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The far-infrared laser magnetic resonance spectrum of the SH radical
JOURNAL OF MOLECULAR SPECTROSCOPY
153,41-58 ( 1992)
The Far-Infrared Laser Magnetic Resonance Spectrum of the SH Radical STEPHEN H. ASHWORTH AND JOHN M. BROWN The PhysicalChemistry Laboratory,South Parks Road, Oxford. OXI 3QZ, England We have extended the observations in the far-infrared laser magnetic resonance spectrum of the SH radical in its ground *II state to cover the first three rotational transitions in the ‘TIXlz component. Signals were seen from all naturally occurring isotopes of sulfur except the least abundant, % (0.02%). The measurements have been analyzed, together with selected data from previous work, to determine an improved set of molecular parameters for 32SH in its ground state. The impli~tions of these parameters are discussed. The magnetic and electric nuclear hyperfine parameters for 33SHare significantly improved over previous work. The frequencies of rotational transitions in 32SHin the absence of a magnetic field are calculated from the parameter set to aid in the detection of this radical in astrophysical sources. 0 1992 Academic PB.. 1~. 1. INTRODUCTION
The spectroscopic properties of the SH radical have been broadly established from a variety of ex~~ments. However, the molecule is irn~~nt enough to merit more detailed study. It enjoys a nearest neighbour relationship to the OH radical with which it provides illuminating comparisons. It is also an important astrophysical molecule because of the relatively high cosmic abundance of sulfur. In particular, improved molecular parameters for the molecule in its X211 state are needed. These can be used, for example, to calculate accurate frequencies in the far-infrared spectrum to help searches for the molecule in space at these wavelengths by the burgeoning methods of far-infrared ~tronomy ( I). The previous spectroscopic studies of SH in its X211 state can be conveniently listed in order of increasing frequency. Meerts and Dymanus have made direct measurements of the lambda-type doubling frequencies in molecular beam electric resonance (MBER) experiments of both SH (2) and SD (3). There have also been several studies by gas phase EPR. The dominant isotopomer 32S‘H has been studied in the J = $ level by McDonald (4), Radford and Linzer (5), and by Tanimoto and Uehara ( 6). It has also been detected in the J = 2 level by Brown and This~ethwaite ( 7), Uehara and Morino (a), and Tanimoto and Uehara (6). Miller ( 9) has measured some hyperhne splittings in the J = f EPR spectrum of 33SH, using a sample in natural abundance. Moving up to the far-infrared region, there has been one study so far. Davies et al. (10) have recorded two pure rotational transitions in the 21’13,2 component, one for SH (J = 2 + 4) and the other for SD (J = s + $) by laser magnetic resonance (LMR). The first vibrational-rotational spectra recorded were those for SD by Rohrbeck ei al. (II), Lowe fl2), and Zeitz et al. (13) using CO LMR. The higher frequency part of the fund~ent~ band of SH itself has been recorded by Bernath, Amano, and Wong using difference frequency spectroscopy ( 14) and Benidar et al. using FTIR ( 15). Finally, the A 2Z+-X211 transition in the electronic spectrum of SH has been recorded and analyzed by Ramsay ( 16). 41
0022-2852192$5.00 Copyright 0 1992 by Academic Press, Inc. All nghts of reproduction in any form resewed.
ASHWORTH
42
AND
BROWN
In the present work, we have extended the far-infrared LMR spectrum of the SH radical. The first three rotational transitions in the ‘II 3,2 component have been studied and signals recorded for 32SH, 34SH and 33SH. The observed resonances have been fitted with selected measurements from previous work to derive an improved set of molecular parameters for SH in its ground state. The implications of these parameters for the structure of SH are discussed. We have also computed the zero-field far-infrared spectrum of 3’SH from these parameters. 2. EXPERIMENTAL
DETAILS
The far-infrared spectra were recorded at the Boulder Laboratories of NIST using the LMR spectrometer described previously ( 17). The SH radicals were produced continuously in the detection region by one of two methods: (i) the reaction of H atoms with elemental sulfur, and (ii) the reaction of H2S with fluorine atoms. In the first method a coating of elemental sulfur was laid down on the inside of a short length of glass tubing. The tube was first tightly packed with sulfur and then gently warmed to fuse the sulfur onto the glass. The remaining loose sulfur was then carefully removed. This tube was connected to the H-atom discharge source by a length of PTFE tubing. The H atoms were generated in a microwave discharge in 2. I Torr He and 0.5 Torr Hz. In the second method. F atoms were produced in the microwave discharge. The H$ was introduced via a second tube opening at the end of the PTFE tube which connected the F-atom discharge source to the detection region. The total pressure was about 240 mTorr: 20 mTorr H2S, 100 mTorr F2 ( 10% in He), and the balance He. Both methods proved to be extremely efficient ways of generating SH radicals and signal-to-noise ratios in excess of 2000: 1 were obtained with 0.3 set output time constant. The magnetic flux densities were measured with a rotating coil probe which was calibrated from time to time against a proton NMR gaussmeter. The overall uncertainty in the flux density measurements is 10m5 T below 0.1 T and 10-4B0 above 0.1 T, where B,, is the magnetic flux density. The FIR LMR observations are summarized in Table I. The uncertainty in the laser frequencies which are given in this table arises mainly from the irreproducability in setting the laser to the peak of its gain curve (ca. 1 MHz). The polarization of the radiation relative to the applied magnetic field can
TABLE I Summary of Transitions Observed by LMR Laser line
J’c
;+;
J
Frequency/GHe 1385.6461
Pump lOP(24)
p* 216.4
Gas ‘%D,OD
k+f
1391.9721
9R( 14)
215.4
CHsOD
f+)
1950.5816
SR(28)
153.7
‘%DsOH
i+f
2488.5534
lOR(36)
120.5
CDzFz
FAR-INFRARED
43
LMR OF SH
be changed by rotating a Brewster-angle window between the gain medium and the sample volume through 90”. 3. RESULTS AND ANALYSIS
3.1. Observations The transitions observed in the present study are summarized in Table I together with the laser lines used. The spectra are slightly complicated by the presence of the various naturally occurring SH isotopomers. These are, however, readily distinguished because of the widely different relative abundances (“S: 95.02%, 33S:0.75%, 34S:4.2 I%, 36S. . 0 *02% ) . ‘?GH, the least abundant isotopomer, was not detected. The isotope pattern can be used as an aid to assignment obviating the need to perform laser pulling experiments to obtain the signs of tuning rates. If the zero-field frequency is greater than the laser frequency, the resonance associated with the most abundant isotopomer, 32SHf occurs at higher flux density than that of 34SH and vice versa (18). Previous work on SH (3, 10) provided molecular parameters which gave unambiguous assignments of the spectra recorded in this work, using the predictive program described elsewhere (18, 19). The isotope structure can be clearly seen in Fig. 1. The 32SH signais have been truncated somewhat so that the 33SH signals are more obvious. Each signal consists of two clearly resolved A-doublets. The 33S hyperfine structure (I = 2) is also well resolved. In addition, evidence of the proton hyperfine structure can be seen on the 33SH and 34SH signals. The response of the system was not fast enough to show such proton hyperfine structure on the 32SH signals with the relatively high scan speed used to record this spectrum.
215.4 urn IT polarfsaiion
32s
1 3%
3% -
I
,
1
/
0.9
I.0
1.1
1.2
I
I-3
Flux density/T FIG. 1. A portion of the far-infrared LMR spectrum of the SH radical in its X’fI state, recorded with the 2 15.4~pm laser line of CD30D in K polarization (a = 0). The transition is J = $ + $, MJ = -3 + -4 for each of the three naturally occurring isotopomers, “SH, 33SH,and %H. The large splitting for each isotopomer is the lambda-type doubling. The quartet hyperfme structure for 33SH can clearly be seen. Note that the “SH signals go off scale.
44
ASHWORTH
AND BROWN 216.4um lT polarisation
I
1
,
I
@38
@37
I
I
I
039
/
O-40 Flux density/T
FIG. 2. Part of the far-infrared LMR spectrum of 33SH in natural abundance, recorded with the 2 l&4pm laser line of ‘%DaOD in K polarization (A&I’= 0). The quartet pattern arises from the “S magnetic and electric hyperfine interactions; the small doubling arises from the proton hyperfme structure. The other two weak, broader lines at approximately 0.385 and 0.410 T arise from another species. The spectrum was recorded with an output time constant of 300 msec.
Both proton and 33Shyperfine structure are easily observable in Fig. 2. The former, however, is not fully resolved. In addition there are two weak transitions at approximately 0.385 and 0.41 T. These are high-field components of an extensive series of weak lines which we have tentatively assigned to I-f&. This assignment is currently under investigation. In favorable cases it proved possible to saturate the transitions. Figure 3 shows one component of a 32SH A-doublet. The doubling here is a result of the proton hyperfme interaction, and the saturation dips are easily seen. Another notable feature of this spectrum is that the Doppler limited hyperfme components are almost completely resolved. Although the transition is tuning relatively quickly so the lines are inherently narrow ( du / d B cc I/ linewidth), significantly narrower lines were obtained using H$ + F rather than using H + S because of the much lower pressure employed. The J = ; + 5 spectrum is shown in Fig. 4. All the far-infrared transitions observed in this work occur in the 2IIs,2 manifold. The detailed measurements are given in Table II. The observation oftransitions within the ‘IIt p manifold would provide interesting complemental info~ation. We were 2164pm 0 polarisatbn
0%05
O%?O
01615
0~%20
Flux density/T
FIG. 3. A small portion of the far-infrared LMR spectrum of %H, recorded with the 216.4-pm laser line of “CDaOD in g polarization (L\M = f I ). The Lamb dips at the centers of the two proton hyperfine components can be clearly seen. The signal was recorded with an output time constant of 100 msec.
FAR-INFRARED
LMR OF SH
45
unable, however, to observe these transitions in the far-infrared LMR spectrum because of two adverse factors. The magnitude of the spin-orbit splitting in SH is about 395 cm-‘, so the population of the upper 211I ,2 state would be around 15% of that of the ‘IIJ,~ state assuming thermal equilibrium at a temperature of 300 K. Although such a population of the 2111,2manifold ought to be sufficient, the low tunability of the 2111,2 state means that very close coincidences between molecular and laser frequencies are required, typically within 400 MHz (the contending interval for transitions involving the 2113,2levels is 30 GHz). Second, the low tunability of the ‘IIr12 transitions means that their linewidths in a magnetic resonance experiment would be very broad and severely under-modulated. It is, therefore, quite understandable that, when searches were made for the 211,,2 transitions on the basis of predictions made with the best parameters available, the signals were not detected. The measurements of the LMR spectrum were used with the earlier molecular beam (2, 3), EPR (5, 6), and LMR data ( IO) to determine the appropriate molecular parameters in the effective Hamiltonian for a 211state: &ff = H, + &XX+
f&d
+ HLD
+ I?r,, + ffhfs
+ f&j
+ fke,m,-
(1)
This Hamiltonian has been described in detail elsewhere ( 19). The rotationally dependent terms in the Hamiltonian are formulated in terms of N2 rather than R2 (20). The basis set was truncated without loss in accuracy at matrix elements with AJ = *2. Each datum was weighted in the fit, inversely as the square ofthe experimental uncertainty (which for LMR data arises primarily from the knowledge of the laser frequency as used in the ex~~ment). As can be seen from Table I, there is no direct information on SH in the *II t ,z spin component in our work. We have therefore used Ramsay’s measurements on the A 2Z ‘-X 211 electronic transition to determine the spin-orbit and spin-rotation parameters. We have refit Ramsay’s data with the effective Hamiltonian in Eq. ( 1) to determine the parameter values given in Table III. We chose to constrain the parameter AD to zero in the fit so that A and y are strictly effective parameters, having absorbed the effect ofAD (21). The data set which is given in Table II consists of: (a) the lambda-doubling frequencies for 32SH measured by molecular beam electric resonance by Meerts and Dymanus (2,3) with an accuracy about 1 kHz. This includes measurements of the Zeeman splittings for the J = 1 level (3) (accuracy about 30 kHz). (b) EPR data for 32SH in the J = z and $ levels measured by Radford and Linzer (5) and Tanimoto and Uehara (6)) respectively. The accuracies of these data are 50 and 100 kHz. (c) The present observations in the fm-infrared LMR spectra of 32SH, 33SH, 34SH and 32SD. The accuracy was taken to be 1 MHz. We have remeasured the resonances for 32SDreported by Davies et al. ( IO) because of their rather low accuracy. For the 33SH isotopomer, the average of the four 33Shyperhne components was used in this fit because the program is only capable of dealing with the interaction of a single nucleus at the moment. The 33Ssplittings were used to determine the hype&me parameters in a separate fit (see below). Certain molecular parameters are not determinable directly from this data set. In such cases, values were obtained from other sources and the parameter was constrained
46
ASHWORTH
AND BROWN
TABLE II Details of the Fit of the Data for “SH in the % State %l, manifold J = ; data (2, Upper state F 1 1
MF 1 -1
state
Lower
FltlX
MF
P
Density”
-
1 1
1 -1
+ +
-1
P”
-
F
0.01 0.01
8.446558
6
0.134
+
0.01
8.445677
15
0.067
0.01
8.444331
66
-
1
1
1
-
1
0
+
1
0
+
0.01
8.446091
0
-
1
1
+
0.01
8.444745
-28
1
0
-
1
0
+
0.00
8.445211
-2
1
0
-
0
0
+
0.00
8.459034
-
0
0
+
0.01
8.459914
-66
-
0
0
+
0.01
8.458154
-38
1 1
-1 1
1
Upper state
F
P
5
1
; ;
Lower state
F
P
+
1
2
+
f
1
+
;
f ;
2 2
+ -
f
;
3
-
3
30 30 30 30
0.060
30
-0.064
5
0.000 0.000
5
0.076
30
-0.060
30
(2) uncertainty
Frequency
J f
J
30
-0.076
3
manifold MBER data
NW
-0.134
38
-
1
uncertainty
Rake
@HII -11
0 -1
Tuning
*c
@HI) 8.443864
1 1
Frquency
Clf,:,
-
@HE) 0.1114862
2
-
0.1115452
0.1
2
-
0.100293
3.2
1
-
0.122737
;
2
+
0.4424781
0.0
0.5
;
3
+
0.4426277
0.3
0.5
1.8
2
-0.2
-4.7
&HI) 0.5 0.5 3 3
;
3
-
f!
