.
combination sum relation (31). The ground-state used was the following,
combination
AF; = R(J - 1) - P(J + 1) = [48” - 60; - 4DI;,K2](J
difference
relation
+ M) - SDl;(J + ‘/2)3, (1)
while for the upper state, AF; = R(J) - P(J) = [48’ - 60; - 4D;,F](J The combination
+ ‘/2) - 8D;(J
+ ‘/2)3. (2)
sum relation was of the form,
R(J - 1) + P(J) = 2[V0 + (OlB- CXC)~] - 2cPJ2,
(3)
where OlB= (B” - B’), (Ye= (C” - C’), and p is the effective K value for the contribution discussed above. The wavenumbers of lines listed in Table I have been used to form the necessary values of AF!!, AF;, and combination sums which were then fitted to Eqs. (l), (2), and (3), respectively, using least-squares regression analysis programs (32). The results of these three fittings are listed in columns 2, 3, and 4 of Table II. The quality of the fitting for the ground state is illustrated in Fig. 3A. The data points in the figure were obtained by dividing the AF; by the appropriate (J + 1/2) and then plotting this number versus (J + ‘/)* in the traditional manner (3Z). The line put through these points was determined by using the regression analysis values of 4[B” - D,p] as the y intercept and -8DI; as the slope. Except for the few points lying below (J + 1/2)2= 100, the points stay within the dotted lines (99% confidence levels), or fit the solid line to an accuracy of about 2 to 3 x lop4 cm-‘. A similar illustrative plot of the combination sum data and regression analysis results is shown in Fig. 3B. The line through the data points which used the regression results of 2[v, + (cP - &)F] as the y intercept and -2& as the slope fitted the experimental points almost exactly. The ability to plot the combination sums
499
THE v6 BAND OF CID6 TABLE II Results of Various Data Fits for v&A;) of C,D,” CM.
1
-1.
2
001. 3
sa [W-$1
Cal.4 amELsI4
XE
0.461385(20)
D" J
001. 5 EREQFIT 0.461391(13)
3.63(17)xlo-7
[W-D$l
-
3.89(7hlo-7 0.460509
0.460505(22) 3.84mklo-7
?i ",*a*&~
-
a*
6.8O(42)x1O-4 0
E&D{-D$
2336.768(Z)
2336.768(l)
8.823(12)1dO-~
8.822(14)xlo-4
0
0
GSCD - Ground State Combination wAllcpankitiesinulitsofal-1; Differences 6 DSCD - Upper State Combination Differences.
in this manner despite the small perturbation observed in this band was in marked contrast to the results obtained for v6 of C,H, (5), where the much more severe perturbation caused a sharp break in the sum plot after J = 10. The wavenumbers given in Table I may also be fitted by means of a least-squares treatment of the equation, eR
= a + bm + cm2 + dm3 + em4,
(4)
where the coefficients have the following meanings: a = vo, b = (B’ + B”), c = (-OlB + pJ), d = -2(D; + DI;), and e = pJ. The variable m has the value (J + 1) for the R-branch lines and (-J) for the P-branch lines (31). The results of this fitting are reported in column 5 of Table II. The calculated wavenumbers and the residuals (obs. - talc.) are listed along with the observed wavenumbers in Table I. The overall fit of the data was very good (1.3 x low3 cm-‘). The observed line positions in Table I are systematically lower (-0.05 to 0.15 cm-‘) than those reported previously (1, 14). Figure 2 shows a record of the observed R branch from R(9) to R(30), and below it the same R lines calculated as to position and envelope from constants determined in the above analyses. As expected, the envelopes of the unresolved J manifolds were found to be quite sensitive to the value of (OH - crc). Since OlBwas well determined from the various analyses it was thought that oc could be extracted by calculating a series of J-manifold envelopes. The value of o? was fixed to that in column 4 of Table II and (Yewas varied until a good match was obtained. The R( 10) manifold was chosen first for this calculation since at J = 10 no perturbations were noticeable and contributions from DJK terms were negligible. Figure 4 shows a series of envelopes obtained with values of (Ye ranging from 0.0 x 1O-4 to 6.0 x low4 cm-‘. It may be seen that the observed and calculated envelopes agree
100
200
300
=2336.768(2km-’
400
500
600
J2
700
(J l f,’
900
900
1000
1100
1200
=8.82302) x 1OAcm-l
1400
(B)
(A)
1300
4
v6
1500
FIG. 3. (A) A plot of the GSCD data (0) according to Eq. (1). The solid line was drawn from the regression analysis fitting of the experimental data. The dotted lines indicate 9% confidence limits of this line. The B* is the effective value [B” - DJKs]. The previous best available value of B” from Jones and Stoicheff (15) is also indicated on the plot. (B) A plot of the combination sum relation according to Eq. (3). The experimental data are denoted by 0. The solid line is from the regression analysis. The effective band origin v$ is v,, + (cP - ac)s.
cl
4674JJ 1
=3.83(17? x lO”cm-
c3D6
501
THE i+, BAND OF C3Ds
R(10) C,D, v,(A;)
cYc,=o.ox1041
=6.0x10-’
FIG. 4. The evaluation of oc = (C” - C’) by computer simulation of the R(lO) manifold. The value of 4.5(5) x low4cm-’ was determined by fixing the other molecular constants to the values listed in the last column of Table III and varying oc until a match was obtained.
