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Diode laser overtone spectroscopy of hydrogen sulfide
I1 November
1994
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical
Physics Letters 229 (1994)
609-615
Diode laser overtone spectroscopy of hydrogen sulfide R. Gro13klo13,S .B. Rai I, R. Stuber, W. Demtriider Fachbereich Physik, Universitdt Kaiserslautern, D-67663 Kaiserslautern, Germany Received
19 August
1994
Abstract Overtone spectra of a B-type band of H2S in the range 11930-12300 cm-’ have been measured with an externally modulated tunable diode laser and a multipass absorption cell. The assignment of about 230 rotational lines, supported by the analysis of some lines of the isotopomer Hz%, allowed the determination of the molecular constants of the upper state, which is probably the (2, 2, 2) vibrational state, and revealed the existence of perturbations.
1. Introduction Hydrogen sulfide H2S is, like the water molecule H20, a near oblate asymmetric top. However, its spectrum is more complex due to the heavier mass of the sulfur atom and the mixture of isotopes (natural abundance of 95% 32S and 4.2% 34S). The rotational constants of the (0,0,O) vibrational ground state are well known from microwave spectroscopy [l-3] and far-infrared studies [4,5]. Little is, however, known about higher excited vibrational states and their mutual interactions. Bands corresponding to the excitation of the fundamental vibrational frequencies ~1, 23 and ~3 [ 6- 111 or their lower combinations have been studied up to excitation energies of 11000 cm-’ [ 12-191, using classical absorption spectroscopy, Fourier-transform or laser spectroscopy. Cross [ 131 and later Innes et al. [ 151 made attempts to analyze bands above 10000 cm-’ from low resolution spectra with only partly resolved lines. Recently nearly 130 rotational lines of H2.S have been measured with diode laser spectroscopy in the 12200 cm-’ re1On leave from the Department versity, Varanasi, India. Elsevier Science B.V. .SSDIOOO9-2614(94)01079-X
of Physics, Banaras Hindu Uni-
gion by Tate et al. [ 201, but no rotational assignment was given. In this Letter, we report the measurement and the partial analysis of Doppler-limited H;?S spectra in the region 11930-12300 cm-’ obtained with a continuously tunable diode laser spectrometer.
2. Experimental The experimental apparatus, shown in Fig. 1, has already been described in our earlier papers [ 21,221 and is therefore only briefly discussed here. The radiation from a single mode GaAlAs diode laser with antireflection coatings and external cavity, consisting of a collimating lens and a tunable Littrow grating, is phase- and amplitude-modulated in an external electro-optic LiTaOs modulator. The beam with 1 mW power passes 70 times through a multipass absorption cell with spherical dielectric mirrors, containing HzS gas at a pressure of 100 mbar and 99.5% purity (purchased from Aldrich Chemie) . The transmitted laser power was monitored by a sensitive photodiode with subsequent lock-in detection. The computer controls
R.GroJkloJ et nl./Chemical Physics Letters 229 (1994) 609-615
610
c 4
experiment EOM
diodelaser
Fig. 1. Experimental apparatus.
the wavelength tuning and stores the measured spectra. The absolute wavelengths were measured with an accuracy of lOA cm-’ by a travelling Michelson wavemeter. Two different diode lasers with maximum outputs at 840 and 820 nm were necessary to cover the whole measured spectral range.
3. Rotational analysis The rotational structure of the measured H2S band in the range 11930-12300cm-’ is illustratedin Fig. 2. It shows well-developed P- and R-branch structures on both sides of a weak Q branch. This clearly indicates a B-type band with AKc = AK, = f 1. An enlarged section of the spectrum between 12173 and 12182 cm-’ is shown in Fig. 3. The intense P- and R-lines with Ka = 0, Kc = J and Kc = 0, K, = J could be readily identified. The assignment of the intense P- and R-lines up to J’ = 14, based on the method of ground state differences, allowed an initial least-squares fit, using an asymmetric rotor program of Luckhaus and Quack [ 231. For this initial fit, the ground state constants, which are accurately known from Flaud et al. [5], were used as fixed known constants. Also the higher-order constants A’ and H’ of the upper state were set equal to those of the ground state and were used as fixed parameters. The only variable fit parameter are therefore the band origin ~0 and the rotational constants A, B and C.
The upper state constants obtained from this fit were used to search for further P-, Q- and R-lines with different values of K, and Kc, It was found, that rotational lines with intermediate K,, Kc values are rather weak and in many cases the predicted lines could not be found. The correct assignments of the new lines were always checked by the corresponding ground state combination differences. The assignments of nearly 230 lines of both isotopomers H232Sand Hz~~S,which represent about 30% of all measured lines, are listed in Table 1. From a least-squares fit of all assigned lines the molecular constants of the upper state were determined using the asymmetric rotor program [ 23 1. They correspond to 75 different upper levels. From these 217 assigned lines 88 transitions to 24 upper levels showed deviations AV = V&s- y,,lc > 0.02 cm-‘, which is twice as large as the experimental uncertainty. Since these lines are apparently perturbed, they were excluded from the final fit for the determination of the unperturbed molecular constants, which are compiled in Table 2. For this fit only the constants H’ were kept fixed at the ground state values of Flaud et al. [ 51, while the constants ~0, A’, B’, C’ and the A’ are free fit parameters. The standard deviation of this final fit was CT= 0.007 cm-‘. This fit was used to calculate the deviations AZJlisted in Table 1. Since the relative natural abundance of the isotopomers H234S and H232S is 4.2:95, only the most intense P- and R-lines of H234S could be unambigu-
R.GroJkloJ et al. /Chemical Physics Letters 229 (1994) 609-615
~ zl
2500
A
2000
>
5
1500
.r
1000
5
500 0 12000
wavenumber
[cm-l]
Fig. 2. The rotational structure of the measured H2S band in the range 11930-12300 cm-‘.
wavenumber [cm-‘] Fig. 3. Enlarged section of the spectrum between 12173 and 12182 cm- l. The lines marked by 0 could not be assigned.
