ARTICLE pubs.acs.org/JPCA
Rotational and Rovibrational Spectroscopy of CH3NC of the Ground and ν4 = 1 Vibrational States Petr Pracna,†,* Jirí Urban,† Ondrej Votava,† Zuzana Meltzerova,‡ Stepan Urban,‡ Veli-Matti Horneman,§ and Brian J. Drouin|| †
)
J. Heyrovsky Institute of Physical Chemistry, v.v.i., Academy of Sciences of the Czech Republic, Dolejskova 3, 18223 Prague 8, Czech Republic ‡ Department of Analytical Chemistry, Institute of Chemical Technology, Technicka 5, 16628 Prague 6, Czech Republic § Department of Physics, University of Oulu, Box 3000, 90014 Oulu, Finland Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Mail Stop 183-301, Pasadena, California 91109-8099, United States
bS Supporting Information ABSTRACT: The parallel vibration-rotation band ν4 of methyl isocyanide (CH3NC), with a band center at 944.9 cm-1, was studied by FTIR spectroscopy between 890 and 980 cm-1 in order to improve the ground-state rotational constants. Such improvement is essential for the scheduled studies of excited vibrational levels and their mutual anharmonic resonances occurring at higher values of the K rotational number. Ground-state combination differences generated from this band, spanning values of J/K from 0 to 85/13, were combined with rotational data from the literature and newly measured rotational transitions, extending the J/K range from 3/0 up to 31/14, and fitted simultaneously with a fully quantitative reproduction of the data. The infrared data of the ν4 band were analyzed together with rotational data of the ν4 = 1 level, spanning values of J/K from 4/0 to 14/12. The fit in the approximation of an isolated vibrational state, with the transitions perturbed by weak local resonances excluded, yields reproduction of the data within experimental uncertainties.
1. INTRODUCTION The systematic investigation of high-resolution rovibrational spectra of methyl isocyanide (CH3NC) was initiated in the 1990s. The aim was to contribute by analyses of FTIR spectra to a detailed understanding of the rovibrational structure in the context of the problem of monomolecular isomerization of CH3NC to CH3CN. This reaction has been a subject of many kinetic studies1-5 because it revealed a significant disagreement with the statistical behavior (Rice-Ramsperger-Kassel-Marcus theory) for unimolecular reactions.6 In their studies, Plíva and co-workers analyzed all fundamental vibrational levels.7-10 For the determination of the axial rotational constant A0 and the centrifugal distortion constant D0k they exploited the method of combination loops applied to the ν7 þ ν8 combination band and the (ν7 þ ν8) - ν8 hot band.11 There also exists an earlier series of microwave investigations of the vibrational ground state,12 the lowest excited vibrational levels ν8 = 1-4 corresponding to the bending mode of the CNC chain13-15 and the lowest fundamental level ν4 = 1.16 All these studies confined themselves quite naturally only to the lower K rotational states because the intensities in methyl isocyanide r 2011 American Chemical Society
spectra decrease rapidly with growing K due to the large value of A-B ≈ 4.9 cm-1. None of these studies reached the higher K rotational states through which all excited levels of the CNC bending mode are strongly coupled. Description of such systems requires that all vibrationally excited levels are studied as one global interconnected system, as has been shown in the recent investigations of a structurally similar molecule, methyl acetylene CH3CCH.17-22 It is the aim of the present investigations to describe in such manner quantitatively these anharmonic resonances in the CH3NC molecule which are obviously crucial for understanding the intramolecular vibrational redistribution of energy that plays an important role in the mentioned kinetic studies. Using information available from earlier studies of CH3NC, it is possible to estimate the onset of such localized anharmonic resonances from K = 9 in the ν8 = 1 level. In higher excited levels of the CNC bending mode the resonances progressively move to Received: September 21, 2010 Revised: December 23, 2010 Published: January 26, 2011 1063
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The Journal of Physical Chemistry A lower values of K, and the complexity of resonances increases dramatically with excited levels of the other vibrational modes entering the game. In the present work we begin the investigation by a new analysis of the vibrational ground state, which is essential for all further analyses of the vibrationally excited levels with an accurate account of the intervibrational couplings. We combine here the results of the submillimeter wave measurements of rotational transitions in the vibrational ground state with the ground-state combination differences generated from significantly extended assignments in the parallel fundamental ν4 band corresponding to the C-N valence vibration. The IR data from this band are also analyzed simultaneously with rotational data of the ν4 = 1 level and provide a set of considerably improved parameters of the upper state.