almost exactly for c& = 4.5 x 10m4 cm-‘, while for oc = 3.0 x 10e4 and 6.0 x lop4 cm-’ the calculated envelopes fall significantly above and below the observed envelopes, respectively. It was therefore concluded that the best value of & was 4.5 x 1O-4 cm-l. To carry out the calculation above it was necessary to assume values of c”, &, and 0;; in addition to the molecular constants determined in this paper (B”, B’, v,, DI;, and D$). The value of C” = 0.3196 cm-l used in earlier work (13) was assumed. The present work produced an observed D’j = 3.83 x lo-’ cm-’ which agreed very well with Duncan’s value ofD’j = 3.74 x IO-’ cm-l calculated from force field considerations (33). It therefore appeared reasonable to use Duncan’s values of DljK = -3.57 x lo-’ cm-’ and 0;; = 1.07 x lo-’ cm-’ (33) in the simulations. This decision was further reinforced when the calculated D’Jand DI;Kvalues for C3H6 were also found to agree well with very recent observed values.3 It was further assumed that DiK = DIfK and Di = 0;. The simulation program used (PERTCOR) is similar to that described by Cartwright and Mills (6) and DiLauro and Mills (36). The maximum values ofJ and K were set at 50 and the statistical weights were taken from Herzberg (37) and were assumed as for X,Y, (D&; i.e., for K = 3p, 3p 2 1, 3p ? 2, 3p they are 249:240:240:249 and for K = 0, J even:J odd they are 8: 16. These values can also be verified using the et al. have reported a diode laser study of the Y,,, + v,,(P) band of &He near 1892.5 cm-’ foundl); = 1.072(54) x 10-6cm-‘, and DyK = - 1.29(19) x 10-6cm-1. Rubiner al. (35) have the pure rotational Raman spectrum of C,H, and with consideration of the effective K strucdetermined 0; = 1.0 x low6 cm-’ and DyX = -1.3 x 10e6 cm-‘. Duncan has calculated Dl; = 0.96 x 10mBcm-r and DL = -1.22 x lo-@ cm-l (33). 3 Weber (34). They reexamined ture have
502
NIELSEN,
DAUNT,
AND
HALSEY
recent work of Weber (38). The calculated lineshapes for all J values in both P and R branches were found to agree well with observed contours (Fig. 2). This appeared to be true even for split manifolds except in the localized region of the splittings. 4. DISCUSSION
The results of the data analyses are collected in Table II. The numbers in Table II have been obtained from the averages of the several data sets fitted individually, and also from analysis ofthe averaged data sets (line-wavenumbers). The molecular parameters show very good internal consistency. The error in the values is given by the numbers in parentheses following the constant (99% confidence intervals). It may be seen that the value of vO + (o? - CC)@ from the combination sum fit TABLE Comparison
with Previous
m1uMRFs. Cc’ B"
O-46079(20)
D;
l.o(l.o)xlo-7
"0
aB
0.4630(23)
III Studies”
IR
(d)
FaxE Fmmk)
0.4607(3)
FRESEm SImY 0.461388(20)(f)
3.74xlo-7
3.83(17)xlo-7
2336.02(10)
2336.87(l)
2336.764(4)
8.5xlo-4
9.0(l)xlo-4
8.823(12)~lO-~
CiC
4.5(5)xlo-4
EJ
0
0.3196(')
C"
D;;c
%
(a)
-3.57xlo-7
-3.57x10-7(h)
1.07xlo-7
1.07x10-7(h)
-
All quantities in units of an-'.
(b) Ref. 15.. (c) Ref. 1. (d) Ref. 2. (e) Ref. 33. (f) !imluatedbyassuningI;T=
9 atid L.-&U?of B"-D$
c,f~01. 2, ~,le
II.
(g) Ref. 13. (h) Assuned equal to force field value. Note: Column
6; 3rd line should
read #2336.764(2).
Footnote
(d) should
read Ref. 14.
THE v,BANDOFC,D,
503
agrees exactly with the value from the wavenumber fit. The B”, D’j, B’, D;, OB, and pJ values determined from the various fittings agree very well with one another. The reasons for this good agreement are believed to be (i) the ability in the case of this band to attribute the maximum of each J manifold to essentially the same low value of K and (ii) the fact that the weak perturbation present affects only levels with K > 15 in contrast to vs of C3H6. The ability to plot the data and fit them as accurately as is shown in Fig. 3 would not have been possible otherwise. The collected results from previous investigations and from the present work are listed in Table III. Several differences may be noted: the present value of the band origin term v0 + (cP - (Y”)@ = 2336.768 cm-l differs greatly from the earlier medium resolution work by 0.748 cm-l (1) and 0.102 cm-’ (14), respectively. The former work contained a J misassignment as noted in Ref. (14). The discrepancy with the more recent work is most likely caused by the limited resolution available in that work. It should be noted that if it is assumed that 3 = 9, then v0 = 2336.764 cm-‘. Significant differences also exist between the present value of [B” - Ohs] = 0.461385 cm-’ and the previous ir values of 0.4630 cm-’ (1) and 0.4607 cm-’ (14). The differences here are believed to be due to the same causes as for the v, discrepancies. There is also a value of B” from the rotational Raman study of Jones and Stoicheff (15) ofB” = 0.46079( 15) cm-r (see Fig. 3A). This value falls significantly below the present value (ir - R = 0.000598 cm-‘). As discussed by Weber (3&r, 39) this discrepancy between rotational Raman results and highresolution ir or microwave data usually stems from one of two reasons: (i) the neglect of the effect of the centrifugal distortion constant DJK on the observed maxima and (ii) the presence of underlying “hot” bands from rotational transitions originating in excited vibrational states in the Raman data. For cyclopropane the effects of “hot” bands are not expected to be as serious as the neglect of centrifugal distortion contributions. In support of this conclusion it is noted that the value of B” reported by McCubbin et al. (5) from the high-resolution ir analysis of v6 of C3H, was 0.67024(15) cm-‘, while the early rotational Raman value of Jones and Stoicheff (15) was 0.66962(20) cm-l, a difference of 0.00064 cm-‘. The recent diode laser study of v10 + vrl of C3H, (34) has verified the earlier ir results by reporting B” = 0.670277(28) cm-‘. Very recently, two new rotational Raman studies of C,H, have been reported. Both ofthese studies took proper account of the effects of the underlying K structure. The study of Kainnady and Weber (3&z) reported B” = 0.670144(12) cm-’ and that of Rubin et al. (35) reported B” = 0.67028(15) cm-‘. These recent studies affirm the conclusion that the discrepancy for the B” values of CBD, mentioned above is caused by the neglect of D JKin the earlier Raman work (1.5). The present B” difference of 5.98 x 10m4cm-’ for C3D6 is of the same magnitude as the earlier observed difference for C3H6 of 6.4 x lo-” cm-’ before the full centrifugal distortion effects were taken into account. The determination of (CUB- aC) = 4,323 x lo-’ cm-l and a” = 8.823 x lop4 cm-’ from the present study permits a detailed explanation of the observed structure of the Q branch and the J manifolds. The equation for the K lines in each J manifold can be reduced to 4,;
= v. + (B’ + B”)m - cxBm2 - 4DI;m3 + [(Q? - ore) - 2D’;,m]K2,
(5)
504
NIELSEN,
DAUNT, AND HALSEY
where we have assumed pJ = p”” = pK = 0. The first four terms on the right side of Eq. (5) are constant for each K line in a particular J manifold. The degradation of the manifold is thus given only by the last term. Since (cu” - cyc>is positive and D’jKis negative, the J manifolds degrade to higher wavenumbers, as can be seen in Fig. 2. The (crB - c&) constant being positive also means that the K-subband origins degrade to the high wavenumber side of L+,.As a consequence, all the subband origins from K = 0 to K = 30 lie in a region 70.40 cm-’ above v. = 2336.764 cm-l. As is usually assumed, the band origin was found to be at the base of the sharp edge of the Q branch. Even though all the subband origins lie above uo, no Q branch lines were observed above that wavenumber. The equation for the Q-branch lines (31), again ignoring the p terms, reduces to I/,$ = v. + (& - aC)K2 - dJ(J
+ 1).