2
+
0.4471876
;
2
-
f
-4.3
2
3
+
;
+ -
0.4379154
;
3 3
1.0941871
-0.2
0.5
3
4
+
;
4
-
1.0944596
-0.2
;
3
+
1.0935326
4 4
+ -
4 3
-
; ;
; I2
4
+
f
5
-
oi ;
5
+
2.1587239
1
0.4
2
1.0951179
3.1
2
2.1582986
0.2
1
0.0
1
f
5
-
;
4
+
2.1564902
;
4
-
1
+
+ -
0.4
5
5 5
2.1605318
y
; ‘i?
3.7148864
1.0
2
+
6
+
+
6
-
3.7154892
-0.7
-1.0
1
2
a\ Paritv label. Proto;; hyperfinc siructnre not resolved. Deuterium hyperfine rtructure not resolved. Uncertainty of sew implies rem weight in the fit.
to this value in the fit. We have already mentioned the need to use the optical data (16) for values of the spin-orbit and spin-rotation parameters. The vibrational dependence of the major parameters (A, B, D, p, and q) is also needed so that the isotopic scaling can be performed reliably. These dependences have been measured accurately in the infrared by Bernath et al. ( 14). We have refitted their data using our Hamiltonian (which differs slightly from theirs). The values determined for the vibrational dependences are given in Table III. The Zeeman parameters required to describe a molecule in a ‘II state have been defined by Brown et al. ( 19). Four of the six parameters (gL, g,, g$ and g:‘) are determinable from the data. Of the remaining two, gS was constrained to the free spin value corrected for relativistic effects as computed by Veseth (22) at 2.00213. The anisotropic correction to the spin g-factor was estimated from Curl’s relationship ( 23),
FAR-INFRARED
LMR OF SH
47
TABLE 11---Cmtinued
Uncertainty Density”
(-4
0.778175
9.21570
-80
11.675
0.777898
9,21571
-72
11.675
50
0.776556
9.21574
-52
11.727
50
0.776075
9.21574
-17
Il.727
50
0.774924
9.21576
-13
xl.779
50
0.774442
9.21577
19
ii.779
50
0.797677
9.21577
3
11.666
50
0.797193
9.21577
20
11.668
30
0.795556
9.21577
36
11.727
50
0.795062
9.21577
11.727
50
0.793445
9.21578
11.767
50
0.792975
9.21578
-32
11.787
50
0.776173
9.21573
-36
11.675
50
0.777694
9.21573
-19
11.675
50
0.776553
9.21572
-27
11.727
50
0.776076
9.21572
-54
11.727
50
0.774923
9.2157l
-41
11.779
50
0.774436
9.21571
36
ii.779
50
0.797670
9.21561
120
11.668
50
0.797191
9.21579
65
11.668
50
0.795554
9.21578
62
11.727
50
0.795075
9.21577
57
11.727
50
0.793440
9.21575
60
11.787
50
0.792970
9.21574
-12
11.787
50
Den&y’
(&is)
@HI)
Rate;
1.589532
9.11440
232
5.502
1.589817
9.11440
178
5.502
100
1.597863
9.11395
-134
5.452
100 100
VW
-17 26
Rata
WI 50
Uncerthty
as 0.776
X 10m2.
WI 100
1.5S8635
9.11395
-180
5.452
1.606467
9.11383
-131
5.399
106
1.606757
9.11383
-144
5.399
100 100
1.615582
9.~1379
-95
5.342
1.815885
9.11379
-150
5.342
100
1.625191
9.11378
-47
5.282
100
1.625499
9.11378
-104
5.282
100
1.756753
*s&563
129
3.492
loo
1.757075
9.11563
82
5.492
106
1.763143
9.11519
116
5.44s
100
1.763452
9.11519
61
5.449
106
1.770201
9.11523
95
5.402
100
1.770493
9.11523
56
5.402
100
1.777999
9.11583
60
5.349
100
1.778283
9.11563
-9
5.349
160
1.786413
9.11595
-23
3.2Q2
1W
1.786677
e.lm5
-55
5.292
106
ASHWORTH
48
AND BROWN
TABLE II-Continued R(;),1391.9721GH.,
215.4jnn,
MI
%H %iH
+ _f
_;
P 1
_;
-
_;
-
_j-
+
-j
+
;
=SH J%B
MJ
‘%H
;
_f
-
=SH
1 2
_J
_
JJSH
;
-f
+
-)
+
_f
-
-;
-
%A
-f
;
“SH %H
-f
%i 3’SH
f _$
2
CD.OH,
Plux
Upper state
-5
+
_f
+
_;
-+
;
1 5 _+ ; -; ; _f ; _;
Tuning Ratec
Unceltainty
P
Density”
_j
+
0.91464
0.69
9.583
1.0
_)
+
0.91530
0.62
9.583
1.0
-j
-
0.94951
0.25
9.583
1.0
-;
-
0.95019
-0.08
9.583
1.0
+
1.04418
-0.12
9.595
1.0
+
1.04481
9.595
1.0
_;
-
1.07900
-1.01
9.595
1.0
-as
-
1.07979
-2.39
9.595
1.0
_f
+
1.16564
-1.15
9.606
1.0
_;
+
1.16635
-1.79
9.606
1.0
-5
-
1.20030
-1.54
9.606
1.0
_f
-
1.20102
-2.25
9.606
1.0
+
0.58483
-0.84
14.965
1.0
-
0.60665
-0.60
14.970
1.0
MI f
9B(14)
o-c
MJ
-2 _j:
3_
(MW
0.02
(MW
=SH
-“-;
-
A_;
=SH
9-i
+
_d
3%
-1
;
-
.A_;
+
1.00828
-1.28
8.759
1.0
%H
_d
f
+
3-i
_
1.04554
-1.15
8.771
1.0
J’SK
_.q
-
A_;
+
0.74554
0.52
14.985
1.0
%H
_“_+
+
-“-:_
_
0.76741
0.55
14.990
1.0
“SH
_d
;
_
_“_f
+
1.28227
-1.15
9.812
1.0
%H
_d
;
+
-“-f
_
1.31903
-1.45
8.824
1.0
-f
R(]),1385.6461GHa,
Upperstate MI MJ P =SH
2
_f
“SH
1 I f
_s
=SH =SH
_) f
=SH %iH
_; ;
%iH =SH
-f f
“SH 3%
_f ;
%H
MI
1
f 1 f ;
_
_;
+
-5
+
-;
-
_f
-
_f
+
-f
+
-f
-
-f
-
_;
+
_)
+
216.4pm,
-;
MJ -3 _J_ 1 -;
%D#D,
lOP(24) uncertainty
FluX
Tuning
P
Density’
Ilaw
+ +
0.25244
0.35
9.522
0.25308
0.33
9.522
0.5
-
0.28736
-0.31
9.522
0.5
-0.33
Lower state
WI) 0.5
_:_
-
0.28801
9.522
0.5
-;
+
0.38267
0.94
9.534
1.0
-5
+
0.38336
0.51
9.534
1.0
3
_;
-
0.41733
1.84
9.534
1.0
I 1 f
_J
_
0.41801
1.50
9.534
1.0
+
0.50483
0.55
9.545
1.0
0.50550
0.36
9.545
1.0
-
0.53950
0.50
9.546
1.0
+
0.54019
0.09
9.546
1.0
0.74190
1.22
3.311
1.0
0.26
3.330
1.0
3.384
1.0
f -;
1 f ;
I
-f 3 1-b -;
YXi
.A-$
_
1 s i -i _“_f
?SH
_“_;
+
A-;
_
0.84208
=SH
-d-f
_
A-;
+
1.11312
=SH
A__;
+
A-$
_
1.21063
0.07
3.402
1.0
“SH
-“-;
_
A_;
+
1.45399
0.03
3.450
1.0
=SH
A-5
+
-“-;
_
1.54954
=SH
;
-
;
_jT
+
0.16100
_f
+
%H
_;
-+
-
=SH
;
_)
+
=SH
1 ?
I 1 _.$
+ -
-f
-
_;
+
=SH
_f
_f
J’SH %H
t -1 ;
“SH
1 ? ;
=SH =SH =SH
-f
‘“SH %H
; -f
t 1 f
+ -
f
-
+
+
f
+
_; 1 ? _f ; 1 1 1 2 -f + _; I 5 -;
3.468
1.0
0.86
14.913
0.5
0.16152
0.81
14.913
0.5
0.18322
0.20
14.917
0.5
-
0.18374
0.18
14.917
0.5
+
0.32229
0.81
14.932
1.0
0.32284
0.20
14.932
1.0
0.34432
0.43
14.937
1.0
14.937
1.0
3 , -5 -5 J 1 J i
-0.14
+ _
-0.11
-;
-
_f
+
0.27976
-0.31
8.616
0.5
_;
+
0.28018
-0.27
8.616
0.5
0.31801
-0.27
8.627
0.5
0.31842
-0.17
8.627
0.5
-i -f
1
-
0.34488
-0.20
“SH
_d
f
_
A_;
+
0.42361
1.68
8.643
1.0
“SH
-d
;
+
-d-i
_
0.46156
1.81
8.655
1.0
FAR-INFRARED
LMR OF SH
49
TABLE II-Continued R(f),l365&461GB1, Upper state MI
Lower state
MJ
P
MI
216.4pm, “CDsOD,
lOP(24) (cont.)
