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High-resolution infrared spectrum of propyne: The 30 μm region
JOURNAL
OF MOLECULAR
High-Resolution
SPECTROSCOPY
144.389-415 (1990)
Infrared Spectrum of Propyne: The 30 pm Region GEORGES
Lahoratoire
GRANER
d ‘Infkarouge. .IwciP au C’NRS. C’rklersitP Paris-Sad. F-91 405 0r.sa.v Cedes. France
Bdtiment 350.
AND
GEORG Ph!,sikalisrh-Che1nisc~te.s
WAGNER
lnstitut. Justus-Liehip L~nirerxtdt. Heirtrictz-Bt!HIRing 58. D-6300 Giessen. Germanj
A high-resolution (0.002 cm -’ ) spectrum of propyne in the region of 30 pm has been used to improve the constants of 8,” and to analyze its hot bands. For vIO. it was found necessary to use WJ. nJAr T),w, and even qhhn and qnhkh constants to tit the high K series correctly. A standard deviation of 0.00021 cm-’ was obtained. The assignments were more challenging for the hot bands. Finally. more than ‘1000 transitions were assigned in the 2u~~-v~C: band and more than 1500 in 2v?,-u?A. The final fit, also including us, and microwave data will be presented in a future paper. 6 1990 Academic Press. Inc INTRODUCTION
In the last decade, propyne (or methylacetylene CHj-C~-C-H) has been the subject of many spectroscopic investigations ( l-23 ). There are many reasons for this interest. Propyne has been detected in the planet Titan (24, 25 ) and in interstellar clouds (26) through its infrared and microwave spectra. It has also been detected in the northern aurora1 region of Jupiter (27) and tentatively identified at the south pole of Saturn (24). Moreover, many IR bands of this compound lie in the region of the CO? lasers so that laser-Stark spectroscopy has been possible (3, 8, 13 ) and optically pumped laser emissions have been produced in the far- and the mid-infrared regions (,28-30.4) and assigned ( 4, 22, 23). The fact that the lowest vibrational mode of propyne is low ( vlg = 33 1 cm -‘) and that it is an E-type level is also an important feature. It enhances its importance for astrophysical applications and opens the way to the study of hot bands. a difficult but interesting topic for most molecules. Through the study of hot bands in the 10 pm region, we have recently been able to obtain a value for the il0 rotational constant of propyne (31, 32). The uIO band itself has only recently been recorded and analyzed at high resolution (20). As was suggested in the conclusion of Ref. ( 20). it was obvious that the study had to be completed by a careful study of the hot bands, especially the two strong components ~Y$-v~~ and 2v’&-u~~. The availability of a spectrometer with a better resolving power led us to undertake the study of these hot bands. Their assignment is the main subject of this present paper. Their complete analysis will be reported in a forthcoming paper. As a by-product. better information on the fundamental vlg itself 389
0022-2852/90
$3.00
Copyright C 1990 by Academic Press. Inc. All rights of reproduction in any form rexwed.
390
GRANER
AND
WAGNER
became available, in particular after the hot bands blends and overlaps became clear. EXPERIMENTAL
had been assigned,
when many
DETAILS
Recording Condilior~s Two spectra hereafter called A and B were recorded on the BRUKER IFS 120 HR Fourier transform spectrometer of the Giessen University. The theoretical resolution limit of this spectrometer is 0.00 12 cm -’ , without apodization. For comparison, the Doppler width for propyne at 300 K is 0.65 X I Om3 cm-’ (FWHM). Spectrum .4, an exploratory spectrum, was recorded with a liquid helium cooled Ge:Cu detector, a 3.5~pm beam splitter, and an optical band-pass filter 3 15-63 1 cm -’ Propyne was put in a 2%cm-long cell at a pressure of 2.66 mbar (266 Pa ). The cell windows were made of CsBr. The relatively high pressure led us to limit the resolution of the spectrometer to 0.0044 cm -‘. A total of 200 scans were coadded. This spectrum could be investigated above 323 cm-‘. For spectrum B, the same beam splitter was used. but with a liquid helium cooled Si bolometer and a low-pass optical filter cutting at 375 cm-‘. A 298-cm-long cell. with CsI windows, was employed and the pressure could be lowered to 0.998 mbar (99.8 Pa). This time the nominal resolution was set at 0.0020 cm-‘. A total of 300 scans were coadded. The spectrum was excellent up to 360 cm ’ and too noisy above 365 cm-‘. Therefore a few very-high-1 R lines are not available under optimal conditions in either of the two spectra. Most of the analysis was made using spectrum B. A handful of lines from spectrum .4 were also used, after proper care had been taken in the calibration problems.
Calibrution There are no accepted wavenumber standards in the 30 pm region so that calibration is somewhat problematic. We shall therefore discuss it in some detail. In Refs. (32. _10), calibration was based on the OCS v2 band at 520 cm -’ (33) and transferred through D20 lines. For spectrum B of the present work, no extra calibration spectrum was recorded. Many residual water vapor lines were seen in the spectrum. Thirteen of them. between factor. We ignored lines above 256 and 298 cm-‘, were used to derive a calibration 298 cm-‘, which were likely to be partly overlapped by propyne lines. The wavenumbers used for H20 were those obtained by J. W. C. Johns (34) and published in Ref. (35). Later, a careful study of all calibration standards in the medium and far infrared (36) led the Giessen group to propose new values for water vapor wavenumbers in this region. The lines between 256 and 298 cm-’ which are of a good quality both in Ref. (36) and in spectrum B and a few strong lines up to 343 cm -’ (but with a smaller weight) were used here to derive a calibration factor. Table I gives a list of calibrated water lines with the standard lines used for the calibration (36). The standard deviation of the fit was 53 X lop6 cm-l. As indicated in Ref. (36), the values are systematically below those of Johns by r3 X 10 p4 cm -‘.
PROPYNE
AT 30 pm
391
TABLE I Hz0 Lines Used for Calibration T’HIS WORK
1371
112906
256. 112 972
.099916
257.099 931
138 632
265. 138 650 266. 845 102
,559349
267. 559 350 267.757 693
757 716
271.
842 399
276. 147 829
147 721’
277.
425 548
278. 257 327
257 115’
278. 519 162 351 472’
280. 351 681 281. 155 723
155 700
282.257 841
,257997’ .488909’ ,377a22 ,785811 ,603376
283. 488 978 284. 284.785 812 285. 603 296 290 726 969
726 972
298. 416 828
,416628’ ,741153
298. 304 879 847
880 162+
314. 741 856
742 Il4+
323. 929 344
,929334+
335. 157 118
157 172+
340. 549 439
549 273+
343. 204 988
1
205 064+
*weight 0 +weight 0.1. probably overlapped by propyne.
Finally Table II reports the wavenumbers of a few prominent lines of C3H4 taken in the spectrum of Ref. (20) and in the present spectrum B. In comparing these values, one should not forget the different resolutions of the spectra. This table shows a small discrepancy. of about 2 X lop4 cm-‘, between the two columns. To summarize: the accuracy of the wavenumber scale that we finally used in the present work (i.e., spectrum B with the second calibration) is probably not better than 0.0002 cm -I. On the other hand, the internal consistency of the propyne spectrum. as shown by least-squares fits on selected lines, is better than 5 X 10 P5 cm -’ . However, it should be recalled that unblended lines are almost impossible to find in the propyne spectrum. THE Y,O FUNDAMENTAL
BAND
Description of the Spectrum The perpendicular band vi0 has a separation between subbands 2( .4’-A{- B’) s 0.57 cm-’ identical to the 2B value in the P and R branches. Therefore all the lines with
392
GRANER AND WAGNER TABLE II Comparison of Some Prominent Lines of C3H4 Using Different Calibrations I201
THIS WORK
298.120 872
120 969
301. 133 336
133 803
306.252
917
253 203
314.041
005
,041 219
326.991
860
,991 950
329. 178 361
178 038
334.462
693
462 896
342. 357 561
357 633
349.171
116
171440
355.038
446
038 779
(a) Calibration
based on 1341 1351
(b) Calibration
based on [361
the same J. hJ + KS AK value are gathered in a small range. The spectrum thus most of the resolved comprises a very dense central part 322-332 cmP’, containing Q branches of vi0 and of its hot bands, and two less congested regions at lower and higher wavenumbers, containing mainly the A J = - 1 and A J = + 1 transitions, respectively. The peak-finder program detected about 1800 peaks in the central region. which should contain about 2500 transitions of sizeable strength at a conservative estimate. Figures l-3 show small parts of the spectrum. Assignrnmts
Using the results of Ref. (20). it was straightforward to assign the transitions outside the range J < 50, K. AK = -9 to +9 to which the analysis in Ref. (20) was mainly confined. J values up to 60 and even 66 were reached and K. AK = 10, 11, 12 subbands were assigned unambiguously. The series K. AK = - 10 and - 11 were more difficult to find and could not be ascertained until the Hamiltonian used was modified as explained below. As for K * AK = - 12, we cannot yet put forward satisfactory assignments. For these high K series, the line intensities are low, much smaller than those of overlapping hot band transitions. Moreover, ground state combination differences are difficult or impossible to use since A J = -AK series (i.e., ‘R and RP) have then vanished and Q branches are barely visible. We therefore must rely heavily upon the quality of the predictions. Each measured line was given a weight 1.0. I. 0.0 I. or 0 according to the overlaps suspected or known, especially after the major hot bands had been assigned. A typical problem has been encountered with the R Rj (J) series. We were surprised to find a systematic deviation of GO.0004 cm -’ in the fits for many J values. although the lines were apparently well behaved. This was explained later by the fact that the RR4 (J)
PROPYNE
AT
393
30 urn
1;
I
’
3J7)'1,
RRqiB) ,; ii
0 ,,,‘1,,“11111”““~‘11’1’~,‘,,,~1,’,,1(’~, 333.6 333 7 333
8
-
333
‘)
RR,(10)
,’ RR,(7) RR,(6)
‘j
RR'tgj 3 9
RR&l*)
334.0
WavPnumber/cm~'
FIG. I. Part of the spectrum B of propyne (L = 298 cm, p = 99.8 Pa, resolving power ? 0.0020 cm ’ ). The transitions belonging to Yr0 are denoted by C (for cold). to Zs~~-u?~ by H (for hot), and to ?u~,~-Y~~ by 2 (for zero), except for the ‘RK(J) lines of Z which are only designated by K(J) for short. One line belonging to 2v~&v~~ is denoted by S (for superhot ). We have not indicated a certain number of weak transitions belonging to high J values of RQ12, RQII, RQIo, and RQs branches of C and H,
series of 2~7;~ v?d stays for 2 1 G J G 37 within 0.0026 cm -’ of RR4 uIo, and they are therefore not resolved. Due to the high probability of blends in the Q-branch region, we decided not to use any Q transition in the least-squares fit, except for RQo which brings additional information.
337
3
337
4
337.5 Wavenumber/cm-'
FIG. 2. Another part of the same spectrum. Notations C. H and S as in Fig. lines of 2v$ - Y;; are only designated by K(J) for short.
337
6
I. As in Fig. 1. the ‘&(J)
394
GRANER
AND
WAGNER
FIG. 3. Part of the Q-branch region of the same spectrum. Same notations. We have not indicated certain number of weak transitions corresponding to “Q6 and “Q) of H and to ‘Qz and ‘Q4 of Z.
a
As explained in Ref (JO), there was not need in this case to use an elaborate model including the I( 2, - 1) resonance. So we worked with a simple program for unperturbed perpendicular bands, using 2 X 2 matrices and including only the I( 2,2) rovibrational interaction. The ground state constants used were those given in Table I of Ref. ( 20). In particular, Hz was fixed to 0. In the first stage, the diagonal term for the excited state was the usual one: (Jh-f(~(
JAI) = vlo + (A’ - B’)k’ - D;,J(
+ 1) - ‘(A<)&/
- D;J’(J
+ TJ( J + 1 )W + r&?
t H;J3(J+
+ B’J(J
J + 1 )k’ - Dik4
+ H&J’( The nondiagonal
+ 1)’ 1 )3
/ + 1 )‘k’ + Hk,,J( J + 1 )li” + H;-k6.
( 1)
term was:
(vrO = 1, J, k, Ito = +l IHI vIo = 1, J, k +- 2, /,. = +-1) = ;[J(J+
1) - k(k +- l)]“‘[J(J
+ 1) - (li k l)(li k 2)]“’
X [qiO + &J(J+
I) + q$J2(J+
I)‘+
q:,(X
f 2)‘].
(2)
Note that the q’s used in Eq. (2) are defined according to Cartwright and Mills (37) and are therefore four times larger than those of Ref. (20). In these formulas. X-is a signed quantity. Later we shall use K = ) kl . Then I takes implicitly the sign of k - 1. It was soon obvious that this model was not sufficient and that we had to add progressively to the diagonal terms of Eq. ( 1) the supplement { 7)J./.P(J + 1)’ + TjJKJ(J + 1 )k’ + ?j/&Y + TUXJ(J+
l)/Y4 + T],w@ + nKKKKP}lil.
(3)
PROPYNE
AT
395
30 pm
The first three terms of Eq. (3) have already been found to be significant by Wlodarczak ez al. (21) for propyne and also for H3GeF by Burger et al. (38, 39). They were also used, under the names of 0,. BJK, and ok., by Duckett et al. (40) and Halonen et al. (41). But we were forced to introduce also qKin- and ~~~~~ (since 7JKK was not found significant) in order to fit correctly the ‘Pi,, and ‘Pi I series: systematic deviations of several thousandths of cm -’ were obtained when these high-order terms were omitted. It is not unlikely that a qKKKK&“I term would have slightly improved the fits and helped to assign the elusive ‘PI2 series, but we balked at this extension. The second column of Table III lists the parameters obtained in our preferred fit. The standard deviation of this fit is 0.2 10 X 10v3 cm -‘. Note that among the H’s, only H;( -HZ was found significant. In the nondiagonal term (2), neither the (2 + 2)’ term nor the J2(J + 1)’ term was found to be significant. In fact, even with this model, there are a few systematic deviations. The ‘PI0 lines have positive deviations of 6 to 7 X 10m4 cm-’ and the ‘PII lines have negative deviations of 4 to 5 X 10m4 cm-‘. Moreover. even if we consider that the weak ‘“PI2 series is certainly overlapped in many places it is surprising that no line of this series
TABLE 111 Molecular
Constants
Determined
T
for v,” of Propyne
IR only 330.938
VI0
AC
IR + MW 55 (5)
330.93856
4. 7336522 1104)
4.7336548
A”
B’
B’
7.98653
D;
D,
2.478
(23) x IO 9
2.467 (131 x lO-9
D,
1. 779 (99) x IO-8
1.734 (62) x 10-R
1.434(120)x
I397
2. 1699 (431 x IO-3
D,-D;
k&H;
-2
2 1691 142) x 10-3
(711 x IO”
7 986OY (32) x IO 1
IO-”
162186~x10~
1 1139(19)X
10-z
I II47 IS) x 10-z 3.799 (14) x 10”
-7.00(55)X
IO-”
7 07 (2XJ x lo-”
-9.84Llbo)x
IO”’
I1 36 (27) x 10-10
I. 71 (34) x IO-’
I66
2 88 (31) x 1(k9
Errorr
g,ven bctwcen quored.
5 301X7)x 10-12
5.21 187) x 10-12
5.59894 (183) x IO4
5.59763 (122, x 10-I
Ground state cons,ants
arc three rrmdard
pxmheser
Expermental
unccrminty
x IO.*. D,,=S.45,17
1
I 820 (471 x IO 9
errors expressed
on the band center
are those gwen ,n 1201, namely
x IO-‘? UK=0
(34) P 10-T
2.83 131) x lW9
I.859 (67) x IO-9
dlgc
(II71 x 10-e
2.133 (821 x IO-R
3.799 (14) x 104
D,=9$0462
(41 (93)
A’.
D;,
HK,=1.769
(All in cm-‘)
I” ““!lr of the lasf
is about
0 CfNl2 cm-’
Ao=S 308410. B,=O.28S059769,
x 10’. D1=9.83 x In,
tI,=o.
H,,=3.018
I IO”.
GRANER
396
AND
WAGNER
could be found. It is to be noted that Wlodarczak et a/. (21) did not publish microwave transition for kl = - 10 or - 11 in the v10 = 1 state.
any
Discussion The fact that the high-order 7’s are only effective parameters is obvious when we compare the contributions of vlk-k3, vKA-k5, vKtikk7. and vKKKtik9 for k’ = 10 (corresponding to K-AK = -11). These contributions are 3.8 X 10-j. -1.7 X lo-‘, 2.9 X 10m2, and -5.3 X lop3 cm-‘, respectively, whereas one would expect a regular decrease of the contributions. The situation is clearly worse for k’ = 13, corresponding to KS AK = + 12. The values are now 0.83, -0.063,O. 18, and 0.056 cm-‘, respectively. We have tried to avoid the use of the high-order terms of Eq. (3) by introducing several interactions. (a)
We added the 1( 2, - 1) resonance
under the form
(u,~ = 1, J, k, I,,, = +I lHlur,, = 2rlo(2k
+ l)[J(J+
= 1, J, k + 1, Ilo = ?l)
(4)
1) - k(k t I)]“‘.
This term links levels which are rather far apart and do not cross, so that when the term rIo is let free, the fit diverges. If yIo is fixed to a certain value, it has a very small effect on the results of the fit. For instance, Yr. = 2 X lo-’ cm-’ gives a change of only 25 X 10m6 cm -’ on the predicted wavenumber of ‘P,?( 24), one of the transitions for which we expected an effect. Now, this value of VI0is much too large to be reasonable. In molecules where it has been determined, r, is usually of the same magnitude as cl, or even smaller. Cho et al. (42) pointed out that the contribution of the nondiagonal term (4 ) is equivalent to a small addition to diagonal parameters B’, .4’-B’, .4r, and 17/i. It is likely that, at a higher order, this contribution to the diagonal energy appears as the terms of Eq. (3). (b) Although the next vibrational state, v9 = 1, is farther apart (band center at 639 cm-l), for high enough K values, a level crossing occurs. Using constants from Ref. (43), the subband energies (i.e., for J = 0) of Ki = 9 and 10 of v9 = 1 are calculated at 949 and 1034 cm -‘, respectively, whereas the KI = - 10 and - 11 subbands of vro = 1 have energies of 926 and 1041 cm-‘, respectively. One could therefore imagine a resonance with Al = k2, Ak = + 1, and an interaction term quite similar to Eq. (4 ). We had hoped that such a term would improve the small systematic deviations of ‘PI0 and ‘PI,. This attempt was also negative. (c) We explored another possibility: that the effects observed were due to the constraint H,’ = 0. We fixed Hi to different values and fitted the data again. The standard deviation went to a minimum around H”k. = 2 X 10 +Gcm -I, which is not an unreasonable value, but ‘PII lines were still far off. Therefore we decided to keep Hi at zero for the moment. (d) A last possibility should be examined. Let us assume that the calibration factor used is slightly wrong so that the ‘PII (37 ) line at 300 cm ml and the RRI1 ( 35 ) line at 355 cm-r are in error by +2 X lop4 and -2 X 10e4 cm -‘, respectively. This could be compensated by adjusting the 7’s of formula (3). in this case by a change of r]J,
PROPYNE
1 X lo-” cm-’ that a calibration
AT 30
pm
397
on qJK, about 10% of its present value. It is therefore error is responsible for the observed effects.
very unlikely
These considerations show that we have more or less reached our limits. Further progress will depend not only on a better model but also on a determination of Hi and on a better calibration. In a last trial to detect any anomaly in our results, we fitted simultaneously our IR data and the rotational transitions in the ulo = 1 state published by the Lille group (21 ), the latter being given a weight of 5000. The results of this fit are given in the last column of Table III. They are essentially identical to those obtained with the IR data only. The rms deviation of the microwave data is 77 kHz, as compared to 64 kHz in Ref. (21). We also predicted a few high K rotational transitions in the hope of assigning new experimental microwave peaks. G. Wlodarczak and J. Demaison actually found in their archives a few of these lines, but for technical reasons they were not deemed good enough to be introduced in the fit. The lists of observed and/or predicted lines of uio are not given here to save space. They will be provided on request by the first author (G. Graner) .’ HOT
BANDS:
HOW
THEY
WERE
ASSIGNED
The assignment of the rovibrational transitions belonging to the hot bands entailed the use of three computer programs which will be briefly described. We were also guided by a gross estimate of the intensities to be expected. We shall come back to this point later. First Step: Program POLY In the first place, we looked for a series of lines with a reasonable spacing, compatible with the classical 2B values. When such a series was found, it was followed visually as long as it was clear. Then the wavenumbers of these lines were least-squares fitted to a polynomial in an arbitrary running number. Each line was weighted 1, 0.1, 0.0 1., or 0 as explained for uiO. Polynomials of increasing degrees were tried, with the provision that all parameters should remain statistically significant. The program can also detect the lines deviating by more than three standard deviations: these lines are automatically given a zero weight and a new run performed. When a satisfactory polynomial has been found, it is used for extrapolation on both sides of the series. As a result of this first step, we have at our disposal a series of typically 20 or 30 lines and the SD of the fits is usually 1 X 10m4 cm-r or less in the present case. For the next step, the lines with weights 0 or 0.01 are replaced by the smoothed values. This is very important for dense spectra like the present ones. Second Step: The Program TOUTHOT The program TOUT was written long ago to assign series in symmetric top spectra. It has been used with great success for many molecules including CH3Br (44), CHjFT (45). and CF3H (46). ’ A few copies are on deposit in the Editorial
office of the Journal
o/‘hfoleculur
.S~ectrosc’op?~
GRANER
398
AND WAGNER
TABLE IV Automatic Assignment of Series AUTOMATIC
ASSIGNMENT OF SE&IE_S_
A SERIES OF R LINES I- TRY
K,, FOR THE
IS FOUND:
J ?
I(
‘?
SERIES]
al TRY Ji, for the FIRST lmc J,, + I for the SECOND J,, + 2 for the THIRD L‘IZ...
I 10
hi ADD
Jg and “y agam. ? to Jo .lnd try agal”
cl ADD
?- TRY
K,j+I
FOR THE
e,c SERIES
31 k~lh J,,
il.5THERE
A CHOICE
WITH
@ IMI?
SUCCESS
?I
The principle of this program is explained in Table IV. It is based on the use of ground state combination differences (GSCD). which are often well known from microwave spectroscopy and/or other infrared bands. Program TOUT can be used with almost no change to assign hot bands of the general from v, + v,-vy,, where us is an .41-type mode. But. a new version called TOUTHOT had to be written for hot bands v, + vt- vl. where vt is an E-type degenerate mode, in the present case v, + vlo-vlO. The differences are the following: (a) Instead of GSCD, we must use lower state combination differences ( LSCD ). In the present case, they are differences among the rotational levels of VI0 = 1. Whereas the GSCD can usually be expressed analytically, the LSCD are obtained numerically from a list of energies. Such a list, calculated from Ref. (21). was kindly provided by G. Wlodarczak and J. Demaison. It was used for (vg + vlo)~2-v10 and (us + vlo)o-~,o in the 9-11 ,um region, and to initiate the present work. Later, we used the energies obtained by the present study of v l0. Since they are based on an accurate value of .4o (32), these energies are correct in absolute values and can be used among differem K values as well as among different J values. (b) The usual GSCD do not depend upon AK; i.e., RR - RP differences are identical to ‘R - ‘P or even QR - QP differences. On the other hand, LSCD depend on AK, or more precisely on the sign of I”, since the energy expressions ( 1) and (3 ) of the lower state explicitly contain 1. In other words, if a certain rovibrational level E’ of vlo = 2 or another excited state is reached by two transitions v,, = E’ ~ E” (v,” = 1, &,. K”, 1”) and vg = E’ - E” (v,o = 1. JB. K”, I”), the difference v,., ~ VB = E” 1. JR, K”, I”) E” (~10 = 1. J,4, K”. /“) is sensitive. not only to the J and (v10 = K” values, as usual. but also to the sign of I”. This point is important as will be shown later.