2. EXPERIMENTAL DETAILS The sample of CH3NC was prepared according to the literature23 by dehydration of methyl formamide (CH3NHCOH) by p-toluenesulfonyl chloride in quinoline heated to 75 °C under a vacuum of 15 Torr (2 kPa). The product was collected in a receiver trap cooled by dry ice and acetone to -70 °C. Maintaining the low pressure in the reaction is essential for avoiding the risk of inflammation of the product at the reaction temperature. Manipulation with the gaseous sample at spectroscopic conditions (room temperature, pressure below 150 Pa) even more reduces the inflammation risk. The measurements of rotational transitions were performed with the Prague High Resolution Spectrometer.24 The source signal was synthesized by a swept signal generator HP 83650 B (Agilent) operating between 10 MHz and 50 GHz. The frequencies above 50 GHz were generated by frequency multipliers. A set of high-power semiconductor amplifiers ensured sufficient radiation power before frequency multiplication. Semiconductor Schotky diodes operating at room temperature were used as detectors. The spectra were recorded in the range from 139 to 305 GHz with a second-harmonic lock-in detection of signal modulated at 28 kHz. For better determination of the lines it was necessary to change the depth of modulation applied to the signal from the signal generator. It varied from 50 kHz for stronger lines (transition with the rotational quantum number K up to 6) to 90 kHz for weaker lines. The final modulation depth, which depends on the combination of frequency multipliers, was kept within the Doppler line widths. The optical path length of a conventional 280 cm long glass cell was doubled using a roof-top mirror and a THz polarizer from TYDEX (www.tydex.ru). The pressure of the sample was varied according to transition intensities between 0.5 and 1.9 Pa and measured with a capacitance gauge (Leybold) with a relative uncertainty of about 5%. The uncertainty of measurements is estimated to be better than 20 kHz for isolated lines with a good signal-to-noise ratio. A similar spectrometer25 operating at 580-643 GHz was employed at the molecular spectroscopy laboratory of the Jet Propulsion Laboratory (JPL). Transitions due to CH3NC were detected with a marginal signal-to-noise ratio in a systematic study of a discharged gas mixture of 97% N2 and 3% CH4, held at 13.3 Pa and 200 K. These pressure/temperature conditions are representative of the stratosphere of Saturn’s satellite, Titan, and the study revealed qualitative and quantitative agreement with known components of the Titanian atmosphere. The infrared experimental work was performed by using the Bruker IFS 120 HR Fourier transform spectrometer in the
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Infrared Laboratory at the University of Oulu. The CH3NC sample was purified with cold traps before evaporating it into a White cell,26a,26b which was provided with potassium bromide (KBr) windows. Two series of recordings were performed under different conditions. The absorption path lengths were 3.2 and 35.2 m and the sample pressures 11.9 and 122.7 Pa (spectra I and II), respectively. The total recording times in these measurements were 75.2 and 137.8 h, respectively. During the measurements the sample gas was kept at room temperature. The instrument was equipped with a Globar source and a KBr beamsplitter made by Bruker Inc. Infrared radiation was detected with a liquid nitrogen cooled mercury-cadmium-telluride detector. Spectral resolution was better than 0.0013 cm-1 for small well-separated lines. The uncertainty of such unperturbed lines was estimated to be better than 0.0002 cm-1. The spectra were calibrated with CO2 peaks.27 The peak positions were calculated using the optimized center of gravity (CG) method28 using well-interpolated spectra.