FllK
MI
P
Density”
Tuning
Uncehinty
Rat@
(MHz)
(hz,
J’SA
_d
f
-
_d -f
+
0.55837
0.42
8.670
1.0
3’SH
_d
;
+
A-5
-
0.59605
0.48
8.681
1.0
%H
f
-;
-
+
_:_
+
0.58379
0.71
4.122
1.0
-5
-
_ai
+
0.58499
0.31
4.122
1.0
-;
+
-;
-
0.66561
-0.30
4.117
1.0
-;
+
-;
-
0.66678
-0.47
4.117
1.0
_;
-
_f
+
1.16611
-0.05
4.142
1.0
-;
-
-3%
+
1.16717
0.12
4.142
1.0
3=SH
-f
J%H JlSH
f _f
%.H “‘SH
; -f
3’SH 3’SR
; -f
-;
+
-f
+
_; ; _f ; _; ; -;
-;
-
1.24787
0.62
4.136
1.0
-f
-
1.24908
0.22
4.136
1.0
3’SH
_d
f
-
_d
6
+
1.03828
0.14
2.403
1.0
3’SH
_d
f
+
-4
f
-
1.17231
0.40
2.432
1.0
R(;),1950.5816GHs, Upper state
Lower state
3’SH
A-;
P +
3’SH
A-4
-
MI
MI
MI MI .A-; .A__;
153.7/rm, “CDJOH, Flu
P _ +
R(;;),248&5534GHs,
Density’
(iii*,
1.76463
-3.63
1.81926
-367.35
2-5
+
0.24884
-“-;
_
2-3
+
1.51577
%B
_A-:_
+
9-g
-
0.56309
32SH
9-f
-
-“-;
+
3’SH
A-;
+
9-i
%B
A-;
-
?5H
A-)
3%
_d
3’SH
-f
Tuning
uncertainty
Raiec 8.717
(MHz) 1.0
8.731
01
120.5~1, CDsFz, lOR(36)
-
3’SH
BR(28)
-0.23 0.76
3.391
-1.0
3.439
1.0
-0.41
3.390
1.0
0.34842
-0.15
2.421
1.0
-
0.78866
-0.38
2.425
1.0
A-:;
+
0.58150
-0.67
1.451
1.0
+
3-i
-
1.31642
-0.28
1.450
1.0
A-5
_
3-t
+
1.65934
47.69
0.475
“SH
9-g
-
9-g
+
0.14778
0.31
5.703
1.0
3’SH
9-i
+
9-i
-
0.33409
0.08
5.716
1.0
3=SH
3-f
-
A-:_
+
0.17792
0.75
4.734
1.0
3=SH
_A-;
+
A-;
-
0.40231
0.25
4.745
1.0
3aSH
9-f
-
_“_$
+
0.22386
0.04
3.764
1.0
3’SH
A-f
+
-“-“s
-
0.50567
0.05
3.773
1.0
3%
_d
;
-
A-5
+
0.30125
0.39
2.795
1.0
JWI
_d
;
+
-d-i
-
0.68037
0.14
3*SH
_d
;
-
_d
+
+
0.46104
;
;
0’
2.801
1.0
-0.03
1.825
1.0
31SH
_d
+
_d
_
1.03986
-0.15
1.828
1.0
3%H
-“-;
-
9-f
+
0.78423
-0.34
1.081
1.0
‘%H
A-;
+
2-g
-
1.78564
-0.20
1.081
1.0
“SH
_d
-
-1
+
3.98059
0.09
0.854
1.0
;
g
=‘SH
A-;
-
A-5
+
0.90405
0.29
5.744
1.0
%H
-d-i
+
3-5
-
1.08763
0.23
5.758
1.0
%H
A-5
-
9-g
+
1.09004
0.36
4.758
1.0
3’SH
-d-f
+
3-i
-
1.31109
0.31
4.770
1.0
J’SH
9-t
-
_d
+
1.36856
15.09
3.773
-“5
01
The data for four different isotopomers of SH are very accurate and therefore likely to show effects of the breakdown of the Born-Oppenheimer approximation in the isotopic scaling. Watson has shown how to model such effects (24), and we have included his parameter &, , the correction for the equilibrium rotational constant Be, in our fits for both the H and S atoms. Both were determinable in the final fit.
50
ASHWORTH
AND
BROWN
TABLE II-Continued R(~),1016.8972GJ.h, 294.8/m, 9R(8), CHJOD Upper state MI
P
MJ
Lowu state MI MI P
Flux
-6 Raw
Density’
uncehinty
+
-8
_;
-
0.45340
-0.41
5.361
WI) 1.0
-
-8
-f
+
0.47078
-0.01
5.362
1.0
+
_I
-3
-
0.75372
-0.06
3.225
1.0
+
0.78363
-0.10
3.226
1.0
-
0.28975
0.18
8.359
1.0 1.0
=SD
_e
-;
%D
_e
-;
J’SD
-‘_;
“SD
2-f
-
2-f
“SD
__c -;
+
_e
“SD
2-f
“SD
_I
‘=SD
-‘-;
“SD
_e
%D
_*
‘=SD
-‘_f
“SD
_e
%D
-1
“SD
_e
-t
-
..s_;
+
0.30120
0.12
8.362
+
-0
_f
-
0.38934
0.27
6.217
1.0
-
_c
-ST
+
0.40470
0.14
6.220
1.0
-
0.59331
0.25
4.076
1.0
_e
-f
+
0.61659
0.13
4.078
1.0
+
_*
.+
-
1.03805
-0.23
2.351
1.0
-
_e
_g
+
1.08033
-0.10
2.349
1.0
;
+
_I
f
-
1.24684
-0.10
1.931
1.0
;
-
_e
;
+
1.29491
-0.08
1.933
1.0
-f
f )
-;
+ -
2-t
The data set was fitted to experimental accuracy by this effective Hamiltonian. The standard deviation of the fit relative to the experimental uncertainty was S = 0.9626. The results are given in Tables II (residuals) and III (parameter values and standard deviations for the dominant isotopomer, 32SH). The 33Shyperhne splittings were fitted separately, using a computer program which is capable of dealing with two independent hyperhne interactions. Most of the parameters for 33SH were taken from Table IV, suitably scaled for this particular isotopomer. The experimental measurements are given in Table V; the parameter values used and determined in the fit are given in Table VI. Three hyperfme parameters were determined from the 33S splittings, h3,2, which equals a + gb + c) in terms of the Frosch and Foley parameters (25), eqoQ and eqzQ. The other three magnetic hyperhne parameters, h , ,*, b, and a’were constrained to values obtained by scaling from the corresponding quantities for “OH (26). The three other parameters determined in the fit B, q, and g, were simply used to ensure that the center of the hyperfine patterns occurred at the observed fields. 4. DISCUSSION
In this paper, we report the observation and analysis of the far-infrared LMR spectra of four different isotopic forms of the SH radical in the 2) = 0 level of its ground 211 state. This has resulted in a significant refinement of its molecular parameters. This can be seen in Table VI, where we have listed the values for the rotational constant B. and the centrifugal distortion correction Do determined from the electronic (16), the infrared spectrum ( 14), and from the previous infrared study (IO), as well as the present work. In general the differences between the parameters are much larger than expected from statistical uncertainties. These reflect different assumptions for the effective Hamiltonian used in fitting the data. The improvement in our knowledge of the rotational constant for 32S‘H means that we can refine the equilibrium bond length for this molecule. Using the value for CQdetermined from the refit of the infrared data of Bernath et al. (14), we obtain B, = 9.599545(65) cm-’ or 287.7871( 19) GHz, where the error estimate has been computed in neglect of any nonlinear dependence of B. on the vibrational quantum number. From this value we obtain,
FAR-INFRARED
51
LMR OF SH
TABLE IIt Parameter Values Determined for 32SH in the v = 0 Level of the X *B State Value.
Correlation’
Parameter
...
a.4
V&e
Conektion’
77917.557(62)+ -11297.15(42)’ -4.40(
1oy
5.613
QB
0.0144796(12)
6.217
OjJ x 105
7200.0
8.42966(23)
10’
%
283.6121#(33)
-0.284334(30) PO + 2qD X
...
0.2294 x lo6
-0.218(U)
0.1616
x 10s
qjJ X 10’
5+c
-0.030994(60~
527.8
d
..
g:
9s
2.00213f
.
..*
0.422(14)
6
531.9
f.
8.~~(~)~ -0.146(4?)”
-0.0108(20)d
a9
0.032574(30)
. . ...
0.315(13)
++a
a
13.67(10)‘ -0.33X(56)
-0.06340@3(97) 0.027343(59) 0.00776(
. . . 0.3055
x 10s
3.305 38.65 ...
gt
1.0094848(33)
2.501
0,“’ x 10’
0.10073(50)
1.182
g, x 103
-0.3321(17)
2.495
91 - 9:’
0.01434(17)
1.182
5.58569W
.. -0.95605(98)
1.073
PN &i(S)
-0.70(12)
1.399
&x(W
a) Parameter value in GHz where appropriate. b) The correlation coefficient is the appropriate diagonal element of the inverse of the correlation matrix. c) Figures in parentheses are one standard deviation of the least squares fit given in units of the last quoted decimal place. d) Parameter determined in the refit of infrared data (14) and constrained to this value in the present fit. e ) Origin of the fundamen~l band determined from the infrared data ( II) as 2599.0499 (2 1) cm-‘. f) Parameter determined in the refit of optical data ( 16) alone and constrained to this value in the present fit. g) Parameter constrained to this value in the fit.
r, = 0.13406630(45)
nm.
(3)
It has been possible to fit all sulfur and hydrogen isotopic forms simultaneously to a single model using the appropriate isotopic scaling factors. The effects of the breakdown of the Born-Oppenheimer separation on the isotopic scaling of the equilibrium rotational constant B, proved to be significant for both the hydrogen and sulfur atoms. The value obtained for the former is &(H) = -0.95605 (98), which agrees reasonably well with the corresponding value estimated for OH of - 1.7 (27). Somewhat surprisingly, this appears to be the first time that data for XH and XD have been fitted simultaneously. The corresponding correction parameter for the sulfur atom in SH is just determinable and is of a similar magnitude, -0.70( 12). The heavy atom correction parameter has also been measured for SeH (27) but has been determined to be much larger, - 17.8 ( 8 ). This possibly arises because of the similarity in magnitude of the spin-orbit splitting and the vibrational interval for this molecule. Four of the six g-factors for SH in its X2.11state have been determined in our work (see Table III). Because of the lack of information on SH in the 2111,,2component, we have been forced to constrain the electron spin g-factor, gs to a theoretical value (22). The major parameter which has been determined is the orbital g-factor, g$_, which is related to the relati~sti~lly corrected parameter gL by &=gL+&L>
(4)
52
ASHWORTH
AND BROWN
TABLE IV
Details of the Fit of the 3%H Data R(;) Upper
1391.9721 GE&, SR(l4),
state
Lower
216.4 /mt, CHsOD
state
FlUr
I
Density’
0.7
9.69
1.03538
0.5
es*
1.04113
0.7
9.5s
1.04181
0.3
9.59
1.04737
0.4
1.05341 -3
_;
-2
-
g
$ f f
;
;
-;
-f _g _; -2
-; -4
_)
-:
-3
-8 -f
; _; t -; ;
1.05407
t f
_f _f
i f
_; -1
-1
_f
_#
-1 _f
5
-;
if
_)
#
_;
f
-3
-$
_g
-4
_f
-$
_;
_$
a b E d)
I
0.0
9.59
-0.2
9.59
1.06960
+ + + + +
1.07033
-0.2
0.6
9.59
9.59
1.07587
-0.7
9.59
1.07656
-1.1
9.59
1.08208
-0.4
9.59
1.0827%
-1.0
9.39
+
1.08846
-1.0
9.59
+
1.08908
-0.8
9.59
1385.6461 GH:,
lOP(24),
216.4 #XII, “%DJOD 0.37337
-0.6
9.53
0.37411
-1.4
9.53
_
0.37966
-0.5
9.53
-
0.38036
-1.1
9.53
-
0.38584
-0.6
9.53
-
0.38647
-0.3
9.53
;
-
0.39181
-0.2
9.53
-
0.39249
-0.6
9.53
$
+
0.40819
0.1
+
0.40882
0.2
9.53
+
0.41417
0.9
9.53
_$
+
0.41485
0.5
9.53
;
i
0.42036
0.9
9.53
+
0.42104
0.5
9.53
+
0.42659
1.7
9.53
+
0.42733
0.8
9.53
_; ; _f
-f
_f
-;
9.59
-
f
;
-t _$
9.59
-0.1
+
R _t
Rate’
1.03470
1.04806
_f
Tuning (b&
-5 :_
-5 1 _;
parity label. Flux density in Tesla. Tuning Proton hype&e structure
9.53
ratein mT/MHa. from predictions.
where AgL is a nonadiabatic correction to the g-factor in the effective Zeeman Hamiltonian ( 19). If we assume the same relativistic correction for gl, as for g, we obtain gl. = 0.999905. The value determined for gL in Table III gives AgL = 0.5793( 33) X 10m3. This parameter is a measure of the difference in the rotational admixture of excited 22 and 2A states into the ‘II state (28) and makes an interesting comparison with the rotational g-factor, g: which measures the sum of these contributions. The rotational g-factor measured in our work is g,, which is the difference of the nuclear and electronic contributions, gr=gY-g;. For 32SH, the nuclear contribution
can be calculated to be 0.5361
X
(5) 10W3so that g:
FAR-INFRARED
LMR
OF SH
53
TABLE IV-Continued
upperState MJ
-f _;
# g
-;
t
-3
)
-f
-f
_f
-;
-t -;
f _; _;
-$
_)
f
-8
-1
;
-3 _p -f -f
;
-$
t g
i _;
-4
;
4
_;
-1
-$ -4
-4
if
-;
#
_)
f
-‘r
f
-;
-f
-;
-;
-f
-$
4
-)
-4
f -f $ -4
) _f
1.103oP
0.4
3.38
LlO615’
1.0
3.38
1.16670~
1.0
3.35
1.1153P
1.1
3.38
1.11566*
1.1
3.36
-
1.12181’
0.9
3.37
-
l.12245d
0.8
-
3.38
3.38
1.20138’
-0.5
3.40
+
1.20262’
-0.5
3.40
+ +
1.26660
0.1
1.20754’
0.1
3.40
+
1.2131@
0.2
3.40
+
1.21374’
0.2
3.40
+
l.2168Td
0.3
3.40
+
1.2265od
0.3
3.40
-
0.41441’
-0.1
-
0.41483’
-0.1
8.64
-
6.42034’
-0.7
8.64
3.40
8.64
-
0.4207s’
-0.7
8.64
-
0.42637’
-1.1
8.64
-
0.421370~
-1.1
f
-
0.43210d
-
1
+
f _f
_f
z
-$
0.4
B +
-;
RAW
l.10320d
-
f
Tatig
r.kBsi@
1
4 -
-4
-;
Flus
hf?
