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Ground state spectroscopic constants of isothiocyanic acid, HNCS, from its microwave and millimeter wave spectra combined with far infrared data
JOURNAL
OF MOLECULAR
Ground
SPECTROSCOPY
78, 189-202 (1979)
State Spectroscopic Constants of lsothiocyanic HNCS, from Its Microwave and Millimeter Wave Spectra Combined With Far Infrared Data KOICHI
YAMADA
Physikalisch-Chemisches Heinrich-Buff-Ring
AND MANFRED
Acid,
WINNEWISSER
Institut, Justus Liebig-Universitiit Giessen. 58, D-6300 Giessen, West Germany
GISBERT WINNEWISSER Max-Planck-lnstitut
fiir Radioastronomie, Auf dem Hiigel69, D-5300 Bonn. West Germany AND
L. B. Department
SZALANSKI
AND M.
C. L. GERRY
of Chemistry, The University of British Vancouver, B.C.. V6T I W5, Canada
Columbia,
The microwave and millimeter wave spectra of isothiocyanic acid, HNCS, in the ground vibrational state have been investigated in the frequency region 8-300 GHz. The a-type R-branch transitions have been assigned up to J = 25 and K, = 4, and the a-type “Q, branch transitions up to J = 45. No b-type transitions could be identified in the frequency region covered. The far infrared data reported by Krakow, Lord, and Neely [J. Mol. Spectrosc. 27, 148 (1%8)] were combined with our millimeter wave data in order to determine reliable spectroscopic constants. The rotational Hamiltonian, Watson’s formalism with S reduction, has been extended empirically to higher order to facilitate the fitting of the large centrifugal distortion effects. The obtained constants are: A = 1357.3 GHz; D, = 1.19393 kHz; d, = -13.781 Hz:
B = 5883.4627 MHz: DJx = -1025.37 kHz; d, = -4.59 Hz.
C = 5845.6113 MHz; Dx = 51.57 GHz;
The 14N quadrupole coupling constant has also been determined:
xaa = 1.114 MHz.
I. INTRODUCTION
The rotational spectra of isothiocyanic acid, HNCS, and all singly substituted isotopic species, have been investigated extensively in the present series of studies by microwave (mw) and millimeter wave (mmw) spectroscopy. The precision of the transition frequencies for QRKbranches measured earlier (I -4) has been improved and the frequency range of observations has been extended. The u-type Q branch “QI has been measured for the first time for each of these molecules except for HNC34S. Recently the part of the present investigation concerning DNCS was reported (5). The present paper concerns our measurements of the mw 189
0022-2852/79/120189-14$02.00/O Copyright
0 1979 by Academic
AU rights of reproduction
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Inc.
in any form reserved.
190
YAMADA
ET AL.
and mmw spectra of the parent isotopic species, H14N12C32S,and the centrifugal distortion analysis of the observed spectra. The analysis and the results of the spectra for the isotopic species H15NCS, HN13CS, and HNC34S will be published in a separate paper together with a new evaluation of the rs structure of this molecule in the light of recent ab initio calculations indicating a bent chain of the heavy atoms. The measured a-type spectra supply us with precise information about the J-dependent terms in the rotational Hamiltonian of the molecule. However, the terms which depend purely upon the K, quantum number could not be determined from our spectra, due to lack of b-type rotational transitions. As mentioned in the previous paper (5), in DNCS the b-type transitions for K, = 1 t 0 have been identified, but it was not possible to locate the corresponding transitions for the H species. In the frequency range of our spectrometers, the Boltzmann factor is unfavorable and it is difficult to predict the line positions forJ values as high as 100, which fall in the measurable frequency range. To date, no b-type transition has been identified for HNCS by microwave techniques, though the far infrared (fir) spectrum shows strong b-type transitions (6). We used the fir data reported by Krakow et al. (6) as complementary information in order to determine the spectroscopic parameters which will reproduce all of the observed rotational spectrum and allow the calculation of the rotational energy levels of the molecule. As the earlier work established (4, 6), the K, rotational energy, i.e., the energy of rotation about the axis of least moment of inertia, is quite anomalous in the sense that high order terms in the Hamiltonian are needed to reproduce them and similarly the K, dependence of the a-type R-branch transitions is anomalous. The centrifugal distortion effect is very large and terms up to PI2 in the Hamiltonian are required to fit the observed frequencies to the conventional power series expansion in the K, quantum number. II. OBSERVED
SPECTRA
AND ASSIGNMENT