611
612
R.Gro@kloJ et al. /Chemical
Table 1 The observed line positions and their rotational lines due to the H234S molecule J’
KL
14 14 13 13 13 13 12 12 12 12 11 11 11 11 10 10 10 10 10 10 10 9 9 9 9 9 9 9 9 9 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 I 7 7 7 7 I I
0
1 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 2 2 0 0 1 1 1
1 1 2 2 0 0 0 1 1
I 1 1 1 2 2 3 3 3 4 4 4 5 5 0 0 0 0 0 1 1
14 14 13 13 13 13 12 12 12 12 11 11 11 11 10 10 10 10 9 9 9 9 9 9 9 8 8 8 8 8 8 8 8 8 8 8 8 I I 7 I 6 6 6 5 5 5 4 4 I I I 7 I I 7
J”
KY
13 13 14 12 14 12 11 13 11 13 12 10 10 12 11 9 9 11 9 11 9 8 10 10 8 9 8 10 9 8 I 9 8 7 9 8 7 8 I 7 8 8 8 I 7 8 8 8 1 6 7 8 8 6 8 7
1 0 1 1 0 0
1 1 0 0 1 1 0 0 1 1 0 0 2 1 1 1 1 0 0 0 2 2 1 1 1 1 1 0 0 2 0 0 2 1 1 4 2 2 3 3 5 4 4 1 1 1 1 1 0 2
K: 13 13 14 12 14 12 11 13 11 13 12 10 10 12 11 9 9 11 8 10 8 8 10 IO 8 9 7 9 9
9
9
8 6 6 8 5 I 5 4 6 4 5
6
assignments.
Physics Letters 229 (1994) 609-615
The lines marked by a dagger represent the perturbed
lines and by a star the
Obs.
Ohs.-talc.
J’
K:,
K:
J”
K;
K;
Obs.
Ohs-talc.
12212.724 12212.724 11948.910 12212.830 11948.910 12212.830 12212.275 11967.012 12212.275 11967.012 11984.486 12211.045 12211.045 11984.486 12001.330 12209.160 12209.160 12001.330 12210.806 11983.681 12210.806 12206.599 12017.530 12017.530 12206.599 12192.321 12209.017 12000.668 12192.320 12209.077 12203.388 12033.124 12049.869 12203.388 12033.124 12049.869 12194.145 12 189.642 12206.693 12206.693 12189.642 12058.607 12174.012 12211.045 12215.138 12158.316 12062.889 12145.498 12226.109 12199.540 12065.131 12048.071 12039.060 12190.279 12048.011 12065.131
-0.001 -0.001 -0.005 -0.001 -0.005 -0.001 0.006 -0.002 0.006 -0.002 0.002 0.003 0.003 0.002 0.005 0.008 0.008 0.005 0.010 0.001 0.010 -0.004 -0.007 -0.007 -0.004 0.003 0.007 0.002 0.002 0.007 -0.009 0.004 -0.003 -0.009 0.004 -0.003 -0.005* 0.002 -0.002 -0.004 -0.002 0.321+ 0.340+ 0.355+ -0.167+ -0.172+ -0.172+ 0.354+ 0.320+ 0.004 0.001 0.003 0.002* 0.003* 0.003 0.002
7 7 7 I I I 1 7 I I I I 7 7 7 I I 7 7 I 7 7 7 I 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 4 4 4 6 6 6 7 7 0 0 0 1 1 1 1 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 4 5 5 5 6 6 6 6
7 6 6 6 6 6 6 6 6 5 5 5 5 4 4 4 3 3 3 1 1 1 0 0 6 6 6 6 6 6 6 6 5 5 5 5 5 5 5 4 4 4 4 3 3 3 2 2 2 2 2 1 1 1 0
6 6 I 8 7 I 8 I 6 8 7 7 6 7 I 6 7 7 6 7 I 6 8 6 7 5 6 7 5 6 7 5 7 6 5 I 6 5 6 7 6 6 5 6 6 5 6 6 6 6 5 5 6 I 5
0
6 5 7 7 5 5 7 7 5 6 6 4 4 3 5 3 2 4 2 0 2 2 1 1 7 5 5 7 5 5 I 5 6 4 4 6 6 4 4 5 3 5 3 2 4 2 1 3 1 3 1 0 2 0
12199.540 12203.672 12186.299 12032.783 12069.805 12069.743 12032.783 12186.299 12203.673 12018.309 12171.256 12075.721 12208.471 12084.027 12155.795 12211.945 12088.712 12136.602 12206.600 12081.572 12132.847 12250.737 11959.314 12259.599 12062.400 12195.025 12079.757 12062.400 12195.025 12019.157 12053.355 12185.749 12047.915 12085.340 12200.000 12047.905 12182.319 12200.036 12085.102 12033.894 12089.990 12167.759 12206.02 1 12093.479 12156.229 12217.629 12101.194 12136.563 12093.363 12150.580 12232.605 12245.621 12154.424 11985.272 12246.282
0.003 0.002 -0.003 0.006 0.010 -0.012 0.001 -0.008 -0.009 0.159’ 0.1611 0.154+ 0.170+ 0.426+ 0.435+ 0.414+ -0.468+ -0.455+ -0.452+ -0.6941 -0.698+ -0.680+ 0.713+ 0.692+ 0.002 0.002 -0.016 0.002 0.001 -0.009 0.010* -0.008* 0.027 0.017 0.024 -0.008 -0.001 -0.012 -0.017 -0.484+ -0.499+ -0.494+ -0.491+ -0.246+ -0.235+ -0.242+ 0.208+ 0.204+ -0.504+ -0.498+ -0.501+ 0.004 0.015 0.014 0.002
2 0 2 2 3 1 1 1 3 1 3 3 4 2 4 5 3 5 I 5 5 8 6 1 1 1 0 0 2 0 0 2 2 2 1 1 1 3 2 4 2 2 5 3 3 5 3 6 4 4 5 5 I 5
I
R.GroJ’kloJ et al./Chemical
613
Physics Letters 229 (1994) 609-615
Table I Continued .I’ 6 6 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
K: 6 6 0 0 0 0 0 1 1
1 1 1 1 2 2 2 2 2 2 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 0 0
I 1 1 1 1 1 I
I 1 2 2 2 2 2 2 2 3 3 3 3 3
0
0 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 3 3 3 2 2 2
I 1 1 I 2 2 1 1 1 0 0 0 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 1
J”
K‘!/
6 7 5 4 6 6 4 6 4 4 6 5 5 6 5 5 4 5 4 5 5 5 4 6 5 5 4 5 4 6 5 4 4 5 6 5 3 5 4 3 5 3 5 4 4 3 5 4 4 3 4 5 4 5 4 4 3 4
5 7 1 1 1 1 1 0 0 2 2 2 0 1 3 1 1 3 3 4 4 2 4 5 5 3 3 5 3 6 4 4 4 4 6 1 1 0 2 0 0 0 2 2 0 2 1 3 1 1
I 3 3 4 4 2 2 4
K;
Obs.