(6)
The sum of the first two terms on the right side of Eq. (6) determines the subband origins. There is the usual restriction that J 2 K, which results in the first allowed line of each K subband having the value J = K. Thus, Eq. (6) reduces to $K = Vo - (rCK2 - a”K. If both &’ and & are positive, ‘as for vg of C3D6, then the first lines of all subbands must lie below vo. In addition, because CUB is positive the remaining J structure (J > K) of each K subband degrades to lower wavenumbers. This gives the final result, as seen in Fig. 1, that all Q-branch lines lie to lower wavenumbers than vo. Although the structure of the Q branch was partially resolved, the density of transitions produced by the close subband spacing makes it impossible to assign specific transitions to these peaks. This was confirmed by the simulation results. The transitions are so close together that even at Doppler limited resolution (-3 x 10m3cm-‘) these lines would not be resolved sufficiently for assignment. A possible explanation for the cause of the weak perturbation in v’6may be a weak x-y Coriolis resonance with the v,(E’) band near 2209 cm-’ or the E’ component of 2v, near 2141 cm-’ (40). A value for L&c1= -0.02 has been reported recently (24). This value seems very small but the separation u6-r+ = 128 cm-’ may be small enough to account for the weak perturbation seen. The vs band has been resolved in a ITCent study in this laboratory into its RRK(J) and ‘p,(J) structure (41), but the small value of 5: (14) causes the Q branches to overlap severely at the center ofthe band.4 This has so far prevented definitive assignment of the observed series. ACKNOWLEDGMENTS The authors would like to thank Professor W. E. Blass for helpful comments and a critical reading of the manuscript. One of us (S.J.D.) would like to thank Professor H. F. Shurvell for the gift of the CBDB samples and Dr. D. E. Ellis for a copy of his thesis. This research was supported by the Planetary Atmospheres program ofthe National Aeronautics and Space Administration (Grant NGL-43-001-006). RECEIVED: August
1, 1979
4 This is quite different from the appearance of the v8 band of C,H, studied by Withstandley, McCubbin, and Polo (9) in which the only regular structure observed was the sawtooth features of the Q branches in the central part of the band.
THE va BAND
505
OF CsDB
REFERENCES 1. Hs. H. GUNTHARD,
R. C. LORD, AND T. K. MCCUBBIN, JR., J. Chem. Phys. 25,768-774
2. J. L. DUNCAN, J. Mol. Spectrosc.
25,451-466
3. J. L. DUNCAN AND D. C. MCKEAN, J. Mol. Spectrosc.
27, 117-142 (l%S).
4. R. WYATT, J. T. ROBERTS,R. E. WENTZ, AND P. M. WILT, J. Chem. Phys. 50,2552-2558 5. T. K. MCCUBBIN, JR., V. WITHSTANDLEY, AND S. R. POLO, J. Mol. Spectrosc. 6. G. J. CARTWRIGHT
AND I. M. MILLS, J. Mol. Spectrosc.
7. F. N. MASRI AND W. E. BLASS, J. Mol. Spectrosc. 8. A. G. MAKI, J. Mol. Spectrosc.
41, 177-181
9. V. WITHSTANDLEY,T. K. MCCUBBIN, JR.,
(1956).
(1968). (1%9).
31,95-99(1%9).
34, 415-439 (1970).
39, 21-28 (1971).
(1972).
AND S.
R. POLO,.I. Mol. Specrrosc.
47,297-300(
1973).
10. P. M. MATHAI, G. G. SHEPHERD,AND H. L. WELSH, Canad. J. Phys. 34, 1448-1459 (1956). II. A. M. PYNDYK AND V. B. PODOBEDOV,Opt. Spectrosc. 35, 31-32 (1973). 12. R. J. BUTCHER AND W. J. JONES,J. Mol. Spectrosc.
47, 64-83 (1973).
13. S. J. DAUNT AND H. F. SHURVELL, J. Raman Spectrosc.
2,463-479
(1974).
14. J. L. DUNCAN AND D. E. ELLIS, J. Mol. Spectrosc. 28,540-557 (l%S); D. E. ELLIS, Ph.D. thesis, University of Aberdeen, 1970. 15. W. J. JONES AND B. P. STOICHEFF, Canad. J. Phys. 42, 2259-2263 (1964). 16. S. J. CYVIN, Specrrochim.
Acta 16, 1022-1030 (1960).
17. J. L. DUNCAN AND G. R. BURNS, J. Mol. Spectrosc. 18. R. A. R. PEARCE AND I. W. LEVIN, Spectrochim.
30, 253-265
(1969).
Acra 32A, 1135-1139 (1976).
19. L. NEMES, Acta Chim. Sci. Hung. 59, 75-83 (1969). 20. J. R. ROBINS, S. J. DAUNT, AND H. F. SHURVELL, J. Raman Specfrosc.
5, 411-416 (1976).
21. C. E. BLOM, P. J. SLINGERLAND,AND C. ALTONA, Mol. Phys. 31, 1359-1376 (1976). 22. C. E. BLOM AND C. ALTONA, Mol. Phys. 31, 1377-1391 (1976). 23. T. P. LEWIS AND I. W. LEVIN, Theoret. Chim. Acra 19, 55-65 (1970). 24. S. KONDO,
T. NAKANAGA,
AND S. SABKI, Spectrochim.