399
PROPYNE AT 30 pm
(c) A special situation occurs when the lower level of a transition is such that k”l” = 1. It is well known that such a level is split by the l(2. 2) resonance into an .4+ and A level (as usual A + is ,4 1 for J even and A, for J odd, and A _ assumes the opposite values). In most cases, the upper level of the transition will also be split in At and A- sublevels. The selection rules are A’ - A’ for P and R branches and .4+-Afor Q branches. Therefore two “families” of series are to be expected. as illustrated in Fig. 4. For the family with the A+ upper level. the Q series originates from an A- sublevel and the P and R series from an At sublevel, whereas it is the opposite for the other family. The program TOUTHOT had to be adapted to look also for these two types of families. Note that in the hot band ~v~~-u,~ the upper level in this case is k’ = I’ = 0. which is not split and has A+ symmetry. Therefore. only one “family” of 'P, , ‘Q, , and ‘R, series is expected and has been found. It is not the case in (4 + v,o)o-vlo, where the l-type vibrational resonance produces a splitting in h-’= 0.
Third S&p: The Program MILL1 An earlier version of this program was written long ago at Orsay and described in Ref. (44). It is a versatile least-squares program which deals with n interacting states of a symmetric top molecule, n being in principle as large as wanted. This program has now been used in several other universities. The latest versions enable us to fit simultaneously rovibrational transitions, purely rotational transitions in excited states, and excited state energies. An important restriction in the program is that the matrices which are diagonalized are of limited size (usually blocks with the same value of li - I). When interactions are such that “infinite chains” occurs, the recourse to other programs with one single matrix for each J value (later factorized in symmetry blocks) becomes compulsory as it was the case for CH3F (47) and CF3H (48). Nevertheless, in moderately perturbed level systems, some modifications enable us to still use MILLI: they are equivalent to using truncated matrices.
v,,=2
k=l=2
AA+ V
,o=l
k=l=l
AA+
--+
AAt
+
FIG 4. Scheme of the levels involved for any (v, + v,.)+*-VT’ transition.
in the K. AK = 1 subbands
of 2u&- IJ~(!.The same scheme is valitl
22 23 24 25 26
2
19
18
9 10 11 12 13 14 15 16 17
40 41 42 43 44 45 46
zt %
z: 33 34 35
z! 29 30
24 25 26
19 20 21
is
10 11 12 13 14 15 16 17
9
i
RR7 334.971902 335.557524 336.144764 336.733729 337.323956 337.915831 338.509572 339.104610 339.701327 340.299515 340.899364 341.500818 342.103513 342.708248 343.314424 343.922220 344.i31448 345.142264 345.754663 346.368642 346.984122 347.601211 348.219830 348.840070 349.461809 350.085128 350.709866 351.336347 351.964396 352.593749 353.225138 353.857914 354.491781 355.128595 355.764790 356.403652 357.044094 357.686021 358.328696 358.975121 RP7 325.259907 324.702766 324.147062 323.594097 323.041948 322.491346 321.943671 321.395859 320.850450 320.306601 319.764481 319.223742 318.685292 318.147873 317.612199 317.078664 316.546209 316.015837
0.00 0.00 1.00 0.00 0.00 0.W 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.10 I.00
1.00 1.00 I.00 1.00 1.00 0.00 0.W 0.00 1.00 1.00 1.00 0.00 0.00 1.00 0.00 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 1.00 0.00 1.00 0.00 l.w 1 .W 0.00 0.W
zi 39 40
% 36
32 33
2
;: 28 29
E 24 25
;:
8 9 10 11 12 13 14 15 16 17 18 19
i;: 39 40 41 42 43 44 45 46 47 48
zz 36
33
314.434437 313.910148 313.388032 312.867613 312.349403 311.831985 311.316536 310.603251 310.291322 309.781152 309.272184 308.765353 308.260498 307.757083 307.254833 306.755655 306.257756 305.762016 305.267ooO 304.774399 RQ7 330.401171 330.415810 330.431773 330.449530 330.468510 330.488930 330.512180 330.535769 330.561661 330.568222 330.617418 330.648106 330.680127 330.713421 330.748855 330.785987 330.824162 330.663996 330.906026 330.949559 330.994580 331.040474 331.089329 331.139499 331.190679 331.243487 331.298483 331.354628 331.412849 331.472478 331.533818 331.596618 331.661048 RR6 333.849831 334.434136 335.019876
314.960070
315.486669
1 1 1
.oo .w .w
0.10 0.10 I.00 0.00 0.00 0.00 0.00 0.00
0.W 0.W
.w
.oo
1 .OO 0.00 0.00 0.00 0.00 0.00 0.10 1 .oo 1 0.10 1.00 1 .w 1 1.00 0.10 0.00 1.00 0.00 0.10 1.00 0.W
0.00 0.00
::
;i 25 26 27 28
;:
11 12 13 14 15 16 17 18 19 20
10
:
:: 43 44
% 40
::
zz
:: 31 32 33
zl
;:
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
9
Transitions 0.10 0.00 0.00 0.00 0.10 0.10 0.00 0.00 0.10 0.00 0.10 0.00 0.00 0.00 1 .W 0.00 0.00 0.01 0.00 0.00 0.00 0.00
Assigned 335.607533 336.196151 336.786662 337.370755 337.972369 338.567660 339.164460 339.762691 340.362907 340.964398 341.567627 342.172237 342.778616 343.386345 343.995745 344.606714 345.219263 345.833393 346.449082 347.066361 347.685231 348.305650 348.927629 349.551229 350.176346 350.802778 351.430474 352.060076 352.691531 353.323555 353.958153 354.594200 355.232790 355.871WO 356.511718 357.153575 RP6 325.278855 324.719826 324.162826 323.607797 323.053758 322.501628 321.951429 321.402299 320.855120 320.309251 319.765731 319.223742 318.682762 318.143943 317.606164 317.071co4 316.536795 316.004655 315.473986 314.944667 314.417777 313.891688 313.368068 0.00 0.00
0.00
0.00 0.00
0.00
0.00
0.00
0.10
0.00
0.00 0.00 0.00 0.00 0.00 0.00
0.00
0.00 0.00 0.00
0.00
0.00
0.10
0.00
0.00
0.00
0.00
0.00
1.cm
.w
1 .w 1 .w 1 1 .w 1 .co 1 .w 1 .w 0.10 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
i .oa 1.oo
0.00 1.00 1.00 1.00
:1:
11 12 13 14 15 16 17 18
10
::
7
41 42 43 44 45 46 47 48
31 32 33 34
330.705479 330.760379 330.817019 330.875159 330.934969 330.996409 331.059479 331.124299 RR5 332.725548 333.308090 333.692399 334.478238 335.065781 335.654697
312.845590 312.326139 311.805896 311.288883 310.773330 310.259953 309.747749 309.237081 308.728917 308.221049 307.716166 307.213WO 306.713200 306.211574 305.713419 305.217000 304.722425 304.229564 RQ6 329.849890 329.862680 329.677638 329.892562 329.910909 329.93m 329.950780 329.972970 329.997320 330.022590 330.049840 330.078792 330.109140 330.141139 330.175020 330.210030 330.247380 330.285330
I.00 1.00 1.00 I.00 0.00 1.00
0.00 0.00 0.00 0.00 0.00 0.00 0.M) 0.00
0.w 0.00 1.00 I.00 0.00 0.00 0.00 0.00 0.10 0.00 1 .w 0.10 0.00 1.00 0.10 1 .w 0.10 1.00
0.00 0.00 0.00 0.00
0.00
.w
1 .W 0.00 0.00 0.00 1 .w 0.00 1.00 0.10 1 1.00 0.00 0.w 0.00
9 10 11 12 13 14 15 16 17 18 19 20 21 93 2: 24 25 26 27 28
316.525835 315.991785 315.459219 314.928630 314.399596 313.871998
321.407326 320.857859
.z
46 47
336.245639 336.837603 337.431371 338.026556 338.623629 339.222135 339.822281 340.423849 341.027175 341.631865 342.238182 342.846610 343.455938 344.066735 344.679374 345.293573 345.909323 346.526632 347.145521 347.765791 348.387740 349.011380 349.636265 350.263021 350.891538 351.521108 352.152945 352.785727 353.419905 354.056OW 354.694600 355.333277 355.973743 356.616249 357.26WW 357.904602 358.552283
in the ?.u$- vf; Hot Band of Propyne
TABLE V
.cm
1 .w
i:&j 1.00 1.00 O.io 1.00 0.00
o.% 0.10
0.00 0.W
0.00 0.00
::$Z 0.00 0.00 0.00 0.00
0.10 0.10
o”:E 0.10
0.00
0.00
0.00 0.00 0.00 0.00 0.00
EZ
0.w 0.00
1
1.00 1.00 1.00 l.w 1.00 1.00 0.00
1.00
0.00
10
:
7
6
4 5
:i 40
::
::
z:
;tJ 30
;z 26 27
;:
F?
i 10 11 12 13 14 15 16 17 ia 19
6 7
ii 39 40 41 42 43 44 45
:z 36
33
:: i:
313.346237 312.822079 312.299739 311.778830 311.259731 310.742997 310.226952 309.712672 309.200683 308.689913 306.181584 307.674161 307.168615 306.665ooO 306.162706 305.662619 305.164343 RQ5 329.296091 329.307363 329.320441 329.334511 329.350507 329.368051 329.388105 329.407641 329.430551 329.454043 329.480304 329.507361 329.535784 329.566831 329.598641 329.632802 329.667610 329.704851 329.742934 329.783300 329.824870 329.867770 329.913490 329.959720 330.008460 330.057590 330.108980 330.161810 330.217080 330.273600 330.331760 330.390750 330.452830 330.579169 RR4 331.597686 332.178838 332.761793 333.346156 333.932014 334.519493 335.108749 0.00 I.00 1.00 1.00 I.00 1.00 1.00
0.00 I.00 0.W 0.00 I.00 0.00 0.10 0.10 0.00 1.00 1.00 0.00 0.10 0.00 0.10 0.10 0.00 0.10 ,.W 0.00 0.00 0.00 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.W 0.00 0.00 0.00 0.00
0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.10 0.00 0.00 0.00 1.00 0.00
11 12 13 14 15 16 17 18 19 20 21 22
10
9
51 52
49 50
‘ii
40 41 42 43 44 45 46 47
z:
35 36 37
;: 23 24 25 26
::
11 12 13 14 15 16 17 18
324.747399 324.187606 323.628857 323.071578 322.516008 321.962199 321.410169 320.858840 320.310231 319.763131 319.217261 318.672638 318.130268 317.589371 317.050193 316.512498
325.309919
336.291593 336.885602 337.480788 338.077858 338.676432 339.276530 339.878379 340.481529 341.086358 341.692747 342.300687 342.910206 343.521295 344.133905 344.748094 345.363823 345.981523 346.600512 347.220261 347.842001 348.465590 349.090749 349.717359 350.345448 350.975177 351.606307 352.239056 352.873305 353.509606 354.147182 354.786077 355.425912 356.068944 356.712451 357.357613 356.004310 358.653132 359.302423 359.954592 360.607717 361.262895 RP4
0.00 1.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 1 .co 0.00 1 .oo 1 .W 0.00 1 .W 0.00
1.00 1.00 1 .W 1 .W 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1 .W 1 .oo 1.00 1 .W 0.00 0.00 l.W 1.00 0.00 0.00 0.00 0.00 0.00
1.00
0.00
335.699370
27 28 29 30
E 22 23 24
11 12 13 14 15 16 17 18 19
E 10
i
5 6
:: 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55
36
315.977164 315.442586 314.910057 314.378987 313.849608 313.321968 312.795709 312.271448 311.748864 311.227147 310.707602 310.189990 309.674069 309.159735 308.647008 308.136134 307.627030 307.118890 306.613067 306.109939 305.607402 305.106670 304.607103 304.11W30 303.615OOO 303.122COO 302.628895 302.138688 301.650380 301.163784 300.678658 300.196344 299.716852 RQ4 328.739631 328.748897 328.760490 328.773146 328.787571 328.803291 328.821231 328.840455 328.860791 328.683503 328.907286 328.933044 328.960241 328.988711 329.019541 329.051572 329.084831 329.120078 329.157546 329.195871 329.235721 329.277691 329.320441 329.365031 329.411781 329.459731 329.560101 329.613411 329.667602 329.724327 329.781410 329.840977 329.902124 329.964072 330.028742 330.093982 330.1615W 330.230589 330.301688 330.373535 330.448902 330.523688 330.601200 RR3 330.467075 331.046141 331.627868 332.210750 332.795101 333.380830 333.968482 334.557767 335.148671 335.740766 336.334760 336.930203 337.527192 338.125761 338.725861 339.327510 339.930659 340.535399 341.141658 341.749447 342.358787 342.969626 343.581995 344.195885 344.811304 345.428213 346.046683 346.666642 347.288131 347.911271 348.535630 349.161669 349.789228 350.418288 351.048872 351.681076 352.314616 352.949698 353.586305 354.225295 354.864212
.w
0.00
0.00
0.00
0.00
0.00
0.00 0.00 0.00 0.00
0.00
0.00 0.00 0.00
0.00
1
0.00
0.00 0.W 1 .w
0.00
0.00
0.00 0.00
0.00
0.00
I.00
0.00 0.00 1.00 0.00 0.00 0.00 1.00 1.00 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 I.00 1.00 1.00 1.00 0.00 0.00
0.00
0.00
0.00
0.00
10 11 12 13 14 ii 16 17 18 19 20 21 22 23
9
2
3 4
40 41 42 43 44 45 46 47 48
329.508551
0.00
0.00
0.00
I.00 0.00 0.00 1.00 1.00 0.w 1.00 1.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.w 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.w 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 1 .w 0.00 0.00 l.W 0.00 0.00 0.00 1.00 0.00 0.00 1.00 0.00
0.00 0.00 0.00
0.00
13
ii
: 10
z: 33
E
E 25 26 27 28
:: 21 22
15 16 17 18
44 45 46 47 48 49 50
355.505634 356.148482 356.792217 357.438600 358.086159 358.735300 359.386407 RP3 325.321975 324.758256 324.196116 323.635727 323.076798 322.519238 321.963909 321.410159 320.857830 320.306601 319.757551 319.209751 318.663859 318.119571 317.576504 317.035784 316.496124 315.958150 315.421927 314.887027 314.354202 313.822571 313.292747 312.764581 312.237759 311.712976 311.189450 310.667931 310.147414 309.628821 309.112043 308.596233 308.081876 307.570985 307.060752 306.551787 306.045106 305.539832 305.035900 304.534134 304.033733 R03 328.180092 328.188602 328.197822 328.209112 328.221803 328.236122 328.252082 328.269422 328.288627 328.309762 0.00
0.10
0.10
0.00 0.00
.w
0.00 0.00 1
0.00
0.00
0.00 0.00 1 .w 1.00 1.00 1.00 0.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.10 0.00 0.10 1.00 0.00 1.00 0.10 1.00 0.10 1.00 0.00 1.00 1.00 0.00 1.00 0.00 0.00 0.00
0.00
0.10 0.00 0.10
0.00 0.00 0.00
0.00
0.00
1.00 0.00 0.00 0.w 1.00 0.00 0.00
10 11 12 13 14 15 16 17 iS 19 20 21 22
9
5 6 7 a
4
:: 39 40
:z 36
:: 33
z: 27 28 29 30
;:
z:
14 15 16 17 18 19 20
330.491 331.072089 331.654788 332.239023 332.825101 333.412596 334.001846 334.592225 335.184024 335.778474 336.373533 336.970302 337.568542 338.168241 338.769311 339.372010 339.976039 340.581479 341.188628 341.796567 342.406217 343.017402 343.629875 344.243555 344.859038 345.475470 346.093882 346.713122 347.334245 347.956122
329.334201 329.912090
328.331778 328.355842 328.381752 328.408452 328.436902 328.467812 328.499702 328.532482 328.567792 328.604382 328.842282 328.681832 328.722911 328.765691 32a.810061 328.856331 328.903721 328.953096 329.003221 329.055611 329.109250 329.164192 329.221381 329.279881 329.339971 329.402081 329.465001 RR9
loo
.w
1.00
1 .w 0.00 1.00 0.00 0.00
0.00 0.00
1
0.00 0.00 0.00 0.00
0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.w 0.00 0.00
0.00
0.00
0.00
0.W
0.00
1.cm 0.10 0.00 0.00 0.00 0.10 0.00
1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.10 1.00 1.00 0.00
ET 52
z 39 40 41 42 43 44 45 46 47 48 49
z:
z; 34
z’:
;:
;;
;z
;:
;:
.z. 9 10 11 12 13 14 15 16 17 18 19
:
4
41 42 43
324.766646 324.202736 323.639847 323.079148 322.52oooa 321.962719 321.406719 320.852206 320.299444 319.748535 319.198843 318.651065 318.104852 317.559834 317.016134 316.474284 315.933480 315.394946 314.856891 314.321025 313.786648 313.253267 312.721560 312.191493 311.682960 311.136071 310.609521 310.085401 309.562652 309.041228 308.521491 308.003414 307.486695 306.971775 306.458436 305.946100 305.436247 304.927871 304.420760 303.915500 303.412595 302.911417 302.412668 301.915321 301.419898 300.926804 300.435619 299.947211
325.329615
-
351.088817 351.719720 352.351981 352.985852 353.621500 354.258900 RP9
348.579859 349.204849 349.831468 350.459720
1
.w
0.10 0.10 1 .w 0.00 1 .w 1.00 0.10 0.00 0.00 1.00 1.00 0.00 0.00 1.00 0.10 1.00 1.00 0.00 0.00 0.00 0.00 0.10 0.00 0.00 1.00 0.00 1.00 1 .w 0.00 0.10 0.00 0.00 0.00 0.00
1.w 0.10 0.10 0.00 0.00
0.10 1 .oo 1 .w
0.00
0.00
0.00
0.00
0.00 0.00 0.w
0.10 0.00 1.00 1.00 1.00 0.00 0.00
0.00 0.10
E
11 12 13 14 15 16 17 18 19
IO
9
8
6 7
6
;4” 25
$7 22
12 13 14 15 16 17 18 19
320.808391 320.247217 319.687656 319.128851 318.571337 318.014943 317.459524 316.905279 316.351985 315.799826 315.248808
299.461OCO RQ2 327.619063 327.625223 327.632703 327.641823 327.652993 327.665113 327.679466 327.695498 327.712611 327.731441 327.752233 327.774793 327.798192 327.823462 327.850202 327.878182 327.907632 327.938702 327.970982 328.005192 328.040842 328.076873 328.115474 328.155282 328.196452 328.238262 328.282972 328.328770 328.375102 328.423382 328.473182 328.524318 328.576942 328.631052 328.686742 326.744511 326.803291 328.863231
0.10 0.00 1.00 1.00 1.00 0.00 0.00 0.00 0.00 0.00 1.00
ii 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57
0.00 0.00 0.00 0.00 0.00 0.00 1.00 I.00 1.00 0.10 0.10 0.00 0.W 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.10 0.00 0.00 0.00 0.00 0.10 0.10 0.00 0.00 1.00 0.10 0.00 0.00 0.00 0.00 0.00
li 15 16 17 16 19 20 21 22 23 24
: 4
22
0.00
1
298.193143
297.164669 296.652420 296.140668 I?01 3271053503 327.059733 327.068153 327.078235 327.091533 327.106823 327.123943 327.142863 327.164579 327.168261 327.213783 327.241583 327.271900 327.304083 327.338513 327.375743 327.413863 327.455152 327.497288 327.543365 327.590403 327.640268 327.691848
297.678635
0.00
298.709303
.w
0.W
0.00
0.00 0.00 0.00 0.00
0.00
1 .oo 0.00 0.00 0.00
0.00 0.00
0.00
1.00
0.00
0.00
0.00
0.00
1
0.00 0.00 0.00
0.00 0.00 0.00
.w 1 .w
0.00
I.00
0.00
0.00 0.00
0.00
l.W
0.00
I.00 I.00 0.00 1 .w
0.00
0.00 I.00 I.00 I.00
0.00
I.00
0.00
I.00 1.00
1.00
0.00 0.00
l.w
0.00
1 .w 0.10 0.00
314.699W5 314.149989 313.602078 313.055381 312.509729 311.964267 311.421767 310.879411 310.338207 309.797942 309.258888 308.720913 308.184471 307.648226 307.113570 306.579907 306.047516 305.516154 304.985635 304.456698 303.928703 303.401135 302.875852 302.351276 301.827689 301.304916 300.783788 300.262992 299.744400 299.226099
41 42 43
IO 11 12 13 14 15 16 17 18 19 20 21 22 23 24
11 12 13 14 15
40 41 42 43 44
2; %
;: 23
::
10 11 12 13 14 15 16 17 16
i i
:z 47 48
44
322.537257 321.983536 321.433030 320.882529 320.336095 319.792135 319.250412 318.710625
323.092969
353.828968 354.446377 355.064505 355.682956 356.301817 356.922466 357.543875 358.165852 358.789387 RR1 330.517040 331.104435 331.692779 332.283710 332.877221 333.472296 334.069798 334.669925 335.272082 335.876984 336.484295 337.093973 337.706220 338.320831 338.937945 339.558462 340.181798 340.806698 341.435048 342.066304 342.700511 343.337289 343.977472 344.620583 345.266678 345.916307 346.568503 347.224141 347.883071 348.545300 349.210815 349.879610 350.552228
TABLE V-Contimtrd 327.745234 327.801002 327.858952 327.919072 327.981482 328.045692 328.112450 328.180100 328.251502 328.324796 328.399569 328.476509 328.555516 328.636342 328.720011 328.805491 RR1 328.194712 328.769871 329.345909 329.922936 330.502142 331.080581 331.659711 332.242347 332.825101 333.408737 333.993525 334.579212 335.165769 335.752804 336.341613 336.930573 337.521452 338.113001 338.705561 339.299071 339.893791 340.489064 341.085508 341.682909 342.281141 342.680978 343.481191 344.082154 344.683807 345.287705 345.891983 346.496810 347.102681 347.709616 348.317864 348.926189 349.535799 350.146522 350.758521 351.370682 351.984193 352.596817 353.213328 0.10 0.10 0.10 0.10 0.10 1.00 1.00 0.00 0.10
0.00 0.10 I.00 1.00 0.00 0.00 0.10 0.00 I.00 0.00 1.00 0.00 I.00 0.00 0.00 1.00 0.00 0.00 0.00 1.00 I.00 1.00 0.00 1 .OO 1.00 0.10 1.00 0.00 0.00 0.00 1.00 0.10 0.00
1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
24 25 26 27 28 29 30 31
1: 11 12 13 14
i
6
:: 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
16 17 18 19 20 21 22 23 24
327.066603 327.074323 327.083383 327.092903 327.103910 327.116291 327.129223 327.143813 327.159363 327.176494 327.195013 327.214973 327.236303 327.258763 327.282951 327.309703 327.336985 327.366283 327.397680 327.430793 327.465163 327.501604 327.540651 327.581215 327.623483 327.668073
RQ1
318.173687 317.639573 317.107590 316.577879 316.051210 315.527424 315.006118 314.487732 313.972209 313.459608 312.950511 312.443509 311.939821 311.439210 310.941948 310.448121 309.957882 309.469972 308.985903 308.505390 308.028003 307.554391 307.084155 306.617318 306.154638 305.694763 305.238942 304.787586 304.338184 303.893300 303.452444 303.015000 302.580480 0.00 0.00 0.10 0.00 1.00 0.10 0.10 0.00 1.00 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.10 0.00 0.10 0.00 0.00 0.00 1.00 0.10 0.00 0.W
1.00 0.10 0.10 1.00 0.10 0.00 1.00 I.00 1.00 1.00 0.00 0.00 1.00 1.00 0.00 0.00 0.10 0.00 0.00 1.00 0.10 1.00 0.00 1.00 0.00 0.10 1 .oO 0.10 0.00 0.00 0.10 0.00 0.00
:
45 46 47
;: 23
::
11 12 13 14 15 16 17 18
326.509190 326.512430
ROO
327.715370 327.763908 327.815472 327.869362 327.925122 327.983282 328.044262 328.107642 328.173352 328.241772 RPO 325.365760 324.797300 324.230440 323.665190 323.101560 322.539751 321.979306 321.420631 320.863626 320.309256 319.755534 319.204164 318.654611 318.107130 317.562231 317.018553 316.477790 315.938797 315.402352 314.868045 314.336388 313.807203 313.280655 312.756768 312.235795 311.716883 311.201343 310.688385 310.178687 309.672005 309.167668 308.667018 308.169020 307.674161 307.182740 306.694060 306.209137 305.726429 305.247543 304.771970 304.299190 303.829470 303.362780 302.899060 302.438250 301.980280 0.00 0.00
0.00 0.00 0.00 0.M) 0.00 0.01 1.00 1.00 I.00 0.01 1.00 1.00 I.00 0.01 0.01 0.01 0.10 I.00 0.05 0.10 1.00 1.00 1.00 1.00 0.10 0.10 0.10 1.00 1.00 0.10 0.01 0.10 0.00 1.00 0.00 0.10 I.00 0.01 0.10 0.00 0.00 0.00 0.W 0.00 0.00 0.00
1.00 1.00 0.00 0.10 o.cKI 0.00 0.00 0.00 0.00 0.00
10 11 12 13 14 -
:
5 6
40 41 42 43 44 45 46
39
58
;z
11 12 13 14 15 16 17 ii 19 20 21