Ohs.-talc.
J’
K:,
K:
J”
K::
K;
Obs.
Ohs.-talc.
I
12150.522 11985.491 12093.821 12189.858 12076.085 12067.015 12 180.606 12076.085 12189.858 12195.531 12062.334 12100.600 12177.613 12062.443 12099.653 12177.711 12195.916 12109.633 12199.404 12104.144 12113.153 12147.126 12194.834 12017.153 12108.321 12141.263 12231.028 12104.945 12218.413 12011.402 12157.133 1223 1.435 12232.825 12151.153 12011.906 12089.144 12 184.026 12089.144 12107.070 12 184.063 12080.032 12174.812 12076.001 12115.900 12172.049 12189.858 12076.519 12112.770 12172.567 12191.686 12157.717 12061.468 12123.198 12033.419 12115.101 12162.343 12203.389 12120.346
0.025 0.019 0.003 0.000 -0.005 0.006* 0.014* -0.007 -0.007 0.022 0.009 0.016 0.029 -0.013 -0.005 0.004 0.006 0.167+ 0.166+ -0.083+ -0.026+ -0.047+ -0.021+ -0.1 lo+ -0.149+ -0.146+ -0.1531 -0.270+ -0.2581 -0.006 -0.017 -0.019 -0.012 -0.007 -0.014 -0.001 0.002 -0.016 -0.015 -0.016 -0.023* -o.oos* 0.081+ 0.051+ 0.036+ 0.065+ -0.030+ -0.029+ -0.0221 -0.024+ 0.555+ 0.558+ 0.544+ -0.105+ -0.099+ -0.100+ -0.104+ -0.023+
4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 0
3 3 4 4 4 4 4 4 4 0 0 0 0 1 1 1 I 1 1 2 2 2 2 2 2 2 3 3 3 3 3 3 3 0 0 0 1 1 1 1 1 1 1 1 2 2 2 2 2 2 0 0 1 1 1 I 1 0
1 I 1 1 1 1 0 0 0 3 3 3 3 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1 1 1 0 0 0 2 2 2 2 2 2 2 2 1 1 1 1 1 1 0 0 0 1
4 3 3 5 5 4 4 3 5 4 2 3 2 3 2 4 3 3 2 4
2 2 3 5 3 3 3 3 5 1 1 I 1 2 0 0 2 0 2 1 1 1 1 1 3 3 4 2 2 2 2 2 4 1 1 1 2 0 0 2 0 0 2 2 3 I 1 1 3 1 I 1 2 0 0 2 0 I
2 2 0 0 2 2 1 1 1 4 2 2 2 2 2 4 1 3 1 3 3 1 2 2 0 2 0 2 2 0 1 1 1 1 1 3 1 1 3 I 1 2 0 2 0 0 2 1 1 I 0 2 0 2 0 1 1 1
12146.798 12220.750 12216.018 12036.732 12069.677 12159.442 12151.374 12218.671 12037.912 12101.537 12177.418 12120.665 12168.207 12119.403 12177.790 12101.616 12129.373 12165.313 12181.585 12090.662 12167.375 12187.665 12152.698 12209.467 12130.365 12073.789 12060.970 12087.435 12161.372 12199.404 12203.938 12151.736 12063.437 12133.442 12169.487 12113.133 12129.876 12171.288 12113.643 12077.661 12162.035 12158.170 12137.821 12099.795 12083.854 12181.872 12162.948 12188.628 12088.376 12152.584 12142.621 12123.698 12105.317 12125.671 12163.689 12112.237 12153.658 12134.370
-0.037+ -0.029+ -0.001 -0.001 0.005 -0.001 0.008 -0.003 0.003 0.005 0.006 0.012 0.008’ -0.001 0.010 -0.008 0.032+ 0.028+ 0.037+ -0.041+ -0.004+ -0.039+ -0.004 0.006 -0.002 -0.002 0.008 0.007 0.00 1 0.009 -0.002 0.003 -0.003 0.001 -0.004 0.017 -0.007 -0.010 0.023 -0.015 0.003* -0.005 -0.001 -0.003 0.010 0.011 0.009 -0.004 -0.006 0.002 -0.007 -0.007 0.00 1 0.002 0.004 -0.007 -0.00 1 -0.003
1 4 4 6 6 4 6 4 3 5 3 5 5 3 5 3 2 2 2 1 3 1 2 0 2 2 1 1 0 2 0 1 1 1 5 3 5 3 3 5 3 4 2 4 2 4 2 4 2 3 3 1 1 1 3 1 0
I I 1 1 0 0 0
3 2 3 2 3 4 4 4 3 2 2 3 4 2 1 3 2 1 3 3 1 2 2 3 3 1 2 1 3 2 1 2 2 2 0 2 I 1
614
R.GroJkloJ
Table 2 Rotational constants given in parentheses
B C A
for the upper state (cm-‘).