3. RESULTS AND DISCUSSION Vibrational Ground State. We reanalyzed the vibrational ground state of methyl isocyanide because the accuracy of the previous investigations was insufficient for our aim of studying the anharmonic resonances occurring at higher values of K ≈ 10 between the progression of vibrational levels ν8 = 1, 2,... of the CNC bending mode. The microwave study12 involved only the low-J rotational transitions from J = 2 r 1 to J = 7 r 6 which provided centrifugal distortion parameters with only limited accuracy. These parameters were later refined in the analysis of the ground-state combination differences (GSCD) generated from the parallel fundamental ν4 band,10 but this study was limited to rotational states with J/K e 65/9. There remained, however, a small disagreement between the rotational constant B determined in these two studies. In our present investigation of the vibrational ground state we combine in a simultaneous fit the highly accurate ground-state rotational data with the GSCD generated from the fundamental ν4 band. The extended assignments of the IR bands ν4 and also ν8 showed that the accuracy of the ground-state parameters obtained from rotational data was not sufficient for the currently studied range of high-J rotational states. This was disclosed by discrepancies between reproduction of the P and R branches for J > 70 in the fits, which was removed only after including the sets of GSCD extended to J ≈ 85. The ν4 parallel band is ideal for obtaining the ground-state parameters from GSCD. First, the difference of constants Δ(A - B) is large enough to make the rotational structure of the band clearly resolved. Second, the band is free from perturbations from other fundamental levels, which makes, with the above-mentioned feature, its assignment a straightforward task. In the simultaneous fit we used the original low-J rotational data12 with the newly measured transitions J = 10 r 9 and 15 r 14 from the currently available range of the Prague microwave spectrometer. To compare the consistency with previous microwave measurements,16 we also recorded the transitions J = 7 r 6 and found an excellent agreement. In the course of the analysis we became aware of previously unpublished measurements from the Jet Propulsion Laboratory for J = 29 r 28 to 32 r 31 and incorporated them in our fits. The experimental data were fitted with a conventional polynomial Hamiltonian for a nondegenerate vibrational level of a 1064
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Table 1. Experimental Frequencies, Errors of Reproduction, and Experimental Uncertainties of Rotational Transitions in the Vibrational Ground State of CH3NC J
a
K
observeda
O-Cb
uncc
J
K
observeda
14
14
300 198.873
J
K
observedd
O-C
unc
O-C
unc
-3
20
1
0
40 211.471
79
100
50
1 2
1 0
40 210.511 60 316.832
29 25
30 30 30
6
0
140 733.927
-34
50
6 6
1 2
140 730.746 140 721.217
-34 -18
50 20
28
0
582 609.639
103
6
3
140 705.310
-20
20
28
1
582 596.594
25
50
2
1
60 315.428
-14
6
4
140 683.056
-15
20
28
2
582 557.735
60
50
2
2
60 311.381
33
30
6
5
140 654.472
7
20
28
3
582 492.867
1
50
3
0
80 421.910
26
60
6
6
140 619.537
15
20
28
4
582 402.110
-53
50
3
1
80 420.062
-3
60
9
0
201 038.956
12
20
28
5
582 285.453
-145
200
3
2
80 414.660
53
60
9
1
201 034.416
13
20
28
6
582 143.146
-62
50
3
3
80 405.504
-8
60
9 9
2 3
201 020.791 200 998.089
8 3
20 20
28 29
9 1
581 561.672 602 652.873
57 -17
90 50
4 4
0 1
100 526.541 100 524.249
31 13
60 60
9
4
200 966.314
-8
20
29
0
602 666.275
-12
50
4
2
100 517.433
18
60
9
5
200 925.485
-15
20
29
2
602 612.626
-77
50
4
3
100 506.072
23
60
9
6
200 875.611
-23
20
29
3
602 545.713
-28
50
4
4
100 490.163
21
60
9
7
200 816.736
-4
20
29
4
602 452.061
35
50
5
0
120 630.590
16
60
9
8
200 748.858
20
20
29
5
602 331.551
-37
50
5
1
120 627.852
6
60
9
9
200 671.973
23
20
29
6
602 184.513
44
50
5
2
120 619.652
-10
60
14 14
0 1
301 523.230 301 516.436
7 6
20 20
29 29
7 9
602 010.769 601 583.767
52 209
50 200
5 5
3 4
120 606.034 120 586.942
8 0
60 60
14
2
301 496.062
10
20
30
0
622 719.555
-101
50
5
5
120 562.410
-6
60
14
3
301 462.105
8
20
30
1
622 705.820
-11
50
6
0
140 733.964
3
60
14
4
301 414.582
7
20
30
2
622 664.343
-14
50
6
1
140 730.754
-26
60
14
5
301 353.482
-20
20
30
3
622 595.327
76
50
6
2
140 721.228
-7
60
14
6
301 278.869
-30
20
30
5
622 374.337
99
50
6
3
140 705.322
-8
60
14
7
301 190.773
-17
20
30
6
622 222.429
22
50
6
4
140 683.086
15
60
14 14 14
8 9 10
301 089.226 300 974.148 300 845.734
21 -28 -8
20 20 20
30 31 31
7 2 3
622 043.126 642 712.517 642 641.301
35 -8 19
50 50 50
6 6
5 6
140 654.460 140 619.518
-5 -4
60 60
14
11
300 703.966
20
20
31
4
642 541.575
0
50
14
12
300 548.855
21
20
31
5
642 413.985
548
500
14
13
300 380.440
-19
20
31
6
642 256.812
-101
50
Present work (in MHz). b Observed - calculated (in kHz). c Experimental uncertainty (in kHz). d Reference 12 (in MHz).