Acta 35A, 181-191 (1979).
25. I. W. LEVIN AND R. A. R. PEARCE,J. Chem. Phys. 69, 2196-2208 (1978). 26. D. E. JENNINGS,Ph.D. thesis, University of Tennessee,
1974.
27. H. M. RANDALL AND J. STRONG, Rev. Sci. Instrum. 2, 585-599 (1931). 28. W. J. BOYD, D. E. JENNINGS,W. E. BLASS, AND N. M. GAILAR, Rev. Sci. Instrum. 45, 1286- 1288 (1974). 29. A. R. H. COLE, Ed., “IUPAC Tables of Wavenumbers for the Calibration of Infrared Spectra,” 2nd ed., Pergamon Press, New York, 1977; A. BALDACCI, V. M. DEVI, D.-W. CHEN, K. NARAHARIRAO, AND B. FRIDOVICH,J. Mol. Spectrosc. 70,143-159(1978); V. M. DEVI, A. BALDACCI, J. GRANGAARD, L. LINDEN, K. NARAHARI RAO, AND B. FRIDOVICH,J. Mol. Spectrosc. 70, 160-162 (1978). 30. W. GORDY
AND R. L. COOK, “Microwave
Molecular Structure, Vol. IX, Techniques of Organic
Chemistry, Chemical Applications of Spectroscopy, Eds.), p. 55, Wiley-Interscience, New York, 1970. 31. H. C. ALLEN AND P. C. CROSS,“Molecular
Part II” (W. West and A. Weissberger,
Vib-Rotors,”
Chap. 7, Wiley, New York, 1963.
32. K. F. LIN, W. E. BLASS, AND N. M. GAILAR, J. Mol. Spectrosc. HAFFORD, M. S. thesis, University of Tennessee, 1972. 33. J. L. DUNCAN, J. Mol. Spectrosc.
60, 225-238
79, 151-157
(1980); J. A.
(1976).
34. W. H. WEBER, D. H. LESLIE, AND C. W. PETERS, Paper RA6 presented at the 33rd Symposium on Molecular Spectroscopy at the Ohio State University, Columbus, Ohio, 1978. 35. B. RUBIN, D. A. STEINER, T. K. MCCUBBIN, JR., AND S. R. POLO, J. Mol. Spectrosc. (1978). 36. C. DILAURO AND I. M. MILLS, J. Mol. Specfrosc.
72,57-61
21, 386-413 (1966).
37. G. HERZBERG, “Molecular Spectra and Molecular Structure, Vol. III, Electronic Spectra and Electronic Structure of Polyatomic Molecules,” p. 94, Van Nostrand, New York, 1%6.
506
NIELSEN,
DAUNT,
AND HALSEY
A. WEBER, in “Raman Spectroscopy of Gases and Liquids” (A. Weber, Ed.), Chap. 3, p. 96 ff., Springer-Verlag, New York, 1979. 386. A. WEBER, Paper WA6 presented at the 34th Symposium on Molecular Spectroscopy at the Ohio State University, Columbus, Ohio. 1979. 39. A. WEBER,in “The Raman Effect” (A. Anderson, Ed.), Vol. 2, p. 63Off.. Dekker, New York, 1973. 40. A. W. BAKER AND R. C. LORD, J. Chem. Phys. 23, 1636-1643 (1955). 41. R. J. LOVELL, S. J. DAUNT, W. E. BLASS, AND G. W. HALSEY, unpublished results. 380.
OF
MOLECULAR
SPECTROSCOPY
81,
494-506 (1980)
Analysis of the z+(A;) Band of Cyclopropane-d, Recorded under High Resolution1,2 A. H. NIELSEN, S. J. DAUNT, AND G. W. HALSEY Molecular
Spectroscopy Laboratory, University of Tennessee,
Department of Physics and Astronomy. Knoxville, Tennessee 37916
The parallel band u6(A!J of C3Ds near 2336 cm-’ has been studied with high resolution (Av = 0.020-0.024 cm-‘) in the infrared. The band has been analyzed using standard techniques and the following parameters have been determined: B” = 0.461388(20) cm-i, 0; = 3.83(17) x lo-’ cm-‘, v0 = 2336.764(2) cm-‘, aS = (B” - B’) = 8.823(12) x 10m4cm-‘, pJ = (0; - DJ) = 0, and a“ = (c” - C’) = 4.5(5) x 10m4cm-‘. 1. INTRODUCTION
In the past 10 years or more much experimental work on the infrared and Raman spectra of the cyclopropanes C,H, (I -13) and CBD, (1, 3, 6, 13-1.5) has appeared in the literature. There have also been several normal coordinate analyses (I, 16-20), ab initio force field studies (21,22), and absolute band intensity studies (23-25) reported. The present paper deals solely with the infrared spectrum of the v6(A;) parallel band of C,D, located at 2336.764 cm-‘. This band has been ascribed to the in-phase CD, antisymmetric stretching vibration. There have been only two previous investigations of this band (1, 14), both at medium resolution. This paper presents the results of the first high-resolution measurement of a CBD, vibration-rotation band. The band has been analyzed using standard methods and values of B”, Dy, CUB= (B” - B’), B’, v,,, pJ = (Dy - D;), and c& have been obtained. Comparison of these new results with previous work and a discussion of these results is given herein. 2. EXPERIMENTAL
DETAILS
All observations were made with the University of Tennessee Smeter Littrowtype vacuum infrared spectrometric system (26) equipped with an 8 x 16 in. (20 x 40 cm) Bausch and Lomb echelle grating blazed at 65” and ruled with 316 lines/cm. The grating was double-passed and used in the thirteenth order for the reported measurements. To keep the energy peaked, the 9 x 18 cm equilateral LiF prism in a Wadsworth-Littrow mounting (27) used for order sorting continuously tracked the grating as it scanned the spectrum. Both the grating and prism drives ’ This research was supported by the Planetary Atmospheres Program of the National Aeronautics and Space Administration (Grant NGL-43-001-006). ’ A preliminary report of this work was presented at the Ohio State University Molecular Spectroscopy Symposium, 1979, Paper ME5. 0022-2852/80/060494-13$02.00/O Copyright All rights
8
1980 by Academic
of reproduction
Press,
Inc.
in any form reserved.