et al./Chemical
The errors arc
hJ hJK hK
8.133(2) 4.4098(3) 9.8116(3) 0.66(6)x 10’ -0.21(3)x102 0.27(3) ~10’ 0.29(3)x103 0.12(12)x10” 0.271 x106 (fixed) -0.1533~10~ (fixed) 0.126~10~ (fixed) 0.1381~10~ (fixed) 0.1354~10” (fixed) -0.485 x IO6 (fixed) 0.123~10~ (fixed)
8.16(2) 4.409( 1) 9.61(4) 0.66~10~ (fixed) -0.21 x10* (fixed) 0.27~10~ (fixed) 0.29 x IO3 (fixed) 0.12~10~ (fixed) 0.271~10~ (fixed) -0.1533~10~ (fixed) 0.126~10~ (fixed) 0.1381~10~ (fixed) 0.1354~10~ (fixed) -0.485 x IO6 (fixed) 0.123~10~ (fixed)
VO
12149.463(2)
12140.36(3)
AJ AJK AK 6J SK HJ
HJK HKJ HK
ously assigned. They are marked in Table 1 by a star. Since the ground state constants of Hz~~S are also given by Flaud et al. [S] we could determine the upper state rotational constants A,,), B,/ and C,! of Hz~~S, which are listed in Table 2. For this fit of only 11 lines for H234S the constants ~0, A’, B’ and C’ were used as fit parameters, while all other constants A’ and H’ were set equal to the constants of Hz~~S in the first column of Table 2. The vibrational assignment of the upper state is still not completely safe. Tate et al. [20] quoted possible assignments(4,2,0),(3,2,1),(5,0,0),(4,0,1),(1, 4, 2) and (0, 4, 3). They did not give any force field calculations which might be used for a definite identification of the upper states. The band origin of the band analyzed in our work is at 12 149.46 cm-‘. When using the force field calculations of Senekowitsch et al. [24] it turns out, that none of the upper states assigned in Ref. [20] match with this measured band origin. A new assignment of the upper state is therefore necessary. It is attempted in the following way: Based on the vibrational constants of Senekowitsch et al., given in Table IV of Ref. [ 241, the term values of possible vibrational states are calculated around the energy of 12150 cm-’ corresponding to our measured band origin. Since the theoretical term values in Ref. [24] around 10000 cm-’ are higher by IO-20 cm-‘,
Physics Letters 229 (1994) 609-615
we searched for vibrational levels with theoretical term values around 12140-12190 cm-‘. This offers three possible upper levels (1, 2, 3) at 12143.5 cm-‘, (2, 2, 2) at 12183 cm-’ and (2,0, 3) at 12186.8 cm-‘. Since the upper levels ( 1, 2, 3) and (2, 0, 3) would correspond to A-type bands, they can be excluded. This leaves as the most probable assignment (2,2,2) for the upper vibrational state, provided the theoretical constants in Ref. [ 241 are sufficiently accurate. Since only about 30% of all measured lines could be assigned up to now, further work is needed to identify the perturbations and to confirm the vibrational assignment.
Acknowledgement We thank the Deutsche Forschungsgemeinschaft for financial support. We also thank Professor Goebel and Dr. Sacher, Marburg for providing us with the antireflection coatings of the laser diodes. We thank Dr. Luckhaus for sending us his asymmetric rotor program.
References Lll C.A. Burrus and W. Gordy, Phys. Rev. 92 (1935) 274. L21C. Huiszoon and A. Dymanus, Physica 31 ( 1965) 1049. L31 P. Helminger, R.L. Cook and EC. De Lucia, J. Chem. Phys. 56 (1972) 4581. [41 R.E. Miller, G.E. Leroi and T.M. Hard, J. Chem. Phys. 50 (1969) 677. [51 J.M. Flaud, C. Camy-Peyret and J.W.C. Johns, Can. J. Phys. 61 (1983) 1462. and J.W.C. [61 C. Camy-Peyret, J.M. Flaud, L. Lechuga-Fossat Johns, J. Mol. Spectry. 109 (1985) 300. [71 H.C. Allen Jr. and E.K. Plyler, J. Chem. Phys. 25 (1956) 1132. [81 L.L. Straw, J. Mol. Spectry. 97 (1983) 9. [91 Wm. Lane, T.H. Edwards, J.R. Gillis, ES. Bonomo and F.J. Murcray, J. Mol. Spectry. 95 ( 1982) 365. J.M. Flaud, C. Camy-Peyret and J.W.C. [lOI L. Lechuga-Fossat, Johns, Can. J. Phys. 62 (1984) 1889. [Ill J.R. Gillis and T.H. Edwards, J. Mol. Spectry. 85 (1981) 55. 1121 L.E. Snyder and T.H. Edwards, J. Mol. Spectry. 3 1 ( 1969) 347. [I31 PC. Cross, Phys. Rev. 48 (1935) 7. [I41 H.R. Grady, PC. Cross and G.W. King, Phys. Rev. 75 (1949) 1450. [I51 K.K. Innes, PC. Cross and E.J. Bair, J. Chem. Phys. 21 (1953) 545.
R.GroJkloJ et al. /Chemical Physics Letters 229 (1994) 609-615 [ 161 H.C. Allen and E.K. Plyler, J. Res. Natl. Bur. Stand. 52 (1954) 205. [ 171 G.L. Ordway, PC. Cross and E.J. Bair, J. Chem. Phys. 23 (1955) 541. [ 181 T.H. Edwards, N.K. Moncur and L.E. Snyder, J. Chem. Phys. 46 (1967) 2139. [ 191 L. Lechuga-Fossat, J.M. Flaud, C. Camy-Peyret, l? Arcas and M. Cuisenier, Mol. Phys. 61 (1987) 23. [20] D.A. Tate, L. Wang and T.F. Gallagher, in: XIth International conference of laser spectroscopy, eds. L. Bloomfield, T. Gallagher and D. Larson (American Institute of Physics, New York, 1993) p.134.
615
[21] R. GroOklo8, H. Wenz, S.B. Rai and W. Demtriider, communicated. [22] R. GroSklol3, P Kersten and W. Demtrijder, Appl. Phys. B. 58 (1994) 137. [23] D. Luckhausand M. Quack, Chem. Phys. Letters 199 (1992) 293. [24] J. Senekowitsch, S. Carter, A. Zilch, H.J. Werner, N.C. Handy and P Rosmus, J. Chem. Phys. 90 (1989) 783.