C3v-symmetric top molecule Evr ðJ, kÞ ¼ Ev þ Bv JðJ þ 1Þ þ ðAv - Bv ÞK 2 - DvJ J 2 ðJ þ 1Þ2 - DvJK JðJ þ 1ÞK 2 - DvK K 4 þ HJv J 3 ðJ þ 1Þ3 v 2 v þ HJK J ðJ þ 1Þ2 K 2 þ HKJ JðJ þ 1ÞK 4 þ HKv K 6
þ LvJ J 4 ðJ þ 1Þ4 þ LvJJK J 3 ðJ þ 1Þ3 K 2 þ LvJK J 2 ðJ þ 1Þ2 K 4 þ LvJKK JðJ þ 1ÞK 6 þ LvK K 8
ð1Þ
In the least-squares fitting, the data were given weights proportional to the inverse square of their estimated experimental uncertainties. Overlapped IR lines were given higher uncertainties based on the extent of discrepancy with the GSCD checks.29 From the assignments in the IR spectrum I we generated more than 1400 GSCD; from spectrum II we added about 450 mostly higher J/K GSCD. The corresponding reproduction of the GSCD and transition frequencies is given in Table S1 of the Supporting Information. The rotational data have markedly higher weights thanks to their extreme accuracy, which was reduced only in several cases of overlapped lines or weaker lines
with a worse signal-to-noise ratio. An overview of the groundstate rotational data with experimental uncertainties and reproduction is given in Table 1. The parameters resulting from the least-squares fit are given in Table 2. The extended span of rotational states yielded a considerable improvement of centrifugal distortion parameters. Their set needed to be extended by the sextic and two octic parameters. The latter were found to be necessary, especially for the quantitative reproduction of the JPL rotational data and high-J GSCD. The axial constants A0 and D0K are entirely decorrelated from the data analyzed here and could be thus kept fixed at previously determined values. This allows a more accurate energy level structure but does not change the energy level differences (i.e., rotational frequencies and GSCD) in the analyzed data. The ground-state constants were kept fixed in further fits of the data pertaining to the excited vibrational state ν4 = 1. Vibrational State ν4 = 1. The vibrational level ν4 = 1 is the lowest nondegenerate (A1) fundamental level of methyl isocyanide lying at 944.9 cm-1. The corresponding parallel band ν4 shown in Figure 1 has a clear rotational structure with a prominent series of K = 3, 6, 9, and 12 transitions in both P and R branches. Thanks to the higher resolution, the Q-branch region in spectrum I is 1065
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Table 2. Energies, Rotational, and Centrifugal Distortion Parameters a (in cm-1 units) of the Vibrational Ground State and the ν4 = 1 Level of CH3NC ν4 = 1
ground state parameter
present work
b
GSCD
c
MW
E
present work
IRd
MWe
944.904032 (8)
944.90042 (3)
5.23871918 (36)
5.234 (27)
0.3333289500 (51) 1.578129 (23)
0.3333245 (44) 1.56776 (94)
0.33332885 1.565
7.534347 (114)
7.2889 (77)
7.518
8.49299 (43)
8.5561 (2)
A
5.247234 f
5.247234 (77)
B DJ 107
0.3353281704 (58) 1.565102 (74)
0.33532524 (38) 1.55407 (158)
0.33532626 1.57
DJK 106
7.589292 (182)
7.4218 (74)
7.575
DK 105
8.5626f
8.5626 (24)
HJ 1014
-2.736 (384)
-3.184 (27)
HJK 1011
7.9758 (168)
7.7606 (18)
HKJ 1010
2.0773 (79)
1.5925 (66)
HK 1010
0.0
-3.04 (15)
LJ 1018 LJJK 1016
1.82 (39) -9.71 (32)
1.82g -9.71g
range of J,Kh
83,13/14,14
65,9/-
-/6,6
84,15/14,12
65,9/-
-/8,6
no. of datah
1875/88
1062/-
-/27
2211/47
943/-
-/23
standard deviationh,i
0.17/25
0.28/-
-/na
0.13/24
0.30/-
-/na
a
Numbers in parentheses are one standard deviation in units of the last significant digit. b Reference 11. c Reference 12. d Reference 10. e Reference 16. f Constrained to the value from ref 11. g Constrained to the ground-state value. h Rovibrational/rotational data. i 10-3 cm-1/kHz.