-if
8.64
1.5
8.64
0.43262d
1.5
8.64
0.45252d
0.2
6.66
f
-)
+
0.452&
0.2
8.66
f :
; -f
+ +
0.458lr”
0.3
8.65
0.45859d
0.3
8.65
$
+
0.46422d
-0.6
8.65
+
0.46464d
-0.7
8.65
+
0.47050d
-1.0
8.66
+
0.47093&
-1.0
8.66
-5 -f -;
-$
-;
-4
-f
.+ -;
-f -if
_)
f
is determined to be 0.8682 ( 17 ) X 1Oe3. Comparing this value with that for Agt above suggests that the contribution to the wavefunction for the X211 state of SH from the 22 states outweighs that from the ‘A states. It is likely that most of this contamination involves the A2Z+ state. Finally, there are two pasty-de~ndent g-factors, g; and g$_ These are a measure of the admixture of *2 states and can be related to the lambda-type doubling parameters:
-4
grer = -B’ The value for g;, which is determined primarily by the MBER Zeeman data (3), is 0.01535 ( 17) as compared with 0.01586 from Eq. (6). The value for g:’ is determined primarily by the EPR data of Radford and Linzer (5) as 0.10072 (50) X 10d2, which again compares well with the estimate from Eq. (7), 0.10025 X lo-*. Nuclear hyperfine parameters have been determined for both the ‘H and 33Snuclei. The former are given in Table III and depend primarily on the MBER data of Meet-&
54
ASHWORTH
AND BROWN
TABLE V Parameter Values Determined for 33SH in the 2’= 0 Level of the X2H State Parameter & fro
Parameter
V&e’
j
-11301548.63*
j
-fo
Value I
-4397.4758976
‘$S hype&e parameters h:
~-
d
234.86’
173.70(28) “Id -9.3(18) %lQ ‘H hype&e parameters
I
bF
79.47’
d
273.6’
eaQ
206(33~
hlr
48.07049385b
bF
ha
17.07654541*
d
9L
1.000484825’
9J
0.~776*
9s $&x 105
sl - 96
0.0143420~62*
9:’ x 162
6.1~2644893b
9N(Sf
1.287642b
9N(W
5.5854’
-63.40929526*
-
27.34261182’ 2.00213*
-
-.540(26)
a) Value in MHz where approptiatt. bj Parameter constrained to this vs;luein the fit and scaled, where appropriate, from the s2SH ~Iue (see Table III). cf One stmdwd d&a&n in units of the last quoted de&& pbxe. d) These parameters are given by: h: = Bf f(6 f c) and h; = a - $(a + c). e) P&ram&r con&mined to this value wbieh was estimated by scrtting from the corresponding ‘70 parameter (see text).
and Dymanus ( 2). These authors have discussed the implication of the proton hypefine p~am~Eers for SH and we shall not elaborate on the subject. However, the value for the % parameters which are given in Table V are new, since they depend on our measurements. Since we have made observations of SH in the 2113,2spin component, we have only been able to determine one magnetic hyperfine parameter, /z~,~,Values for the other three were obtained by scaling those from “OH (26) in the same ratio, This procedure has been shown to be reliable in an analogous study of the SeH radical (27). Miller (9) has also attempted to determine nuclear hyperfke parameter for
TABLE VI A Camparison of the Values Determined for the Rotational Parameters for SH in the II = 0 Level of the 5% State with Those of Previous Studies
Bo/GHe
l?iJ/MHS
283.6<
283.73~(~7~
14.39
14.806(63~
283.57698(90~ ~3.612180(33) [14.39]6
14.4796(12)
IWE Optical, Ref. (15); Infrared, Ref. (14); and FIR, Ref. (10). a) The figures in parentheses are one standard deviation of the least squares fit. in units ofthe last quoted decimal place. b) The centrifugal distortion correction &was not determined in this work. The parameter was constrained to the value determined from the optical spectrum (16).
FAR-INFRARED
II
I
I/, I
OF SH
55
i--I+-I
I
I
I f
I
LMR
"4SH -.m-* 1 ;r;]32SH
I
f
12D5 pm D palarlsation
1
I
I
IO
cl5
0
i
2.0
1-5
Flux dens+’
T
FIG, 4. The far-infrared LMR spectrum of the SH radical, recorded from 0 to 2 Tesla with the 1205wrn laser line of CDzFz in d polarization (AM = + 1). The rotational transition involved is J = f + i in the %,? component. The proton hyperfine structure is not resolved.
33SH in its lowest rotational. level in an EPR study. He interpreted his observations in terms of the magnetic hyperfine parameters introduced by Radford (29) for the situation in which nuclear spin is decoupled, Ehfs = A,MJMI 4 A2MJMI,
(8)
where the upper and lower signs refer to e and fstates, respectively. The relationship between Radford’s parameters and those used in the present paper for the 2113,2component is cl AI
=
h3,2
J(J+
(B
-
1) - (A-
h)b
28)
[(J+
$)’
J(Jf
-
1)
I]
(9)
and
&p-iy)2
A
*
2
(A-2B)*J(J+
J+k 1)’
From his m~suremen~ Miller determined a value for Al of 71.1 + I .O MHz for SH in the J = 3 level. The corresponding value determined from our parameters in Table VisA, = 7 1.O1 + 0.7 1 MHz, in excellent agreement. The fact that the 33Shyperfine parameters for SH seem to scale so well from those of 170H is consistent with the close similarity in the angular behavior of the wavefunction near the heavy atom for these two molecules. More simplistically, the a molecular orbital which contains the open shell electrons in the ground state of SH approximates closely to a 3p atomic orbital on the S atom.
56
ASHWORTH
AND
BROWN
The nuclear electric quadrupole energy of a molecule in a *II state depends on two parameters, eqbQ and eq2Q. In the nuclear spin-decoupled description, the contribution to the total energy for the 2113,2component from this interaction is
[3&f: - J(J+ x [21(2Z1)(25-
1)][3M! - I(Z + l)] 1)(2J)(2J+ 2)(2J+ 3)] ’
(11)
where the upper and lower signs refer to e and j-states, respectively. The values determined from several splittings in the J = 2 + g transition of 33SH are eqoQ = -9.3 f 1.8 MHz and eq2& = 206 + 33 MHz. From his observations, Miller was able to determine only one of these parameters, eqoQ, for which he obtained a value of 13.5 & 2.0 MHz. There is a rather serious disagreement with our value. We have checked to make sure that we are using the same sign convention for eqoQ as Miller; this is indeed the case. We consider our measurements of the 33Ssplittings to be more accurate than Miller’s because (i) we have a much better signal-to-noise ratio and (ii) we measure the hyperfine splittings directly, whereas Miller was only able to record one hyperfine component for each lambda-type doublet (he used the average of these two measurements to determine eqoQ) . For the levels we have studied, the eqoQ and eq2Q terms make comparable contributions to the hyperfme splittings. This is the first determination of these parameters for 33SH; their values make an interesting comparison with those for “OH ( eqoQ = - 1.92 MHz and eq2Q = 66 MHz (26)). The quadrupole moments for the two nuclei are -2.578 fm2 for “0 and -6.4 fm2 for 33S (30). The value determined for eqoQ for 33SH of -9.3 f 1.8 MHz is close to expectation from the ab initio wavefunction of Cade and Huo (31, 32), which gives a value of -13.1 MHz. It is interesting to note that the calculated value for eqoQ for 170H of -2.6 MHz is also larger in magnitude than the experimental value in the same proportion (26). Heterodyne spectrometers working at far-infrared wavelengths have now been developed to be sufficiently compact that they can be used for astronomical or atmospheric observations from an airborne platform (1). These instruments have recently been used to make the first observations of atomic and molecular species in the interstellar clouds at these wavelengths. For example, fine structure transitions have been detected in neutral C (33) and also in C+ (34). Furthermore Betz and Boreiko (35) have detected the first rotational transition (2 + 3) in OH in its *II3,2 component. The identification of these transitions depends on prior laboratory work on the species concerned. Sulfur has quite a high cosmic abundance, and it is likely that SH is present in the interstellar medium. So far, it has not been detected, perhaps because its lambdadoubling transitions occur at unfortunately low frequencies. It is much more likely to be detected through its rotational transitions in the far-infrared. To aid these searches we give the first few pure rotational transition frequencies of 32SH at zero magnetic field in Table VII. These frequencies have been calculated using the parameter values in Table III. We estimate that the transitions within the 2113,2 manifold, which have been observed directly, have an accuracy of 2 MHz. The transitions within the , whose frequencies have been inferred from our model, are about a factor of 2&,2 three less reliable with an accuracy of about 6 MHz. ACKNOWLEDGMENTS We are very grateful to Dr. Harry Radford for supplying us with his raw data on the EPR spectrum of SH (Ref. (5)) and to Dr. Ken Evenson for the use of his far-infrared LMR spectrometer to make the
FAR-INF~RER
LMR OF SH
57
TABLE VII Calculated Transition Frequencies in GHz of Pure Rotational Transitions in ‘*SW in the v = 0 Level of the X *II State
a) Estimated uncertainty = &2MHz. b) Estimated uncertainty = f6MHa.
me~urements reported in this paper. SHA also thanks the Science and En~n~~ng financial support and the travel grant which made this work possible. RECEIVED:
/
Research Council for
January f7, 1992 REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. II. 12. 13. 14. 15. 16. 17. 18. 19.
H. P. ROSER,~~~~~~~~~~~~.33,385-407 f 1991). W. L. MEERTSAND A. DYMANUS,Astrophys. J. 187,445-446 ( 1974). W. L. MEERTSAND A. DYMANLJS, Can. J. Phys. 53,2123-2132 (1975). C. C. MCDONALD, .I Chem. Phys. 39,2%X7-2589 (1963). H. E. RADFORDANDM. LINZER,Phys. Rev. Lett. 10,443-444 ( 1963). M. TANIMOTOAND H. UEHARA,Mol. Phys. 25, 1193-1201 (1973). J. M. BROWNAND P. J. THISTLETHWAIT~ 1I6oi.Phys. 23,635-637 ( 1972). H. UENARAAND Y. MORINO,J. Mol. Spectrosc. 36, 158-161 (1970). T. A. MILLER,J. Chem. Phys. 54, 1658-1664 (1971). P. B. DAVIES,B. J. HANDY, E. K. MURRAY-LLOYD,AND D. K. RUSSELL,Mol. Phys. 36, 1005-1015 (1978). W. ROHRBECK, A. HINZ, AND W. URBAN,Mol. Phys. 41,925-927 ( 1980). R, S. LOWE,Mol. Phys. 41,929-931 ( 1980). D. ZEITZ,W. BOHLE,J. WERNER,A. HINZ, AND W. URBAN,Mol. Phys. 54,953-958 ( 1985). P. F. BERNATH,T. AMANO,AND M. WONG, J. Mol. Spectrosc. 98,20-26 ( 1983). A. BENIDAR,R. FARRENQ,G. GUELACHVILI, AND C. CHACKERIAN, J. Mol. Spectrosc. 147, 383-391 (1991). D. A. RAMSAY, J. Chem. Phys. 20, 1920-1927 (1952). K. M. EVENSON,Faraday Discuss. Chem. Sot. 71,7-14 (1981). J. M. BROWN,A. CARRINGTON, AND T. J. SEARS,Mol. Phys. 37, 1837-1848 ( 1979). J. M. BROWN,M. KAISE,C. M. L. KERR,AND D. J. MILTON,Mol. Phys., 36,553-582 (1978).