1994
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical
Physics Letters 229 (1994)
609-615
Diode laser overtone spectroscopy of hydrogen sulfide R. Gro13klo13,S .B. Rai I, R. Stuber, W. Demtriider Fachbereich Physik, Universitdt Kaiserslautern, D-67663 Kaiserslautern, Germany Received
19 August
1994
Abstract Overtone spectra of a B-type band of H2S in the range 11930-12300 cm-’ have been measured with an externally modulated tunable diode laser and a multipass absorption cell. The assignment of about 230 rotational lines, supported by the analysis of some lines of the isotopomer Hz%, allowed the determination of the molecular constants of the upper state, which is probably the (2, 2, 2) vibrational state, and revealed the existence of perturbations.
1. Introduction Hydrogen sulfide H2S is, like the water molecule H20, a near oblate asymmetric top. However, its spectrum is more complex due to the heavier mass of the sulfur atom and the mixture of isotopes (natural abundance of 95% 32S and 4.2% 34S). The rotational constants of the (0,0,O) vibrational ground state are well known from microwave spectroscopy [l-3] and far-infrared studies [4,5]. Little is, however, known about higher excited vibrational states and their mutual interactions. Bands corresponding to the excitation of the fundamental vibrational frequencies ~1, 23 and ~3 [ 6- 111 or their lower combinations have been studied up to excitation energies of 11000 cm-’ [ 12-191, using classical absorption spectroscopy, Fourier-transform or laser spectroscopy. Cross [ 131 and later Innes et al. [ 151 made attempts to analyze bands above 10000 cm-’ from low resolution spectra with only partly resolved lines. Recently nearly 130 rotational lines of H2.S have been measured with diode laser spectroscopy in the 12200 cm-’ re1On leave from the Department versity, Varanasi, India. Elsevier Science B.V. .SSDIOOO9-2614(94)01079-X
of Physics, Banaras Hindu Uni-
gion by Tate et al. [ 201, but no rotational assignment was given. In this Letter, we report the measurement and the partial analysis of Doppler-limited H;?S spectra in the region 11930-12300 cm-’ obtained with a continuously tunable diode laser spectrometer.
2. Experimental The experimental apparatus, shown in Fig. 1, has already been described in our earlier papers [ 21,221 and is therefore only briefly discussed here. The radiation from a single mode GaAlAs diode laser with antireflection coatings and external cavity, consisting of a collimating lens and a tunable Littrow grating, is phase- and amplitude-modulated in an external electro-optic LiTaOs modulator. The beam with 1 mW power passes 70 times through a multipass absorption cell with spherical dielectric mirrors, containing HzS gas at a pressure of 100 mbar and 99.5% purity (purchased from Aldrich Chemie) . The transmitted laser power was monitored by a sensitive photodiode with subsequent lock-in detection. The computer controls
R.GroJkloJ et nl./Chemical Physics Letters 229 (1994) 609-615
610
c 4
experiment EOM
diodelaser
Fig. 1. Experimental apparatus.
the wavelength tuning and stores the measured spectra. The absolute wavelengths were measured with an accuracy of lOA cm-’ by a travelling Michelson wavemeter. Two different diode lasers with maximum outputs at 840 and 820 nm were necessary to cover the whole measured spectral range.
3. Rotational analysis The rotational structure of the measured H2S band in the range 11930-12300cm-’ is illustratedin Fig. 2. It shows well-developed P- and R-branch structures on both sides of a weak Q branch. This clearly indicates a B-type band with AKc = AK, = f 1. An enlarged section of the spectrum between 12173 and 12182 cm-’ is shown in Fig. 3. The intense P- and R-lines with Ka = 0, Kc = J and Kc = 0, K, = J could be readily identified. The assignment of the intense P- and R-lines up to J’ = 14, based on the method of ground state differences, allowed an initial least-squares fit, using an asymmetric rotor program of Luckhaus and Quack [ 231. For this initial fit, the ground state constants, which are accurately known from Flaud et al. [5], were used as fixed known constants. Also the higher-order constants A’ and H’ of the upper state were set equal to those of the ground state and were used as fixed parameters. The only variable fit parameter are therefore the band origin ~0 and the rotational constants A, B and C.
The upper state constants obtained from this fit were used to search for further P-, Q- and R-lines with different values of K, and Kc, It was found, that rotational lines with intermediate K,, Kc values are rather weak and in many cases the predicted lines could not be found. The correct assignments of the new lines were always checked by the corresponding ground state combination differences. The assignments of nearly 230 lines of both isotopomers H232Sand Hz~~S,which represent about 30% of all measured lines, are listed in Table 1. From a least-squares fit of all assigned lines the molecular constants of the upper state were determined using the asymmetric rotor program [ 23 1. They correspond to 75 different upper levels. From these 217 assigned lines 88 transitions to 24 upper levels showed deviations AV = V&s- y,,lc > 0.02 cm-‘, which is twice as large as the experimental uncertainty. Since these lines are apparently perturbed, they were excluded from the final fit for the determination of the unperturbed molecular constants, which are compiled in Table 2. For this fit only the constants H’ were kept fixed at the ground state values of Flaud et al. [ 51, while the constants ~0, A’, B’, C’ and the A’ are free fit parameters. The standard deviation of this final fit was CT= 0.007 cm-‘. This fit was used to calculate the deviations AZJlisted in Table 1. Since the relative natural abundance of the isotopomers H234S and H232S is 4.2:95, only the most intense P- and R-lines of H234S could be unambigu-
R.GroJkloJ et al. /Chemical Physics Letters 229 (1994) 609-615
~ zl
2500
A
2000
>
5
1500
.r
1000
5
500 0 12000
wavenumber
[cm-l]
Fig. 2. The rotational structure of the measured H2S band in the range 11930-12300 cm-‘.
wavenumber [cm-‘] Fig. 3. Enlarged section of the spectrum between 12173 and 12182 cm- l. The lines marked by 0 could not be assigned.