32:R:go280 327.080410 327.655860 328.232860 328.810830 329.390220 329.972230 330.554490 331.139489 331.725490 332.313700 332.902838 333.494450 334.087650 334.683157 335 280440
326.517260 326.523690 326.531673 326.541001 326.552228 326.565590 326.579819 326.596532 326.614970 326.634710 326.657039 326.680697 326.706320 326.734509 326.764747 326.796948 326.831456 326.867680 326.907140 326.948600 326.992690 327.039190 327.088350 327.140300 327.195ooO 327.252260 327.313236 327.375750 327.441711 327.510666 327.582340 327.657080 327.735150 327.815464 327.900333 327.986809 328.076873 328.170310 328.266400 328.365450 328.467820 328.572270 328.679910
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.10 0.00 0.00 0.01 0.00
1 .oo 1 .w 0.00 0.00 0.10 l.W 1.00 0.10 0.10 0.10 0.10 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 1 .w 1.00 0.00 0.00 0.00 0.01 0.10 1.00 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00
0.10
l.w 0.01
0.00 0.00
:z 27 28
2’: 23 24
zl 9 10 11 12 13 14 15 16 17 16 19 20
3 4 5 6
:
2; 39 40 41 42 43 44 45
36
z: 33
::
;: 27 28
23 24
2
15 16 17 18 19 20
336.480680 337.083820 337.689492 338.297200 338.907008 339.519703 340.134594 340.751340 341.370945 341.993350 342.618195 343.246086 343.877121 344.509695 345.145460 345.783976 346.426285 347.070924 347.718386 348.369020 349.021702 349.678284 350.337028 350.998887 351.663592 352.331491 353.003410 353.676910 354.353110 355.031930 PPl 325.343847 324.773761 324.205287 323.638446 323.072230 322.509583 321.948112 321.388201 320.829995 320.274458 319.720313 319.168462 318.619024 318.071866 317.527885 316.984685 316.444757 315.908026 315.373880 314.840885 314.313459 313.786643 313.264642 312.744833 312.227429 311.712976 311.201343 310.693480
335.879170
0.00 1 .w 0.00
0.00
.w
0.00 1
0.10
0.10 0.00 1.00
1.00
0.00 0.00 1.00 0.10 0.10 0.00 0.00 1 .w
1.00
1.00
0.00
0.10
0.00 0.00 0.00 0.00 0.00
327.063930 327.640268 328.216828 328.797258 329.379940
310.188080 309.684409 309.184921 308.686943 308.192507 307.701567 307.212627 306.726768 306.243400 305.762016 305.284449 304.810193 304.338184 303.868400 303.401335 PO1 325.917125 325.920710 325.924878 325.931482 325.939779 325.949717 325.961396 325.975166 325.990484 326.008249 326.027592 326.050032 326.073892 326.100897 326.129429 326.160781 326.195211 326.232150 326.271570 326.314021 326.358640 326.407106 326.457136 326.511699 326.567349 326.626886 326.688856 326.753885 326.821609 326.891164 326.963925 327.039191 327.117700 327.198800 327.282951 327.369WO 327.458WO 327.549400 D!al 0.00 0.00 0.00 0.00 0.10
0.00 0.00 0.00 0.10 0.10 0.00 0.00 1.00 0.10 0.00 I.00 0.10 1.00 0.00 0.00 0.10 1.00 1.00 0.00 1.00 1.00 0.10 0.10 0.00 0.00 1.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00 0.10 1.00 0.00 0.00 0.00 1.00 0.w 0.00 0.w
: 10 11 12 13 14 15 16 17
6 7
: 9 10 11 12 13 14 15 16 17
6
0.00
1.00 l.W 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
1.cKl
0.00 0.00 0.00 0.00 1.00 1 .w 1.00 1 .w 1.00 1.00
.w
1 .w 1 0.00 1 .m 1.00 l.W 0.00 0.00 0.00 0.00 0.00 0.w 0.10 0.00 0.10 0.00 0.00 0.00 0.00 0.00 0.10
0.00
.oo
0.00 1 0.00 1 .w
0.00
0.00 0.00
0.00
0.00
330.548294 331.135527 331.725492 332.315065 332.908725 333.504407 334.102613 334.704031 335.305838 335.910591 336.519167 337.129957 337.743239 338.359751 336.978543 339.599981 340.225446 340.851637 341.480905 342.113830 342.749296 343.386350 344.026940 344.669665 345.316100 345.964355 346.616020 347.268800 347.924800 348.583ow 349.243999 PP2 322.499988 321.935259 321.372359 320.810708 320.251835 319.694111 319.137745 318.582928 316.029527 317.477364 316.926294 316.376329 315.827734 315.280140 314.733357 314.187955 313.643224 313.099371 312.556668 312.013760 311.472220 310.931451 310.391411 309.852052 309.313443 308.775841 308.238224
329.964072
7
2
3 4
; 10 11 12 13 14 15 16
::
64
:: 50
46 47
4”:
._
40 41 42 dl
37
34
2 :,”
307.701567 307.165775 306.630550 306.096106 305.562377 305.029301 304.497144 303.965737 303.435161 302.905560 302.376608 301.848722 301.321625 300.795635 300.270565 299.746272 299.223161 29a.7wsa3 298.179853 297.659991 297.140925 296.622722 296.105963 295.590118 295.075699 294.562122 294.049700 293.538667 293.028605 292.519740 292.012194 291.505432 291 .oooO64 290.495697 289.992339 PO2 325.349638 325.358075 325.364905 325.373605 325.383920 325.396181 325.409781 325.425338 325.441635 325.459605 325.478777 325.499512 325.520769 325.542852 325.567012 325.590995 325.616985 325.642895 325.669344 325.697365 325.725791 325.755490 325.785585 325.816135 1
.w
1.00 0.00 0.w 0.00 0.00 0.00 0.w 0.00 0.00 0.00 0.00 0.00 0.00 1 .w 0.00 0.00 0.00 0.00 0.00 0.00 1.00 1.00 1 .w 1 .w
1.00 0.w 0.00 1 .w 1 .w 1 .w 1 .w 1 .w 1 .w 1 .w l.w l.w 1 .w 1 .w 1 .w 1 .w 1 .W 0.00 0.00 1 .w 1 .w 0.w 1 .w 1 .w 0.00 1 .w 1 .w 1 .w 1 .w 1 .w 1 .w 0.00 0.00
0.00
46 47
ii
39 40 41 42 43 dd
10 11 12 13 14 15 16 17
9
32zoa724 327.644543 328.223002 328.603291 329.385501 329.968910 330.554209 331.14oaos 331.728888 332.318298 332.908725 333.500533 334.093419 334.687105 335.281864 335.877564 336.474351 337.071343 337.669019 338.268603 338.867895 339.467845 340.068731 340.669742 341.271603 341.873406 342.476246 343.079850 343.683746 344.288151 344.892727 345.498253 346.104244 346.710981 347.317717 347.925649 348.533982 349.142755 349.7523w 350.362533 350.973400 351.585027 352.197300 352.810489 353.423867 354.039124
325.846566 325.878705 325.911298 325.944105 325.977899 326.011424 326.046704 326.082104 326.117714 326.154614 326.192214 326.230294 326.269084
.w
1 .w 1 1 .w 0.00 1 .w 0.00 0.00 1 .w 1 .w 1 .W 1 .w 0.00 1.00 1.00 1.00 1.00 0.00 1.00 0.00 1 .w 0.00 1 .w 0.00 1 .w 0.00 0.00
0.00
1.00 0.00
0.00 0.00
0.00
0.00
1 1 0.00
.w .w
0.00
0.00
0.00
0.00
0.00
0.00
0.00 0.00 0.00
0.00
0.W
0.00 0.00
0.00
0.00 0.00
0.00
0.00
1 .oo 0.00 0.00
0.00 0.00
354.654098 355.270191 355.886517 356.504703 357.122107 357.741669 358.362502 358.983456 PP3 323.051438 322.484326 321.918470 321.355295 320.792980 320.232501 319.673631 319.116352 318.560651 316.006536 317.453942 316.902974 316.352576 315.804831 315.256153 314.712750 314.168877 313.626321 313.084997 312.545417 312.006682 311.469330 310.933221 310.396511 309.864552 309.332063 308.800623 308.270294 307.212627 307.740964
306.685216 306.159252 305.634201 305.109287 304.585904 304.063489 303.541269 303.020554 302.500520 301.981676 301.463135 300.945269 300.427912 299.912300 299.397m 296.682793 298.369751 297.856900
296.833525 297.344632
296.323430
3 4 5 6 7 8 9 IO 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 ::
33 34 35 36 37 36 39 40 41 42 43 44 45 46 47 46 49 50
::
53
48 49 50 51 52 53 54 55
0.10
0.00 1.00
0.10 1.00 0.00 0.10 1.W I.00 0.00 1.W 0.10 0.01 0.10 I.00 0.01 0.00 0.00 0.00 0.10 0.10
0.00 I.00 0.10 0.00 0.00 0.00 0.00 0.00 0.10 1.00 1.00 1.00 0.10 1.00 1.00 1.00 I.00 I.00 0.10 1.00 1.00 0.00 0.00 1.00 0.10 0.00 0.00 0.00 1.00
0.00 1.00 0.00 0.00 0.00 0.00 1.00 1.00
15
14 13
3 4 5 6 7 8 9 10 11 12
34 35 36 37 38 39 40
15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 33 32
9 10 11 12 13 14
3 4 5 6 i
54 55 56 57 58 59 60
334.114811
333.519293 332.925582
325.618515 325.663375 325.710095 325.756845 325.804145 325.853315 325.902045 PR3 327.062783 327.642223 328.222912 328.805371 329.389441 329.975040 330.561661 331.150789 331.740891 332.332558
324.947430 324.972569 324.998075 325.025674 325.053516 325.083265 325.114575 325.146675 325.180125 325.215155 325.250655 325.287517 325.324926 325.364042 325.404245 325.445030 325.487194 325.573655 325.530309
295.614174 295.305406 294.797813 294.290718 293.784795 293.279836 292.775109 PO3 324.770516 324.777043 324.784096 324.793666 324.804666 324.817276 324.631471 324.847422 324.864325 324.883173 324.903426 324.923842
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 24 23 25
0.00 0.W 1.00 0.00 0.00 1.00 0.00
1.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 1.W 0.00 I.00 0.00
0.00 1.00 0.00 0.00 0.00 0.00 0.10 0.10 I.00 0.10 0.00 0.10 1.00 1.00 0.10 I.00 0.00 0.W 0.00 0.00 0.00 1.00 0.00 1.00 1.00 0.10 0.00 0.00 1.00 0.00 1.00
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 4
0.10 I.00 1.00 0.10 1.00 0.10 0.00
310.361198
310.895749 311.431777
0.10
0.10 0.10 0.10 I.00
0.00 1.00 1.00 1.00 1.00 0.10 0.00 0.00 0.00 0.01 0.01 0.10 1.00 1.00 I.00 I.00 1.00
28
4 5 6 7 8 9 10 11 12 13 14 15 16 17 16 19 20 21 22 23 24 25 27 26
35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
31 32 33 34
0.00 0.00 0.W 0.10 0.10 0.00 0.00 0.00 0.00 0.00 0.10 0.00 0.00 0.10 0.00 I.00 1.00 0.10 1.00 0.10 0.00 0.00 0.00 0.00 1.00 0.10 0.00 0.00 l.CO 0.10 0.00 0.00
26 27 26 29 30
1.00 I.00 0.00 1.00 0.00
306.087989 304.567818 304.048611 303.529849 303.012977 302.497155 301.982Wl 301.468030 300.954977 300.442609 299.932165 299.422243 298.913089 298.405156 297.897413 297.392020 296.886272 296.381935 295.678652 295.375699 294.873922 294.373000 293.873466 293.374052 292.675426 PO4 324.192186 324.2OW86 324.209837 324.221146 324.233956 324.247696 324.263256 324.280776 324.299636 324.319864 324.342375 324.365354 324.391041 324.416516 324.444536 324.473646 324.503922 324.536291 324.569656 324.604526 324.640405 324.678157 324.717143 324.757096 324.797166
307.708804 307.182225 306.657110 306.132897 305.610057
309.627901 309.296520 308.765360 308.236634
TABLE V--Continued 334.711902 335.310581 335.909854 336.511053 337.112939 337.715822 338.320131 338.926013 339.532190 340.139446 340.747548 341.358225 341.967993 342.579306 343.191156 343.803545 344.418361 345.032914 345.647696 346.264457 346.880503 347.497656 348.115764 348.734345 349.353150 349.973179 350.593255 351.213791 351.836278 352.458329 353.081178 353.703581 354.327786 354.951952 355.577208 356.202ooO 356.827504 PP4 321.900159 321.334998 320.771485 320.209598 319.649281 319.090609 318.533611 317,978043 317.424124 316.871754 316.321239 315.771608 315.224012 314.677780 314.132916 313.589916 313.048209 312.508200 311.968960 0.10 I.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.10 0.10 I.00 0.10 0.00 0.00 0.00 0.00 0.10 0.00 0.10
1.00 0.10 0.10 0.00 0.00 0.00 0.10 1.00 0.10 0.01 0.00 0.01 0.10 I.00 0.10 0.10 0.10 1.00 1.00 0.10 I.00 1.00 0.10 0.00 0.00 1.00 1.00 1.00 1.00 1.W 0.00 0.00 0.00 0.00
5 6 7
46
4 5 6 7 6 9 10 11 12 13 14 15 16 17 1.3 19 20 21 22 23 24 25 26 27 26 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
29 30 31 32 33 34 35 36 37 38 39 40
352.596817 PP5 320.747067 320.163756 319.622076
324.840096 324.883766 324.928728 324.974716 325.021676 325.069655 325.119102 325.169438 325.220955 325.273057 325.326335 325.380475 PR4 327.057323 327.636223 328.220712 328.604751 329.390451 329.977480 330.566749 331.156319 331.747988 332.341743 332.936217 333.531636 334.129574 334.727905 335.328290 335.929583 336.532465 337.136812 337.742432 338.349351 338.957743 339.566593 340.176721 340.788761 341.402035 342.015157 342.630525 343.246086 343.863230 344.481697 345.100846 345.720993 346.341591 346.963397 347.586212 346.209680 348.833900 349.459030 350.084931 350.712878 351.339794 351.967038
1.00 1.00 I.00
0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.10 0.00 1.00 0.00 0.00 0.10 1.00 0.00 0.00 0.00 1.00 0.00 1.00 1.00 1.00 0.10 0.00 0.10 1.00 1.00 1.00 0.10 0.10 1.00 0.10 1.00 0.10 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 l.W 0.10 1.00 0.00 0.10 0.00 0.00
5 6 7 8
8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62
319.061844 318.503240 317.946430 317.391065 316.837263 316.285179 315.734561 315.185536 314.638087 314.092187 313.547818 313.006017 312.463449 311.923911 311.386715 310.848927 310.313970 309.779842 309.247301 308.716637 308.187370 307.658939 307.132373 306.607131 306.083217 305.560607 305.039333 304.519520 304.C00888 303.483386 302.967470 302.452830 301.938911 301.426514 300.915468 300.406002 299.897004 299.389182 298.882793 298.377243 297.872735 297.369529 296.867358 296.366075 295.665863 295.366860 294.868703 294.371522 293.875216 293.379611 292.885613 292.392311 291.9W288 291.408678 290.917526 PO5 323.611527 323.621287 323.632277 323.644539 0.00 0.00 0.00 0.10
1.00 1.00 1.00 1.00 1.00 0.10 0.0, 0.00 0.00 0.00 0.10 1.00 1.00 1.00 1.00 0.10 0.10 0.00 0.10 1.00 0.00 1.00 1.00 1.00 1.00 0.00 1.00 1.00 0.00 1.00 0.00 0.0, 0.00 0.00 0.10 0.00 0.10 1.00 0.10 1.00 1.00 1.00 I.00 I.00 0.10 1.00 1.00 1.00 0.00 0.00 1.00 1.00 I.00 I.00 0.10
334.139112 334.739252 335.341078 335.944214 336.549144 337.165177 337.762322 336.370601 338.980600 339.592010 340.204985 340.618395 341.433618 342.049538 342.667145
333.539825
I.00 I.00
1.00 0.M) 1.00 1.00 0.00 0.00 0.m 0.00 0.10 1.00 0.00 0.00 0.10
1.00
314.047586 313.501755 312.957849 312.415279 311.874290 311.334870 310.797039 310.260592 309.725713 309.192452 308.660591 308.130356 307.601318 307.074028 306.548399 306.023686 305.500617 304.979019 304.458808 303.939657 303.422460 302.906410 302.391716 301.878241 301.366169 300.855166 300.345576 299.837564 299.330521 298.824242 298.320428 297.817197 297.315474 PO6 323.028338 323.039378
_F
6
46 47 48
‘ii
41 42 43 *‘I
39 40
z
zz
zz 34
E
z:
;: 25 26 27
z
; 9 10 11 12 13 14 15 16 17 18 19 20
6
41 42 43 44
zl
0.00 0.00
1.00 0.01 0.M) 0.w 0.00 0.00 0.01 0.00 1.00 1.00 0.10 1.00 0.10 1.00 0.01 0.00 1.00 1.00 0.00 0.10 1 .OO 0.00 1.00 0.01 1.00 1.00 0.00 1.00 1.00 0.00 0.10 1.00 0.10 ;: 31
;: 25 26 27 26
;:
11 12 13 14 15 16 17 16 19 20
10
:
6 7
8 9 10 11 12 13 14
323.052198 323.066388 323.082198 323.099668 323.118957 323.139333 323.161236 323.184641 323.210067 323.236337 323.264937 323.294719 323.325589 323.358627 323.392687 323.428321 323.465085 323.503806 323.543764 323.585127 323.627977 323.672167 323.717738 323.764713 323.812327 323.862227 323.913037 323.965127 324.018507 324.073347 324.128916 324.186536 324.244066 PR6 327.037543 327.621533 328.206792 328.793681 329.382701 329.972232 330.563619 331.156841 331.751312 332.347358 332.944857 333.543914 334.144286 334.746625 335.349644 335.954760 336.560637 337.167512 337.776912 336.367451 336.998740 339.611320 340.226099 340.641696 341.458518 342.076537 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.10 0.00 0.10 0.00 0.00 1.00 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.10
0.00 0.00 0.00 0.10 0.00 1 .oo 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.10 0.00 1.00 0.00 0.00 0.00 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
11 12 13 14 15 16
10
9
7 R
:: 52
4i 42 43 44 45 46 47 48 49
2’: 30
;:
zz
z
;‘:
10 11 12 13 14 15 16 17 16 19
9
i
_.
0.10 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.10 0.10
20 21
1.00 1.00 1.00 1.00 1.00 1.03 0.00 0.00 1.00 l.CO 0.10 1.00 0.00 1.00 0.m 0.00 0.00 0.00 0.00 0.10 0.00 1.00 1.00 1.00 0.10 0.10 1.00 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.M) 0.00 0.00 0.10 1.00 0.00 0.00 0.10 0.00 0.00 10 11 12 13 14 15 16 17
9
z
;z 24
is 19
0.00
343.316456 PP7 318.433230 317.873649 317.315377 316.758964 316.203915 315.650280 315.098772 314.548376 313.999674 313.452654 312.906620 312.363334 311.820756 311.280182 310.740879 310.203327 309.667257 309.132670 308.599951 308.068461 307.538846 307.010171 306.483219 305.957783 305.434025 304.911099 304.390340 303.870655 303.353141 302.836204 302.321142 301.807692 301.295019 300.783788 300.274024 299.766238 299.259118 298.754071 298.248908 297.745264 297.243789 296.743200 296.243280 295.746171 295.249452 294.753957 !an7 322.441668 322.454463 322.468827 322.484326 322.501882 322.521202 322.541600 322.563657 322.587206 322.612275
17
0.00
342.695886 0.10 0.00 0.00 0.00 0.00 0.10 1.00 0.10 0.00 0.10 0.00 0.00 0.00 1.00 0.00 0.00
322.668506 322.698298 322.728442 322.762186 322.795704 322.832028 322.869167 322.907047 322.948729 322.989471 323.031522 323.077083 323.123160 323.169955 323.218904 323.268808 PR7 327.022320 327.607766 326.194515 328.782625 329.373002 329.964072 330.557426 331.151874 331.747087 332.344731 332.942361 333.543914 334.145488 334.749029 335.354125 335.959933 336.567810 337.176499 337.787287 338.398918 339.012010 339.626160 340.242529 340.859616 341.477794 342.098467 342.718719 343.340927 343.963850 344.588162 345.214258 345.842984 346.470270 347.100460 347.730074 PI’8 317.271543 316.713654 316.157091 315.602261 315.049084 314.497500 1.00 1.00 1.00 1.00 1 .OO 0.10
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.10 0.00 1.00 0.00 0.00 0.00 0.10 0.00 0.00 0.00 1.00 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.10 0.00 0.00
0.00
322.638921
40 41 42 43 44 45 46 47 46 49 50 51
:7 ::
2
E 21 22
14 15 16 17 18
313.947263 313.399172 312.852421 312.307209 311.763370 311.222013 310.680491 310.141992 309.604554 309.068727 308.534402 307.999971 307.470470 306.941683 306.413701 305.886850 305.380075 304.836925 304.316054 303.795569 303.276442 302.759117 302.242948 301.728383 301.215022 300.703257 300.193499 299.684225 299.176822 298.670073 298.165737 297.662640 297.160367 296.659266 296.160661 295.662486 295.164920 294.670326
1.00 0.10 1.00 0.00 1.00 0.00 1 .OO 1.00 1.00 1.00 0.10 0.00 0.00 0.00 0.00 0.10 0.00 0.00 1.00 1.00 0.10 0.10 0.00 0.00 1.00 0.01 0.10 1.M) 0.10 0.00 1.00 0.00 1.00 0.10 I.00 0.10 0.10 0.10
406
GRANER INTENSITIES
AND
WAGNER
IN HOT
BANDS
Intensity considerations are useful in ascertaining subband assignments found with TOUTHOT if ambiguities exist for the J”, k’“, and 1” values and when it is not clear whether a subband belongs to 2u?;-v?,j or to ~zJ?~-v?~, which we shall hereafter call hot band (2) and hot band (0). respectively. For these hot bands, the rovibrational selection rules are the following, according to Amat’s rule AK - Al = 3p. Forhotband(2),AK=+lfor1”=+1,/‘=?2 For hot band (0), AK = Tl for I” = fl, I’ = 0. In other words, the KS AK = n subband of hot band (2) and the K * AK = -n subband of hot band (0) share a common lower level. Now, how does one decide, a priori, whether a subband belongs to hot band (2) or to hot band (0)? Let us assume, as an example, that we have assigned a K subband with I” = -1. It can therefore be either ‘PA-> ‘QK, and ‘Rk- of hot band (2) or RPk-, “Q-, and RRK of hot band (0). Several criteria are to be taken into account. First, let us consider the strong-weak-weak alternation. In propyne, due to the three equivalent H atoms of the CH3 group, nuclear spin statistics give an intensity twice as strong for k” - 1” = 3p as for k” - I” # 3~. This means that for hot band (2), the subbands with KS AK = * * * -8, -5, -2. 1, 4, 7 - - - are enhanced, whereas for hot band (0), the enhanced subbands are Km AK = * * * -7, -4. -1,2, 5, 8 . . *. Therefore, this relative enhancement tvitkin a hot band does not allow us to choose, because the enhancement is the same for the ‘(P, Q, R)K subband of hot band (2 ) and the R(P, Q, R)K subband of hot band (0) and vice versa. A second argument is that, in well-behaved perpendicular bands, AJ = AKtransitions are stronger than AJ = -AK transitions. Therefore, if we find here that the P series is stronger than the R series, we are probably dealing with hot band (2 ), and with hot band (0) if it is the opposite. Another minor criterium already mentioned earlier concerns K” = I” = 1. Hot band (2) has two R( P, (2, R), families (with very close upper energy levels) for this case. whereas hot band (0) has only one ‘(P, Q, R), family. Finally, the comparison of intensities of lines belonging to the two hot bands, when it is feasible, is also informative. The vibrational factors of the transition moment matrix elements are in the ratios 1: 1: fi for vlo, hot band (O), and hot band (2), respectively, which gives 1: I:2 after squaring. Since the Boltzmann factor at 300 K is 0.2 1, the vibrational intensities of these three bands are in the ratios 1:0.2 1:0.42 (the authors are grateful to Dr. A. Ruoff for clarifying this point). Therefore, if we take a certain transition (e.g., ‘PI(( J)) in the three bands, the intensities should roughly be: I X (spin statistics) in vlo; 0.42 X I X (spin statistics) in hot band (2); 0.21 X 1 X (spin statistics) in hot band (0). Due to the high density of the spectrum, this property cannot easily be checked but it is clear that hot band (0) is significantly weaker than hot band (2). The nuclear spin weights give spectacular effects, as can be seen clearly in Figs. 1 and 2, especially for hot band (3). If we consider this hot band, and compare it with the fundamental vIo. we find as a first approximation that -For K values with K # 3p and K - I# 3p, the K . AK subband (2) has an intensity which is 42% of the intensity of the K. AK subband
of hot band of v,~.