494
THE y6 BAND OF C,D,
495
operated under computer control and all data were digitally recorded at - 1 x 10T3 cm-l intervals. The detector was a Santa Barbara Research Corporation InSb photovoltaic detector operating at 77 K. The source was a carbon rod furnace operating at 2600°C (28). The C3D, was obtained from Merck, Sharpe and Dohme and was the same sample as that used in an earlier Raman study (23). The only impurities observed were small amounts of CO, and C3D,H. A l-m stainless-steel cell with KBr windows situated inside the vacuum tank was filled by means of a gas-handling system external to the spectrometer. All observations were made at room temperature (22°C). The C3D, band extends from about 2290 to 2370 cm-’ (Fig. 1) and therefore overlaps a portion of the CO, fundamental v3 at 2350 cm-‘. This fact makes it convenient to use the CO* lines (29) for calibration of the C3D, lines. The small impurity of CO, in the sample gave rise to easily visible lines, denoted by circles in Figs. 1 and 2. Two complete scans were made across the band at a pressure of 0.3 Torr of the C3D, with the small impurity of COz, and one run was made at a pressure of 1.8 Torr of the C3D6 augmented by an added pressure of 0.2 Torr of pure 12C1602 obtained from Matheson Gas Products. The calibration lines were fitted to a thirdorder polynomial with a standard deviation of 1.3 x lop3 cm-‘. The spectral resolution of the spectrometer (FWHM of single lines) varied from 0.020 at 2290 cm-l to 0.024 at 2375 cm-‘. The line position measurements from the different scans were reproducible to about 1 x 10m3cm-‘. 3. ANALYSIS
The complete band is shown in Fig. 1 with the J “lines” from P(38) to R(38) labeled. With the resolution available the assignment was straightforward, in
FIG.1.Survey scan of the v6(A;) parallel band of cyclopropane-d,. The experimental conditions are described in the text. The lines denoted by circles are due to an impurity of CO, in the sample.
496
NIELSEN,
DAUNT, AND HALSEY TABLE I
Observed” and Calculatedb Wavenumbers J
in cm-’ for the v~(A~) Band of Cyclopropane-d, R(J)
P(J) talc.
%S.
&
(3alc.
LX?&
0
k-)
his-
2337.6888
2338.6054 tf) 2339.5203 (d’
2338.6081
-2.7
2339.5255
-5.2
-4.8
2340.4405
2340.4412
-0.7
2333.0662
-4.5
2341.3537
2341.3551
-1.4
2332.1338
2332.1364
-2.6
2342.2650
2342.2671
-2.1
6
2331.2019
2331.2050
-3.1
2343.1763
2343.1773
-1.0
7
2330.2719
2330.2718
0.1
2344.0863
2344.0857
0.6
8
2329.3369
2329.3369
0.0
2344.9941
2344.9923
1.8
9
2328.4000
2328.4004
-0.4
2345.8974
2345.8970
0.4
10
2327.4638
2327.4621
1.7
2346.8004
2346.7999
0.5
11
2326.5223
2326.5222
0.1
2347.7027
2347.7009
1.8
12
2325.5819
2325.5806
1.3
2348.6012
2348.6000
1.2
13
2324.6394
2324.6374
2.0
2349.4987
2349.4972
1.5
14
2323.6948
2323.6926
2.2
2350.3939
2350.3926
1.3
15
2322.7465
2322.7461
0.4
2351.2860
2351.2860
0.0
16
2321.7991
2321.7979
1.2
2352.1762
2352.1775
-1.3
17
2320.8487
2320.8482
0.5
2353.0661
2353.0671
-1.0
18
2319.8973
2319.8968
0.5
2353.9557
2353.9548
0.9
19
2318.9453
2318.9439
1.4
2354.8412
2354.8405
0.7
20
2317.9900
2317.9894
0.6
2355.7253
2355.7242
1.1
1
2335~8522(c)
2335.8450
7.2
2
2334.9263(c)
2334.9205
5.8
3
2333.9894(d)
2333.9942
4
2333.0617(d)
5
(a) Allvalues areaverages ofthn?esepamte-uremn Cc) and (f).
tsexcepttkeemrkedwith
(b) CTa&&db?ii values using the equaticn " = 2336.7678+0.9219006C&w8.822x10-4m2-1.55678 k)cmlyIl7zmmdinhight?rpressuresran. in fittings. (d) these lines wxe k?) mtlmaswed.
EadlybleMedwithC-branchesandnotinclukd
given weights of 0 in the regression analysis by wighting routine &I
zalmstarrpletelyotscured by P(14) of co2.
(f)Qllyllx?amainhig~pfessurescan.
contrast to the earlier studies (1,14). The K structure of the .I manifolds was unresolved with the present resolution. The Q branch shaded off toward lower wavenumbers and is discussed in the following section. There also appear to be two secondary Q branches on the low wavenumber side of the main Q branch. These are assigned to Q branches of “hot” bands. Utilizing the formulation found in Gordy and Cook (30) for fractional populations it was found that -67% of the molecules are in the ground state at 300 K. The v14 state at 524.5 cm-’ (13) contains 10.9% of the molecules with other states progressively less: ~~~(717cm-‘, 4.3%), v,(614.5 cm-l, 3.5%), v,&386.5 cm-‘, 1.9%), ~~(800 cm-‘, 1.5%), ~~~(964.0 cm-‘, 1.3%), 2~,,(0.9%). The stronger “hot” band has been assigned to vg + v14 - ~14
THE ve BAND OF C,D, TABLE
I-Continued
P(J)
2 aa.
497
R(J)
Qlc.
a.
Qlc.