611
612
R.Gro@kloJ et al. /Chemical
Table 1 The observed line positions and their rotational lines due to the H234S molecule J’
KL
14 14 13 13 13 13 12 12 12 12 11 11 11 11 10 10 10 10 10 10 10 9 9 9 9 9 9 9 9 9 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 I 7 7 7 7 I I
0
1 0 0
1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 2 2 0 0 1 1 1
1 1 2 2 0 0 0 1 1
I 1 1 1 2 2 3 3 3 4 4 4 5 5 0 0 0 0 0 1 1
14 14 13 13 13 13 12 12 12 12 11 11 11 11 10 10 10 10 9 9 9 9 9 9 9 8 8 8 8 8 8 8 8 8 8 8 8 I I 7 I 6 6 6 5 5 5 4 4 I I I 7 I I 7
J”
KY
13 13 14 12 14 12 11 13 11 13 12 10 10 12 11 9 9 11 9 11 9 8 10 10 8 9 8 10 9 8 I 9 8 7 9 8 7 8 I 7 8 8 8 I 7 8 8 8 1 6 7 8 8 6 8 7
1 0 1 1 0 0
1 1 0 0 1 1 0 0 1 1 0 0 2 1 1 1 1 0 0 0 2 2 1 1 1 1 1 0 0 2 0 0 2 1 1 4 2 2 3 3 5 4 4 1 1 1 1 1 0 2
K: 13 13 14 12 14 12 11 13 11 13 12 10 10 12 11 9 9 11 8 10 8 8 10 IO 8 9 7 9 9
9
9
8 6 6 8 5 I 5 4 6 4 5
6
assignments.
Physics Letters 229 (1994) 609-615
The lines marked by a dagger represent the perturbed
lines and by a star the
Obs.
Ohs.-talc.
J’
K:,
K:
J”
K;
K;
Obs.
Ohs-talc.
12212.724 12212.724 11948.910 12212.830 11948.910 12212.830 12212.275 11967.012 12212.275 11967.012 11984.486 12211.045 12211.045 11984.486 12001.330 12209.160 12209.160 12001.330 12210.806 11983.681 12210.806 12206.599 12017.530 12017.530 12206.599 12192.321 12209.017 12000.668 12192.320 12209.077 12203.388 12033.124 12049.869 12203.388 12033.124 12049.869 12194.145 12 189.642 12206.693 12206.693 12189.642 12058.607 12174.012 12211.045 12215.138 12158.316 12062.889 12145.498 12226.109 12199.540 12065.131 12048.071 12039.060 12190.279 12048.011 12065.131
-0.001 -0.001 -0.005 -0.001 -0.005 -0.001 0.006 -0.002 0.006 -0.002 0.002 0.003 0.003 0.002 0.005 0.008 0.008 0.005 0.010 0.001 0.010 -0.004 -0.007 -0.007 -0.004 0.003 0.007 0.002 0.002 0.007 -0.009 0.004 -0.003 -0.009 0.004 -0.003 -0.005* 0.002 -0.002 -0.004 -0.002 0.321+ 0.340+ 0.355+ -0.167+ -0.172+ -0.172+ 0.354+ 0.320+ 0.004 0.001 0.003 0.002* 0.003* 0.003 0.002
7 7 7 I I I 1 7 I I I I 7 7 7 I I 7 7 I 7 7 7 I 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 4 4 4 6 6 6 7 7 0 0 0 1 1 1 1 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 4 5 5 5 6 6 6 6
7 6 6 6 6 6 6 6 6 5 5 5 5 4 4 4 3 3 3 1 1 1 0 0 6 6 6 6 6 6 6 6 5 5 5 5 5 5 5 4 4 4 4 3 3 3 2 2 2 2 2 1 1 1 0
6 6 I 8 7 I 8 I 6 8 7 7 6 7 I 6 7 7 6 7 I 6 8 6 7 5 6 7 5 6 7 5 7 6 5 I 6 5 6 7 6 6 5 6 6 5 6 6 6 6 5 5 6 I 5
0
6 5 7 7 5 5 7 7 5 6 6 4 4 3 5 3 2 4 2 0 2 2 1 1 7 5 5 7 5 5 I 5 6 4 4 6 6 4 4 5 3 5 3 2 4 2 1 3 1 3 1 0 2 0
12199.540 12203.672 12186.299 12032.783 12069.805 12069.743 12032.783 12186.299 12203.673 12018.309 12171.256 12075.721 12208.471 12084.027 12155.795 12211.945 12088.712 12136.602 12206.600 12081.572 12132.847 12250.737 11959.314 12259.599 12062.400 12195.025 12079.757 12062.400 12195.025 12019.157 12053.355 12185.749 12047.915 12085.340 12200.000 12047.905 12182.319 12200.036 12085.102 12033.894 12089.990 12167.759 12206.02 1 12093.479 12156.229 12217.629 12101.194 12136.563 12093.363 12150.580 12232.605 12245.621 12154.424 11985.272 12246.282
0.003 0.002 -0.003 0.006 0.010 -0.012 0.001 -0.008 -0.009 0.159’ 0.1611 0.154+ 0.170+ 0.426+ 0.435+ 0.414+ -0.468+ -0.455+ -0.452+ -0.6941 -0.698+ -0.680+ 0.713+ 0.692+ 0.002 0.002 -0.016 0.002 0.001 -0.009 0.010* -0.008* 0.027 0.017 0.024 -0.008 -0.001 -0.012 -0.017 -0.484+ -0.499+ -0.494+ -0.491+ -0.246+ -0.235+ -0.242+ 0.208+ 0.204+ -0.504+ -0.498+ -0.501+ 0.004 0.015 0.014 0.002
2 0 2 2 3 1 1 1 3 1 3 3 4 2 4 5 3 5 I 5 5 8 6 1 1 1 0 0 2 0 0 2 2 2 1 1 1 3 2 4 2 2 5 3 3 5 3 6 4 4 5 5 I 5
I
R.GroJ’kloJ et al./Chemical
613
Physics Letters 229 (1994) 609-615
Table I Continued .I’ 6 6 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
K: 6 6 0 0 0 0 0 1 1
1 1 1 1 2 2 2 2 2 2 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 0 0
I 1 1 1 1 1 I
I 1 2 2 2 2 2 2 2 3 3 3 3 3
0
0 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 3 3 3 2 2 2
I 1 1 I 2 2 1 1 1 0 0 0 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 1
J”
K‘!/
6 7 5 4 6 6 4 6 4 4 6 5 5 6 5 5 4 5 4 5 5 5 4 6 5 5 4 5 4 6 5 4 4 5 6 5 3 5 4 3 5 3 5 4 4 3 5 4 4 3 4 5 4 5 4 4 3 4
5 7 1 1 1 1 1 0 0 2 2 2 0 1 3 1 1 3 3 4 4 2 4 5 5 3 3 5 3 6 4 4 4 4 6 1 1 0 2 0 0 0 2 2 0 2 1 3 1 1
I 3 3 4 4 2 2 4
K;
Obs.