PROPYNE
-For
AT
30
pm
values such that K = 3p, and therefore
407
K - 1 Z 3p, the intensity
ratio is
21%. -For values such that K - 1 = 3p, and therefore reaches 84%. The reader can check qualitatively seem different due to overlaps. ASSIGNMENTS
K # 3p, the intensity
these ratios in Figs. 1 and 2, although
IN THE
HOT
ratio
they often
BANDS
Hot Band (2) The first series which was assigned with the help of POLY and of TOUTHOT was the RR7 series of hot band (2). It is extremely close to the corresponding series of vIO. For low J values, the hot band lines are ~0.030 cm-’ below the cold band lines: they coincide around J E 28 and are slightly above for higher J values. A similar pattern is found for most of the series of hot band (2 ) which were easily assigned, with the notable exceptions of the subbands KS AK = 1 and 0 which are less obvious, for different reasons. The ‘P7 and ‘Pa series were also found only in a later stage, when a correct global model was available. Finally, we have assigned 17 subbands of hot band ( 2). from KAK = -8 to f7, including two subbands for Ku AK = 1. The highest J value was reached for ‘P2 (66 ). We have in the end established a list of 2090 transitions, 1272 of which have a nonzero weight. They correspond to 743 different energy levels with a nonzero weight. The whole list of transitions is given in Table V. It should be noted that for most P and R series, the low J lines are obscured because they lie in the region of Q branches. For the two subbands with K* AK = 1, it was found that in the upper level ( v10 = 2. Ilo = 2. k = 2). which is split by an A4+ A doubling, the A + level is above the -4 -
v J+l
J J-l FIG. 5. Scheme of levels for the 2u&v~~
transition.
10 11 12 13 14 15
:
:P 55
:? 52
zl 39 40 41 42 43 44 45 46 47 48 49
z:: 36
z: 33
::
;: 26 27 28
:: 21 22 23
11 12 13 14 15 16 17 18
10
:
7
316.875234 316.315527 315.756779 315.199674 314.644453 314.090627 313.536433 312.987886 312.439101 311.891567 311.346082 310.802061 310.259953 309.718942 309.179903 308.642566 308.106714 307.572665 307.040354 306.509586 305.980527 305.45325s 304.927557 304.403677 303.681326 303.360962 302.642047 302.325066 301.809918 301.295021 300.783788 300.274023 299.765693 299.259118 298.754071 298.251349 297.750261 297.250394 296.752412 296.256700 295.762614 295.270242 294.779552 294.290718 293.803269 293.317992 292.834257 292.352728 291.872545 PQ7 320.886250 320.898510 320.912610 320.928670 320.945874 320.965040 320.985244 321 .C07860 321.031884
0.10
0.00
0.00 0.10 0.00 1 .oo 1 .w 0.10
0.00
0.00 0.00
0.10
1 .oo
l.w 0.10 1 .oo
1.00
1.00 1.00 l.w
0.00
1 .w 1.00
0.00
0.10 0.10 1 .cQ 0.10
0.00
.oo
0.00 0.10 I.043 1.00 1.M) 0.00 1.00 1 .Oo 1 .oo Cl.10 1 .co cJ.cQ 1 .co 0.10 0.00 1.00 I.00 0.00 1 .m 1 .cO 1.00 0. IO 0.00 1 .m 1 .oo 1 1 .oo 1 .oo 0.10
Ei 31 32
;,” 28
15 16 17 18 19 20 21 22 23 24 25
zi 39 40
:z 36
z: 33
z:
;z 27 28
17 18 19 20 21 22 23 24
16
321.057058 321.084086 321.112579 321.142690 321.174790 321.208466 321.243173 321.280118 321.318333 321.357960 321.399029 321.442859 321.487803 321.534619 321.582659 321.631904 321.683399 321.737079 321.791389 321.846569 321.905689 321.965709 322.026809 322.089829 322.155049 PR7 325.469005 326.054394 326.642177 327.230263 327.820442 328.412182 329.005681 329.600321 330.1s6s40 330.794989 331.394839 331.995728 332.598547 333.202697 333.808716 334.416235 335.025305 335.635924 336.248103 336.861933 337.477232 338.094500 338.713182 339.332940 339.954099 340.577909 341.202938 341.629110 342.457236 343.087366 343.718135 344.350854 344.985374 PP6
.oo
0.00
0.00 0.00 0.00 1 .oo 1 .Oil 0.00 0.00 0.00 0.00 1 .m 0.00 0.00 0.00 0.00 0.M)
0.00 0.10
0.00
0.00
0.00
0.00
0.00 0.00 0.00
0.00
0.00
0.00
0.00 0.00 0.00
0.00
0.00
0.00 0.00
0.00
0.W 0.00 0.00
0.00 1.00
1 .oo 0.10 0.00
0.00
1
0.00
0.00 0.00
0.10
1.00 1.00 1.00 1.00 I.00 0.00 0.00 0.10
:
6 7
10 11 12 13 14 15 16 17
::
45 46 47 48 49 50
16 17 18 19 20
ii
9 10 11 12 13 Id
i
6
Transltlons 318.036311 317.474390 316.914077 316.355374 315.798430 315.242778 314.689266 314.136698 313.586602 313.037400 312.490262 311.944593 311.400400 310.858110 310.317378 309.778620 309.241430 308.705883 308.172358 307.640297 307.110315 306.581570 306.054660 305.529950 305.006820 304.485576 303.965940 303.448107 302.932302 302.418074 301.905960 301.39577s 300.886893 300.380406 299.875438 299.372305 2s8.871104 298.372333 297.874600 297.379516 296.886272 296.393770 295.904165 295.416243 294.929770 294.446060 293.963930 PO6 321.474461 321.485544 321.498223 321.512640 321.528377 321.545694 321.564920 321.585730 321.608068 321.631904 321.657640 321.684120
Assigned
.oo
1 .oo 0.00 1 .OO 1 .m 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
1.m 1.oo
.w
0.00 1.00 0.00 1.00 0.00 0.00 1 .w 0.00 0.00 0.00 0.00 1 1 .w 1 .Oo 0.00
0.00 0.00 0.00 0.00
1 1 .oo 0.00
0.00 0.00 0.00
0.00 0.00 0.00 0.00 321.744174 321.776205 321.809570 321.845156 321.881589 321.921285 321.962083 322.004064 322.048050 322.093798 322.140880 322.190260 322.240491 322.293880 322.348767 322.404100 322.462199 322.522084 322.583188 322.646608 322.711467 322.778075 322.846760 322.917370 322.989470 PR6 325.485615 326.069690 326.655489 327.242540 327.831688 328.421732 329.014196 329.607498 330.202805 330.799515 331.397633 331.997010 332.599011 333.202689 333.807606 334.413499 335.021786 335.631440 336.243071 336.855832 337.470646 336.086870 338.704921 339.324620 339.945992 340.568939 341.193777 341.820051 342.448295 343.078323 343.709493 344.342903 344.978382
321.713396
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.10 0.10 0.00 0.00 0.00 0.00 0.W 0.10 0.00 0.00 0.00 o.c!o 0.M) o.ca 0.00 0.00 0.00 0.00 0.00 0.10
0.00 1.00 1.00 0.10 0.00 0.10 0.00 0.00 0.00 1.00 0.10 0.00 0.00 0.10 1.00 0.10 0.10 0.00 0.00 0.00 0.00 0.03 0.00 1.00 0.00 0.10
40 41 42 43 44 45 46 47 48 49 50
3”: 39
:z
21 22 23
1s ::
13 14 15 16 17
ii
40 41 42 43 44 45 46 47 48 49 50 51
39
III the 7 _v ”Lo- v *’ IO Hot Band of Propyne
TABLE VI
346.252500 346.892749 347.534056 348.177827 348.622466 349.469216 350.117883 350.768030 361.419417 352.073353 352.728880 353.385570 PP5 319.194331 318.630739 318.069029 317.508723 316.950016 316.392900 315.837244 315.283145 314.731471 314.181532 313.632251 313.085206 312.539593 311.996016 311.454170 310.914057 310.375861 309.839457 309.304554 308.772170 308.241360 307.712470 307.185500 306.660382 306.137458 305.616323 305.097220 304.580187 304.065030 303.552021 303.040643 302.531838 302.024939 301.519873 301.017370 300.516203 300.017691 299.520718 299.026184 298.533706 298.042660 297.553910 297.067120 296.582460 296.099138 295.618250
345.614390
Z% 0.00 0.00 0.00 0.00 0.01 0.01 0.00
::i% 0.01 0.01
K% 0.00 0.01 0.00 0.00 0.01 0.01 0.00 0.00 0.01 0.01 0.01 0.00 0.00 O.CO 0.00 0.00 0.01 0.01 0.00 0.01 0.00 0.01 0.00 0.01 0.01
EZ 0.00
0.01 0.00 0.01
0.10 1 .oO
0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00
2% 0.00
8 9 10
i
43 44 45 46 47 48
ii
13 14 15 16 17 18 19
ii
7 8
325.499510 326.081746 326.666021 327.251410 327.839580 328.427092
294.661735 294.186121 293.712226 293.240159
295.139020
0.00 0.00 0.00 0.00 0.10 0.10
0.00 0.00 0.00 0.00 0.00
;:
18 19 20
,
12 13 14 15 16 17
4
:: 40 41 42 43 44 45 46 47 48 49 50
:z 34 35 36 37
Z?
24 25 26 27 28 29
;z
Z?
12 13 14 15 16 17 18 19
330.205704 330.800554 331.398466 331.997018 332.597336 333.199709 333.803820 334.409819 335.016877 335.627202 336.238006 336.850649 337.465603 336.081959 338.700570 339.321052 339.943051 340.567408 341.193085 341.621022 342.449882 343.062228 343.716251 344.351546 344.969368 345.627654 346.269011 346.911996 347.556734 348.203607 348.852181 349.501967 350.154474 350.607906 351.463346 352.120546 352.779032 353.439374 PP4 320.349644 319.784005 319.220908 318.658535 318.098273 317.539858 316.983130 316.427829 315.674319 315.323102 314.773510 314.226048 313.679585 313.136886 312.595377 312.056058 311.518980 310.983918 310.451334
329.611842
329.019559
.w
.w
0.01 0.01 0.01 1 .w 1 1.00 0.01 1 .oo 0.10 1.00 0.00 1 .oo 0.10 1 .oo 1 .oo 1 .oo 1.00 0.10 0.01
0.00
0.00
0.00 0.10 0.10
0.10
0.00 1 .oo 0.00
0.00 0.00 0.00
0.00
0.00
0.10
0.00 0.00 0.00
0.10
0.00
1
0.00
0.00 0.00
0.00 0.10 0.00
0.10 1 .w
0.00
0.10
0.00
0.00
0.00 0.00 0.00
0.00
0.00
0.00 0.00
23
11 12 13 14 15 16 17 18 19 20 21 22 23
E?
:z 57 58 59
42 43 44 45 46 47 48 49 50 51 52 53 54
;:: 26 27
291.764786 291.304622 PO4 322.641957 322.650679 322.660569 322.671268 322.684394 322.698298 322.715252 322.733466 322.753806 322.775482 322.799504 322.824400 322.852835 322.883093 322.915150 322.948729 322.985498 323.023815 323.064590 323.107870
292.226070
309.392768 308.866864 308.343836 307.822801 307.304265 306.787794 306.273778 305.762016 305.252721 304.745784 304.240580 303.738032 303.237498 302.739298 302.242946 301.749135 301.256648 300.766238 300.277823 299.791495 299.307610 298.624242 298.342913 297.863301 297.385714 296.909465 296.434845 295.961397 295.489868 295.019282 294.548938 294.083027 293.617005 293.152141 292.688509
309.920886
.oo
1 .w I 0.00 1 .w 1.00 0.01 0.00 0.00
0.00
0.01
0.10
0.01 1.00 0.01 0.01 1 .oo 0.01 I.00 0.10 1 .oo
0.01 0.01 0.01 0. IO 1 .w 1 .ocl 1 .oo 1 .W 1 .oo 1 .W 0.10 0.00 1 .W 0.01 I.00 0.10 0.10 1 .W 0.10 0.01 1.00 0.00 0.10 1 .W 1.W 1.00 0.01 1 .W 1 .Ocl 1 .OO I.00 0.01 0.01 1.00 0.00 0.00 I.00 0.00 0.00
i: 40 41
:: 37
z: 33 34
::
;z 24 25 26 27 28
i 9 10 11 12 13 14 15 16 17 18 19 20 21
4 5 6
42 43 44
%I
;;:
74 25 26 323.152750 323.200634 323.250687 323.302808 323.357319 323.414738 323.473536 323.534802 323.598330 323.663690 323.731100 323.801550 323.874024 323.947640 324.023820 324.101869 324.181340 324.263260 324.346460 324.432380 324.518733 PR4 325.508730 326.089438 326.672710 327.257190 327.843570 328.431340 329.020870 329.612640 330.205704 330.802054 331 .3978W 331.997880 332.598802 333.202689 333.807606 334.415519 335.025320 335.636562 336.251393 336.867570 337.486698 338.107580 338.730940 339.356255 339.984103 340.613710 341.245860 341.880317 342.516636 343.154815 343.795160 344.437750 345.082050 345.728402 346.376610 347.026619 347.678452 .348.331500 0.00 1 .W 0. IO 0.00 0.00 0.00 0.00 0.00 0.01 0.10 0.00 0.00 0.01 0.10 0.10 0.10 1 .W 0.01 0.01 0.00 0.10 0.00 0.00 1 .W 1 .W 0.00 0.00 1 .cO 1 .W 1.00 0.00 0.00 0.00 0.01 0.W 0.01 0.01 0.10
1.00 1.00 0.10 0.10 0.10 0.01 0.10 0.00 0.00 0.00 0.W 0.10 0.00 0.01 0.10 0.00 0.00 0.00 0.00 0.10
0.00
:::
6
5
38 39 40 41 42 43 44
:z 21
14 15 16 17 18
:;
:?
44 45 46 47 48 49
348.986803 349.643480 350.301480 350.961010 351.622092 352.284540 352.948790 353.613670 354.280260 354.947973 355.614353 356.284990 PP3 321.502014 320.934729 320.369814 319.805843 319.242528 318.682254 318.121842 317.562231 317.W5799 316.449224 315.894142 315.338853 314.784950 314.232229 313.679585 313.126622 312.575096 312.023428 311.472273 310.921258 310.370325 309.819644 309.269437 308.719230 308.169162 307.619058 307.068757 306.519980 305.969420 305.419457 304.870270 304.321ooO 303.771390 303.222168 302.673COO 302.123645 301.574490 301.025334 300.475964 299.927745 299.378154 298.828382 PQ3 323.220174 323.230658 323.236357 323.245330
.w
0.01 0.00 1 .w 0.10
0.01 0.01 0.01
0.10
1
0.00
1 .w 0.10 0.00 1 .w
0.00
0.01 0.01
0.00
.w
0.00 1 1 .w
0.01
0.01
0.00
.w
1 .w 0.00 0.00 1 1 .w
0.00
1.00 1 .w 0.10 1 .w 0.10 0.00 0.10 0.00 1 .w 0.10 0.00 1 .w 1.00 0.01 0.01 1 .w
0.00 0.10 0.00 0.00 0.00 0.00 0.01 0.00 0.00
0.01
0.00 0.00
:: 21 22 23 24 25
14 15 16 17 18
2: 39 40 41 42
i;
:: 34
;: 30 31
27
19 20 21 22 23 24
16 ‘7
1: iic
10 11 12 13
;
9
323.255418 323.266417 323.280116 323.294719 323.309225 323.325589 323.342180 323.359320 323.377615 323.396450 323.414738 323.435428 323.454369 323.475180 323.494989 323.515434 323.534802 323.557222 323.577423 323.599360 323.620396 323.641431 323.663063 323.683580 323.704480 323.725493 323.747580 323.769133 323.789623 323.811430 323.832560 323.853810 323.874024 323.895107 323.917842 323.938340 PR3 325.514930 326.094280 326.674280 327.257300 327.839580 328.423370 329.OlW80 329.596670 330.185220 330.772633 331.362180 331.952253 332.543250 333.132730 333.723767 334.314977 334.906546 335.498258 336.090429 336.681870 337.273842 337.866663 338.458641
1.00
1% 0.00 0.00 1 .oo 0.01 0.10
F% 0.00 0.00 1.00 1 .OO
0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.W
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1.00 0.00 0.00 0.00
PROPYNE
AT 30
pm
413
level, the separation being well represented, with a standard deviation of 2 X IO-’ cm-‘by AE = a[J(J+ l)]‘+ b[J(J+ 1)13 + c[J(J+ 1)14with a = 1.19 X 10v7, h = -6.63 X lo-‘” and c = -1.56 X lo-l5 cm-l. Hot Band (0) The first two series assigned in hot band (0) were ‘P7 and ‘P4. They both lie about 1.5 cm-’ below the same series of vlo. Further assignments were made easier by an important point illustrated by Fig. 5: thesubbandK”=n+l,l”= l.AK=Al=-IandthesubbandK”=n-l,f”=-1, AK = A/ = + 1 share the same upper level I(’ = n, 1’ = 0. In other words, six transitions, namely,PP,+,(J+ l),PQn+i(J),PRn+~(Jl).RPn-~(J+ l),RQ,_,(J),andRR,.-~(J - I ), all reach the same upper level. Since we know A0 (32) very well, the energies of the ulo = 1 state determined in the first part of this paper are very reliable even for different K values. They can be employed for a nonclassical use of LSCD to determine one of the two subbands if the other one is known or to check dubious assignments. Even if several of the six above mentioned transitions are blended, enough remain for a valid check. Finally, we have assigned 13 subbands from K- AK = -7 to +5. The highest Jvalue reached is for ‘P, (64) but, as a rule, it was not possible to go as far in J as for hot band (2). The final list comprises 1560 transitions, 914 of which have a nonzero weight. Due to the remark made earlier, this corresponds to only 363 different energy levels with a nonzero weight. The whole list of transitions is given in Table VI.
DISCUSSION
AND
FURTHER
WORK
We have converted the wavenumbers of both hot bands into upper level energies using the very accurate lower level energies (in the vIo = 1 state) determined in the first part of the present work. These energies of the vIO = 2 state were then leastsquares fitted to a model including the I( 2, 2) interaction between the I = 0 and the 1 = +-2 components. But it was soon clear to us that it was not possible to ignore the level v9 = 1, located near nlo = 2. With the u9 band having been just studied at Oulu by K. Pekkala (see the accompanying paper (43)). we were aware that a Fermi resonance was present, affecting mainly the K’ = 1, u9 = 1, l9 = - 1 levels on one hand andtheK’= 1.u lo = 2, I9 = +2 levels on the other. It resulted in a shift of aboui 0.020 cm -I. Other interactions could also be suspected between the two vibrational levels, It appeared therefore more reasonable to fit all the energy levels together. This will be reported in a further paper where we treat together vIo = 2, l9 = 0, k2 levels, rovibrational transitions of v9. and also rotational transitions in both levels (49). It should be mentioned that from the present work, accurate energies of the vi0 = 2 state became available. They were used to assign with no ambiguity one RR5 series belonging to the “superhot” band 3~~~~2~~~. Two lines of this series are shown on Figs. 1 and 2. We hope to be able in the near future to assign other transitions of these “superhot” bands. Since the 3vi0 band lies near IO pm, the knowledge of the vl(, = 3 levels is crucial for a better understanding of the complex band system of propyne in the 10 pm region.
414
GRANER
AND
WAGNER
ACKNOWLEDGMENTS The authors thank Brenda P. Winnewisser, reading of the manuscript.
INSU and from the France-German
RECEIVED:
Hans Biirger, Rauno Anttila, and Karl Pekkala for a critical
Support from the “Action program
ThCmatique
PROCOPE
Programmee
PlanCtologie”
of the French
is gratefully acknowledged.