21
2317.0329
2317.0333 -0.4
2356.6064
2356.6061
0.3
22
2316.0740
2316.0756 -1.6
2357.4844
2357.4659
-1.5
23
2315.1168
2315.1163
0.5
2358.3615
2358.3637
-2.2
24
2314.1532
2314.1556 -2.4
2359.2385
2359.2396
-1.1
25
2313.1920
2313.1932 -1.2
2360.1124
2360.1135
-1.1
26
2312.2291
2312.2294 -0.3
2360.9852
2360.9854
-0.2
27
2311.2636
2311.2640 -0.4
2361.8575
2361.8552
2.3
28
2310.2946
2310.2971 -2.5
2362.7230
2362.7230
0.0
29
2309.3285
2309.3287 -0.2
2363.5672
2363.5888
-1.6 -1.0
30
2308.3565
2308.3588 -2.3
2364.4515
2364.4525
31
2307.38Zl(d) 2307.3875 -5.4
2365.3168
2365.3142
2.6
32
2306.4158
2306.4146
1.2
2366.1783(d)
2366.1739
4.4
33
2305.4422
2305.4403
1.9
2367.0341
2367.0314
2.7
34
2304.4672
2304.4645
2.7
2367.8t349(f)
2367.0869
-2.0
35
2303.4903
2303.4873
3.0
2368.7416
2360.7403
1.3
36
2302.5072
2302.5087 -1.5
2369.5916
2369.5915
0.1
37
2301.5301
2301.5286
2370.4360td)
2370.4407
-4.7
38
2300.5452
2300.5471 -1.9
1.5
A more detailed record of the R branch is shown in Fig. 2. It may be seen that from about R(15) onward the lines appeared to develop a “splitting” which was not interpretable with the standard K* model. This “splitting” was therefore attributed to some unidentified perturbation. The v6 band of C,H, studied with high resolution by McCubbin et al. (5) exhibited a similar but much more severe perturbation. As discussed by McCubbin et al. (5), this perturbation will not affect the fitting of the lines to the usual combination relations used for determination of the ground state constants. The same cannot be assumed true for the upper state difference and sum relations. The maxima of the J manifolds were used in the fittings and the K-dependent terms were considered as effective contributions to the J-dependent terms. From computer simulations of the manifolds it was found that the maxima occurred at K = 1, 2, or 3 as J went from 0 to 35. From J = 15 onward, where the “splitting” began to be apparent in the manifolds, the maxima remained at K = 3, which is well below the K value of the observed resonance. Since the value of DJK was later found to be fairly small, the contributions of K = 1 and 2 to J manifolds forJ < 15 were not considered significant. The remaining manifolds had their maxima at -K = 3 and therefore the fitting was done on lines that would have the effective assignment QPS(J) or QR3(J). These facts are believed to be responsible for the consistency of the separate analyses reported below. The molecular constants were obtained from the measured wavenumbers by means of the usual upper and lower state combination difference relations and the
498
NIELSEN,
DAUNT, AND HALSEY
FIG. 2. An expanded portion of the R branch of vs of CaDa. The upper trace shows the observed spectrum. The lower trace is a computer simulation with the constants in the last column of Table III. The CO, impurity lines are marked with circles. The lines of C3D6 show signs of a weak perturbation for K > 15, which shows up as a “splitting” of the manifolds here for J 2 19.
combination sum relation (31). The ground-state used was the following,
combination
AF; = R(J - 1) - P(J + 1) = [48” - 60; - 4DI;,K2](J
difference
relation
+ M) - SDl;(J + ‘/2)3, (1)
while for the upper state, AF; = R(J) - P(J) = [48’ - 60; - 4D;,F](J The combination
+ ‘/2) - 8D;(J
+ ‘/2)3. (2)
sum relation was of the form,
R(J - 1) + P(J) = 2[V0 + (OlB- CXC)~] - 2cPJ2,
(3)
where OlB= (B” - B’), (Ye= (C” - C’), and p is the effective K value for the contribution discussed above. The wavenumbers of lines listed in Table I have been used to form the necessary values of AF!!, AF;, and combination sums which were then fitted to Eqs. (l), (2), and (3), respectively, using least-squares regression analysis programs (32). The results of these three fittings are listed in columns 2, 3, and 4 of Table II. The quality of the fitting for the ground state is illustrated in Fig. 3A. The data points in the figure were obtained by dividing the AF; by the appropriate (J + 1/2) and then plotting this number versus (J + ‘/)* in the traditional manner (3Z). The line put through these points was determined by using the regression analysis values of 4[B” - D,p] as the y intercept and -8DI; as the slope. Except for the few points lying below (J + 1/2)2= 100, the points stay within the dotted lines (99% confidence levels), or fit the solid line to an accuracy of about 2 to 3 x lop4 cm-‘. A similar illustrative plot of the combination sum data and regression analysis results is shown in Fig. 3B. The line through the data points which used the regression results of 2[v, + (cP - &)F] as the y intercept and -2& as the slope fitted the experimental points almost exactly. The ability to plot the combination sums
499
THE v6 BAND OF CID6 TABLE II Results of Various Data Fits for v&A;) of C,D,” CM.
1
-1.
2
001. 3
sa [W-$1
Cal.4 amELsI4
XE
0.461385(20)
D" J
001. 5 EREQFIT 0.461391(13)
3.63(17)xlo-7
[W-D$l
-
3.89(7hlo-7 0.460509
0.460505(22) 3.84mklo-7
?i ",*a*&~
-
a*
6.8O(42)x1O-4 0
E&D{-D$
2336.768(Z)
2336.768(l)
8.823(12)1dO-~
8.822(14)xlo-4
0
0
GSCD - Ground State Combination wAllcpankitiesinulitsofal-1; Differences 6 DSCD - Upper State Combination Differences.