58
ASHWORTH
AND BROWN
20. J. M. BROWN, E. A. COLBOURN,J. K. G. WATSON, AND F. D. WAYNE, J. Mol. Spearox. 74, 294318 (1979). 21. J. M. BROWN AND J. K. G. WATSON, J. Mol. Spectrosc. 65, 65-74 ( 1977). 22. L. VESETH,J. Mol. Spectrosc. 63, 180-192 ( 1976). 23. R. F. CURL, Mol. Phys. 9,585-597 (1965). 24. J. K. G. WATSON, J. Mol. Spectrosc. 80, 41 l-42 1 ( 1980). 25. R. A. FROSCHAND H. M. FOLEY,Phys. Rev. 88, 1337-1349 (1952). 26. K. R. LEOPOLD,K. M. EVENSON,E. R. COMBEN,AND J. M. BROWN,.I. :Wol. Spectrosc. 122,440-454 (1987). 27. S. H. ASHWORTHAND J. M. BROWN,J. Chem. Sot. Farudq Truns. 86, 1995-2004 ( 1990). 28. J. M. BROWNAND H. UEHARA,Mol. Pltys. 24, 1169-l 174 (1972). 29. H. E. RADFORD,Phys Rev. 122, 144-130 (1961). 30. I. M. MILLS,T. CVITAS, K. HOMANN,N. KALLAY, AND K. KUTCHITSU,“Quantities Units and Symbols in Physical Chemistry,” Blackwell, Oxford, 1988. 31. P. E. CADEAND M. W. Hue, J. Chem. P!I_w.47,649-672 ( 1967). 32. P. E. CADE, J. Chem. Phys. 47,2390-2406 ( 1967). 33. D. J. JAFFE,A. I. HARRIS, M. SILVER,R. GENZEL, AND A. L. BETZ, Asfrophys. J. Lea. 290, L59-L62 (1985). 34. R. T. BOREIKO,A. L. BETZ, AND J. ZMUIDZINAS,AstrophJJJ.J. Lett. 325, L47-L51 ( 1988). 35. A. L. BETZ AND R. T. BOREIKO,Astrophys. J. Lett. 346, LlOl-L104 (1989).
153,41-58 ( 1992)
The Far-Infrared Laser Magnetic Resonance Spectrum of the SH Radical STEPHEN H. ASHWORTH AND JOHN M. BROWN The PhysicalChemistry Laboratory,South Parks Road, Oxford. OXI 3QZ, England We have extended the observations in the far-infrared laser magnetic resonance spectrum of the SH radical in its ground *II state to cover the first three rotational transitions in the ‘TIXlz component. Signals were seen from all naturally occurring isotopes of sulfur except the least abundant, % (0.02%). The measurements have been analyzed, together with selected data from previous work, to determine an improved set of molecular parameters for 32SH in its ground state. The impli~tions of these parameters are discussed. The magnetic and electric nuclear hyperfine parameters for 33SHare significantly improved over previous work. The frequencies of rotational transitions in 32SHin the absence of a magnetic field are calculated from the parameter set to aid in the detection of this radical in astrophysical sources. 0 1992 Academic PB.. 1~. 1. INTRODUCTION
The spectroscopic properties of the SH radical have been broadly established from a variety of ex~~ments. However, the molecule is irn~~nt enough to merit more detailed study. It enjoys a nearest neighbour relationship to the OH radical with which it provides illuminating comparisons. It is also an important astrophysical molecule because of the relatively high cosmic abundance of sulfur. In particular, improved molecular parameters for the molecule in its X211 state are needed. These can be used, for example, to calculate accurate frequencies in the far-infrared spectrum to help searches for the molecule in space at these wavelengths by the burgeoning methods of far-infrared ~tronomy ( I). The previous spectroscopic studies of SH in its X211 state can be conveniently listed in order of increasing frequency. Meerts and Dymanus have made direct measurements of the lambda-type doubling frequencies in molecular beam electric resonance (MBER) experiments of both SH (2) and SD (3). There have also been several studies by gas phase EPR. The dominant isotopomer 32S‘H has been studied in the J = $ level by McDonald (4), Radford and Linzer (5), and by Tanimoto and Uehara ( 6). It has also been detected in the J = 2 level by Brown and This~ethwaite ( 7), Uehara and Morino (a), and Tanimoto and Uehara (6). Miller ( 9) has measured some hyperhne splittings in the J = f EPR spectrum of 33SH, using a sample in natural abundance. Moving up to the far-infrared region, there has been one study so far. Davies et al. (10) have recorded two pure rotational transitions in the 21’13,2 component, one for SH (J = 2 + 4) and the other for SD (J = s + $) by laser magnetic resonance (LMR). The first vibrational-rotational spectra recorded were those for SD by Rohrbeck ei al. (II), Lowe fl2), and Zeitz et al. (13) using CO LMR. The higher frequency part of the fund~ent~ band of SH itself has been recorded by Bernath, Amano, and Wong using difference frequency spectroscopy ( 14) and Benidar et al. using FTIR ( 15). Finally, the A 2Z+-X211 transition in the electronic spectrum of SH has been recorded and analyzed by Ramsay ( 16). 41
0022-2852192$5.00 Copyright 0 1992 by Academic Press, Inc. All nghts of reproduction in any form resewed.
ASHWORTH
42
AND
BROWN
In the present work, we have extended the far-infrared LMR spectrum of the SH radical. The first three rotational transitions in the ‘II 3,2 component have been studied and signals recorded for 32SH, 34SH and 33SH. The observed resonances have been fitted with selected measurements from previous work to derive an improved set of molecular parameters for SH in its ground state. The implications of these parameters for the structure of SH are discussed. We have also computed the zero-field far-infrared spectrum of 3’SH from these parameters. 2. EXPERIMENTAL
DETAILS
The far-infrared spectra were recorded at the Boulder Laboratories of NIST using the LMR spectrometer described previously ( 17). The SH radicals were produced continuously in the detection region by one of two methods: (i) the reaction of H atoms with elemental sulfur, and (ii) the reaction of H2S with fluorine atoms. In the first method a coating of elemental sulfur was laid down on the inside of a short length of glass tubing. The tube was first tightly packed with sulfur and then gently warmed to fuse the sulfur onto the glass. The remaining loose sulfur was then carefully removed. This tube was connected to the H-atom discharge source by a length of PTFE tubing. The H atoms were generated in a microwave discharge in 2. I Torr He and 0.5 Torr Hz. In the second method. F atoms were produced in the microwave discharge. The H$ was introduced via a second tube opening at the end of the PTFE tube which connected the F-atom discharge source to the detection region. The total pressure was about 240 mTorr: 20 mTorr H2S, 100 mTorr F2 ( 10% in He), and the balance He. Both methods proved to be extremely efficient ways of generating SH radicals and signal-to-noise ratios in excess of 2000: 1 were obtained with 0.3 set output time constant. The magnetic flux densities were measured with a rotating coil probe which was calibrated from time to time against a proton NMR gaussmeter. The overall uncertainty in the flux density measurements is 10m5 T below 0.1 T and 10-4B0 above 0.1 T, where B,, is the magnetic flux density. The FIR LMR observations are summarized in Table I. The uncertainty in the laser frequencies which are given in this table arises mainly from the irreproducability in setting the laser to the peak of its gain curve (ca. 1 MHz). The polarization of the radiation relative to the applied magnetic field can
TABLE I Summary of Transitions Observed by LMR Laser line
J’c
;+;
J
Frequency/GHe 1385.6461
Pump lOP(24)
p* 216.4
Gas ‘%D,OD
k+f
1391.9721
9R( 14)
215.4
CHsOD
f+)
1950.5816
SR(28)
153.7
‘%DsOH
i+f
2488.5534
lOR(36)
120.5
CDzFz
FAR-INFRARED
43
LMR OF SH
be changed by rotating a Brewster-angle window between the gain medium and the sample volume through 90”. 3. RESULTS AND ANALYSIS
3.1. Observations The transitions observed in the present study are summarized in Table I together with the laser lines used. The spectra are slightly complicated by the presence of the various naturally occurring SH isotopomers. These are, however, readily distinguished because of the widely different relative abundances (“S: 95.02%, 33S:0.75%, 34S:4.2 I%, 36S. . 0 *02% ) . ‘?GH, the least abundant isotopomer, was not detected. The isotope pattern can be used as an aid to assignment obviating the need to perform laser pulling experiments to obtain the signs of tuning rates. If the zero-field frequency is greater than the laser frequency, the resonance associated with the most abundant isotopomer, 32SHf occurs at higher flux density than that of 34SH and vice versa (18). Previous work on SH (3, 10) provided molecular parameters which gave unambiguous assignments of the spectra recorded in this work, using the predictive program described elsewhere (18, 19). The isotope structure can be clearly seen in Fig. 1. The 32SH signais have been truncated somewhat so that the 33SH signals are more obvious. Each signal consists of two clearly resolved A-doublets. The 33S hyperfine structure (I = 2) is also well resolved. In addition, evidence of the proton hyperfine structure can be seen on the 33SH and 34SH signals. The response of the system was not fast enough to show such proton hyperfine structure on the 32SH signals with the relatively high scan speed used to record this spectrum.
215.4 urn IT polarfsaiion
32s
1 3%
3% -
I
,
1
/
0.9
I.0
1.1
1.2
I
I-3
Flux density/T FIG. 1. A portion of the far-infrared LMR spectrum of the SH radical in its X’fI state, recorded with the 2 15.4~pm laser line of CD30D in K polarization (a = 0). The transition is J = $ + $, MJ = -3 + -4 for each of the three naturally occurring isotopomers, “SH, 33SH,and %H. The large splitting for each isotopomer is the lambda-type doubling. The quartet hyperfme structure for 33SH can clearly be seen. Note that the “SH signals go off scale.
44
ASHWORTH
AND BROWN 216.4um lT polarisation
I
1
,
I
@38
@37
I
I
I
039
/
O-40 Flux density/T
FIG. 2. Part of the far-infrared LMR spectrum of 33SH in natural abundance, recorded with the 2 l&4pm laser line of ‘%DaOD in K polarization (A&I’= 0). The quartet pattern arises from the “S magnetic and electric hyperfine interactions; the small doubling arises from the proton hyperfme structure. The other two weak, broader lines at approximately 0.385 and 0.410 T arise from another species. The spectrum was recorded with an output time constant of 300 msec.
Both proton and 33Shyperfine structure are easily observable in Fig. 2. The former, however, is not fully resolved. In addition there are two weak transitions at approximately 0.385 and 0.41 T. These are high-field components of an extensive series of weak lines which we have tentatively assigned to I-f&. This assignment is currently under investigation. In favorable cases it proved possible to saturate the transitions. Figure 3 shows one component of a 32SH A-doublet. The doubling here is a result of the proton hyperfme interaction, and the saturation dips are easily seen. Another notable feature of this spectrum is that the Doppler limited hyperfme components are almost completely resolved. Although the transition is tuning relatively quickly so the lines are inherently narrow ( du / d B cc I/ linewidth), significantly narrower lines were obtained using H$ + F rather than using H + S because of the much lower pressure employed. The J = ; + 5 spectrum is shown in Fig. 4. All the far-infrared transitions observed in this work occur in the 2IIs,2 manifold. The detailed measurements are given in Table II. The observation oftransitions within the ‘IIt p manifold would provide interesting complemental info~ation. We were 2164pm 0 polarisatbn
0%05
O%?O
01615
0~%20
Flux density/T
FIG. 3. A small portion of the far-infrared LMR spectrum of %H, recorded with the 216.4-pm laser line of “CDaOD in g polarization (L\M = f I ). The Lamb dips at the centers of the two proton hyperfine components can be clearly seen. The signal was recorded with an output time constant of 100 msec.