Figure 1. Overview spectrum of the ν4 band of CH3NC (spectrum I) with the prominent series of K = 3, 6, 9, and 12 transtions in the P and R branches enhanced by the hydrogen spin statistics and the progression of the Q branches of the fundamental and hot bands.
now much less congested and contains many isolated lines. The typical pattern of hot band Q branches is clearly seen in the overview spectrum. The hot bands are associated with the combinations with the lowest degenerate bending mode ν8 and correspond to the bands (ν4 þ ν8) - ν8 and (ν4 þ 2ν8) 2ν8. The presence of hot bands is an unavoidable source of frequent overlaps with the lines of the fundamental ν4 band. This reduces the wavenumber precision of lines, especially those of the weaker high-K transitions. We were able to assign over 1800 transitions from spectrum I and over 1000 transitions from spectrum II. The infrared data were fitted simultaneously with the available rotational data from literature16 and the newly measured transitions for J = 10 r 9 and 15 r 14. The fit has been done at the present stage in the approximation of an isolated vibrational state with the effective Hamiltonian given by eq 1, with exclusion of data influenced by local perturbations having an origin mainly in the overtone level ν8 = 3 . The perturbations can be now reliably estimated from the preliminary assignments of the hot bands ν8 = 2 r 1 and 3 r 2 which are studied together with rotational data. A global analysis
Figure 2. Diagram of J-reduced energies Ered = Evr(J,k) - B0J(J þ 1) þ D0J J2(J þ 1)2 - H0J J3(J þ 1)3 of resonant crossings of the K = 3 and 4 levels of ν4 = 1° with the levels of the Vl88 = 3(1,-3 vibrational state. The vibrational angular momentum quantum number is used as a superscript to the right column of rotational quantum number K. Preliminary values of Ev = 792.48, B = 0.3392, A = 5.2248 in the ν8 = 3(1 level and Ev = 833.87, B = 0.3391, A = 5.2247, Aζ = 4.8736 in the ν8 = 3(3 level (in cm-1) were used. The positions of resonant level crossings due to the anharmonic and ΔK = þ2, Δl = -1 interactions are marked by the full and dashed circles, respectively.
of the levels system ν8 = 1, 2, 3 and ν4 = 1 with the account of all significant intervibrational couplings will be the subject of a 1066
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Table 3. Experimental Frequencies, Errors of Reproduction, and Experimental Uncertainties of Rotational Transitions in the Vibrational State ν4 = 1 of CH3NC O-Cb uncc
J
K
observedd
20
4
0
99 927.244
104
60
20
4
1
99 924.810
-72
60
55
50
4
2
99 918.102
-8
90
43
50
4
3
99 906.944
119
60
268 40
20 20
5 5
0 1
119 911.328 119 908.618
9 8
60 60
119 900.498
12
60
119 886.956
9
Another weak perturbation is also observed in the K = 9 levels, which is tentatively attributed to a (ΔK = -2, Δl = þ1) resonance with K = 7 of ν7 = 1þ1. Therefore, these levels with J > 35 were also given zero weights in the fit. With exclusion of the mentioned levels we were able to fit all the available infrared and rotational data within their experimental uncertainties. Reproduction of rotational data is shown in Table 3. It is also included, together with the reproduction of the infrared data, in Table S2 of the Supporting Information. The validity of the model of an isolated vibrational state is supported by the closeness of the centrifugal distortion parameters to the ground-state values as documented in Table 2.