in this manner despite the small perturbation observed in this band was in marked contrast to the results obtained for v6 of C,H, (5), where the much more severe perturbation caused a sharp break in the sum plot after J = 10. The wavenumbers given in Table I may also be fitted by means of a least-squares treatment of the equation, eR
= a + bm + cm2 + dm3 + em4,
(4)
where the coefficients have the following meanings: a = vo, b = (B’ + B”), c = (-OlB + pJ), d = -2(D; + DI;), and e = pJ. The variable m has the value (J + 1) for the R-branch lines and (-J) for the P-branch lines (31). The results of this fitting are reported in column 5 of Table II. The calculated wavenumbers and the residuals (obs. - talc.) are listed along with the observed wavenumbers in Table I. The overall fit of the data was very good (1.3 x low3 cm-‘). The observed line positions in Table I are systematically lower (-0.05 to 0.15 cm-‘) than those reported previously (1, 14). Figure 2 shows a record of the observed R branch from R(9) to R(30), and below it the same R lines calculated as to position and envelope from constants determined in the above analyses. As expected, the envelopes of the unresolved J manifolds were found to be quite sensitive to the value of (OH - crc). Since OlBwas well determined from the various analyses it was thought that oc could be extracted by calculating a series of J-manifold envelopes. The value of o? was fixed to that in column 4 of Table II and (Yewas varied until a good match was obtained. The R( 10) manifold was chosen first for this calculation since at J = 10 no perturbations were noticeable and contributions from DJK terms were negligible. Figure 4 shows a series of envelopes obtained with values of (Ye ranging from 0.0 x 1O-4 to 6.0 x low4 cm-‘. It may be seen that the observed and calculated envelopes agree
100
200
300
=2336.768(2km-’
400
500
600
J2
700
(J l f,’
900
900
1000
1100
1200
=8.82302) x 1OAcm-l
1400
(B)
(A)
1300
4
v6
1500
FIG. 3. (A) A plot of the GSCD data (0) according to Eq. (1). The solid line was drawn from the regression analysis fitting of the experimental data. The dotted lines indicate 9% confidence limits of this line. The B* is the effective value [B” - DJKs]. The previous best available value of B” from Jones and Stoicheff (15) is also indicated on the plot. (B) A plot of the combination sum relation according to Eq. (3). The experimental data are denoted by 0. The solid line is from the regression analysis. The effective band origin v$ is v,, + (cP - ac)s.
cl
4674JJ 1
=3.83(17? x lO”cm-
c3D6
501
THE i+, BAND OF C3Ds
R(10) C,D, v,(A;)
cYc,=o.ox1041
=6.0x10-’
FIG. 4. The evaluation of oc = (C” - C’) by computer simulation of the R(lO) manifold. The value of 4.5(5) x low4cm-’ was determined by fixing the other molecular constants to the values listed in the last column of Table III and varying oc until a match was obtained.
almost exactly for c& = 4.5 x 10m4 cm-‘, while for oc = 3.0 x 10e4 and 6.0 x lop4 cm-’ the calculated envelopes fall significantly above and below the observed envelopes, respectively. It was therefore concluded that the best value of & was 4.5 x 1O-4 cm-l. To carry out the calculation above it was necessary to assume values of c”, &, and 0;; in addition to the molecular constants determined in this paper (B”, B’, v,, DI;, and D$). The value of C” = 0.3196 cm-l used in earlier work (13) was assumed. The present work produced an observed D’j = 3.83 x lo-’ cm-’ which agreed very well with Duncan’s value ofD’j = 3.74 x IO-’ cm-l calculated from force field considerations (33). It therefore appeared reasonable to use Duncan’s values of DljK = -3.57 x lo-’ cm-’ and 0;; = 1.07 x lo-’ cm-’ (33) in the simulations. This decision was further reinforced when the calculated D’Jand DI;Kvalues for C3H6 were also found to agree well with very recent observed values.3 It was further assumed that DiK = DIfK and Di = 0;. The simulation program used (PERTCOR) is similar to that described by Cartwright and Mills (6) and DiLauro and Mills (36). The maximum values ofJ and K were set at 50 and the statistical weights were taken from Herzberg (37) and were assumed as for X,Y, (D&; i.e., for K = 3p, 3p 2 1, 3p ? 2, 3p they are 249:240:240:249 and for K = 0, J even:J odd they are 8: 16. These values can also be verified using the et al. have reported a diode laser study of the Y,,, + v,,(P) band of &He near 1892.5 cm-’ foundl); = 1.072(54) x 10-6cm-‘, and DyK = - 1.29(19) x 10-6cm-1. Rubiner al. (35) have the pure rotational Raman spectrum of C,H, and with consideration of the effective K strucdetermined 0; = 1.0 x low6 cm-’ and DyX = -1.3 x 10e6 cm-‘. Duncan has calculated Dl; = 0.96 x 10mBcm-r and DL = -1.22 x lo-@ cm-l (33). 3 Weber (34). They reexamined ture have
502
NIELSEN,
DAUNT,
AND
HALSEY
recent work of Weber (38). The calculated lineshapes for all J values in both P and R branches were found to agree well with observed contours (Fig. 2). This appeared to be true even for split manifolds except in the localized region of the splittings. 4. DISCUSSION
The results of the data analyses are collected in Table II. The numbers in Table II have been obtained from the averages of the several data sets fitted individually, and also from analysis ofthe averaged data sets (line-wavenumbers). The molecular parameters show very good internal consistency. The error in the values is given by the numbers in parentheses following the constant (99% confidence intervals). It may be seen that the value of vO + (o? - CC)@ from the combination sum fit TABLE Comparison
with Previous
m1uMRFs. Cc’ B"
O-46079(20)
D;
l.o(l.o)xlo-7
"0
aB
0.4630(23)
III Studies”
IR
(d)
FaxE Fmmk)
0.4607(3)
FRESEm SImY 0.461388(20)(f)
3.74xlo-7
3.83(17)xlo-7
2336.02(10)
2336.87(l)
2336.764(4)
8.5xlo-4
9.0(l)xlo-4
8.823(12)~lO-~
CiC
4.5(5)xlo-4
EJ
0
0.3196(')
C"
D;;c
%
(a)
-3.57xlo-7
-3.57x10-7(h)
1.07xlo-7
1.07x10-7(h)
-
All quantities in units of an-'.
(b) Ref. 15.. (c) Ref. 1. (d) Ref. 2. (e) Ref. 33. (f) !imluatedbyassuningI;T=
9 atid L.-&U?of B"-D$
c,f~01. 2, ~,le
II.
(g) Ref. 13. (h) Assuned equal to force field value. Note: Column
6; 3rd line should
read #2336.764(2).
Footnote
(d) should
read Ref. 14.