FAR-INFRARED
LMR OF SH
45
unable, however, to observe these transitions in the far-infrared LMR spectrum because of two adverse factors. The magnitude of the spin-orbit splitting in SH is about 395 cm-‘, so the population of the upper 211I ,2 state would be around 15% of that of the ‘IIJ,~ state assuming thermal equilibrium at a temperature of 300 K. Although such a population of the 2111,2manifold ought to be sufficient, the low tunability of the 2111,2 state means that very close coincidences between molecular and laser frequencies are required, typically within 400 MHz (the contending interval for transitions involving the 2113,2levels is 30 GHz). Second, the low tunability of the ‘IIr12 transitions means that their linewidths in a magnetic resonance experiment would be very broad and severely under-modulated. It is, therefore, quite understandable that, when searches were made for the 211,,2 transitions on the basis of predictions made with the best parameters available, the signals were not detected. The measurements of the LMR spectrum were used with the earlier molecular beam (2, 3), EPR (5, 6), and LMR data ( IO) to determine the appropriate molecular parameters in the effective Hamiltonian for a 211state: &ff = H, + &XX+
f&d
+ HLD
+ I?r,, + ffhfs
+ f&j
+ fke,m,-
(1)
This Hamiltonian has been described in detail elsewhere ( 19). The rotationally dependent terms in the Hamiltonian are formulated in terms of N2 rather than R2 (20). The basis set was truncated without loss in accuracy at matrix elements with AJ = *2. Each datum was weighted in the fit, inversely as the square ofthe experimental uncertainty (which for LMR data arises primarily from the knowledge of the laser frequency as used in the ex~~ment). As can be seen from Table I, there is no direct information on SH in the *II t ,z spin component in our work. We have therefore used Ramsay’s measurements on the A 2Z ‘-X 211 electronic transition to determine the spin-orbit and spin-rotation parameters. We have refit Ramsay’s data with the effective Hamiltonian in Eq. ( 1) to determine the parameter values given in Table III. We chose to constrain the parameter AD to zero in the fit so that A and y are strictly effective parameters, having absorbed the effect ofAD (21). The data set which is given in Table II consists of: (a) the lambda-doubling frequencies for 32SH measured by molecular beam electric resonance by Meerts and Dymanus (2,3) with an accuracy about 1 kHz. This includes measurements of the Zeeman splittings for the J = 1 level (3) (accuracy about 30 kHz). (b) EPR data for 32SH in the J = z and $ levels measured by Radford and Linzer (5) and Tanimoto and Uehara (6)) respectively. The accuracies of these data are 50 and 100 kHz. (c) The present observations in the fm-infrared LMR spectra of 32SH, 33SH, 34SH and 32SD. The accuracy was taken to be 1 MHz. We have remeasured the resonances for 32SDreported by Davies et al. ( IO) because of their rather low accuracy. For the 33SH isotopomer, the average of the four 33Shyperhne components was used in this fit because the program is only capable of dealing with the interaction of a single nucleus at the moment. The 33Ssplittings were used to determine the hype&me parameters in a separate fit (see below). Certain molecular parameters are not determinable directly from this data set. In such cases, values were obtained from other sources and the parameter was constrained
46
ASHWORTH
AND BROWN
TABLE II Details of the Fit of the Data for “SH in the % State %l, manifold J = ; data (2, Upper state F 1 1
MF 1 -1
state
Lower
FltlX
MF
P
Density”
-
1 1
1 -1
+ +
-1
P”
-
F
0.01 0.01
8.446558
6
0.134
+
0.01
8.445677
15
0.067
0.01
8.444331
66
-
1
1
1
-
1
0
+
1
0
+
0.01
8.446091
0
-
1
1
+
0.01
8.444745
-28
1
0
-
1
0
+
0.00
8.445211
-2
1
0
-
0
0
+
0.00
8.459034
-
0
0
+
0.01
8.459914
-66
-
0
0
+
0.01
8.458154
-38
1 1
-1 1
1
Upper state
F
P
5
1
; ;
Lower state
F
P
+
1
2
+
f
1
+
;
f ;
2 2
+ -
f
;
3
-
3
30 30 30 30
0.060
30
-0.064
5
0.000 0.000
5
0.076
30
-0.060
30
(2) uncertainty
Frequency
J f
J
30
-0.076
3
manifold MBER data
NW
-0.134
38
-
1
uncertainty
Rake
@HII -11
0 -1
Tuning
*c
@HI) 8.443864
1 1
Frquency
Clf,:,
-
@HE) 0.1114862
2
-
0.1115452
0.1
2
-
0.100293
3.2
1
-
0.122737
;
2
+
0.4424781
0.0
0.5
;
3
+
0.4426277
0.3
0.5
1.8
2
-0.2
-4.7
&HI) 0.5 0.5 3 3
;
3
-
f!
2
+
0.4471876
;
2
-
f
-4.3
2
3
+
;
+ -
0.4379154
;
3 3
1.0941871
-0.2
0.5
3
4
+
;
4
-
1.0944596
-0.2
;
3
+
1.0935326
4 4
+ -
4 3
-
; ;
; I2
4
+
f
5
-
oi ;
5
+
2.1587239
1
0.4
2
1.0951179
3.1
2
2.1582986
0.2
1
0.0
1
f
5
-
;
4
+
2.1564902
;
4
-
1
+
+ -
0.4
5
5 5
2.1605318
y
; ‘i?
3.7148864
1.0
2
+
6
+
+
6
-
3.7154892
-0.7
-1.0
1
2
a\ Paritv label. Proto;; hyperfinc siructnre not resolved. Deuterium hyperfine rtructure not resolved. Uncertainty of sew implies rem weight in the fit.
to this value in the fit. We have already mentioned the need to use the optical data (16) for values of the spin-orbit and spin-rotation parameters. The vibrational dependence of the major parameters (A, B, D, p, and q) is also needed so that the isotopic scaling can be performed reliably. These dependences have been measured accurately in the infrared by Bernath et al. ( 14). We have refitted their data using our Hamiltonian (which differs slightly from theirs). The values determined for the vibrational dependences are given in Table III. The Zeeman parameters required to describe a molecule in a ‘II state have been defined by Brown et al. ( 19). Four of the six parameters (gL, g,, g$ and g:‘) are determinable from the data. Of the remaining two, gS was constrained to the free spin value corrected for relativistic effects as computed by Veseth (22) at 2.00213. The anisotropic correction to the spin g-factor was estimated from Curl’s relationship ( 23),
FAR-INFRARED
LMR OF SH
47
TABLE 11---Cmtinued
Uncertainty Density”
(-4
0.778175
9.21570
-80
11.675
0.777898
9,21571
-72
11.675
50
0.776556
9.21574
-52
11.727
50
0.776075
9.21574
-17
Il.727
50
0.774924
9.21576
-13
xl.779
50
0.774442
9.21577
19
ii.779
50
0.797677
9.21577
3
11.666
50
0.797193
9.21577
20
11.668
30
0.795556
9.21577
36
11.727
50
0.795062
9.21577
11.727
50
0.793445
9.21578
11.767
50
0.792975
9.21578
-32
11.787
50
0.776173
9.21573
-36
11.675
50
0.777694
9.21573
-19
11.675
50
0.776553
9.21572
-27
11.727
50
0.776076
9.21572
-54
11.727
50
0.774923
9.2157l
-41
11.779
50
0.774436
9.21571
36
ii.779
50
0.797670
9.21561
120
11.668
50
0.797191
9.21579
65
11.668
50
0.795554
9.21578
62
11.727
50
0.795075
9.21577
57
11.727
50
0.793440
9.21575
60
11.787
50
0.792970
9.21574
-12
11.787
50
Den&y’
(&is)
@HI)
Rate;
1.589532
9.11440
232
5.502
1.589817
9.11440
178
5.502
100
1.597863
9.11395
-134
5.452
100 100
VW
-17 26
Rata
WI 50
Uncerthty
as 0.776
X 10m2.
WI 100
1.5S8635
9.11395
-180
5.452
1.606467
9.11383
-131
5.399
106
1.606757
9.11383
-144
5.399
100 100
1.615582
9.~1379
-95
5.342
1.815885
9.11379
-150
5.342
100
1.625191
9.11378
-47
5.282
100
1.625499
9.11378
-104
5.282
100
1.756753
*s&563
129
3.492
loo
1.757075
9.11563
82
5.492
106
1.763143
9.11519
116
5.44s
100
1.763452
9.11519
61
5.449
106
1.770201
9.11523
95
5.402
100
1.770493
9.11523
56
5.402
100
1.777999
9.11583
60
5.349
100
1.778283
9.11563
-9
5.349
160
1.786413
9.11595
-23
3.2Q2
1W
1.786677
e.lm5
-55
5.292
106
ASHWORTH
48
AND BROWN
TABLE II-Continued R(;),1391.9721GH.,
215.4jnn,
MI
%H %iH
+ _f
_;
P 1
_;
-
_;
-
_j-
+
-j
+
;
=SH J%B
MJ
‘%H
;
_f
-
=SH
1 2
_J
_
JJSH
;
-f
+
-)
+
_f
-
-;
-
%A
-f
;
“SH %H
-f
%i 3’SH
f _$
2
CD.OH,
Plux
Upper state
-5
+
_f
+
_;
-+
;
1 5 _+ ; -; ; _f ; _;
Tuning Ratec
Unceltainty
P
Density”
_j
+
0.91464
0.69
9.583
1.0
_)
+
0.91530
0.62
9.583
1.0
-j
-
0.94951
0.25
9.583
1.0
-;
-
0.95019
-0.08
9.583
1.0
+
1.04418
-0.12
9.595
1.0
+
1.04481
9.595
1.0
_;
-
1.07900
-1.01
9.595
1.0
-as
-
1.07979
-2.39
9.595
1.0
_f
+
1.16564
-1.15
9.606
1.0
_;
+
1.16635
-1.79
9.606
1.0
-5
-
1.20030
-1.54
9.606
1.0
_f
-
1.20102
-2.25
9.606
1.0
+
0.58483
-0.84
14.965
1.0
-
0.60665
-0.60
14.970
1.0
MI f
9B(14)
o-c
MJ
-2 _j:
3_
(MW
0.02
(MW
=SH
-“-;
-
A_;
=SH
9-i
+
_d
3%
-1
;
-
.A_;
+
1.00828
-1.28
8.759
1.0
%H
_d
f
+
3-i
_
1.04554
-1.15
8.771
1.0
J’SK
_.q
-
A_;
+
0.74554
0.52
14.985
1.0
%H
_“_+
+
-“-:_
_
0.76741
0.55
14.990
1.0
“SH
_d
;
_
_“_f
+
1.28227
-1.15
9.812
1.0
%H
_d
;
+
-“-f
_
1.31903
-1.45
8.824
1.0
-f
R(]),1385.6461GHa,
Upperstate MI MJ P =SH
2
_f
“SH
1 I f
_s
=SH =SH
_) f
=SH %iH
_; ;
%iH =SH
-f f
“SH 3%
_f ;
%H
MI
1
f 1 f ;
_
_;
+
-5
+
-;
-
_f
-
_f
+
-f
+
-f
-
-f
-
_;
+
_)
+
216.4pm,
-;
MJ -3 _J_ 1 -;
%D#D,
lOP(24) uncertainty
FluX
Tuning
P
Density’
Ilaw
+ +
0.25244
0.35
9.522
0.25308
0.33
9.522
0.5
-
0.28736
-0.31
9.522
0.5
-0.33
Lower state
WI) 0.5
_:_
-
0.28801
9.522
0.5
-;
+
0.38267
0.94
9.534
1.0
-5
+
0.38336
0.51
9.534
1.0
3
_;
-
0.41733
1.84
9.534
1.0
I 1 f
_J
_
0.41801
1.50
9.534
1.0
+
0.50483
0.55
9.545
1.0
0.50550
0.36
9.545
1.0
-
0.53950
0.50
9.546
1.0
+
0.54019
0.09
9.546
1.0
0.74190
1.22
3.311
1.0
0.26
3.330
1.0
3.384
1.0
f -;
1 f ;
I
-f 3 1-b -;
YXi
.A-$
_
1 s i -i _“_f
?SH
_“_;
+
A-;
_
0.84208
=SH
-d-f
_
A-;
+
1.11312
=SH
A__;
+
A-$
_
1.21063
0.07
3.402
1.0
“SH
-“-;
_
A_;
+
1.45399
0.03
3.450
1.0
=SH
A-5
+
-“-;
_
1.54954
=SH
;
-
;
_jT
+
0.16100
_f
+
%H
_;
-+
-
=SH
;
_)
+
=SH
1 ?