J
K
observeda
6
0
139 894.787
-29
6
1
139 891.641
-16
6
2
139 882.236
6
3
139 866.433
6 6
4 5
139 844.556e 139 815.922
6
6
139 781.201
24
20
5
2
9
0
199 840.071
-15
20
5
3
9
1
199 835.579
2
20
5
4
119 868.302e 304
9
2
199 822.042
-12
20
6
0
139 894.798
-18
60
9
3
199 799.524
5
20
6
1
139 891.634
-23
60
9
4
199 768.304e
325
20
6
2
139 882.196
15
60
9 9
5 6
199 727.437 199 677.916
-3 2
20 20
6 6
3 4
139 866.414 24 139 844.562e 274
60 60
9
7
199 619.422
9
20
6
5
139 815.896
14
60
9
8
199 551.953
1
20
6
6
139 781.188
11
60
9
9
199 475.545
-3
20
8
0
179 859.320
7
90
14 0
299 724.628
-14
20
8
1
179 855.270
16
90
14 1
299 717.884
-13
20
8
2
179 843.180
101
90
14 2
299 697.653
-11
20
8
3
179 822.900
110
90
14 3 14 4
299 663.971 299 617.145e
22 386
20 20
8 8
4 5
179 794.640c 248 179 758.000 107
90 60
14 5
299 556.122
15
20
8
6
179 713.340
90
14 6
299 482.009
0
20
14 7
299 394.483
0
20
299 293.548
-4
’ ASSOCIATED CONTENT
14 8
20
14 9
299 179.192
-49
20
bS Supporting Information. Text files giving the spectral data (wavenumbers and frequencies of transitions) for the ground and ν4 = 1 vibrational states are denoted as S1 and S2, respectively. This material is available free of charge via the Internet at http:// pubs.acs.org.
14 10 299 051.614
35
20
14 11 298 910.599 14 12 298 756.330
-1 -9
20 20
O-C unc
38
60 60
a Present work (in MHz). b Observed - calculated (in kHz). c Experimental uncertainty (in kHz). d Reference 16 (in MHz). e Zero weight in the fit.
4. CONCLUSION We investigated the vibrational ground state and vibrational state ν4 = 1 of CH3NC in order to prepare the ground for studies of the progression of vibrational states ν8 = 1-4 and their mutual anharmonic resonances. For this purpose we needed a significant improvement of accuracy of the ground-state rotational energies. We achieved this by analyzing simultaneously the ground-state combination differences generated from the vibration-rotation transitions of the ν4 band with rotational transitions available from the literature and retrieved from the new measurements. The vibration-rotation wavenumbers of the ν4 band were analyzed together with rotational data from the excited ν4 = 1 state in the approximation of an isolated vibrational level, with exclusion of transitions perturbed by weak local resonances. The set of refined rotational and centrifugal distortion parameters up to the eighth order of expansion of the effective Hamiltonian provides a quantitative reproduction of all experimental data.
’ AUTHOR INFORMATION Corresponding Author
forthcoming paper after measurements of new rotational data in these excited levels are completed. The perturbation of the K = 3 and 4 levels of ν4 = 1 comes from the weak quartic anharmonic resonance with the ν8 = 3-3 level as shown in the J-reduced energy diagram in Figure 2. The closer coincidence occurs for K = 4 at low J values and is the reason for the large residuals observed in rotational spectra. For K = 3, the spacing between the two levels is larger for low J and the anharmonic interaction has no significant influence on fitting the rotational data. However, the difference of rotational constants B of these states B(ν4 = 1) < B(ν8 = 3) brings the K = 3 levels into a resonance crossing at higher values of J ≈ 60, which was clearly observed in the IR spectrum. Therefore, the infrared data pertaining to the K = 3 and 4 levels were given zero weights in the fit, while only the K = 4 rotational data were excluded. It should be noted that the K = 3 levels of ν4 = 1 cross also the K = 5 levels of ν8 = 3-1 at J ≈ 75. The corresponding higher order (ΔK = þ2, Δl = -1) resonance was assumed to be the main reason for the problematic reproduction of the K = 3 data in the previous analysis of the ν4 band.10
*Phone: þ420-26605 3426. Fax: þ420-28658 2307. E-mail:
[email protected].
’ ACKNOWLEDGMENT This work was supported by the Grant Agency of the Academy of Sciences of the Czech Republic (project IAA400400706) and the Ministry of Education, Youth and Sports of the Czech Republic (research program LC06071). Portions of this research were performed at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. ’ REFERENCES (1) SnaveIy, D. L.; Zare, R. N.; Miller, J. A.; Chandler, D. W. J. Phys. Chem. 1986, 90, 3544–3549. (2) Troe, J. J. Chem. Phys. 1977, 66, 4758–4775. (3) Rossi, M. J.; Pladziewicz, J. R.; Barker, J. R. J. Chem. Phys. 1983, 78, 6695–6708. (4) Hippler, H.; Troe, J.; Wendelken, H. J. J. Chem. Phys. 1983, 78, 6709–6717. 1067
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