THE v,BANDOFC,D,
503
agrees exactly with the value from the wavenumber fit. The B”, D’j, B’, D;, OB, and pJ values determined from the various fittings agree very well with one another. The reasons for this good agreement are believed to be (i) the ability in the case of this band to attribute the maximum of each J manifold to essentially the same low value of K and (ii) the fact that the weak perturbation present affects only levels with K > 15 in contrast to vs of C3H6. The ability to plot the data and fit them as accurately as is shown in Fig. 3 would not have been possible otherwise. The collected results from previous investigations and from the present work are listed in Table III. Several differences may be noted: the present value of the band origin term v0 + (cP - (Y”)@ = 2336.768 cm-l differs greatly from the earlier medium resolution work by 0.748 cm-l (1) and 0.102 cm-’ (14), respectively. The former work contained a J misassignment as noted in Ref. (14). The discrepancy with the more recent work is most likely caused by the limited resolution available in that work. It should be noted that if it is assumed that 3 = 9, then v0 = 2336.764 cm-‘. Significant differences also exist between the present value of [B” - Ohs] = 0.461385 cm-’ and the previous ir values of 0.4630 cm-’ (1) and 0.4607 cm-’ (14). The differences here are believed to be due to the same causes as for the v, discrepancies. There is also a value of B” from the rotational Raman study of Jones and Stoicheff (15) ofB” = 0.46079( 15) cm-r (see Fig. 3A). This value falls significantly below the present value (ir - R = 0.000598 cm-‘). As discussed by Weber (3&r, 39) this discrepancy between rotational Raman results and highresolution ir or microwave data usually stems from one of two reasons: (i) the neglect of the effect of the centrifugal distortion constant DJK on the observed maxima and (ii) the presence of underlying “hot” bands from rotational transitions originating in excited vibrational states in the Raman data. For cyclopropane the effects of “hot” bands are not expected to be as serious as the neglect of centrifugal distortion contributions. In support of this conclusion it is noted that the value of B” reported by McCubbin et al. (5) from the high-resolution ir analysis of v6 of C3H, was 0.67024(15) cm-‘, while the early rotational Raman value of Jones and Stoicheff (15) was 0.66962(20) cm-l, a difference of 0.00064 cm-‘. The recent diode laser study of v10 + vrl of C3H, (34) has verified the earlier ir results by reporting B” = 0.670277(28) cm-‘. Very recently, two new rotational Raman studies of C,H, have been reported. Both ofthese studies took proper account of the effects of the underlying K structure. The study of Kainnady and Weber (3&z) reported B” = 0.670144(12) cm-’ and that of Rubin et al. (35) reported B” = 0.67028(15) cm-‘. These recent studies affirm the conclusion that the discrepancy for the B” values of CBD, mentioned above is caused by the neglect of D JKin the earlier Raman work (1.5). The present B” difference of 5.98 x 10m4cm-’ for C3D6 is of the same magnitude as the earlier observed difference for C3H6 of 6.4 x lo-” cm-’ before the full centrifugal distortion effects were taken into account. The determination of (CUB- aC) = 4,323 x lo-’ cm-l and a” = 8.823 x lop4 cm-’ from the present study permits a detailed explanation of the observed structure of the Q branch and the J manifolds. The equation for the K lines in each J manifold can be reduced to 4,;
= v. + (B’ + B”)m - cxBm2 - 4DI;m3 + [(Q? - ore) - 2D’;,m]K2,
(5)
504
NIELSEN,
DAUNT, AND HALSEY
where we have assumed pJ = p”” = pK = 0. The first four terms on the right side of Eq. (5) are constant for each K line in a particular J manifold. The degradation of the manifold is thus given only by the last term. Since (cu” - cyc>is positive and D’jKis negative, the J manifolds degrade to higher wavenumbers, as can be seen in Fig. 2. The (crB - c&) constant being positive also means that the K-subband origins degrade to the high wavenumber side of L+,.As a consequence, all the subband origins from K = 0 to K = 30 lie in a region 70.40 cm-’ above v. = 2336.764 cm-l. As is usually assumed, the band origin was found to be at the base of the sharp edge of the Q branch. Even though all the subband origins lie above uo, no Q branch lines were observed above that wavenumber. The equation for the Q-branch lines (31), again ignoring the p terms, reduces to I/,$ = v. + (& - aC)K2 - dJ(J
+ 1).
(6)
The sum of the first two terms on the right side of Eq. (6) determines the subband origins. There is the usual restriction that J 2 K, which results in the first allowed line of each K subband having the value J = K. Thus, Eq. (6) reduces to $K = Vo - (rCK2 - a”K. If both &’ and & are positive, ‘as for vg of C3D6, then the first lines of all subbands must lie below vo. In addition, because CUB is positive the remaining J structure (J > K) of each K subband degrades to lower wavenumbers. This gives the final result, as seen in Fig. 1, that all Q-branch lines lie to lower wavenumbers than vo. Although the structure of the Q branch was partially resolved, the density of transitions produced by the close subband spacing makes it impossible to assign specific transitions to these peaks. This was confirmed by the simulation results. The transitions are so close together that even at Doppler limited resolution (-3 x 10m3cm-‘) these lines would not be resolved sufficiently for assignment. A possible explanation for the cause of the weak perturbation in v’6may be a weak x-y Coriolis resonance with the v,(E’) band near 2209 cm-’ or the E’ component of 2v, near 2141 cm-’ (40). A value for L&c1= -0.02 has been reported recently (24). This value seems very small but the separation u6-r+ = 128 cm-’ may be small enough to account for the weak perturbation seen. The vs band has been resolved in a ITCent study in this laboratory into its RRK(J) and ‘p,(J) structure (41), but the small value of 5: (14) causes the Q branches to overlap severely at the center ofthe band.4 This has so far prevented definitive assignment of the observed series. ACKNOWLEDGMENTS The authors would like to thank Professor W. E. Blass for helpful comments and a critical reading of the manuscript. One of us (S.J.D.) would like to thank Professor H. F. Shurvell for the gift of the CBDB samples and Dr. D. E. Ellis for a copy of his thesis. This research was supported by the Planetary Atmospheres program ofthe National Aeronautics and Space Administration (Grant NGL-43-001-006). RECEIVED: August
1, 1979
4 This is quite different from the appearance of the v8 band of C,H, studied by Withstandley, McCubbin, and Polo (9) in which the only regular structure observed was the sawtooth features of the Q branches in the central part of the band.
THE va BAND
505
OF CsDB
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