July 19, 1990 REFERENCES
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3. F. MEYER, J. DUPRE, C. MEYER, C. LAMBEAU, M. DE VLEESCHOUWER. J. G. LAHAYE. AND A. FAST. Int. J. Itfiured Millitneter IIicves 3, 83-95 ( 1982 ). 4. H. N. RUTT. D. N. TRAVIS, AND K. C. HAWKINS. Inl. J. ItQkwed Millitneicr Clhws 5, 1201-12 19 ( 1984). 5. J. M. WARES AND J. A. ROBERTS, J. Chetn. P/I?J. 82, 5-8 ( 1985 ), 6. N. F. HENFREY AND B. A. THRIISH, J. .tlo/. .Spec/rosc. 113, 426-450 ( 1985). 7. T. AL ADLOUNI, F. MEYER, J. DIIPRE, AND C. MEYER, C’. R. .kud. Sci. Paris 300, 553-555 ( 1985). 8. F. MEYER, J. DUPRE. C. MEYER, J. G. LAHAYE, AND A. FAYT. Cutlad. J. Ph~:s. 63, 1184-l 188 ( 1985 ). 9. V. PRAKASH AND J. A. ROBERTS, J. C%em. Pigs. 84, 1193-l 195 (1986). 10. W. M. RHEE AND J. A. ROBERTS, J. Chctn. PI1y.s. 85,6940-6944 ( 1986 ). 11. J. M. WARE, V. PRAKASH, AND J. A. ROBERTS. J. .Zlo/. Specfrmc.. 116, 17-22 (1986). 12. W. M. RHEE. J. A. ROBERTS. AND V. PRAKASH, J. .kfto/. Speclrosc. 120, 169-174 ( 1986). 13. T. AL ADLOUNI. F. MEYER. C. MEYER. J. G. LAHAYE. AND A. FAYT, Inr. J. It$ured Millitnetcr ~+‘UWS 7,405-419 (1986). 14. W. M. RHEE AND J. A. ROBERTS, J. MO/. Spe&mc. 126, 356-369 ( 1987). 15 N. F. HENFREY AND B. A. THRUSH, J A/o/. Spcvfrosc. 121, 139-149 ( 1987). 16. N. F. HENFREY AND B. A. THRUSH, J. Mol. Sp~tn~. 121. 150-166 (1987). 17. T. AL ADLOUNI, F. MEYER, C. MEYER, D. E. JENNINGS,AND J. J. HILLMAN, In,. .J. In/ktrc~d ,Ifi//itnc~rcv Hitves 38, 1083-1096 ( 1987). 18. H. TAM. I. AN, AND J. A. ROBERTS. J. A/o/. Specttwc. 126, 349-358 ( 1989). 19. L. A. BAYLOR. E. WEITZ, AND P. HOFMANN. J. Chm. Phys. 90, 615-627 ( 1989). 20. V. M. HORNEMAN. G. GRANER, H. FAKOUR. AND C. TARRAGO. J. Mol. Spe~~(.Iro.sc. 137, l-8 ( 1989 ). 137,432
(1989).
21. G. WLODARCZAK, R. BOCQLIET. A. BAUER. AND J. DEMAISON. J. MO/. Speorosc~. 129, 371-380
( 1988).
22. T. AL ADLOUNI AND G. GRANER. Mikrochim .lctu ( RTett) II. 399-40 I ( I988 ). 23. T. AL ADLOUNI ANDG. GRANER. J. 3/o/. Spec~ros~~. 127, 186-199 ( 1988). 24. R. HANEL, B. CONRATH. F. M. FI.ASAR. V. KUNDE. W. MAGUIRE. J. PEARL, J. PIRRAGLI,~, R. SAMUELSON, L. HERATH. M. ALLISON. D. CRUIKSHANK. D. GAUTIER, P. GIERASCH. L. HORN, R. KOPPANY. AND C. PONNAMPERUMA.&ivnw
212, 192-200
25. A. COLISTENIS.B. BEZARD. AND D. GA~TIER. IU.CZIS80, 54-76
( 1981 ). ( 1989).
26. See T. B. H. KUIPER.E. N. RODRIGUEZKUIPER,D. F. DICKINSON,B. E. TURNER, AND B. ZUCKERMANN.
A.slroph?_;. J. 276, 2 1l-220
( I984 ) and
references therein.
27. S. J. KIM, J. CALDWELL. A. RIVOLO, R. WAGNER. AND G. S. ORTON. Icunrs 64, 233-248
( 1985).
28. T. Y. CHANG AND J. D. MCGEE. .4pp/. Phys. Lctt. 19, 103-105 ( 1971).
2Y. T. Y. CHANC;AND J. D. MCGEE. IEEE .I. Qmznfutt? Ekwron. QE-9, 62-65 30 T. A. FISCHERAND C. WITTIG, .4pp/. P/ty.s. Lett. 39, 6-8 ( 198 1 ).
( 1976).
31. G. GRANER, J. DEMAISON, G. WLODARCZAK, R. ANTTILA, J. HILLMAN, AND D. E. JENNINGS.MO/. Phys. 64. 921-932 (1988). 32. G. GRANER, V. M. HORNEMAN, G. BLANQUET. J. WALRAND. M. TAKAMI. AND L. JORISSEN.J. MO/. Specfmsc. 135, 32-44 ( 1989). 33.
K. JOLMA, V. M. HORNEMAN. J. KAUPPINEN, AND A. G. MAKI, J. MO/. Spectrosc (1985).
34. J. W. C. JOHNS. J. Opt. Sot. .-ltner. B. 2, 1340-1354
(1985).
113,
167-174
PROPYNE
3.5.G. GUELACHVILI
AT
30 pm
415
AND K. NARAHARI RAO, ‘*Handbook of Infrared Standards.” Academic Press, New
York. 1986. 36. G. WAGNER, B. P. WINNEWISSER, AND M. WINNEWISSER, “Eleventh Colloquium on High Resolution Molecular Spectroscopy, Giessen. September 1989.” Communication F25. 37. G. J. CARTWRIGHTAND 1. M. MILLS. J. Mol. Spec’fnx 34, 415-439 ( 1970). 38. H. BURGER.R. EUJEN.M. LITZ. AND S. CRADOCK, J. Mol. Specfrmc. 138, 332-345 ( 1989). 39. S. CRADOCK,H. BURGER,R. EUGEN.M. LITZ,AND A. RAHNER, J. :Lfol Specmsc. 142, IO-23 ( 1990). 40. J. A. DUCKETT.A. G. ROBIETTE,AND 1. M. MILLS. .I. hfool.Specfrosc. 62, 34-52 ( 1976). 41. L. HALONEN.J. KAUPPINEN.AND G. L. CALDOW. J. Chen~. F%JT 81, 2157-2269 ( 1984): 86, 58885889 (1987). 42. H. G. CHO. Y. MATSUO, AND R. H. SCHWENDEM~N.J. Mol. Spe~rrosc. 137, 215-229 ( 1989). 43. K. PEKKALA. J. Mol. Spmru~c. 144, 416-428 ( 1990 ). 44. C. BETRENCOURT,G. GRANER. D. E. JENNINGS,AND W. E. BLASS. J. Md. Spectrosc~. 69, 179-198 (1978). 45. G. GRANER .&NDG. GUELACHVILI,J. Mol. Spec/rmc. 89. 19-41 ( 198 I ). 46. G. GRANER AND G. GUELACHVILI.J. MO/. Spec~ms~~. 107, 2 15-228 ( 1984 ). 47. J. P. CHAMPION, A. G. ROBIETTE,1. M. MILLS, AND G. GRANER. J. ftfol. .Spectro.w 96, 422-441 (1982). 48. J. P. CHAMPIONAND G. GRANER, hlc11.Phys. 58. 475-484 ( 1986). 49. K. PEKKALA, G. GRANER. G. WLODARCZAK.AND 3. DEMAISON,to be published.
OF MOLECULAR
High-Resolution
SPECTROSCOPY
144.389-415 (1990)
Infrared Spectrum of Propyne: The 30 pm Region GEORGES
Lahoratoire
GRANER
d ‘Infkarouge. .IwciP au C’NRS. C’rklersitP Paris-Sad. F-91 405 0r.sa.v Cedes. France
Bdtiment 350.
AND
GEORG Ph!,sikalisrh-Che1nisc~te.s
WAGNER
lnstitut. Justus-Liehip L~nirerxtdt. Heirtrictz-Bt!HIRing 58. D-6300 Giessen. Germanj
A high-resolution (0.002 cm -’ ) spectrum of propyne in the region of 30 pm has been used to improve the constants of 8,” and to analyze its hot bands. For vIO. it was found necessary to use WJ. nJAr T),w, and even qhhn and qnhkh constants to tit the high K series correctly. A standard deviation of 0.00021 cm-’ was obtained. The assignments were more challenging for the hot bands. Finally. more than ‘1000 transitions were assigned in the 2u~~-v~C: band and more than 1500 in 2v?,-u?A. The final fit, also including us, and microwave data will be presented in a future paper. 6 1990 Academic Press. Inc INTRODUCTION
In the last decade, propyne (or methylacetylene CHj-C~-C-H) has been the subject of many spectroscopic investigations ( l-23 ). There are many reasons for this interest. Propyne has been detected in the planet Titan (24, 25 ) and in interstellar clouds (26) through its infrared and microwave spectra. It has also been detected in the northern aurora1 region of Jupiter (27) and tentatively identified at the south pole of Saturn (24). Moreover, many IR bands of this compound lie in the region of the CO? lasers so that laser-Stark spectroscopy has been possible (3, 8, 13 ) and optically pumped laser emissions have been produced in the far- and the mid-infrared regions (,28-30.4) and assigned ( 4, 22, 23). The fact that the lowest vibrational mode of propyne is low ( vlg = 33 1 cm -‘) and that it is an E-type level is also an important feature. It enhances its importance for astrophysical applications and opens the way to the study of hot bands. a difficult but interesting topic for most molecules. Through the study of hot bands in the 10 pm region, we have recently been able to obtain a value for the il0 rotational constant of propyne (31, 32). The uIO band itself has only recently been recorded and analyzed at high resolution (20). As was suggested in the conclusion of Ref. ( 20). it was obvious that the study had to be completed by a careful study of the hot bands, especially the two strong components ~Y$-v~~ and 2v’&-u~~. The availability of a spectrometer with a better resolving power led us to undertake the study of these hot bands. Their assignment is the main subject of this present paper. Their complete analysis will be reported in a forthcoming paper. As a by-product. better information on the fundamental vlg itself 389
0022-2852/90
$3.00
Copyright C 1990 by Academic Press. Inc. All rights of reproduction in any form rexwed.
390
GRANER
AND
WAGNER
became available, in particular after the hot bands blends and overlaps became clear. EXPERIMENTAL
had been assigned,
when many
DETAILS
Recording Condilior~s Two spectra hereafter called A and B were recorded on the BRUKER IFS 120 HR Fourier transform spectrometer of the Giessen University. The theoretical resolution limit of this spectrometer is 0.00 12 cm -’ , without apodization. For comparison, the Doppler width for propyne at 300 K is 0.65 X I Om3 cm-’ (FWHM). Spectrum .4, an exploratory spectrum, was recorded with a liquid helium cooled Ge:Cu detector, a 3.5~pm beam splitter, and an optical band-pass filter 3 15-63 1 cm -’ Propyne was put in a 2%cm-long cell at a pressure of 2.66 mbar (266 Pa ). The cell windows were made of CsBr. The relatively high pressure led us to limit the resolution of the spectrometer to 0.0044 cm -‘. A total of 200 scans were coadded. This spectrum could be investigated above 323 cm-‘. For spectrum B, the same beam splitter was used. but with a liquid helium cooled Si bolometer and a low-pass optical filter cutting at 375 cm-‘. A 298-cm-long cell. with CsI windows, was employed and the pressure could be lowered to 0.998 mbar (99.8 Pa). This time the nominal resolution was set at 0.0020 cm-‘. A total of 300 scans were coadded. The spectrum was excellent up to 360 cm ’ and too noisy above 365 cm-‘. Therefore a few very-high-1 R lines are not available under optimal conditions in either of the two spectra. Most of the analysis was made using spectrum B. A handful of lines from spectrum .4 were also used, after proper care had been taken in the calibration problems.
Calibrution There are no accepted wavenumber standards in the 30 pm region so that calibration is somewhat problematic. We shall therefore discuss it in some detail. In Refs. (32. _10), calibration was based on the OCS v2 band at 520 cm -’ (33) and transferred through D20 lines. For spectrum B of the present work, no extra calibration spectrum was recorded. Many residual water vapor lines were seen in the spectrum. Thirteen of them. between factor. We ignored lines above 256 and 298 cm-‘, were used to derive a calibration 298 cm-‘, which were likely to be partly overlapped by propyne lines. The wavenumbers used for H20 were those obtained by J. W. C. Johns (34) and published in Ref. (35). Later, a careful study of all calibration standards in the medium and far infrared (36) led the Giessen group to propose new values for water vapor wavenumbers in this region. The lines between 256 and 298 cm-’ which are of a good quality both in Ref. (36) and in spectrum B and a few strong lines up to 343 cm -’ (but with a smaller weight) were used here to derive a calibration factor. Table I gives a list of calibrated water lines with the standard lines used for the calibration (36). The standard deviation of the fit was 53 X lop6 cm-l. As indicated in Ref. (36), the values are systematically below those of Johns by r3 X 10 p4 cm -‘.
PROPYNE
AT 30 pm
391
TABLE I Hz0 Lines Used for Calibration T’HIS WORK
1371
112906
256. 112 972
.099916
257.099 931
138 632
265. 138 650 266. 845 102
,559349
267. 559 350 267.757 693
757 716
271.
842 399
276. 147 829
147 721’
277.
425 548
278. 257 327
257 115’
278. 519 162 351 472’
280. 351 681 281. 155 723
155 700
282.257 841
,257997’ .488909’ ,377a22 ,785811 ,603376
283. 488 978 284. 284.785 812 285. 603 296 290 726 969
726 972
298. 416 828
,416628’ ,741153
298. 304 879 847
880 162+
314. 741 856
742 Il4+
323. 929 344
,929334+
335. 157 118
157 172+
340. 549 439
549 273+
343. 204 988
1
205 064+
*weight 0 +weight 0.1. probably overlapped by propyne.
Finally Table II reports the wavenumbers of a few prominent lines of C3H4 taken in the spectrum of Ref. (20) and in the present spectrum B. In comparing these values, one should not forget the different resolutions of the spectra. This table shows a small discrepancy. of about 2 X lop4 cm-‘, between the two columns. To summarize: the accuracy of the wavenumber scale that we finally used in the present work (i.e., spectrum B with the second calibration) is probably not better than 0.0002 cm -I. On the other hand, the internal consistency of the propyne spectrum. as shown by least-squares fits on selected lines, is better than 5 X 10 P5 cm -’ . However, it should be recalled that unblended lines are almost impossible to find in the propyne spectrum. THE Y,O FUNDAMENTAL
BAND
Description of the Spectrum The perpendicular band vi0 has a separation between subbands 2( .4’-A{- B’) s 0.57 cm-’ identical to the 2B value in the P and R branches. Therefore all the lines with
392
GRANER AND WAGNER TABLE II Comparison of Some Prominent Lines of C3H4 Using Different Calibrations I201
THIS WORK
298.120 872
120 969
301. 133 336
133 803
306.252
917
253 203
314.041
005
,041 219
326.991
860
,991 950
329. 178 361
178 038
334.462
693
462 896
342. 357 561
357 633
349.171
116
171440
355.038
446
038 779
(a) Calibration
based on 1341 1351
(b) Calibration
based on [361
the same J. hJ + KS AK value are gathered in a small range. The spectrum thus most of the resolved comprises a very dense central part 322-332 cmP’, containing Q branches of vi0 and of its hot bands, and two less congested regions at lower and higher wavenumbers, containing mainly the A J = - 1 and A J = + 1 transitions, respectively. The peak-finder program detected about 1800 peaks in the central region. which should contain about 2500 transitions of sizeable strength at a conservative estimate. Figures l-3 show small parts of the spectrum. Assignrnmts
Using the results of Ref. (20). it was straightforward to assign the transitions outside the range J < 50, K. AK = -9 to +9 to which the analysis in Ref. (20) was mainly confined. J values up to 60 and even 66 were reached and K. AK = 10, 11, 12 subbands were assigned unambiguously. The series K. AK = - 10 and - 11 were more difficult to find and could not be ascertained until the Hamiltonian used was modified as explained below. As for K * AK = - 12, we cannot yet put forward satisfactory assignments. For these high K series, the line intensities are low, much smaller than those of overlapping hot band transitions. Moreover, ground state combination differences are difficult or impossible to use since A J = -AK series (i.e., ‘R and RP) have then vanished and Q branches are barely visible. We therefore must rely heavily upon the quality of the predictions. Each measured line was given a weight 1.0. I. 0.0 I. or 0 according to the overlaps suspected or known, especially after the major hot bands had been assigned. A typical problem has been encountered with the R Rj (J) series. We were surprised to find a systematic deviation of GO.0004 cm -’ in the fits for many J values. although the lines were apparently well behaved. This was explained later by the fact that the RR4 (J)
PROPYNE
AT
393
30 urn
1;
I
’
3J7)'1,
RRqiB) ,; ii
0 ,,,‘1,,“11111”““~‘11’1’~,‘,,,~1,’,,1(’~, 333.6 333 7 333
8
-
333
‘)
RR,(10)
,’ RR,(7) RR,(6)
‘j
RR'tgj 3 9
RR&l*)
334.0
WavPnumber/cm~'
FIG. I. Part of the spectrum B of propyne (L = 298 cm, p = 99.8 Pa, resolving power ? 0.0020 cm ’ ). The transitions belonging to Yr0 are denoted by C (for cold). to Zs~~-u?~ by H (for hot), and to ?u~,~-Y~~ by 2 (for zero), except for the ‘RK(J) lines of Z which are only designated by K(J) for short. One line belonging to 2v~&v~~ is denoted by S (for superhot ). We have not indicated a certain number of weak transitions belonging to high J values of RQ12, RQII, RQIo, and RQs branches of C and H,
series of 2~7;~ v?d stays for 2 1 G J G 37 within 0.0026 cm -’ of RR4 uIo, and they are therefore not resolved. Due to the high probability of blends in the Q-branch region, we decided not to use any Q transition in the least-squares fit, except for RQo which brings additional information.
337
3
337
4
337.5 Wavenumber/cm-'
FIG. 2. Another part of the same spectrum. Notations C. H and S as in Fig. lines of 2v$ - Y;; are only designated by K(J) for short.
337
6
I. As in Fig. 1. the ‘&(J)
394
GRANER
AND
WAGNER
FIG. 3. Part of the Q-branch region of the same spectrum. Same notations. We have not indicated certain number of weak transitions corresponding to “Q6 and “Q) of H and to ‘Qz and ‘Q4 of Z.
a
As explained in Ref (JO), there was not need in this case to use an elaborate model including the I( 2, - 1) resonance. So we worked with a simple program for unperturbed perpendicular bands, using 2 X 2 matrices and including only the I( 2,2) rovibrational interaction. The ground state constants used were those given in Table I of Ref. ( 20). In particular, Hz was fixed to 0. In the first stage, the diagonal term for the excited state was the usual one: (Jh-f(~(
JAI) = vlo + (A’ - B’)k’ - D;,J(
+ 1) - ‘(A<)&/
- D;J’(J
+ TJ( J + 1 )W + r&?
t H;J3(J+
+ B’J(J
J + 1 )k’ - Dik4
+ H&J’( The nondiagonal
+ 1)’ 1 )3
/ + 1 )‘k’ + Hk,,J( J + 1 )li” + H;-k6.
( 1)
term was:
(vrO = 1, J, k, Ito = +l IHI vIo = 1, J, k +- 2, /,. = +-1) = ;[J(J+
1) - k(k +- l)]“‘[J(J
+ 1) - (li k l)(li k 2)]“’
X [qiO + &J(J+
I) + q$J2(J+
I)‘+
q:,(X
f 2)‘].
(2)
Note that the q’s used in Eq. (2) are defined according to Cartwright and Mills (37) and are therefore four times larger than those of Ref. (20). In these formulas. X-is a signed quantity. Later we shall use K = ) kl . Then I takes implicitly the sign of k - 1. It was soon obvious that this model was not sufficient and that we had to add progressively to the diagonal terms of Eq. ( 1) the supplement { 7)J./.P(J + 1)’ + TjJKJ(J + 1 )k’ + ?j/&Y + TUXJ(J+
l)/Y4 + T],w@ + nKKKKP}lil.
(3)
PROPYNE
AT
395
30 pm
The first three terms of Eq. (3) have already been found to be significant by Wlodarczak ez al. (21) for propyne and also for H3GeF by Burger et al. (38, 39). They were also used, under the names of 0,. BJK, and ok., by Duckett et al. (40) and Halonen et al. (41). But we were forced to introduce also qKin- and ~~~~~ (since 7JKK was not found significant) in order to fit correctly the ‘Pi,, and ‘Pi I series: systematic deviations of several thousandths of cm -’ were obtained when these high-order terms were omitted. It is not unlikely that a qKKKK&“I term would have slightly improved the fits and helped to assign the elusive ‘PI2 series, but we balked at this extension. The second column of Table III lists the parameters obtained in our preferred fit. The standard deviation of this fit is 0.2 10 X 10v3 cm -‘. Note that among the H’s, only H;( -HZ was found significant. In the nondiagonal term (2), neither the (2 + 2)’ term nor the J2(J + 1)’ term was found to be significant. In fact, even with this model, there are a few systematic deviations. The ‘PI0 lines have positive deviations of 6 to 7 X 10m4 cm-’ and the ‘PII lines have negative deviations of 4 to 5 X 10m4 cm-‘. Moreover. even if we consider that the weak ‘“PI2 series is certainly overlapped in many places it is surprising that no line of this series
TABLE 111 Molecular
Constants
Determined
T
for v,” of Propyne
IR only 330.938
VI0
AC
IR + MW 55 (5)
330.93856
4. 7336522 1104)
4.7336548
A”
B’
B’
7.98653
D;
D,
2.478
(23) x IO 9
2.467 (131 x lO-9
D,
1. 779 (99) x IO-8
1.734 (62) x 10-R
1.434(120)x
I397
2. 1699 (431 x IO-3
D,-D;
k&H;
-2
2 1691 142) x 10-3
(711 x IO”
7 986OY (32) x IO 1
IO-”
162186~x10~
1 1139(19)X
10-z
I II47 IS) x 10-z 3.799 (14) x 10”
-7.00(55)X
IO-”
7 07 (2XJ x lo-”
-9.84Llbo)x
IO”’
I1 36 (27) x 10-10
I. 71 (34) x IO-’
I66
2 88 (31) x 1(k9
Errorr
g,ven bctwcen quored.
5 301X7)x 10-12
5.21 187) x 10-12
5.59894 (183) x IO4
5.59763 (122, x 10-I
Ground state cons,ants
arc three rrmdard
pxmheser
Expermental
unccrminty
x IO.*. D,,=S.45,17
1
I 820 (471 x IO 9
errors expressed
on the band center
are those gwen ,n 1201, namely
x IO-‘? UK=0
(34) P 10-T
2.83 131) x lW9
I.859 (67) x IO-9
dlgc
(II71 x 10-e
2.133 (821 x IO-R
3.799 (14) x 104
D,=9$0462
(41 (93)
A’.
D;,
HK,=1.769
(All in cm-‘)
I” ““!lr of the lasf
is about
0 CfNl2 cm-’
Ao=S 308410. B,=O.28S059769,
x 10’. D1=9.83 x In,
tI,=o.
H,,=3.018
I IO”.
GRANER
396
AND
WAGNER
could be found. It is to be noted that Wlodarczak et a/. (21) did not publish microwave transition for kl = - 10 or - 11 in the v10 = 1 state.
any
Discussion The fact that the high-order 7’s are only effective parameters is obvious when we compare the contributions of vlk-k3, vKA-k5, vKtikk7. and vKKKtik9 for k’ = 10 (corresponding to K-AK = -11). These contributions are 3.8 X 10-j. -1.7 X lo-‘, 2.9 X 10m2, and -5.3 X lop3 cm-‘, respectively, whereas one would expect a regular decrease of the contributions. The situation is clearly worse for k’ = 13, corresponding to KS AK = + 12. The values are now 0.83, -0.063,O. 18, and 0.056 cm-‘, respectively. We have tried to avoid the use of the high-order terms of Eq. (3) by introducing several interactions. (a)
We added the 1( 2, - 1) resonance
under the form
(u,~ = 1, J, k, I,,, = +I lHlur,, = 2rlo(2k
+ l)[J(J+
= 1, J, k + 1, Ilo = ?l)
(4)
1) - k(k t I)]“‘.