The method for preparing the HNCS samples and the procedure of measuring the mw and mmw spectra have been explained in detail in our earlier papers (5, 7). The frequency ranges covered for this molecule in our laboratories extend from 8 to 50 GHz and from 70 to 300 GHz. The u-type R-branch transitions, aR,, were easily assigned for K, = 0, 1,2, and 3, because they are the strongest of the lines which compose the band structure for eachJ. The assignment could be confirmed in the mw region by the Stark effect, the hyperfine structure due to the 14N nucleus, and the limited number of K, components for each J transition due to J > K,. The lines arising from levels with K, = 4, @R4, were rather difficult to identify because the lines are weak, with comparable intensity to that of some of the vibrational satellites as can be deduced from Fig. 1. Since our spectrometers do not reach the frequency region where J = 5 t 4 transitions appear, the hyperhne structure of the aR4 (4) transition has not been observed, but it should be resolvable. Therefore, none of the criteria for assigning the lines as mentioned above was applicable to this branch of transitions. In addition, the prediction of the line frequencies for the *R4 transitions from the data for lower K, transitions was impossible because the large
SPECTROSCOPIC
CONSTANTS OF HNCS
191
E/cm-’ 800 Z--i i
1
1-z 3-i
o-* b-Cm
1-t’
40104
MHz
a
b
V5~ 1
“6; 1
C Vlb State “4; 1
J 1-i
0
o-’
K, GS
rovrb panty for even _I
FIG. 1. Energy level diagram showing the K, rotational levels in the ground vibrational state and in the three bending excited vibrational states, labeled according to Ref. (7). The rovibrational parity for even J levels is indicated by + and -. The network of local resonances has been discussed in Ref. (7).
centrifugal distortion effects prevent any meaningful extrapolation of the line position. Therefore, the vibrational satellites of the lowest three bending excited states were examined first [see Fig. 1 and Ref. (7)], since the K, = 0 and 1 lines for each excited state were about as intense as the K, = 4 lines in the ground vibrational state. The lines in these excited vibrational states have now been identified successfully up to K, = 2 (7). The relatively intense lines which were still left unassigned have been consequently identified as the qR4branch by the method of elimination. The ‘JQ1transitions have been assigned by using the predicted frequencies based on the assigned qR,transitions. The assignment was confirmed by the unresolved and very slow Stark lobes. The hyperfine splitting due to the 14N nucleus could not be observed for these transitions. Similarly it was also not observed in the qQl transitions of DNCS. The measured transition frequencies and their assignments are given in Table I. The observed hyperfine components for the low frequency transitions of the IiRRK branches are also listed. The table also contains the fir transitions reported by Krakow et al. (6) which have been used in the present work for determining the spectroscopic parameters. III. CENTRIFUGAL
DISTORTION ANALYSIS
The rotational transitions measured were analyzed by using Watson’s Hamiltonian for an asymmetric rotor in the S reduction (8). However, the Hamiltonian given by Watson includes only terms up to the sixth order and is not sufficient to
192
YAMADA ET AL. TABLE I Rotational Transitions of HNCS TSANSIILON JPPEH LOHEF: STATE STATi. :IrlANO Mnll TRANSITIONS ;t U, 1J - u( c, 01 F= iI F= l1 F= ci 2i G, 2) - 1( 01 11 F= 32 F= Z1 F= lC F= Z2 F= i1 3( u, 31 - zt ;, 2) -( 3, 4) - 3( ;, 3J o( j, 5) - C( c, 5J a( 3, 9) - 7( ?, 7) 3( s* 3) - 81 L, 8) iTl( U,lJJ - Y( i, 9) 11( ,l,ilJ - iC( Lti*J 1:t J,l') - ll( 3,llJ ;Jl U,l3J - i2( li,lZJ 1-i 2,141 - 13( 1.13) i5( $915) - :ht C,14J ic,( O,lbJ - iSI G,15) ;J( 0,18J - 171 S*lTJ IV1 11,13J - 181 Ctl8J L',( b.22) - 2cc i,2Gl 2-t L,24J - ?3( C,23J i5( L.25) - ZL( :,2*1 2( 1, 1) F= 3F= 2iF= F= LF= :Z( 1, 2) F= 3F= 2F;F= 2F= I3( 1, 2) J( 1, 31 -( i, 31 -( 1, 4) c,( 1, 5) Ct I, b) b( 1, 7J b( 1, 0) 3( 1, 6) ?( 1, '3) LJI 1, 9) lJ( l,LOJ iit 1,111 12( isilJ lL( 1.121 i3( lrlll -
it 2 2 C 2 1 11 2 1 c 2 i 2( 24 3( 3( 5t II
7( 7t 8( 8( 9( 9( lG( ll( ll( i2(
1, 0)
1, 1)
1, 1, 1, 1, is
11 2) 2) 31 4) 1, 5) 1, 6) 1, 7J 1, 7) 1, 8) I, 81 it 9) iriO) IrlOJ l*llJ l*Ll)
OBSERVE0
CALCULATE0 + H.F. SHIFTS (STANDARO
liT24.066 11724.018 117;,.347 li72b.500 23458.108 23458.099 23458.099 23458.421 2345e.r25 23457.533 zg;'o';; . 76373.366 9383C.05G lL555fl.074 117285.805 12dG13.249 1+071ro.375 152467.130 i64193.525 175929.509 187b45.017 211094.597 222810.626 2+626r.989 261429.903 293149.911 23499.377 23499.352 23*99.651 23496.947 23499.352 23494.352 23423.691 23423.649 23423.972 23423.285 23u23.b49 23423.649 352-9.001; 35135.440 4i.998.52i
468k7.190 7C4')7.25@ 702:0.15& a3995.194 93692.459 lk5743.8b4 ltiJ*03.258 117492.254 i17113.84O 12w32r.141 140968.131 14C53r(.lC8 152735.541
OEV.