I 1 _.$
+ -
-f
-
_;
+
=SH
_f
_f
J’SH %H
t -1 ;
“SH
1 ? ;
=SH =SH =SH
-f
‘“SH %H
; -f
t 1 f
+ -
f
-
+
+
f
+
_; 1 ? _f ; 1 1 1 2 -f + _; I 5 -;
3.468
1.0
0.86
14.913
0.5
0.16152
0.81
14.913
0.5
0.18322
0.20
14.917
0.5
-
0.18374
0.18
14.917
0.5
+
0.32229
0.81
14.932
1.0
0.32284
0.20
14.932
1.0
0.34432
0.43
14.937
1.0
14.937
1.0
3 , -5 -5 J 1 J i
-0.14
+ _
-0.11
-;
-
_f
+
0.27976
-0.31
8.616
0.5
_;
+
0.28018
-0.27
8.616
0.5
0.31801
-0.27
8.627
0.5
0.31842
-0.17
8.627
0.5
-i -f
1
-
0.34488
-0.20
“SH
_d
f
_
A_;
+
0.42361
1.68
8.643
1.0
“SH
-d
;
+
-d-i
_
0.46156
1.81
8.655
1.0
FAR-INFRARED
LMR OF SH
49
TABLE II-Continued R(f),l365&461GB1, Upper state MI
Lower state
MJ
P
MI
216.4pm, “CDsOD,
lOP(24) (cont.)
FllK
MI
P
Density”
Tuning
Uncehinty
Rat@
(MHz)
(hz,
J’SA
_d
f
-
_d -f
+
0.55837
0.42
8.670
1.0
3’SH
_d
;
+
A-5
-
0.59605
0.48
8.681
1.0
%H
f
-;
-
+
_:_
+
0.58379
0.71
4.122
1.0
-5
-
_ai
+
0.58499
0.31
4.122
1.0
-;
+
-;
-
0.66561
-0.30
4.117
1.0
-;
+
-;
-
0.66678
-0.47
4.117
1.0
_;
-
_f
+
1.16611
-0.05
4.142
1.0
-;
-
-3%
+
1.16717
0.12
4.142
1.0
3=SH
-f
J%H JlSH
f _f
%.H “‘SH
; -f
3’SH 3’SR
; -f
-;
+
-f
+
_; ; _f ; _; ; -;
-;
-
1.24787
0.62
4.136
1.0
-f
-
1.24908
0.22
4.136
1.0
3’SH
_d
f
-
_d
6
+
1.03828
0.14
2.403
1.0
3’SH
_d
f
+
-4
f
-
1.17231
0.40
2.432
1.0
R(;),1950.5816GHs, Upper state
Lower state
3’SH
A-;
P +
3’SH
A-4
-
MI
MI
MI MI .A-; .A__;
153.7/rm, “CDJOH, Flu
P _ +
R(;;),248&5534GHs,
Density’
(iii*,
1.76463
-3.63
1.81926
-367.35
2-5
+
0.24884
-“-;
_
2-3
+
1.51577
%B
_A-:_
+
9-g
-
0.56309
32SH
9-f
-
-“-;
+
3’SH
A-;
+
9-i
%B
A-;
-
?5H
A-)
3%
_d
3’SH
-f
Tuning
uncertainty
Raiec 8.717
(MHz) 1.0
8.731
01
120.5~1, CDsFz, lOR(36)
-
3’SH
BR(28)
-0.23 0.76
3.391
-1.0
3.439
1.0
-0.41
3.390
1.0
0.34842
-0.15
2.421
1.0
-
0.78866
-0.38
2.425
1.0
A-:;
+
0.58150
-0.67
1.451
1.0
+
3-i
-
1.31642
-0.28
1.450
1.0
A-5
_
3-t
+
1.65934
47.69
0.475
“SH
9-g
-
9-g
+
0.14778
0.31
5.703
1.0
3’SH
9-i
+
9-i
-
0.33409
0.08
5.716
1.0
3=SH
3-f
-
A-:_
+
0.17792
0.75
4.734
1.0
3=SH
_A-;
+
A-;
-
0.40231
0.25
4.745
1.0
3aSH
9-f
-
_“_$
+
0.22386
0.04
3.764
1.0
3’SH
A-f
+
-“-“s
-
0.50567
0.05
3.773
1.0
3%
_d
;
-
A-5
+
0.30125
0.39
2.795
1.0
JWI
_d
;
+
-d-i
-
0.68037
0.14
3*SH
_d
;
-
_d
+
+
0.46104
;
;
0’
2.801
1.0
-0.03
1.825
1.0
31SH
_d
+
_d
_
1.03986
-0.15
1.828
1.0
3%H
-“-;
-
9-f
+
0.78423
-0.34
1.081
1.0
‘%H
A-;
+
2-g
-
1.78564
-0.20
1.081
1.0
“SH
_d
-
-1
+
3.98059
0.09
0.854
1.0
;
g
=‘SH
A-;
-
A-5
+
0.90405
0.29
5.744
1.0
%H
-d-i
+
3-5
-
1.08763
0.23
5.758
1.0
%H
A-5
-
9-g
+
1.09004
0.36
4.758
1.0
3’SH
-d-f
+
3-i
-
1.31109
0.31
4.770
1.0
J’SH
9-t
-
_d
+
1.36856
15.09
3.773
-“5
01
The data for four different isotopomers of SH are very accurate and therefore likely to show effects of the breakdown of the Born-Oppenheimer approximation in the isotopic scaling. Watson has shown how to model such effects (24), and we have included his parameter &, , the correction for the equilibrium rotational constant Be, in our fits for both the H and S atoms. Both were determinable in the final fit.
50
ASHWORTH
AND
BROWN
TABLE II-Continued R(~),1016.8972GJ.h, 294.8/m, 9R(8), CHJOD Upper state MI
P
MJ
Lowu state MI MI P
Flux
-6 Raw
Density’
uncehinty
+
-8
_;
-
0.45340
-0.41
5.361
WI) 1.0
-
-8
-f
+
0.47078
-0.01
5.362
1.0
+
_I
-3
-
0.75372
-0.06
3.225
1.0
+
0.78363
-0.10
3.226
1.0
-
0.28975
0.18
8.359
1.0 1.0
=SD
_e
-;
%D
_e
-;
J’SD
-‘_;
“SD
2-f
-
2-f
“SD
__c -;
+
_e
“SD
2-f
“SD
_I
‘=SD
-‘-;
“SD
_e
%D
_*
‘=SD
-‘_f
“SD
_e
%D
-1
“SD
_e
-t
-
..s_;
+
0.30120
0.12
8.362
+
-0
_f
-
0.38934
0.27
6.217
1.0
-
_c
-ST
+
0.40470
0.14
6.220
1.0
-
0.59331
0.25
4.076
1.0
_e
-f
+
0.61659
0.13
4.078
1.0
+
_*
.+
-
1.03805
-0.23
2.351
1.0
-
_e
_g
+
1.08033
-0.10
2.349
1.0
;
+
_I
f
-
1.24684
-0.10
1.931
1.0
;
-
_e
;
+
1.29491
-0.08
1.933
1.0
-f
f )
-;
+ -
2-t
The data set was fitted to experimental accuracy by this effective Hamiltonian. The standard deviation of the fit relative to the experimental uncertainty was S = 0.9626. The results are given in Tables II (residuals) and III (parameter values and standard deviations for the dominant isotopomer, 32SH). The 33Shyperhne splittings were fitted separately, using a computer program which is capable of dealing with two independent hyperhne interactions. Most of the parameters for 33SH were taken from Table IV, suitably scaled for this particular isotopomer. The experimental measurements are given in Table V; the parameter values used and determined in the fit are given in Table VI. Three hyperfme parameters were determined from the 33S splittings, h3,2, which equals a + gb + c) in terms of the Frosch and Foley parameters (25), eqoQ and eqzQ. The other three magnetic hyperhne parameters, h , ,*, b, and a’were constrained to values obtained by scaling from the corresponding quantities for “OH (26). The three other parameters determined in the fit B, q, and g, were simply used to ensure that the center of the hyperfine patterns occurred at the observed fields. 4. DISCUSSION
In this paper, we report the observation and analysis of the far-infrared LMR spectra of four different isotopic forms of the SH radical in the 2) = 0 level of its ground 211 state. This has resulted in a significant refinement of its molecular parameters. This can be seen in Table VI, where we have listed the values for the rotational constant B. and the centrifugal distortion correction Do determined from the electronic (16), the infrared spectrum ( 14), and from the previous infrared study (IO), as well as the present work. In general the differences between the parameters are much larger than expected from statistical uncertainties. These reflect different assumptions for the effective Hamiltonian used in fitting the data. The improvement in our knowledge of the rotational constant for 32S‘H means that we can refine the equilibrium bond length for this molecule. Using the value for CQdetermined from the refit of the infrared data of Bernath et al. (14), we obtain B, = 9.599545(65) cm-’ or 287.7871( 19) GHz, where the error estimate has been computed in neglect of any nonlinear dependence of B. on the vibrational quantum number. From this value we obtain,
FAR-INFRARED
51
LMR OF SH
TABLE IIt Parameter Values Determined for 32SH in the v = 0 Level of the X *B State Value.
Correlation’
Parameter
...
a.4
V&e
Conektion’
77917.557(62)+ -11297.15(42)’ -4.40(
1oy
5.613
QB
0.0144796(12)
6.217
OjJ x 105
7200.0
8.42966(23)
10’
%
283.6121#(33)
-0.284334(30) PO + 2qD X
...
0.2294 x lo6
-0.218(U)
0.1616
x 10s
qjJ X 10’
5+c
-0.030994(60~
527.8
d
..
g:
9s
2.00213f
.
..*
0.422(14)
6
531.9
f.
8.~~(~)~ -0.146(4?)”
-0.0108(20)d
a9
0.032574(30)
. . ...
0.315(13)
++a
a
13.67(10)‘ -0.33X(56)
-0.06340@3(97) 0.027343(59) 0.00776(
. . . 0.3055
x 10s
3.305 38.65 ...
gt
1.0094848(33)
2.501
0,“’ x 10’
0.10073(50)
1.182
g, x 103
-0.3321(17)
2.495
91 - 9:’
0.01434(17)
1.182
5.58569W
.. -0.95605(98)
1.073
PN &i(S)
-0.70(12)
1.399
&x(W
a) Parameter value in GHz where appropriate. b) The correlation coefficient is the appropriate diagonal element of the inverse of the correlation matrix. c) Figures in parentheses are one standard deviation of the least squares fit given in units of the last quoted decimal place. d) Parameter determined in the refit of infrared data (14) and constrained to this value in the present fit. e ) Origin of the fundamen~l band determined from the infrared data ( II) as 2599.0499 (2 1) cm-‘. f) Parameter determined in the refit of optical data ( 16) alone and constrained to this value in the present fit. g) Parameter constrained to this value in the fit.
r, = 0.13406630(45)
nm.
(3)
It has been possible to fit all sulfur and hydrogen isotopic forms simultaneously to a single model using the appropriate isotopic scaling factors. The effects of the breakdown of the Born-Oppenheimer separation on the isotopic scaling of the equilibrium rotational constant B, proved to be significant for both the hydrogen and sulfur atoms. The value obtained for the former is &(H) = -0.95605 (98), which agrees reasonably well with the corresponding value estimated for OH of - 1.7 (27). Somewhat surprisingly, this appears to be the first time that data for XH and XD have been fitted simultaneously. The corresponding correction parameter for the sulfur atom in SH is just determinable and is of a similar magnitude, -0.70( 12). The heavy atom correction parameter has also been measured for SeH (27) but has been determined to be much larger, - 17.8 ( 8 ). This possibly arises because of the similarity in magnitude of the spin-orbit splitting and the vibrational interval for this molecule. Four of the six g-factors for SH in its X2.11state have been determined in our work (see Table III). Because of the lack of information on SH in the 2111,,2component, we have been forced to constrain the electron spin g-factor, gs to a theoretical value (22). The major parameter which has been determined is the orbital g-factor, g$_, which is related to the relati~sti~lly corrected parameter gL by &=gL+&L>
(4)
52
ASHWORTH
AND BROWN
TABLE IV
Details of the Fit of the 3%H Data R(;) Upper
1391.9721 GE&, SR(l4),
state
Lower
216.4 /mt, CHsOD
state
FlUr
I
Density’
0.7
9.69
1.03538
0.5
es*
1.04113
0.7
9.5s
1.04181
0.3
9.59
1.04737
0.4
1.05341 -3
_;
-2
-
g
$ f f
;
;
-;
-f _g _; -2
-; -4
_)
-:
-3
-8 -f
; _; t -; ;
1.05407
t f
_f _f
i f
_; -1
-1
_f
_#
-1 _f
5
-;
if
_)
#
_;
f
-3
-$
_g
-4
_f
-$
_;
_$
a b E d)
I
0.0
9.59
-0.2
9.59
1.06960
+ + + + +
1.07033
-0.2
0.6
9.59
9.59
1.07587
-0.7
9.59
1.07656
-1.1
9.59
1.08208
-0.4
9.59
1.0827%
-1.0
9.39
+
1.08846
-1.0
9.59
+
1.08908
-0.8
9.59
1385.6461 GH:,
lOP(24),
216.4 #XII, “%DJOD 0.37337
-0.6
9.53
0.37411
-1.4
9.53
_
0.37966
-0.5
9.53
-
0.38036
-1.1
9.53
-
0.38584
-0.6
9.53
-
0.38647
-0.3
9.53
;
-
0.39181
-0.2
9.53
-
0.39249
-0.6
9.53
$
+
0.40819
0.1
+
0.40882
0.2
9.53
+
0.41417
0.9
9.53
_$
+
0.41485
0.5
9.53
;
i
0.42036
0.9
9.53
+
0.42104
0.5
9.53
+
0.42659
1.7
9.53
+
0.42733
0.8
9.53
_; ; _f
-f
_f
-;
9.59
-
f
;
-t _$
9.59
-0.1
+
R _t
Rate’
1.03470
1.04806
_f
Tuning (b&
-5 :_
-5 1 _;
parity label. Flux density in Tesla. Tuning Proton hype&e structure
9.53
ratein mT/MHa. from predictions.