This term links levels which are rather far apart and do not cross, so that when the term rIo is let free, the fit diverges. If yIo is fixed to a certain value, it has a very small effect on the results of the fit. For instance, Yr. = 2 X lo-’ cm-’ gives a change of only 25 X 10m6 cm -’ on the predicted wavenumber of ‘P,?( 24), one of the transitions for which we expected an effect. Now, this value of VI0is much too large to be reasonable. In molecules where it has been determined, r, is usually of the same magnitude as cl, or even smaller. Cho et al. (42) pointed out that the contribution of the nondiagonal term (4 ) is equivalent to a small addition to diagonal parameters B’, .4’-B’, .4r, and 17/i. It is likely that, at a higher order, this contribution to the diagonal energy appears as the terms of Eq. (3). (b) Although the next vibrational state, v9 = 1, is farther apart (band center at 639 cm-l), for high enough K values, a level crossing occurs. Using constants from Ref. (43), the subband energies (i.e., for J = 0) of Ki = 9 and 10 of v9 = 1 are calculated at 949 and 1034 cm -‘, respectively, whereas the KI = - 10 and - 11 subbands of vro = 1 have energies of 926 and 1041 cm-‘, respectively. One could therefore imagine a resonance with Al = k2, Ak = + 1, and an interaction term quite similar to Eq. (4 ). We had hoped that such a term would improve the small systematic deviations of ‘PI0 and ‘PI,. This attempt was also negative. (c) We explored another possibility: that the effects observed were due to the constraint H,’ = 0. We fixed Hi to different values and fitted the data again. The standard deviation went to a minimum around H”k. = 2 X 10 +Gcm -I, which is not an unreasonable value, but ‘PII lines were still far off. Therefore we decided to keep Hi at zero for the moment. (d) A last possibility should be examined. Let us assume that the calibration factor used is slightly wrong so that the ‘PII (37 ) line at 300 cm ml and the RRI1 ( 35 ) line at 355 cm-r are in error by +2 X lop4 and -2 X 10e4 cm -‘, respectively. This could be compensated by adjusting the 7’s of formula (3). in this case by a change of r]J,
PROPYNE
1 X lo-” cm-’ that a calibration
AT 30
pm
397
on qJK, about 10% of its present value. It is therefore error is responsible for the observed effects.
very unlikely
These considerations show that we have more or less reached our limits. Further progress will depend not only on a better model but also on a determination of Hi and on a better calibration. In a last trial to detect any anomaly in our results, we fitted simultaneously our IR data and the rotational transitions in the ulo = 1 state published by the Lille group (21 ), the latter being given a weight of 5000. The results of this fit are given in the last column of Table III. They are essentially identical to those obtained with the IR data only. The rms deviation of the microwave data is 77 kHz, as compared to 64 kHz in Ref. (21). We also predicted a few high K rotational transitions in the hope of assigning new experimental microwave peaks. G. Wlodarczak and J. Demaison actually found in their archives a few of these lines, but for technical reasons they were not deemed good enough to be introduced in the fit. The lists of observed and/or predicted lines of uio are not given here to save space. They will be provided on request by the first author (G. Graner) .’ HOT
BANDS:
HOW
THEY
WERE
ASSIGNED
The assignment of the rovibrational transitions belonging to the hot bands entailed the use of three computer programs which will be briefly described. We were also guided by a gross estimate of the intensities to be expected. We shall come back to this point later. First Step: Program POLY In the first place, we looked for a series of lines with a reasonable spacing, compatible with the classical 2B values. When such a series was found, it was followed visually as long as it was clear. Then the wavenumbers of these lines were least-squares fitted to a polynomial in an arbitrary running number. Each line was weighted 1, 0.1, 0.0 1., or 0 as explained for uiO. Polynomials of increasing degrees were tried, with the provision that all parameters should remain statistically significant. The program can also detect the lines deviating by more than three standard deviations: these lines are automatically given a zero weight and a new run performed. When a satisfactory polynomial has been found, it is used for extrapolation on both sides of the series. As a result of this first step, we have at our disposal a series of typically 20 or 30 lines and the SD of the fits is usually 1 X 10m4 cm-r or less in the present case. For the next step, the lines with weights 0 or 0.01 are replaced by the smoothed values. This is very important for dense spectra like the present ones. Second Step: The Program TOUTHOT The program TOUT was written long ago to assign series in symmetric top spectra. It has been used with great success for many molecules including CH3Br (44), CHjFT (45). and CF3H (46). ’ A few copies are on deposit in the Editorial
office of the Journal
o/‘hfoleculur
.S~ectrosc’op?~
GRANER
398
AND WAGNER
TABLE IV Automatic Assignment of Series AUTOMATIC
ASSIGNMENT OF SE&IE_S_
A SERIES OF R LINES I- TRY
K,, FOR THE
IS FOUND:
J ?
I(
‘?
SERIES]
al TRY Ji, for the FIRST lmc J,, + I for the SECOND J,, + 2 for the THIRD L‘IZ...
I 10
hi ADD
Jg and “y agam. ? to Jo .lnd try agal”
cl ADD
?- TRY
K,j+I
FOR THE
e,c SERIES
31 k~lh J,,
il.5THERE
A CHOICE
WITH
@ IMI?
SUCCESS
?I
The principle of this program is explained in Table IV. It is based on the use of ground state combination differences (GSCD). which are often well known from microwave spectroscopy and/or other infrared bands. Program TOUT can be used with almost no change to assign hot bands of the general from v, + v,-vy,, where us is an .41-type mode. But. a new version called TOUTHOT had to be written for hot bands v, + vt- vl. where vt is an E-type degenerate mode, in the present case v, + vlo-vlO. The differences are the following: (a) Instead of GSCD, we must use lower state combination differences ( LSCD ). In the present case, they are differences among the rotational levels of VI0 = 1. Whereas the GSCD can usually be expressed analytically, the LSCD are obtained numerically from a list of energies. Such a list, calculated from Ref. (21). was kindly provided by G. Wlodarczak and J. Demaison. It was used for (vg + vlo)~2-v10 and (us + vlo)o-~,o in the 9-11 ,um region, and to initiate the present work. Later, we used the energies obtained by the present study of v l0. Since they are based on an accurate value of .4o (32), these energies are correct in absolute values and can be used among differem K values as well as among different J values. (b) The usual GSCD do not depend upon AK; i.e., RR - RP differences are identical to ‘R - ‘P or even QR - QP differences. On the other hand, LSCD depend on AK, or more precisely on the sign of I”, since the energy expressions ( 1) and (3 ) of the lower state explicitly contain 1. In other words, if a certain rovibrational level E’ of vlo = 2 or another excited state is reached by two transitions v,, = E’ ~ E” (v,” = 1, &,. K”, 1”) and vg = E’ - E” (v,o = 1. JB. K”, I”), the difference v,., ~ VB = E” 1. JR, K”, I”) E” (~10 = 1. J,4, K”. /“) is sensitive. not only to the J and (v10 = K” values, as usual. but also to the sign of I”. This point is important as will be shown later.
399
PROPYNE AT 30 pm
(c) A special situation occurs when the lower level of a transition is such that k”l” = 1. It is well known that such a level is split by the l(2. 2) resonance into an .4+ and A level (as usual A + is ,4 1 for J even and A, for J odd, and A _ assumes the opposite values). In most cases, the upper level of the transition will also be split in At and A- sublevels. The selection rules are A’ - A’ for P and R branches and .4+-Afor Q branches. Therefore two “families” of series are to be expected. as illustrated in Fig. 4. For the family with the A+ upper level. the Q series originates from an A- sublevel and the P and R series from an At sublevel, whereas it is the opposite for the other family. The program TOUTHOT had to be adapted to look also for these two types of families. Note that in the hot band ~v~~-u,~ the upper level in this case is k’ = I’ = 0. which is not split and has A+ symmetry. Therefore. only one “family” of 'P, , ‘Q, , and ‘R, series is expected and has been found. It is not the case in (4 + v,o)o-vlo, where the l-type vibrational resonance produces a splitting in h-’= 0.
Third S&p: The Program MILL1 An earlier version of this program was written long ago at Orsay and described in Ref. (44). It is a versatile least-squares program which deals with n interacting states of a symmetric top molecule, n being in principle as large as wanted. This program has now been used in several other universities. The latest versions enable us to fit simultaneously rovibrational transitions, purely rotational transitions in excited states, and excited state energies. An important restriction in the program is that the matrices which are diagonalized are of limited size (usually blocks with the same value of li - I). When interactions are such that “infinite chains” occurs, the recourse to other programs with one single matrix for each J value (later factorized in symmetry blocks) becomes compulsory as it was the case for CH3F (47) and CF3H (48). Nevertheless, in moderately perturbed level systems, some modifications enable us to still use MILLI: they are equivalent to using truncated matrices.
v,,=2
k=l=2
AA+ V
,o=l
k=l=l
AA+
--+
AAt
+
FIG 4. Scheme of the levels involved for any (v, + v,.)+*-VT’ transition.
in the K. AK = 1 subbands
of 2u&- IJ~(!.The same scheme is valitl
22 23 24 25 26
2
19
18
9 10 11 12 13 14 15 16 17
40 41 42 43 44 45 46
zt %
z: 33 34 35
z! 29 30
24 25 26
19 20 21
is
10 11 12 13 14 15 16 17
9
i
RR7 334.971902 335.557524 336.144764 336.733729 337.323956 337.915831 338.509572 339.104610 339.701327 340.299515 340.899364 341.500818 342.103513 342.708248 343.314424 343.922220 344.i31448 345.142264 345.754663 346.368642 346.984122 347.601211 348.219830 348.840070 349.461809 350.085128 350.709866 351.336347 351.964396 352.593749 353.225138 353.857914 354.491781 355.128595 355.764790 356.403652 357.044094 357.686021 358.328696 358.975121 RP7 325.259907 324.702766 324.147062 323.594097 323.041948 322.491346 321.943671 321.395859 320.850450 320.306601 319.764481 319.223742 318.685292 318.147873 317.612199 317.078664 316.546209 316.015837
0.00 0.00 1.00 0.00 0.00 0.W 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.10 I.00
1.00 1.00 I.00 1.00 1.00 0.00 0.W 0.00 1.00 1.00 1.00 0.00 0.00 1.00 0.00 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 1.00 0.00 1.00 0.00 l.w 1 .W 0.00 0.W
zi 39 40
% 36
32 33
2
;: 28 29
E 24 25
;:
8 9 10 11 12 13 14 15 16 17 18 19
i;: 39 40 41 42 43 44 45 46 47 48
zz 36
33
314.434437 313.910148 313.388032 312.867613 312.349403 311.831985 311.316536 310.603251 310.291322 309.781152 309.272184 308.765353 308.260498 307.757083 307.254833 306.755655 306.257756 305.762016 305.267ooO 304.774399 RQ7 330.401171 330.415810 330.431773 330.449530 330.468510 330.488930 330.512180 330.535769 330.561661 330.568222 330.617418 330.648106 330.680127 330.713421 330.748855 330.785987 330.824162 330.663996 330.906026 330.949559 330.994580 331.040474 331.089329 331.139499 331.190679 331.243487 331.298483 331.354628 331.412849 331.472478 331.533818 331.596618 331.661048 RR6 333.849831 334.434136 335.019876
314.960070
315.486669
1 1 1
.oo .w .w
0.10 0.10 I.00 0.00 0.00 0.00 0.00 0.00
0.W 0.W
.w
.oo
1 .OO 0.00 0.00 0.00 0.00 0.00 0.10 1 .oo 1 0.10 1.00 1 .w 1 1.00 0.10 0.00 1.00 0.00 0.10 1.00 0.W
0.00 0.00
::
;i 25 26 27 28
;:
11 12 13 14 15 16 17 18 19 20
10
:
:: 43 44
% 40
::
zz
:: 31 32 33
zl
;:
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
9
Transitions 0.10 0.00 0.00 0.00 0.10 0.10 0.00 0.00 0.10 0.00 0.10 0.00 0.00 0.00 1 .W 0.00 0.00 0.01 0.00 0.00 0.00 0.00
Assigned 335.607533 336.196151 336.786662 337.370755 337.972369 338.567660 339.164460 339.762691 340.362907 340.964398 341.567627 342.172237 342.778616 343.386345 343.995745 344.606714 345.219263 345.833393 346.449082 347.066361 347.685231 348.305650 348.927629 349.551229 350.176346 350.802778 351.430474 352.060076 352.691531 353.323555 353.958153 354.594200 355.232790 355.871WO 356.511718 357.153575 RP6 325.278855 324.719826 324.162826 323.607797 323.053758 322.501628 321.951429 321.402299 320.855120 320.309251 319.765731 319.223742 318.682762 318.143943 317.606164 317.071co4 316.536795 316.004655 315.473986 314.944667 314.417777 313.891688 313.368068 0.00 0.00
0.00
0.00 0.00
0.00
0.00
0.00
0.10
0.00
0.00 0.00 0.00 0.00 0.00 0.00
0.00
0.00 0.00 0.00
0.00
0.00
0.10
0.00
0.00
0.00
0.00
0.00
1.cm
.w
1 .w 1 .w 1 1 .w 1 .co 1 .w 1 .w 0.10 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
i .oa 1.oo
0.00 1.00 1.00 1.00
:1:
11 12 13 14 15 16 17 18
10
::
7
41 42 43 44 45 46 47 48
31 32 33 34
330.705479 330.760379 330.817019 330.875159 330.934969 330.996409 331.059479 331.124299 RR5 332.725548 333.308090 333.692399 334.478238 335.065781 335.654697
312.845590 312.326139 311.805896 311.288883 310.773330 310.259953 309.747749 309.237081 308.728917 308.221049 307.716166 307.213WO 306.713200 306.211574 305.713419 305.217000 304.722425 304.229564 RQ6 329.849890 329.862680 329.677638 329.892562 329.910909 329.93m 329.950780 329.972970 329.997320 330.022590 330.049840 330.078792 330.109140 330.141139 330.175020 330.210030 330.247380 330.285330
I.00 1.00 1.00 I.00 0.00 1.00
0.00 0.00 0.00 0.00 0.00 0.00 0.M) 0.00
0.w 0.00 1.00 I.00 0.00 0.00 0.00 0.00 0.10 0.00 1 .w 0.10 0.00 1.00 0.10 1 .w 0.10 1.00
0.00 0.00 0.00 0.00
0.00
.w
1 .W 0.00 0.00 0.00 1 .w 0.00 1.00 0.10 1 1.00 0.00 0.w 0.00
9 10 11 12 13 14 15 16 17 18 19 20 21 93 2: 24 25 26 27 28
316.525835 315.991785 315.459219 314.928630 314.399596 313.871998
321.407326 320.857859
.z
46 47
336.245639 336.837603 337.431371 338.026556 338.623629 339.222135 339.822281 340.423849 341.027175 341.631865 342.238182 342.846610 343.455938 344.066735 344.679374 345.293573 345.909323 346.526632 347.145521 347.765791 348.387740 349.011380 349.636265 350.263021 350.891538 351.521108 352.152945 352.785727 353.419905 354.056OW 354.694600 355.333277 355.973743 356.616249 357.26WW 357.904602 358.552283
in the ?.u$- vf; Hot Band of Propyne
TABLE V
.cm
1 .w
i:&j 1.00 1.00 O.io 1.00 0.00
o.% 0.10
0.00 0.W
0.00 0.00
::$Z 0.00 0.00 0.00 0.00
0.10 0.10
o”:E 0.10
0.00
0.00
0.00 0.00 0.00 0.00 0.00
EZ
0.w 0.00
1
1.00 1.00 1.00 l.w 1.00 1.00 0.00
1.00
0.00
10
:
7
6
4 5
:i 40
::
::
z:
;tJ 30
;z 26 27
;:
F?
i 10 11 12 13 14 15 16 17 ia 19
6 7
ii 39 40 41 42 43 44 45
:z 36
33
:: i:
313.346237 312.822079 312.299739 311.778830 311.259731 310.742997 310.226952 309.712672 309.200683 308.689913 306.181584 307.674161 307.168615 306.665ooO 306.162706 305.662619 305.164343 RQ5 329.296091 329.307363 329.320441 329.334511 329.350507 329.368051 329.388105 329.407641 329.430551 329.454043 329.480304 329.507361 329.535784 329.566831 329.598641 329.632802 329.667610 329.704851 329.742934 329.783300 329.824870 329.867770 329.913490 329.959720 330.008460 330.057590 330.108980 330.161810 330.217080 330.273600 330.331760 330.390750 330.452830 330.579169 RR4 331.597686 332.178838 332.761793 333.346156 333.932014 334.519493 335.108749 0.00 I.00 1.00 1.00 I.00 1.00 1.00
0.00 I.00 0.W 0.00 I.00 0.00 0.10 0.10 0.00 1.00 1.00 0.00 0.10 0.00 0.10 0.10 0.00 0.10 ,.W 0.00 0.00 0.00 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.W 0.00 0.00 0.00 0.00
0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.10 0.00 0.00 0.00 1.00 0.00
11 12 13 14 15 16 17 18 19 20 21 22
10
9
51 52
49 50
‘ii
40 41 42 43 44 45 46 47
z:
35 36 37
;: 23 24 25 26
::
11 12 13 14 15 16 17 18
324.747399 324.187606 323.628857 323.071578 322.516008 321.962199 321.410169 320.858840 320.310231 319.763131 319.217261 318.672638 318.130268 317.589371 317.050193 316.512498
325.309919
336.291593 336.885602 337.480788 338.077858 338.676432 339.276530 339.878379 340.481529 341.086358 341.692747 342.300687 342.910206 343.521295 344.133905 344.748094 345.363823 345.981523 346.600512 347.220261 347.842001 348.465590 349.090749 349.717359 350.345448 350.975177 351.606307 352.239056 352.873305 353.509606 354.147182 354.786077 355.425912 356.068944 356.712451 357.357613 356.004310 358.653132 359.302423 359.954592 360.607717 361.262895 RP4
0.00 1.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 1 .co 0.00 1 .oo 1 .W 0.00 1 .W 0.00
1.00 1.00 1 .W 1 .W 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1 .W 1 .oo 1.00 1 .W 0.00 0.00 l.W 1.00 0.00 0.00 0.00 0.00 0.00
1.00
0.00
335.699370
27 28 29 30
E 22 23 24
11 12 13 14 15 16 17 18 19
E 10
i
5 6
:: 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55
36
315.977164 315.442586 314.910057 314.378987 313.849608 313.321968 312.795709 312.271448 311.748864 311.227147 310.707602 310.189990 309.674069 309.159735 308.647008 308.136134 307.627030 307.118890 306.613067 306.109939 305.607402 305.106670 304.607103 304.11W30 303.615OOO 303.122COO 302.628895 302.138688 301.650380 301.163784 300.678658 300.196344 299.716852 RQ4 328.739631 328.748897 328.760490 328.773146 328.787571 328.803291 328.821231 328.840455 328.860791 328.683503 328.907286 328.933044 328.960241 328.988711 329.019541 329.051572 329.084831 329.120078 329.157546 329.195871 329.235721 329.277691 329.320441 329.365031 329.411781 329.459731 329.560101 329.613411 329.667602 329.724327 329.781410 329.840977 329.902124 329.964072 330.028742 330.093982 330.1615W 330.230589 330.301688 330.373535 330.448902 330.523688 330.601200 RR3 330.467075 331.046141 331.627868 332.210750 332.795101 333.380830 333.968482 334.557767 335.148671 335.740766 336.334760 336.930203 337.527192 338.125761 338.725861 339.327510 339.930659 340.535399 341.141658 341.749447 342.358787 342.969626 343.581995 344.195885 344.811304 345.428213 346.046683 346.666642 347.288131 347.911271 348.535630 349.161669 349.789228 350.418288 351.048872 351.681076 352.314616 352.949698 353.586305 354.225295 354.864212
.w
0.00
0.00
0.00
0.00
0.00
0.00 0.00 0.00 0.00
0.00
0.00 0.00 0.00
0.00
1
0.00
0.00 0.W 1 .w
0.00
0.00
0.00 0.00
0.00
0.00
I.00
0.00 0.00 1.00 0.00 0.00 0.00 1.00 1.00 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 I.00 1.00 1.00 1.00 0.00 0.00
0.00
0.00
0.00
0.00
10 11 12 13 14 ii 16 17 18 19 20 21 22 23
9
2
3 4
40 41 42 43 44 45 46 47 48
329.508551
0.00
0.00
0.00
I.00 0.00 0.00 1.00 1.00 0.w 1.00 1.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.w 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.w 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 1 .w 0.00 0.00 l.W 0.00 0.00 0.00 1.00 0.00 0.00 1.00 0.00
0.00 0.00 0.00
0.00
13
ii
: 10
z: 33
E
E 25 26 27 28
:: 21 22
15 16 17 18
44 45 46 47 48 49 50
355.505634 356.148482 356.792217 357.438600 358.086159 358.735300 359.386407 RP3 325.321975 324.758256 324.196116 323.635727 323.076798 322.519238 321.963909 321.410159 320.857830 320.306601 319.757551 319.209751 318.663859 318.119571 317.576504 317.035784 316.496124 315.958150 315.421927 314.887027 314.354202 313.822571 313.292747 312.764581 312.237759 311.712976 311.189450 310.667931 310.147414 309.628821 309.112043 308.596233 308.081876 307.570985 307.060752 306.551787 306.045106 305.539832 305.035900 304.534134 304.033733 R03 328.180092 328.188602 328.197822 328.209112 328.221803 328.236122 328.252082 328.269422 328.288627 328.309762 0.00
0.10
0.10
0.00 0.00
.w
0.00 0.00 1
0.00
0.00
0.00 0.00 1 .w 1.00 1.00 1.00 0.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.10 0.00 0.10 1.00 0.00 1.00 0.10 1.00 0.10 1.00 0.00 1.00 1.00 0.00 1.00 0.00 0.00 0.00
0.00
0.10 0.00 0.10
0.00 0.00 0.00
0.00
0.00
1.00 0.00 0.00 0.w 1.00 0.00 0.00
10 11 12 13 14 15 16 17 iS 19 20 21 22
9
5 6 7 a
4
:: 39 40
:z 36
:: 33
z: 27 28 29 30
;:
z:
14 15 16 17 18 19 20
330.491 331.072089 331.654788 332.239023 332.825101 333.412596 334.001846 334.592225 335.184024 335.778474 336.373533 336.970302 337.568542 338.168241 338.769311 339.372010 339.976039 340.581479 341.188628 341.796567 342.406217 343.017402 343.629875 344.243555 344.859038 345.475470 346.093882 346.713122 347.334245 347.956122
329.334201 329.912090
328.331778 328.355842 328.381752 328.408452 328.436902 328.467812 328.499702 328.532482 328.567792 328.604382 328.842282 328.681832 328.722911 328.765691 32a.810061 328.856331 328.903721 328.953096 329.003221 329.055611 329.109250 329.164192 329.221381 329.279881 329.339971 329.402081 329.465001 RR9
loo
.w
1.00
1 .w 0.00 1.00 0.00 0.00
0.00 0.00
1
0.00 0.00 0.00 0.00
0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.w 0.00 0.00
0.00
0.00
0.00
0.W
0.00
1.cm 0.10 0.00 0.00 0.00 0.10 0.00
1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.10 1.00 1.00 0.00
ET 52
z 39 40 41 42 43 44 45 46 47 48 49
z:
z; 34
z’:
;:
;;
;z
;:
;:
.z. 9 10 11 12 13 14 15 16 17 18 19
:
4
41 42 43