Ohs.-talc.
J’
K:,
K:
J”
K::
K;
Obs.
Ohs.-talc.
I
12150.522 11985.491 12093.821 12189.858 12076.085 12067.015 12 180.606 12076.085 12189.858 12195.531 12062.334 12100.600 12177.613 12062.443 12099.653 12177.711 12195.916 12109.633 12199.404 12104.144 12113.153 12147.126 12194.834 12017.153 12108.321 12141.263 12231.028 12104.945 12218.413 12011.402 12157.133 1223 1.435 12232.825 12151.153 12011.906 12089.144 12 184.026 12089.144 12107.070 12 184.063 12080.032 12174.812 12076.001 12115.900 12172.049 12189.858 12076.519 12112.770 12172.567 12191.686 12157.717 12061.468 12123.198 12033.419 12115.101 12162.343 12203.389 12120.346
0.025 0.019 0.003 0.000 -0.005 0.006* 0.014* -0.007 -0.007 0.022 0.009 0.016 0.029 -0.013 -0.005 0.004 0.006 0.167+ 0.166+ -0.083+ -0.026+ -0.047+ -0.021+ -0.1 lo+ -0.149+ -0.146+ -0.1531 -0.270+ -0.2581 -0.006 -0.017 -0.019 -0.012 -0.007 -0.014 -0.001 0.002 -0.016 -0.015 -0.016 -0.023* -o.oos* 0.081+ 0.051+ 0.036+ 0.065+ -0.030+ -0.029+ -0.0221 -0.024+ 0.555+ 0.558+ 0.544+ -0.105+ -0.099+ -0.100+ -0.104+ -0.023+
4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 0
3 3 4 4 4 4 4 4 4 0 0 0 0 1 1 1 I 1 1 2 2 2 2 2 2 2 3 3 3 3 3 3 3 0 0 0 1 1 1 1 1 1 1 1 2 2 2 2 2 2 0 0 1 1 1 I 1 0
1 I 1 1 1 1 0 0 0 3 3 3 3 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1 1 1 0 0 0 2 2 2 2 2 2 2 2 1 1 1 1 1 1 0 0 0 1
4 3 3 5 5 4 4 3 5 4 2 3 2 3 2 4 3 3 2 4
2 2 3 5 3 3 3 3 5 1 1 I 1 2 0 0 2 0 2 1 1 1 1 1 3 3 4 2 2 2 2 2 4 1 1 1 2 0 0 2 0 0 2 2 3 I 1 1 3 1 I 1 2 0 0 2 0 I
2 2 0 0 2 2 1 1 1 4 2 2 2 2 2 4 1 3 1 3 3 1 2 2 0 2 0 2 2 0 1 1 1 1 1 3 1 1 3 I 1 2 0 2 0 0 2 1 1 I 0 2 0 2 0 1 1 1
12146.798 12220.750 12216.018 12036.732 12069.677 12159.442 12151.374 12218.671 12037.912 12101.537 12177.418 12120.665 12168.207 12119.403 12177.790 12101.616 12129.373 12165.313 12181.585 12090.662 12167.375 12187.665 12152.698 12209.467 12130.365 12073.789 12060.970 12087.435 12161.372 12199.404 12203.938 12151.736 12063.437 12133.442 12169.487 12113.133 12129.876 12171.288 12113.643 12077.661 12162.035 12158.170 12137.821 12099.795 12083.854 12181.872 12162.948 12188.628 12088.376 12152.584 12142.621 12123.698 12105.317 12125.671 12163.689 12112.237 12153.658 12134.370
-0.037+ -0.029+ -0.001 -0.001 0.005 -0.001 0.008 -0.003 0.003 0.005 0.006 0.012 0.008’ -0.001 0.010 -0.008 0.032+ 0.028+ 0.037+ -0.041+ -0.004+ -0.039+ -0.004 0.006 -0.002 -0.002 0.008 0.007 0.00 1 0.009 -0.002 0.003 -0.003 0.001 -0.004 0.017 -0.007 -0.010 0.023 -0.015 0.003* -0.005 -0.001 -0.003 0.010 0.011 0.009 -0.004 -0.006 0.002 -0.007 -0.007 0.00 1 0.002 0.004 -0.007 -0.00 1 -0.003
1 4 4 6 6 4 6 4 3 5 3 5 5 3 5 3 2 2 2 1 3 1 2 0 2 2 1 1 0 2 0 1 1 1 5 3 5 3 3 5 3 4 2 4 2 4 2 4 2 3 3 1 1 1 3 1 0
I I 1 1 0 0 0
3 2 3 2 3 4 4 4 3 2 2 3 4 2 1 3 2 1 3 3 1 2 2 3 3 1 2 1 3 2 1 2 2 2 0 2 I 1
614
R.GroJkloJ
Table 2 Rotational constants given in parentheses
B C A
for the upper state (cm-‘).