where AgL is a nonadiabatic correction to the g-factor in the effective Zeeman Hamiltonian ( 19). If we assume the same relativistic correction for gl, as for g, we obtain gl. = 0.999905. The value determined for gL in Table III gives AgL = 0.5793( 33) X 10m3. This parameter is a measure of the difference in the rotational admixture of excited 22 and 2A states into the ‘II state (28) and makes an interesting comparison with the rotational g-factor, g: which measures the sum of these contributions. The rotational g-factor measured in our work is g,, which is the difference of the nuclear and electronic contributions, gr=gY-g;. For 32SH, the nuclear contribution
can be calculated to be 0.5361
X
(5) 10W3so that g:
FAR-INFRARED
LMR
OF SH
53
TABLE IV-Continued
upperState MJ
-f _;
# g
-;
t
-3
)
-f
-f
_f
-;
-t -;
f _; _;
-$
_)
f
-8
-1
;
-3 _p -f -f
;
-$
t g
i _;
-4
;
4
_;
-1
-$ -4
-4
if
-;
#
_)
f
-‘r
f
-;
-f
-;
-;
-f
-$
4
-)
-4
f -f $ -4
) _f
1.103oP
0.4
3.38
LlO615’
1.0
3.38
1.16670~
1.0
3.35
1.1153P
1.1
3.38
1.11566*
1.1
3.36
-
1.12181’
0.9
3.37
-
l.12245d
0.8
-
3.38
3.38
1.20138’
-0.5
3.40
+
1.20262’
-0.5
3.40
+ +
1.26660
0.1
1.20754’
0.1
3.40
+
1.2131@
0.2
3.40
+
1.21374’
0.2
3.40
+
l.2168Td
0.3
3.40
+
1.2265od
0.3
3.40
-
0.41441’
-0.1
-
0.41483’
-0.1
8.64
-
6.42034’
-0.7
8.64
3.40
8.64
-
0.4207s’
-0.7
8.64
-
0.42637’
-1.1
8.64
-
0.421370~
-1.1
f
-
0.43210d
-
1
+
f _f
_f
z
-$
0.4
B +
-;
RAW
l.10320d
-
f
Tatig
r.kBsi@
1
4 -
-4
-;
Flus
hf?
-if
8.64
1.5
8.64
0.43262d
1.5
8.64
0.45252d
0.2
6.66
f
-)
+
0.452&
0.2
8.66
f :
; -f
+ +
0.458lr”
0.3
8.65
0.45859d
0.3
8.65
$
+
0.46422d
-0.6
8.65
+
0.46464d
-0.7
8.65
+
0.47050d
-1.0
8.66
+
0.47093&
-1.0
8.66
-5 -f -;
-$
-;
-4
-f
.+ -;
-f -if
_)
f
is determined to be 0.8682 ( 17 ) X 1Oe3. Comparing this value with that for Agt above suggests that the contribution to the wavefunction for the X211 state of SH from the 22 states outweighs that from the ‘A states. It is likely that most of this contamination involves the A2Z+ state. Finally, there are two pasty-de~ndent g-factors, g; and g$_ These are a measure of the admixture of *2 states and can be related to the lambda-type doubling parameters:
-4
grer = -B’ The value for g;, which is determined primarily by the MBER Zeeman data (3), is 0.01535 ( 17) as compared with 0.01586 from Eq. (6). The value for g:’ is determined primarily by the EPR data of Radford and Linzer (5) as 0.10072 (50) X 10d2, which again compares well with the estimate from Eq. (7), 0.10025 X lo-*. Nuclear hyperfine parameters have been determined for both the ‘H and 33Snuclei. The former are given in Table III and depend primarily on the MBER data of Meet-&
54
ASHWORTH
AND BROWN
TABLE V Parameter Values Determined for 33SH in the 2’= 0 Level of the X2H State Parameter & fro
Parameter
V&e’
j
-11301548.63*
j
-fo
Value I
-4397.4758976
‘$S hype&e parameters h:
~-
d
234.86’
173.70(28) “Id -9.3(18) %lQ ‘H hype&e parameters
I
bF
79.47’
d
273.6’
eaQ
206(33~
hlr
48.07049385b
bF
ha
17.07654541*
d
9L
1.000484825’
9J
0.~776*
9s $&x 105
sl - 96
0.0143420~62*
9:’ x 162
6.1~2644893b
9N(Sf
1.287642b
9N(W
5.5854’
-63.40929526*
-
27.34261182’ 2.00213*
-
-.540(26)
a) Value in MHz where approptiatt. bj Parameter constrained to this vs;luein the fit and scaled, where appropriate, from the s2SH ~Iue (see Table III). cf One stmdwd d&a&n in units of the last quoted de&& pbxe. d) These parameters are given by: h: = Bf f(6 f c) and h; = a - $(a + c). e) P&ram&r con&mined to this value wbieh was estimated by scrtting from the corresponding ‘70 parameter (see text).
and Dymanus ( 2). These authors have discussed the implication of the proton hypefine p~am~Eers for SH and we shall not elaborate on the subject. However, the value for the % parameters which are given in Table V are new, since they depend on our measurements. Since we have made observations of SH in the 2113,2spin component, we have only been able to determine one magnetic hyperfine parameter, /z~,~,Values for the other three were obtained by scaling those from “OH (26) in the same ratio, This procedure has been shown to be reliable in an analogous study of the SeH radical (27). Miller (9) has also attempted to determine nuclear hyperfke parameter for
TABLE VI A Camparison of the Values Determined for the Rotational Parameters for SH in the II = 0 Level of the 5% State with Those of Previous Studies
Bo/GHe
l?iJ/MHS
283.6<
283.73~(~7~
14.39
14.806(63~
283.57698(90~ ~3.612180(33) [14.39]6
14.4796(12)
IWE Optical, Ref. (15); Infrared, Ref. (14); and FIR, Ref. (10). a) The figures in parentheses are one standard deviation of the least squares fit. in units ofthe last quoted decimal place. b) The centrifugal distortion correction &was not determined in this work. The parameter was constrained to the value determined from the optical spectrum (16).
FAR-INFRARED
II
I
I/, I
OF SH
55
i--I+-I
I
I
I f
I
LMR
"4SH -.m-* 1 ;r;]32SH
I
f
12D5 pm D palarlsation
1
I
I
IO
cl5
0
i
2.0
1-5
Flux dens+’
T
FIG, 4. The far-infrared LMR spectrum of the SH radical, recorded from 0 to 2 Tesla with the 1205wrn laser line of CDzFz in d polarization (AM = + 1). The rotational transition involved is J = f + i in the %,? component. The proton hyperfine structure is not resolved.
33SH in its lowest rotational. level in an EPR study. He interpreted his observations in terms of the magnetic hyperfine parameters introduced by Radford (29) for the situation in which nuclear spin is decoupled, Ehfs = A,MJMI 4 A2MJMI,
(8)
where the upper and lower signs refer to e and fstates, respectively. The relationship between Radford’s parameters and those used in the present paper for the 2113,2component is cl AI
=
h3,2
J(J+
(B
-
1) - (A-
h)b
28)
[(J+
$)’
J(Jf
-
1)
I]
(9)
and
&p-iy)2
A
*
2
(A-2B)*J(J+
J+k 1)’
From his m~suremen~ Miller determined a value for Al of 71.1 + I .O MHz for SH in the J = 3 level. The corresponding value determined from our parameters in Table VisA, = 7 1.O1 + 0.7 1 MHz, in excellent agreement. The fact that the 33Shyperfine parameters for SH seem to scale so well from those of 170H is consistent with the close similarity in the angular behavior of the wavefunction near the heavy atom for these two molecules. More simplistically, the a molecular orbital which contains the open shell electrons in the ground state of SH approximates closely to a 3p atomic orbital on the S atom.
56
ASHWORTH
AND
BROWN
The nuclear electric quadrupole energy of a molecule in a *II state depends on two parameters, eqbQ and eq2Q. In the nuclear spin-decoupled description, the contribution to the total energy for the 2113,2component from this interaction is
[3&f: - J(J+ x [21(2Z1)(25-
1)][3M! - I(Z + l)] 1)(2J)(2J+ 2)(2J+ 3)] ’
(11)
where the upper and lower signs refer to e and j-states, respectively. The values determined from several splittings in the J = 2 + g transition of 33SH are eqoQ = -9.3 f 1.8 MHz and eq2& = 206 + 33 MHz. From his observations, Miller was able to determine only one of these parameters, eqoQ, for which he obtained a value of 13.5 & 2.0 MHz. There is a rather serious disagreement with our value. We have checked to make sure that we are using the same sign convention for eqoQ as Miller; this is indeed the case. We consider our measurements of the 33Ssplittings to be more accurate than Miller’s because (i) we have a much better signal-to-noise ratio and (ii) we measure the hyperfine splittings directly, whereas Miller was only able to record one hyperfine component for each lambda-type doublet (he used the average of these two measurements to determine eqoQ) . For the levels we have studied, the eqoQ and eq2Q terms make comparable contributions to the hyperfme splittings. This is the first determination of these parameters for 33SH; their values make an interesting comparison with those for “OH ( eqoQ = - 1.92 MHz and eq2Q = 66 MHz (26)). The quadrupole moments for the two nuclei are -2.578 fm2 for “0 and -6.4 fm2 for 33S (30). The value determined for eqoQ for 33SH of -9.3 f 1.8 MHz is close to expectation from the ab initio wavefunction of Cade and Huo (31, 32), which gives a value of -13.1 MHz. It is interesting to note that the calculated value for eqoQ for 170H of -2.6 MHz is also larger in magnitude than the experimental value in the same proportion (26). Heterodyne spectrometers working at far-infrared wavelengths have now been developed to be sufficiently compact that they can be used for astronomical or atmospheric observations from an airborne platform (1). These instruments have recently been used to make the first observations of atomic and molecular species in the interstellar clouds at these wavelengths. For example, fine structure transitions have been detected in neutral C (33) and also in C+ (34). Furthermore Betz and Boreiko (35) have detected the first rotational transition (2 + 3) in OH in its *II3,2 component. The identification of these transitions depends on prior laboratory work on the species concerned. Sulfur has quite a high cosmic abundance, and it is likely that SH is present in the interstellar medium. So far, it has not been detected, perhaps because its lambdadoubling transitions occur at unfortunately low frequencies. It is much more likely to be detected through its rotational transitions in the far-infrared. To aid these searches we give the first few pure rotational transition frequencies of 32SH at zero magnetic field in Table VII. These frequencies have been calculated using the parameter values in Table III. We estimate that the transitions within the 2113,2 manifold, which have been observed directly, have an accuracy of 2 MHz. The transitions within the , whose frequencies have been inferred from our model, are about a factor of 2&,2 three less reliable with an accuracy of about 6 MHz. ACKNOWLEDGMENTS We are very grateful to Dr. Harry Radford for supplying us with his raw data on the EPR spectrum of SH (Ref. (5)) and to Dr. Ken Evenson for the use of his far-infrared LMR spectrometer to make the
FAR-INF~RER
LMR OF SH
57
TABLE VII Calculated Transition Frequencies in GHz of Pure Rotational Transitions in ‘*SW in the v = 0 Level of the X *II State
a) Estimated uncertainty = &2MHz. b) Estimated uncertainty = f6MHa.
me~urements reported in this paper. SHA also thanks the Science and En~n~~ng financial support and the travel grant which made this work possible. RECEIVED:
/
Research Council for
January f7, 1992 REFERENCES
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58
ASHWORTH
AND BROWN
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