324.766646 324.202736 323.639847 323.079148 322.52oooa 321.962719 321.406719 320.852206 320.299444 319.748535 319.198843 318.651065 318.104852 317.559834 317.016134 316.474284 315.933480 315.394946 314.856891 314.321025 313.786648 313.253267 312.721560 312.191493 311.682960 311.136071 310.609521 310.085401 309.562652 309.041228 308.521491 308.003414 307.486695 306.971775 306.458436 305.946100 305.436247 304.927871 304.420760 303.915500 303.412595 302.911417 302.412668 301.915321 301.419898 300.926804 300.435619 299.947211
325.329615
-
351.088817 351.719720 352.351981 352.985852 353.621500 354.258900 RP9
348.579859 349.204849 349.831468 350.459720
1
.w
0.10 0.10 1 .w 0.00 1 .w 1.00 0.10 0.00 0.00 1.00 1.00 0.00 0.00 1.00 0.10 1.00 1.00 0.00 0.00 0.00 0.00 0.10 0.00 0.00 1.00 0.00 1.00 1 .w 0.00 0.10 0.00 0.00 0.00 0.00
1.w 0.10 0.10 0.00 0.00
0.10 1 .oo 1 .w
0.00
0.00
0.00
0.00
0.00 0.00 0.w
0.10 0.00 1.00 1.00 1.00 0.00 0.00
0.00 0.10
E
11 12 13 14 15 16 17 18 19
IO
9
8
6 7
6
;4” 25
$7 22
12 13 14 15 16 17 18 19
320.808391 320.247217 319.687656 319.128851 318.571337 318.014943 317.459524 316.905279 316.351985 315.799826 315.248808
299.461OCO RQ2 327.619063 327.625223 327.632703 327.641823 327.652993 327.665113 327.679466 327.695498 327.712611 327.731441 327.752233 327.774793 327.798192 327.823462 327.850202 327.878182 327.907632 327.938702 327.970982 328.005192 328.040842 328.076873 328.115474 328.155282 328.196452 328.238262 328.282972 328.328770 328.375102 328.423382 328.473182 328.524318 328.576942 328.631052 328.686742 326.744511 326.803291 328.863231
0.10 0.00 1.00 1.00 1.00 0.00 0.00 0.00 0.00 0.00 1.00
ii 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57
0.00 0.00 0.00 0.00 0.00 0.00 1.00 I.00 1.00 0.10 0.10 0.00 0.W 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.10 0.00 0.00 0.00 0.00 0.10 0.10 0.00 0.00 1.00 0.10 0.00 0.00 0.00 0.00 0.00
li 15 16 17 16 19 20 21 22 23 24
: 4
22
0.00
1
298.193143
297.164669 296.652420 296.140668 I?01 3271053503 327.059733 327.068153 327.078235 327.091533 327.106823 327.123943 327.142863 327.164579 327.168261 327.213783 327.241583 327.271900 327.304083 327.338513 327.375743 327.413863 327.455152 327.497288 327.543365 327.590403 327.640268 327.691848
297.678635
0.00
298.709303
.w
0.W
0.00
0.00 0.00 0.00 0.00
0.00
1 .oo 0.00 0.00 0.00
0.00 0.00
0.00
1.00
0.00
0.00
0.00
0.00
1
0.00 0.00 0.00
0.00 0.00 0.00
.w 1 .w
0.00
I.00
0.00
0.00 0.00
0.00
l.W
0.00
I.00 I.00 0.00 1 .w
0.00
0.00 I.00 I.00 I.00
0.00
I.00
0.00
I.00 1.00
1.00
0.00 0.00
l.w
0.00
1 .w 0.10 0.00
314.699W5 314.149989 313.602078 313.055381 312.509729 311.964267 311.421767 310.879411 310.338207 309.797942 309.258888 308.720913 308.184471 307.648226 307.113570 306.579907 306.047516 305.516154 304.985635 304.456698 303.928703 303.401135 302.875852 302.351276 301.827689 301.304916 300.783788 300.262992 299.744400 299.226099
41 42 43
IO 11 12 13 14 15 16 17 18 19 20 21 22 23 24
11 12 13 14 15
40 41 42 43 44
2; %
;: 23
::
10 11 12 13 14 15 16 17 16
i i
:z 47 48
44
322.537257 321.983536 321.433030 320.882529 320.336095 319.792135 319.250412 318.710625
323.092969
353.828968 354.446377 355.064505 355.682956 356.301817 356.922466 357.543875 358.165852 358.789387 RR1 330.517040 331.104435 331.692779 332.283710 332.877221 333.472296 334.069798 334.669925 335.272082 335.876984 336.484295 337.093973 337.706220 338.320831 338.937945 339.558462 340.181798 340.806698 341.435048 342.066304 342.700511 343.337289 343.977472 344.620583 345.266678 345.916307 346.568503 347.224141 347.883071 348.545300 349.210815 349.879610 350.552228
TABLE V-Contimtrd 327.745234 327.801002 327.858952 327.919072 327.981482 328.045692 328.112450 328.180100 328.251502 328.324796 328.399569 328.476509 328.555516 328.636342 328.720011 328.805491 RR1 328.194712 328.769871 329.345909 329.922936 330.502142 331.080581 331.659711 332.242347 332.825101 333.408737 333.993525 334.579212 335.165769 335.752804 336.341613 336.930573 337.521452 338.113001 338.705561 339.299071 339.893791 340.489064 341.085508 341.682909 342.281141 342.680978 343.481191 344.082154 344.683807 345.287705 345.891983 346.496810 347.102681 347.709616 348.317864 348.926189 349.535799 350.146522 350.758521 351.370682 351.984193 352.596817 353.213328 0.10 0.10 0.10 0.10 0.10 1.00 1.00 0.00 0.10
0.00 0.10 I.00 1.00 0.00 0.00 0.10 0.00 I.00 0.00 1.00 0.00 I.00 0.00 0.00 1.00 0.00 0.00 0.00 1.00 I.00 1.00 0.00 1 .OO 1.00 0.10 1.00 0.00 0.00 0.00 1.00 0.10 0.00
1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
24 25 26 27 28 29 30 31
1: 11 12 13 14
i
6
:: 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
16 17 18 19 20 21 22 23 24
327.066603 327.074323 327.083383 327.092903 327.103910 327.116291 327.129223 327.143813 327.159363 327.176494 327.195013 327.214973 327.236303 327.258763 327.282951 327.309703 327.336985 327.366283 327.397680 327.430793 327.465163 327.501604 327.540651 327.581215 327.623483 327.668073
RQ1
318.173687 317.639573 317.107590 316.577879 316.051210 315.527424 315.006118 314.487732 313.972209 313.459608 312.950511 312.443509 311.939821 311.439210 310.941948 310.448121 309.957882 309.469972 308.985903 308.505390 308.028003 307.554391 307.084155 306.617318 306.154638 305.694763 305.238942 304.787586 304.338184 303.893300 303.452444 303.015000 302.580480 0.00 0.00 0.10 0.00 1.00 0.10 0.10 0.00 1.00 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.10 0.00 0.10 0.00 0.00 0.00 1.00 0.10 0.00 0.W
1.00 0.10 0.10 1.00 0.10 0.00 1.00 I.00 1.00 1.00 0.00 0.00 1.00 1.00 0.00 0.00 0.10 0.00 0.00 1.00 0.10 1.00 0.00 1.00 0.00 0.10 1 .oO 0.10 0.00 0.00 0.10 0.00 0.00
:
45 46 47
;: 23
::
11 12 13 14 15 16 17 18
326.509190 326.512430
ROO
327.715370 327.763908 327.815472 327.869362 327.925122 327.983282 328.044262 328.107642 328.173352 328.241772 RPO 325.365760 324.797300 324.230440 323.665190 323.101560 322.539751 321.979306 321.420631 320.863626 320.309256 319.755534 319.204164 318.654611 318.107130 317.562231 317.018553 316.477790 315.938797 315.402352 314.868045 314.336388 313.807203 313.280655 312.756768 312.235795 311.716883 311.201343 310.688385 310.178687 309.672005 309.167668 308.667018 308.169020 307.674161 307.182740 306.694060 306.209137 305.726429 305.247543 304.771970 304.299190 303.829470 303.362780 302.899060 302.438250 301.980280 0.00 0.00
0.00 0.00 0.00 0.M) 0.00 0.01 1.00 1.00 I.00 0.01 1.00 1.00 I.00 0.01 0.01 0.01 0.10 I.00 0.05 0.10 1.00 1.00 1.00 1.00 0.10 0.10 0.10 1.00 1.00 0.10 0.01 0.10 0.00 1.00 0.00 0.10 I.00 0.01 0.10 0.00 0.00 0.00 0.W 0.00 0.00 0.00
1.00 1.00 0.00 0.10 o.cKI 0.00 0.00 0.00 0.00 0.00
10 11 12 13 14 -
:
5 6
40 41 42 43 44 45 46
39
58
;z
11 12 13 14 15 16 17 ii 19 20 21
32:R:go280 327.080410 327.655860 328.232860 328.810830 329.390220 329.972230 330.554490 331.139489 331.725490 332.313700 332.902838 333.494450 334.087650 334.683157 335 280440
326.517260 326.523690 326.531673 326.541001 326.552228 326.565590 326.579819 326.596532 326.614970 326.634710 326.657039 326.680697 326.706320 326.734509 326.764747 326.796948 326.831456 326.867680 326.907140 326.948600 326.992690 327.039190 327.088350 327.140300 327.195ooO 327.252260 327.313236 327.375750 327.441711 327.510666 327.582340 327.657080 327.735150 327.815464 327.900333 327.986809 328.076873 328.170310 328.266400 328.365450 328.467820 328.572270 328.679910
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.10 0.00 0.00 0.01 0.00
1 .oo 1 .w 0.00 0.00 0.10 l.W 1.00 0.10 0.10 0.10 0.10 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 1 .w 1.00 0.00 0.00 0.00 0.01 0.10 1.00 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00
0.10
l.w 0.01
0.00 0.00
:z 27 28
2’: 23 24
zl 9 10 11 12 13 14 15 16 17 16 19 20
3 4 5 6
:
2; 39 40 41 42 43 44 45
36
z: 33
::
;: 27 28
23 24
2
15 16 17 18 19 20
336.480680 337.083820 337.689492 338.297200 338.907008 339.519703 340.134594 340.751340 341.370945 341.993350 342.618195 343.246086 343.877121 344.509695 345.145460 345.783976 346.426285 347.070924 347.718386 348.369020 349.021702 349.678284 350.337028 350.998887 351.663592 352.331491 353.003410 353.676910 354.353110 355.031930 PPl 325.343847 324.773761 324.205287 323.638446 323.072230 322.509583 321.948112 321.388201 320.829995 320.274458 319.720313 319.168462 318.619024 318.071866 317.527885 316.984685 316.444757 315.908026 315.373880 314.840885 314.313459 313.786643 313.264642 312.744833 312.227429 311.712976 311.201343 310.693480
335.879170
0.00 1 .w 0.00
0.00
.w
0.00 1
0.10
0.10 0.00 1.00
1.00
0.00 0.00 1.00 0.10 0.10 0.00 0.00 1 .w
1.00
1.00
0.00
0.10
0.00 0.00 0.00 0.00 0.00
327.063930 327.640268 328.216828 328.797258 329.379940
310.188080 309.684409 309.184921 308.686943 308.192507 307.701567 307.212627 306.726768 306.243400 305.762016 305.284449 304.810193 304.338184 303.868400 303.401335 PO1 325.917125 325.920710 325.924878 325.931482 325.939779 325.949717 325.961396 325.975166 325.990484 326.008249 326.027592 326.050032 326.073892 326.100897 326.129429 326.160781 326.195211 326.232150 326.271570 326.314021 326.358640 326.407106 326.457136 326.511699 326.567349 326.626886 326.688856 326.753885 326.821609 326.891164 326.963925 327.039191 327.117700 327.198800 327.282951 327.369WO 327.458WO 327.549400 D!al 0.00 0.00 0.00 0.00 0.10
0.00 0.00 0.00 0.10 0.10 0.00 0.00 1.00 0.10 0.00 I.00 0.10 1.00 0.00 0.00 0.10 1.00 1.00 0.00 1.00 1.00 0.10 0.10 0.00 0.00 1.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00 0.10 1.00 0.00 0.00 0.00 1.00 0.w 0.00 0.w
: 10 11 12 13 14 15 16 17
6 7
: 9 10 11 12 13 14 15 16 17
6
0.00
1.00 l.W 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
1.cKl
0.00 0.00 0.00 0.00 1.00 1 .w 1.00 1 .w 1.00 1.00
.w
1 .w 1 0.00 1 .m 1.00 l.W 0.00 0.00 0.00 0.00 0.00 0.w 0.10 0.00 0.10 0.00 0.00 0.00 0.00 0.00 0.10
0.00
.oo
0.00 1 0.00 1 .w
0.00
0.00 0.00
0.00
0.00
330.548294 331.135527 331.725492 332.315065 332.908725 333.504407 334.102613 334.704031 335.305838 335.910591 336.519167 337.129957 337.743239 338.359751 336.978543 339.599981 340.225446 340.851637 341.480905 342.113830 342.749296 343.386350 344.026940 344.669665 345.316100 345.964355 346.616020 347.268800 347.924800 348.583ow 349.243999 PP2 322.499988 321.935259 321.372359 320.810708 320.251835 319.694111 319.137745 318.582928 316.029527 317.477364 316.926294 316.376329 315.827734 315.280140 314.733357 314.187955 313.643224 313.099371 312.556668 312.013760 311.472220 310.931451 310.391411 309.852052 309.313443 308.775841 308.238224
329.964072
7
2
3 4
; 10 11 12 13 14 15 16
::
64
:: 50
46 47
4”:
._
40 41 42 dl
37
34
2 :,”
307.701567 307.165775 306.630550 306.096106 305.562377 305.029301 304.497144 303.965737 303.435161 302.905560 302.376608 301.848722 301.321625 300.795635 300.270565 299.746272 299.223161 29a.7wsa3 298.179853 297.659991 297.140925 296.622722 296.105963 295.590118 295.075699 294.562122 294.049700 293.538667 293.028605 292.519740 292.012194 291.505432 291 .oooO64 290.495697 289.992339 PO2 325.349638 325.358075 325.364905 325.373605 325.383920 325.396181 325.409781 325.425338 325.441635 325.459605 325.478777 325.499512 325.520769 325.542852 325.567012 325.590995 325.616985 325.642895 325.669344 325.697365 325.725791 325.755490 325.785585 325.816135 1
.w
1.00 0.00 0.w 0.00 0.00 0.00 0.w 0.00 0.00 0.00 0.00 0.00 0.00 1 .w 0.00 0.00 0.00 0.00 0.00 0.00 1.00 1.00 1 .w 1 .w
1.00 0.w 0.00 1 .w 1 .w 1 .w 1 .w 1 .w 1 .w 1 .w l.w l.w 1 .w 1 .w 1 .w 1 .w 1 .W 0.00 0.00 1 .w 1 .w 0.w 1 .w 1 .w 0.00 1 .w 1 .w 1 .w 1 .w 1 .w 1 .w 0.00 0.00
0.00
46 47
ii
39 40 41 42 43 dd
10 11 12 13 14 15 16 17
9
32zoa724 327.644543 328.223002 328.603291 329.385501 329.968910 330.554209 331.14oaos 331.728888 332.318298 332.908725 333.500533 334.093419 334.687105 335.281864 335.877564 336.474351 337.071343 337.669019 338.268603 338.867895 339.467845 340.068731 340.669742 341.271603 341.873406 342.476246 343.079850 343.683746 344.288151 344.892727 345.498253 346.104244 346.710981 347.317717 347.925649 348.533982 349.142755 349.7523w 350.362533 350.973400 351.585027 352.197300 352.810489 353.423867 354.039124
325.846566 325.878705 325.911298 325.944105 325.977899 326.011424 326.046704 326.082104 326.117714 326.154614 326.192214 326.230294 326.269084
.w
1 .w 1 1 .w 0.00 1 .w 0.00 0.00 1 .w 1 .w 1 .W 1 .w 0.00 1.00 1.00 1.00 1.00 0.00 1.00 0.00 1 .w 0.00 1 .w 0.00 1 .w 0.00 0.00
0.00
1.00 0.00
0.00 0.00
0.00
0.00
1 1 0.00
.w .w
0.00
0.00
0.00
0.00
0.00
0.00
0.00 0.00 0.00
0.00
0.W
0.00 0.00
0.00
0.00 0.00
0.00
0.00
1 .oo 0.00 0.00
0.00 0.00
354.654098 355.270191 355.886517 356.504703 357.122107 357.741669 358.362502 358.983456 PP3 323.051438 322.484326 321.918470 321.355295 320.792980 320.232501 319.673631 319.116352 318.560651 316.006536 317.453942 316.902974 316.352576 315.804831 315.256153 314.712750 314.168877 313.626321 313.084997 312.545417 312.006682 311.469330 310.933221 310.396511 309.864552 309.332063 308.800623 308.270294 307.212627 307.740964
306.685216 306.159252 305.634201 305.109287 304.585904 304.063489 303.541269 303.020554 302.500520 301.981676 301.463135 300.945269 300.427912 299.912300 299.397m 296.682793 298.369751 297.856900
296.833525 297.344632
296.323430
3 4 5 6 7 8 9 IO 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 ::
33 34 35 36 37 36 39 40 41 42 43 44 45 46 47 46 49 50
::
53
48 49 50 51 52 53 54 55
0.10
0.00 1.00
0.10 1.00 0.00 0.10 1.W I.00 0.00 1.W 0.10 0.01 0.10 I.00 0.01 0.00 0.00 0.00 0.10 0.10
0.00 I.00 0.10 0.00 0.00 0.00 0.00 0.00 0.10 1.00 1.00 1.00 0.10 1.00 1.00 1.00 I.00 I.00 0.10 1.00 1.00 0.00 0.00 1.00 0.10 0.00 0.00 0.00 1.00
0.00 1.00 0.00 0.00 0.00 0.00 1.00 1.00
15
14 13
3 4 5 6 7 8 9 10 11 12
34 35 36 37 38 39 40
15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 33 32
9 10 11 12 13 14
3 4 5 6 i
54 55 56 57 58 59 60
334.114811
333.519293 332.925582
325.618515 325.663375 325.710095 325.756845 325.804145 325.853315 325.902045 PR3 327.062783 327.642223 328.222912 328.805371 329.389441 329.975040 330.561661 331.150789 331.740891 332.332558
324.947430 324.972569 324.998075 325.025674 325.053516 325.083265 325.114575 325.146675 325.180125 325.215155 325.250655 325.287517 325.324926 325.364042 325.404245 325.445030 325.487194 325.573655 325.530309
295.614174 295.305406 294.797813 294.290718 293.784795 293.279836 292.775109 PO3 324.770516 324.777043 324.784096 324.793666 324.804666 324.817276 324.631471 324.847422 324.864325 324.883173 324.903426 324.923842
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 24 23 25
0.00 0.W 1.00 0.00 0.00 1.00 0.00
1.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 1.W 0.00 I.00 0.00
0.00 1.00 0.00 0.00 0.00 0.00 0.10 0.10 I.00 0.10 0.00 0.10 1.00 1.00 0.10 I.00 0.00 0.W 0.00 0.00 0.00 1.00 0.00 1.00 1.00 0.10 0.00 0.00 1.00 0.00 1.00
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 4
0.10 I.00 1.00 0.10 1.00 0.10 0.00
310.361198
310.895749 311.431777
0.10
0.10 0.10 0.10 I.00
0.00 1.00 1.00 1.00 1.00 0.10 0.00 0.00 0.00 0.01 0.01 0.10 1.00 1.00 I.00 I.00 1.00
28
4 5 6 7 8 9 10 11 12 13 14 15 16 17 16 19 20 21 22 23 24 25 27 26
35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
31 32 33 34
0.00 0.00 0.W 0.10 0.10 0.00 0.00 0.00 0.00 0.00 0.10 0.00 0.00 0.10 0.00 I.00 1.00 0.10 1.00 0.10 0.00 0.00 0.00 0.00 1.00 0.10 0.00 0.00 l.CO 0.10 0.00 0.00
26 27 26 29 30
1.00 I.00 0.00 1.00 0.00
306.087989 304.567818 304.048611 303.529849 303.012977 302.497155 301.982Wl 301.468030 300.954977 300.442609 299.932165 299.422243 298.913089 298.405156 297.897413 297.392020 296.886272 296.381935 295.678652 295.375699 294.873922 294.373000 293.873466 293.374052 292.675426 PO4 324.192186 324.2OW86 324.209837 324.221146 324.233956 324.247696 324.263256 324.280776 324.299636 324.319864 324.342375 324.365354 324.391041 324.416516 324.444536 324.473646 324.503922 324.536291 324.569656 324.604526 324.640405 324.678157 324.717143 324.757096 324.797166
307.708804 307.182225 306.657110 306.132897 305.610057
309.627901 309.296520 308.765360 308.236634
TABLE V--Continued 334.711902 335.310581 335.909854 336.511053 337.112939 337.715822 338.320131 338.926013 339.532190 340.139446 340.747548 341.358225 341.967993 342.579306 343.191156 343.803545 344.418361 345.032914 345.647696 346.264457 346.880503 347.497656 348.115764 348.734345 349.353150 349.973179 350.593255 351.213791 351.836278 352.458329 353.081178 353.703581 354.327786 354.951952 355.577208 356.202ooO 356.827504 PP4 321.900159 321.334998 320.771485 320.209598 319.649281 319.090609 318.533611 317,978043 317.424124 316.871754 316.321239 315.771608 315.224012 314.677780 314.132916 313.589916 313.048209 312.508200 311.968960 0.10 I.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.10 0.10 I.00 0.10 0.00 0.00 0.00 0.00 0.10 0.00 0.10
1.00 0.10 0.10 0.00 0.00 0.00 0.10 1.00 0.10 0.01 0.00 0.01 0.10 I.00 0.10 0.10 0.10 1.00 1.00 0.10 I.00 1.00 0.10 0.00 0.00 1.00 1.00 1.00 1.00 1.W 0.00 0.00 0.00 0.00
5 6 7
46
4 5 6 7 6 9 10 11 12 13 14 15 16 17 1.3 19 20 21 22 23 24 25 26 27 26 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
29 30 31 32 33 34 35 36 37 38 39 40
352.596817 PP5 320.747067 320.163756 319.622076
324.840096 324.883766 324.928728 324.974716 325.021676 325.069655 325.119102 325.169438 325.220955 325.273057 325.326335 325.380475 PR4 327.057323 327.636223 328.220712 328.604751 329.390451 329.977480 330.566749 331.156319 331.747988 332.341743 332.936217 333.531636 334.129574 334.727905 335.328290 335.929583 336.532465 337.136812 337.742432 338.349351 338.957743 339.566593 340.176721 340.788761 341.402035 342.015157 342.630525 343.246086 343.863230 344.481697 345.100846 345.720993 346.341591 346.963397 347.586212 346.209680 348.833900 349.459030 350.084931 350.712878 351.339794 351.967038
1.00 1.00 I.00
0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.10 0.00 1.00 0.00 0.00 0.10 1.00 0.00 0.00 0.00 1.00 0.00 1.00 1.00 1.00 0.10 0.00 0.10 1.00 1.00 1.00 0.10 0.10 1.00 0.10 1.00 0.10 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00 l.W 0.10 1.00 0.00 0.10 0.00 0.00
5 6 7 8
8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62
319.061844 318.503240 317.946430 317.391065 316.837263 316.285179 315.734561 315.185536 314.638087 314.092187 313.547818 313.006017 312.463449 311.923911 311.386715 310.848927 310.313970 309.779842 309.247301 308.716637 308.187370 307.658939 307.132373 306.607131 306.083217 305.560607 305.039333 304.519520 304.C00888 303.483386 302.967470 302.452830 301.938911 301.426514 300.915468 300.406002 299.897004 299.389182 298.882793 298.377243 297.872735 297.369529 296.867358 296.366075 295.665863 295.366860 294.868703 294.371522 293.875216 293.379611 292.885613 292.392311 291.9W288 291.408678 290.917526 PO5 323.611527 323.621287 323.632277 323.644539 0.00 0.00 0.00 0.10
1.00 1.00 1.00 1.00 1.00 0.10 0.0, 0.00 0.00 0.00 0.10 1.00 1.00 1.00 1.00 0.10 0.10 0.00 0.10 1.00 0.00 1.00 1.00 1.00 1.00 0.00 1.00 1.00 0.00 1.00 0.00 0.0, 0.00 0.00 0.10 0.00 0.10 1.00 0.10 1.00 1.00 1.00 I.00 I.00 0.10 1.00 1.00 1.00 0.00 0.00 1.00 1.00 I.00 I.00 0.10
334.139112 334.739252 335.341078 335.944214 336.549144 337.165177 337.762322 336.370601 338.980600 339.592010 340.204985 340.618395 341.433618 342.049538 342.667145
333.539825
I.00 I.00
1.00 0.M) 1.00 1.00 0.00 0.00 0.m 0.00 0.10 1.00 0.00 0.00 0.10
1.00
314.047586 313.501755 312.957849 312.415279 311.874290 311.334870 310.797039 310.260592 309.725713 309.192452 308.660591 308.130356 307.601318 307.074028 306.548399 306.023686 305.500617 304.979019 304.458808 303.939657 303.422460 302.906410 302.391716 301.878241 301.366169 300.855166 300.345576 299.837564 299.330521 298.824242 298.320428 297.817197 297.315474 PO6 323.028338 323.039378
_F
6
46 47 48
‘ii
41 42 43 *‘I
39 40
z
zz
zz 34
E
z:
;: 25 26 27
z
; 9 10 11 12 13 14 15 16 17 18 19 20
6
41 42 43 44
zl
0.00 0.00
1.00 0.01 0.M) 0.w 0.00 0.00 0.01 0.00 1.00 1.00 0.10 1.00 0.10 1.00 0.01 0.00 1.00 1.00 0.00 0.10 1 .OO 0.00 1.00 0.01 1.00 1.00 0.00 1.00 1.00 0.00 0.10 1.00 0.10 ;: 31
;: 25 26 27 26
;:
11 12 13 14 15 16 17 16 19 20
10
:
6 7
8 9 10 11 12 13 14
323.052198 323.066388 323.082198 323.099668 323.118957 323.139333 323.161236 323.184641 323.210067 323.236337 323.264937 323.294719 323.325589 323.358627 323.392687 323.428321 323.465085 323.503806 323.543764 323.585127 323.627977 323.672167 323.717738 323.764713 323.812327 323.862227 323.913037 323.965127 324.018507 324.073347 324.128916 324.186536 324.244066 PR6 327.037543 327.621533 328.206792 328.793681 329.382701 329.972232 330.563619 331.156841 331.751312 332.347358 332.944857 333.543914 334.144286 334.746625 335.349644 335.954760 336.560637 337.167512 337.776912 336.367451 336.998740 339.611320 340.226099 340.641696 341.458518 342.076537 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.10 0.00 0.10 0.00 0.00 1.00 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.10
0.00 0.00 0.00 0.10 0.00 1 .oo 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.10 0.00 1.00 0.00 0.00 0.00 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
11 12 13 14 15 16
10
9
7 R
:: 52
4i 42 43 44 45 46 47 48 49
2’: 30
;:
zz
z
;‘:
10 11 12 13 14 15 16 17 16 19
9
i
_.