et al./Chemical
The errors arc
hJ hJK hK
8.133(2) 4.4098(3) 9.8116(3) 0.66(6)x 10’ -0.21(3)x102 0.27(3) ~10’ 0.29(3)x103 0.12(12)x10” 0.271 x106 (fixed) -0.1533~10~ (fixed) 0.126~10~ (fixed) 0.1381~10~ (fixed) 0.1354~10” (fixed) -0.485 x IO6 (fixed) 0.123~10~ (fixed)
8.16(2) 4.409( 1) 9.61(4) 0.66~10~ (fixed) -0.21 x10* (fixed) 0.27~10~ (fixed) 0.29 x IO3 (fixed) 0.12~10~ (fixed) 0.271~10~ (fixed) -0.1533~10~ (fixed) 0.126~10~ (fixed) 0.1381~10~ (fixed) 0.1354~10~ (fixed) -0.485 x IO6 (fixed) 0.123~10~ (fixed)
VO
12149.463(2)
12140.36(3)
AJ AJK AK 6J SK HJ
HJK HKJ HK
ously assigned. They are marked in Table 1 by a star. Since the ground state constants of Hz~~S are also given by Flaud et al. [S] we could determine the upper state rotational constants A,,), B,/ and C,! of Hz~~S, which are listed in Table 2. For this fit of only 11 lines for H234S the constants ~0, A’, B’ and C’ were used as fit parameters, while all other constants A’ and H’ were set equal to the constants of Hz~~S in the first column of Table 2. The vibrational assignment of the upper state is still not completely safe. Tate et al. [20] quoted possible assignments(4,2,0),(3,2,1),(5,0,0),(4,0,1),(1, 4, 2) and (0, 4, 3). They did not give any force field calculations which might be used for a definite identification of the upper states. The band origin of the band analyzed in our work is at 12 149.46 cm-‘. When using the force field calculations of Senekowitsch et al. [24] it turns out, that none of the upper states assigned in Ref. [20] match with this measured band origin. A new assignment of the upper state is therefore necessary. It is attempted in the following way: Based on the vibrational constants of Senekowitsch et al., given in Table IV of Ref. [ 241, the term values of possible vibrational states are calculated around the energy of 12150 cm-’ corresponding to our measured band origin. Since the theoretical term values in Ref. [24] around 10000 cm-’ are higher by IO-20 cm-‘,
Physics Letters 229 (1994) 609-615
we searched for vibrational levels with theoretical term values around 12140-12190 cm-‘. This offers three possible upper levels (1, 2, 3) at 12143.5 cm-‘, (2, 2, 2) at 12183 cm-’ and (2,0, 3) at 12186.8 cm-‘. Since the upper levels ( 1, 2, 3) and (2, 0, 3) would correspond to A-type bands, they can be excluded. This leaves as the most probable assignment (2,2,2) for the upper vibrational state, provided the theoretical constants in Ref. [ 241 are sufficiently accurate. Since only about 30% of all measured lines could be assigned up to now, further work is needed to identify the perturbations and to confirm the vibrational assignment.
Acknowledgement We thank the Deutsche Forschungsgemeinschaft for financial support. We also thank Professor Goebel and Dr. Sacher, Marburg for providing us with the antireflection coatings of the laser diodes. We thank Dr. Luckhaus for sending us his asymmetric rotor program.
References Lll C.A. Burrus and W. Gordy, Phys. Rev. 92 (1935) 274. L21C. Huiszoon and A. Dymanus, Physica 31 ( 1965) 1049. L31 P. Helminger, R.L. Cook and EC. De Lucia, J. Chem. Phys. 56 (1972) 4581. [41 R.E. Miller, G.E. Leroi and T.M. Hard, J. Chem. Phys. 50 (1969) 677. [51 J.M. Flaud, C. Camy-Peyret and J.W.C. Johns, Can. J. Phys. 61 (1983) 1462. and J.W.C. [61 C. Camy-Peyret, J.M. Flaud, L. Lechuga-Fossat Johns, J. Mol. Spectry. 109 (1985) 300. [71 H.C. Allen Jr. and E.K. Plyler, J. Chem. Phys. 25 (1956) 1132. [81 L.L. Straw, J. Mol. Spectry. 97 (1983) 9. [91 Wm. Lane, T.H. Edwards, J.R. Gillis, ES. Bonomo and F.J. Murcray, J. Mol. Spectry. 95 ( 1982) 365. J.M. Flaud, C. Camy-Peyret and J.W.C. [lOI L. Lechuga-Fossat, Johns, Can. J. Phys. 62 (1984) 1889. [Ill J.R. Gillis and T.H. Edwards, J. Mol. Spectry. 85 (1981) 55. 1121 L.E. Snyder and T.H. Edwards, J. Mol. Spectry. 3 1 ( 1969) 347. [I31 PC. Cross, Phys. Rev. 48 (1935) 7. [I41 H.R. Grady, PC. Cross and G.W. King, Phys. Rev. 75 (1949) 1450. [I51 K.K. Innes, PC. Cross and E.J. Bair, J. Chem. Phys. 21 (1953) 545.
R.GroJkloJ et al. /Chemical Physics Letters 229 (1994) 609-615 [ 161 H.C. Allen and E.K. Plyler, J. Res. Natl. Bur. Stand. 52 (1954) 205. [ 171 G.L. Ordway, PC. Cross and E.J. Bair, J. Chem. Phys. 23 (1955) 541. [ 181 T.H. Edwards, N.K. Moncur and L.E. Snyder, J. Chem. Phys. 46 (1967) 2139. [ 191 L. Lechuga-Fossat, J.M. Flaud, C. Camy-Peyret, l? Arcas and M. Cuisenier, Mol. Phys. 61 (1987) 23. [20] D.A. Tate, L. Wang and T.F. Gallagher, in: XIth International conference of laser spectroscopy, eds. L. Bloomfield, T. Gallagher and D. Larson (American Institute of Physics, New York, 1993) p.134.
615
[21] R. GroOklo8, H. Wenz, S.B. Rai and W. Demtriider, communicated. [22] R. GroSklol3, P Kersten and W. Demtrijder, Appl. Phys. B. 58 (1994) 137. [23] D. Luckhausand M. Quack, Chem. Phys. Letters 199 (1992) 293. [24] J. Senekowitsch, S. Carter, A. Zilch, H.J. Werner, N.C. Handy and P Rosmus, J. Chem. Phys. 90 (1989) 783.