0.10 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.10 0.10
20 21
1.00 1.00 1.00 1.00 1.00 1.03 0.00 0.00 1.00 l.CO 0.10 1.00 0.00 1.00 0.m 0.00 0.00 0.00 0.00 0.10 0.00 1.00 1.00 1.00 0.10 0.10 1.00 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.M) 0.00 0.00 0.10 1.00 0.00 0.00 0.10 0.00 0.00 10 11 12 13 14 15 16 17
9
z
;z 24
is 19
0.00
343.316456 PP7 318.433230 317.873649 317.315377 316.758964 316.203915 315.650280 315.098772 314.548376 313.999674 313.452654 312.906620 312.363334 311.820756 311.280182 310.740879 310.203327 309.667257 309.132670 308.599951 308.068461 307.538846 307.010171 306.483219 305.957783 305.434025 304.911099 304.390340 303.870655 303.353141 302.836204 302.321142 301.807692 301.295019 300.783788 300.274024 299.766238 299.259118 298.754071 298.248908 297.745264 297.243789 296.743200 296.243280 295.746171 295.249452 294.753957 !an7 322.441668 322.454463 322.468827 322.484326 322.501882 322.521202 322.541600 322.563657 322.587206 322.612275
17
0.00
342.695886 0.10 0.00 0.00 0.00 0.00 0.10 1.00 0.10 0.00 0.10 0.00 0.00 0.00 1.00 0.00 0.00
322.668506 322.698298 322.728442 322.762186 322.795704 322.832028 322.869167 322.907047 322.948729 322.989471 323.031522 323.077083 323.123160 323.169955 323.218904 323.268808 PR7 327.022320 327.607766 326.194515 328.782625 329.373002 329.964072 330.557426 331.151874 331.747087 332.344731 332.942361 333.543914 334.145488 334.749029 335.354125 335.959933 336.567810 337.176499 337.787287 338.398918 339.012010 339.626160 340.242529 340.859616 341.477794 342.098467 342.718719 343.340927 343.963850 344.588162 345.214258 345.842984 346.470270 347.100460 347.730074 PI’8 317.271543 316.713654 316.157091 315.602261 315.049084 314.497500 1.00 1.00 1.00 1.00 1 .OO 0.10
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.10 0.00 1.00 0.00 0.00 0.00 0.10 0.00 0.00 0.00 1.00 0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.10 0.00 0.00
0.00
322.638921
40 41 42 43 44 45 46 47 46 49 50 51
:7 ::
2
E 21 22
14 15 16 17 18
313.947263 313.399172 312.852421 312.307209 311.763370 311.222013 310.680491 310.141992 309.604554 309.068727 308.534402 307.999971 307.470470 306.941683 306.413701 305.886850 305.380075 304.836925 304.316054 303.795569 303.276442 302.759117 302.242948 301.728383 301.215022 300.703257 300.193499 299.684225 299.176822 298.670073 298.165737 297.662640 297.160367 296.659266 296.160661 295.662486 295.164920 294.670326
1.00 0.10 1.00 0.00 1.00 0.00 1 .OO 1.00 1.00 1.00 0.10 0.00 0.00 0.00 0.00 0.10 0.00 0.00 1.00 1.00 0.10 0.10 0.00 0.00 1.00 0.01 0.10 1.M) 0.10 0.00 1.00 0.00 1.00 0.10 I.00 0.10 0.10 0.10
406
GRANER INTENSITIES
AND
WAGNER
IN HOT
BANDS
Intensity considerations are useful in ascertaining subband assignments found with TOUTHOT if ambiguities exist for the J”, k’“, and 1” values and when it is not clear whether a subband belongs to 2u?;-v?,j or to ~zJ?~-v?~, which we shall hereafter call hot band (2) and hot band (0). respectively. For these hot bands, the rovibrational selection rules are the following, according to Amat’s rule AK - Al = 3p. Forhotband(2),AK=+lfor1”=+1,/‘=?2 For hot band (0), AK = Tl for I” = fl, I’ = 0. In other words, the KS AK = n subband of hot band (2) and the K * AK = -n subband of hot band (0) share a common lower level. Now, how does one decide, a priori, whether a subband belongs to hot band (2) or to hot band (0)? Let us assume, as an example, that we have assigned a K subband with I” = -1. It can therefore be either ‘PA-> ‘QK, and ‘Rk- of hot band (2) or RPk-, “Q-, and RRK of hot band (0). Several criteria are to be taken into account. First, let us consider the strong-weak-weak alternation. In propyne, due to the three equivalent H atoms of the CH3 group, nuclear spin statistics give an intensity twice as strong for k” - 1” = 3p as for k” - I” # 3~. This means that for hot band (2), the subbands with KS AK = * * * -8, -5, -2. 1, 4, 7 - - - are enhanced, whereas for hot band (0), the enhanced subbands are Km AK = * * * -7, -4. -1,2, 5, 8 . . *. Therefore, this relative enhancement tvitkin a hot band does not allow us to choose, because the enhancement is the same for the ‘(P, Q, R)K subband of hot band (2 ) and the R(P, Q, R)K subband of hot band (0) and vice versa. A second argument is that, in well-behaved perpendicular bands, AJ = AKtransitions are stronger than AJ = -AK transitions. Therefore, if we find here that the P series is stronger than the R series, we are probably dealing with hot band (2 ), and with hot band (0) if it is the opposite. Another minor criterium already mentioned earlier concerns K” = I” = 1. Hot band (2) has two R( P, (2, R), families (with very close upper energy levels) for this case. whereas hot band (0) has only one ‘(P, Q, R), family. Finally, the comparison of intensities of lines belonging to the two hot bands, when it is feasible, is also informative. The vibrational factors of the transition moment matrix elements are in the ratios 1: 1: fi for vlo, hot band (O), and hot band (2), respectively, which gives 1: I:2 after squaring. Since the Boltzmann factor at 300 K is 0.2 1, the vibrational intensities of these three bands are in the ratios 1:0.2 1:0.42 (the authors are grateful to Dr. A. Ruoff for clarifying this point). Therefore, if we take a certain transition (e.g., ‘PI(( J)) in the three bands, the intensities should roughly be: I X (spin statistics) in vlo; 0.42 X I X (spin statistics) in hot band (2); 0.21 X 1 X (spin statistics) in hot band (0). Due to the high density of the spectrum, this property cannot easily be checked but it is clear that hot band (0) is significantly weaker than hot band (2). The nuclear spin weights give spectacular effects, as can be seen clearly in Figs. 1 and 2, especially for hot band (3). If we consider this hot band, and compare it with the fundamental vIo. we find as a first approximation that -For K values with K # 3p and K - I# 3p, the K . AK subband (2) has an intensity which is 42% of the intensity of the K. AK subband
of hot band of v,~.
PROPYNE
-For
AT
30
pm
values such that K = 3p, and therefore
407
K - 1 Z 3p, the intensity
ratio is
21%. -For values such that K - 1 = 3p, and therefore reaches 84%. The reader can check qualitatively seem different due to overlaps. ASSIGNMENTS
K # 3p, the intensity
these ratios in Figs. 1 and 2, although
IN THE
HOT
ratio
they often
BANDS
Hot Band (2) The first series which was assigned with the help of POLY and of TOUTHOT was the RR7 series of hot band (2). It is extremely close to the corresponding series of vIO. For low J values, the hot band lines are ~0.030 cm-’ below the cold band lines: they coincide around J E 28 and are slightly above for higher J values. A similar pattern is found for most of the series of hot band (2 ) which were easily assigned, with the notable exceptions of the subbands KS AK = 1 and 0 which are less obvious, for different reasons. The ‘P7 and ‘Pa series were also found only in a later stage, when a correct global model was available. Finally, we have assigned 17 subbands of hot band ( 2). from KAK = -8 to f7, including two subbands for Ku AK = 1. The highest J value was reached for ‘P2 (66 ). We have in the end established a list of 2090 transitions, 1272 of which have a nonzero weight. They correspond to 743 different energy levels with a nonzero weight. The whole list of transitions is given in Table V. It should be noted that for most P and R series, the low J lines are obscured because they lie in the region of Q branches. For the two subbands with K* AK = 1, it was found that in the upper level ( v10 = 2. Ilo = 2. k = 2). which is split by an A4+ A doubling, the A + level is above the -4 -
v J+l
J J-l FIG. 5. Scheme of levels for the 2u&v~~
transition.
10 11 12 13 14 15
:
:P 55
:? 52
zl 39 40 41 42 43 44 45 46 47 48 49
z:: 36
z: 33
::
;: 26 27 28
:: 21 22 23
11 12 13 14 15 16 17 18
10
:
7
316.875234 316.315527 315.756779 315.199674 314.644453 314.090627 313.536433 312.987886 312.439101 311.891567 311.346082 310.802061 310.259953 309.718942 309.179903 308.642566 308.106714 307.572665 307.040354 306.509586 305.980527 305.45325s 304.927557 304.403677 303.681326 303.360962 302.642047 302.325066 301.809918 301.295021 300.783788 300.274023 299.765693 299.259118 298.754071 298.251349 297.750261 297.250394 296.752412 296.256700 295.762614 295.270242 294.779552 294.290718 293.803269 293.317992 292.834257 292.352728 291.872545 PQ7 320.886250 320.898510 320.912610 320.928670 320.945874 320.965040 320.985244 321 .C07860 321.031884
0.10
0.00
0.00 0.10 0.00 1 .oo 1 .w 0.10
0.00
0.00 0.00
0.10
1 .oo
l.w 0.10 1 .oo
1.00
1.00 1.00 l.w
0.00
1 .w 1.00
0.00
0.10 0.10 1 .cQ 0.10
0.00
.oo
0.00 0.10 I.043 1.00 1.M) 0.00 1.00 1 .Oo 1 .oo Cl.10 1 .co cJ.cQ 1 .co 0.10 0.00 1.00 I.00 0.00 1 .m 1 .cO 1.00 0. IO 0.00 1 .m 1 .oo 1 1 .oo 1 .oo 0.10
Ei 31 32
;,” 28
15 16 17 18 19 20 21 22 23 24 25
zi 39 40
:z 36
z: 33
z:
;z 27 28
17 18 19 20 21 22 23 24
16
321.057058 321.084086 321.112579 321.142690 321.174790 321.208466 321.243173 321.280118 321.318333 321.357960 321.399029 321.442859 321.487803 321.534619 321.582659 321.631904 321.683399 321.737079 321.791389 321.846569 321.905689 321.965709 322.026809 322.089829 322.155049 PR7 325.469005 326.054394 326.642177 327.230263 327.820442 328.412182 329.005681 329.600321 330.1s6s40 330.794989 331.394839 331.995728 332.598547 333.202697 333.808716 334.416235 335.025305 335.635924 336.248103 336.861933 337.477232 338.094500 338.713182 339.332940 339.954099 340.577909 341.202938 341.629110 342.457236 343.087366 343.718135 344.350854 344.985374 PP6
.oo
0.00
0.00 0.00 0.00 1 .oo 1 .Oil 0.00 0.00 0.00 0.00 1 .m 0.00 0.00 0.00 0.00 0.M)
0.00 0.10
0.00
0.00
0.00
0.00
0.00 0.00 0.00
0.00
0.00
0.00
0.00 0.00 0.00
0.00
0.00
0.00 0.00
0.00
0.W 0.00 0.00
0.00 1.00
1 .oo 0.10 0.00
0.00
1
0.00
0.00 0.00
0.10
1.00 1.00 1.00 1.00 I.00 0.00 0.00 0.10
:
6 7
10 11 12 13 14 15 16 17
::
45 46 47 48 49 50
16 17 18 19 20
ii
9 10 11 12 13 Id
i
6
Transltlons 318.036311 317.474390 316.914077 316.355374 315.798430 315.242778 314.689266 314.136698 313.586602 313.037400 312.490262 311.944593 311.400400 310.858110 310.317378 309.778620 309.241430 308.705883 308.172358 307.640297 307.110315 306.581570 306.054660 305.529950 305.006820 304.485576 303.965940 303.448107 302.932302 302.418074 301.905960 301.39577s 300.886893 300.380406 299.875438 299.372305 2s8.871104 298.372333 297.874600 297.379516 296.886272 296.393770 295.904165 295.416243 294.929770 294.446060 293.963930 PO6 321.474461 321.485544 321.498223 321.512640 321.528377 321.545694 321.564920 321.585730 321.608068 321.631904 321.657640 321.684120
Assigned
.oo
1 .oo 0.00 1 .OO 1 .m 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
1.m 1.oo
.w
0.00 1.00 0.00 1.00 0.00 0.00 1 .w 0.00 0.00 0.00 0.00 1 1 .w 1 .Oo 0.00
0.00 0.00 0.00 0.00
1 1 .oo 0.00
0.00 0.00 0.00
0.00 0.00 0.00 0.00 321.744174 321.776205 321.809570 321.845156 321.881589 321.921285 321.962083 322.004064 322.048050 322.093798 322.140880 322.190260 322.240491 322.293880 322.348767 322.404100 322.462199 322.522084 322.583188 322.646608 322.711467 322.778075 322.846760 322.917370 322.989470 PR6 325.485615 326.069690 326.655489 327.242540 327.831688 328.421732 329.014196 329.607498 330.202805 330.799515 331.397633 331.997010 332.599011 333.202689 333.807606 334.413499 335.021786 335.631440 336.243071 336.855832 337.470646 336.086870 338.704921 339.324620 339.945992 340.568939 341.193777 341.820051 342.448295 343.078323 343.709493 344.342903 344.978382
321.713396
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.10 0.10 0.00 0.00 0.00 0.00 0.W 0.10 0.00 0.00 0.00 o.c!o 0.M) o.ca 0.00 0.00 0.00 0.00 0.00 0.10
0.00 1.00 1.00 0.10 0.00 0.10 0.00 0.00 0.00 1.00 0.10 0.00 0.00 0.10 1.00 0.10 0.10 0.00 0.00 0.00 0.00 0.03 0.00 1.00 0.00 0.10
40 41 42 43 44 45 46 47 48 49 50
3”: 39
:z
21 22 23
1s ::
13 14 15 16 17
ii
40 41 42 43 44 45 46 47 48 49 50 51
39
III the 7 _v ”Lo- v *’ IO Hot Band of Propyne
TABLE VI
346.252500 346.892749 347.534056 348.177827 348.622466 349.469216 350.117883 350.768030 361.419417 352.073353 352.728880 353.385570 PP5 319.194331 318.630739 318.069029 317.508723 316.950016 316.392900 315.837244 315.283145 314.731471 314.181532 313.632251 313.085206 312.539593 311.996016 311.454170 310.914057 310.375861 309.839457 309.304554 308.772170 308.241360 307.712470 307.185500 306.660382 306.137458 305.616323 305.097220 304.580187 304.065030 303.552021 303.040643 302.531838 302.024939 301.519873 301.017370 300.516203 300.017691 299.520718 299.026184 298.533706 298.042660 297.553910 297.067120 296.582460 296.099138 295.618250
345.614390
Z% 0.00 0.00 0.00 0.00 0.01 0.01 0.00
::i% 0.01 0.01
K% 0.00 0.01 0.00 0.00 0.01 0.01 0.00 0.00 0.01 0.01 0.01 0.00 0.00 O.CO 0.00 0.00 0.01 0.01 0.00 0.01 0.00 0.01 0.00 0.01 0.01
EZ 0.00
0.01 0.00 0.01
0.10 1 .oO
0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00
2% 0.00
8 9 10
i
43 44 45 46 47 48
ii
13 14 15 16 17 18 19
ii
7 8
325.499510 326.081746 326.666021 327.251410 327.839580 328.427092
294.661735 294.186121 293.712226 293.240159
295.139020
0.00 0.00 0.00 0.00 0.10 0.10
0.00 0.00 0.00 0.00 0.00
;:
18 19 20
,
12 13 14 15 16 17
4
:: 40 41 42 43 44 45 46 47 48 49 50
:z 34 35 36 37
Z?
24 25 26 27 28 29
;z
Z?
12 13 14 15 16 17 18 19
330.205704 330.800554 331.398466 331.997018 332.597336 333.199709 333.803820 334.409819 335.016877 335.627202 336.238006 336.850649 337.465603 336.081959 338.700570 339.321052 339.943051 340.567408 341.193085 341.621022 342.449882 343.062228 343.716251 344.351546 344.969368 345.627654 346.269011 346.911996 347.556734 348.203607 348.852181 349.501967 350.154474 350.607906 351.463346 352.120546 352.779032 353.439374 PP4 320.349644 319.784005 319.220908 318.658535 318.098273 317.539858 316.983130 316.427829 315.674319 315.323102 314.773510 314.226048 313.679585 313.136886 312.595377 312.056058 311.518980 310.983918 310.451334
329.611842
329.019559
.w
.w
0.01 0.01 0.01 1 .w 1 1.00 0.01 1 .oo 0.10 1.00 0.00 1 .oo 0.10 1 .oo 1 .oo 1 .oo 1.00 0.10 0.01
0.00
0.00
0.00 0.10 0.10
0.10
0.00 1 .oo 0.00
0.00 0.00 0.00
0.00
0.00
0.10
0.00 0.00 0.00
0.10
0.00
1
0.00
0.00 0.00
0.00 0.10 0.00
0.10 1 .w
0.00
0.10
0.00
0.00
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323.759397 323.199514
340.158037 340.767887 341.378950 341.991836
36 37 38 39 328.830683 328.894861 328.960897 329.029222 RR5 332.353165 332.936393 333.525807 334.114811 334.704031 335.296927 335.890429 336.484295 337.082450 337.681895 338.280765 338.882797 339.464418 340.091405 340.697883 341.306389 341.916548 342.528728 343.142176 343.757co3 344.374637 344.993893 345.614396 346.236851 346.861450 347.487744 348.115764 348.744682 349.377815 350.011415 350.647926 351.285358 351.924767 1.00 0.10 1.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 I.00 1.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 1.00 0.00 0.00 1.00 1.00 0.00 0.10 0.00 0.00 0.00 O.Cx,
1.00 0.00 0.00 0.00
PROPYNE
AT 30
pm
413
level, the separation being well represented, with a standard deviation of 2 X IO-’ cm-‘by AE = a[J(J+ l)]‘+ b[J(J+ 1)13 + c[J(J+ 1)14with a = 1.19 X 10v7, h = -6.63 X lo-‘” and c = -1.56 X lo-l5 cm-l. Hot Band (0) The first two series assigned in hot band (0) were ‘P7 and ‘P4. They both lie about 1.5 cm-’ below the same series of vlo. Further assignments were made easier by an important point illustrated by Fig. 5: thesubbandK”=n+l,l”= l.AK=Al=-IandthesubbandK”=n-l,f”=-1, AK = A/ = + 1 share the same upper level I(’ = n, 1’ = 0. In other words, six transitions, namely,PP,+,(J+ l),PQn+i(J),PRn+~(Jl).RPn-~(J+ l),RQ,_,(J),andRR,.-~(J - I ), all reach the same upper level. Since we know A0 (32) very well, the energies of the ulo = 1 state determined in the first part of this paper are very reliable even for different K values. They can be employed for a nonclassical use of LSCD to determine one of the two subbands if the other one is known or to check dubious assignments. Even if several of the six above mentioned transitions are blended, enough remain for a valid check. Finally, we have assigned 13 subbands from K- AK = -7 to +5. The highest Jvalue reached is for ‘P, (64) but, as a rule, it was not possible to go as far in J as for hot band (2). The final list comprises 1560 transitions, 914 of which have a nonzero weight. Due to the remark made earlier, this corresponds to only 363 different energy levels with a nonzero weight. The whole list of transitions is given in Table VI.
DISCUSSION
AND
FURTHER
WORK
We have converted the wavenumbers of both hot bands into upper level energies using the very accurate lower level energies (in the vIo = 1 state) determined in the first part of the present work. These energies of the vIO = 2 state were then leastsquares fitted to a model including the I( 2, 2) interaction between the I = 0 and the 1 = +-2 components. But it was soon clear to us that it was not possible to ignore the level v9 = 1, located near nlo = 2. With the u9 band having been just studied at Oulu by K. Pekkala (see the accompanying paper (43)). we were aware that a Fermi resonance was present, affecting mainly the K’ = 1, u9 = 1, l9 = - 1 levels on one hand andtheK’= 1.u lo = 2, I9 = +2 levels on the other. It resulted in a shift of aboui 0.020 cm -I. Other interactions could also be suspected between the two vibrational levels, It appeared therefore more reasonable to fit all the energy levels together. This will be reported in a further paper where we treat together vIo = 2, l9 = 0, k2 levels, rovibrational transitions of v9. and also rotational transitions in both levels (49). It should be mentioned that from the present work, accurate energies of the vi0 = 2 state became available. They were used to assign with no ambiguity one RR5 series belonging to the “superhot” band 3~~~~2~~~. Two lines of this series are shown on Figs. 1 and 2. We hope to be able in the near future to assign other transitions of these “superhot” bands. Since the 3vi0 band lies near IO pm, the knowledge of the vl(, = 3 levels is crucial for a better understanding of the complex band system of propyne in the 10 pm region.
414
GRANER
AND
WAGNER
ACKNOWLEDGMENTS The authors thank Brenda P. Winnewisser, reading of the manuscript.
INSU and from the France-German
RECEIVED:
Hans Biirger, Rauno Anttila, and Karl Pekkala for a critical
Support from the “Action program
ThCmatique
PROCOPE
Programmee
PlanCtologie”
of the French
is gratefully acknowledged.
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