1172Y.C69( -0.056( G.278( -0.557( 23r58.149( -O.OZC( G.OOOt G.278( G.334( [email protected]( 351BT.O89( 46915.981( 70373.341l 93830.071( 105556.077( 1172d5.816( 129Oi3.260( 1407*0.379( 152467.144( 164133.524( 175919.491(' 197645.014( 21IO~l4.614( 222818.631( 246264.951( 281429.7Urt 293149.91Ot 23499.385(
-C.G67( L.270( -0.425( G.lU2( 0.015( 23423.6831 -G.C6U( 6.278( -0.4101 0.121t -0.015( 352i9.t%l 35135.4534 46998.536( 4b847.137( 70497.22ot 70275.135t 93995.21;3( 93692.4&8( 1057r3.859( 105403.276t 117492.252( 117113.9*7( 128824.133( 140988.132~ 14rJ534.135( 152735.561(
O-C
NOd
B
1) 16) 18) 19) 1) 161 16) 18) 19) 19) 21 2J 3) 3) 4) 4J 41 41 4) 4J 5) 5) bJ 61 8) 131 lb)
-0.073
1) 171 181 21) 22) -0) 1) i7J 18) 21) 22) *O) 11 1J 2) 2) 2) 2) 3J 3J 3) 31 3) 3J 3J 3) 31 31
-0.008
,!5.556 33.333 11.111 -0 .OCl
o.a21 0.019 -0.015 -0.021 -0.063 -0.011 -0.011 -0.0"4 -O.C14 0.001 o.oc9 O.OG3 -0eOi7 -0.005 0.038 0.199 0.011
k
46.667 25.000 11.111 8.333 0.333 n P J4 M n r
r n w r r n
M M M HlA H*A w 4b.667
25.OCO 11.111 8.333 a.333 O.OC8
-0.0:4 -O.OiS -;.;'I; . 0.030 O.Gl5 -0.OC9 0.011 0.005 -0.018 c.oc3 -0.oc7 O.O(Ib -O.O@l 0.053 -0.02G
M
46.667 25.000 11.111 8.333 8.333 n n n c r n Ii I M M n H r n n w
193
SPECTROSCOPIC CONSTANTS OF HNCS TABLE TRANSITION LOWEF UPPER STATE STATE
I-Continued
OBSERVED
CALCULATED + O-C SliIFTS (STANOARO OEV.)
:3( 1.13) isi 1,131 ib( irllc) 1st l,lSJ l~( 1ri.j) 1k.t 1*15) ibl l,lb) IY( 1,17) 18( 1.16) 19( lrl6) 13( 1.1)) 21( 1.20~ 21( 1121) 2S( 1,241 25( 1,2*) -
12( 1.12) i3( lsl2) 13( 1,131 iY( 1.13) 14( i,iC~ 15f 1,141 L51 1,151 17( 1,161 17( 1,171 16I Irl?J 26( 1,161 2C( 1,19) 2(r( 1,201 23( 1,231 2~1 1123)
1522+3.736 164u62.601 163952.976 176229.245 175662.056 187975.403 167376.293 211456.441 210765.770 223211.144 222492.731 2C669 0.226 2459CS.016 2610L9.127 293666.779
152243.735( 164482.610( 163952.993( 176229.251( 175661.652( 167975.45uf 16737G.2621 211466.426( 210765.7~5( 223211.141( 222492.720( 246698.873( 245905.014( 231018.690( 293666.7kbt
3( Zr 1) 3( 2, 2) F: 4F= 3F: ZFJF= L-( 2, 2) -?( 2, 31 6( 2, 4) 6( 2, 5) fit 2, 5) %( 2, 71 1( 2, 71 3( 2, d) lO( 2, 01 10( 2, 9) 111 2, 9) iit 2~10) 12( 2,131 12( 2111) 13( L.11) 13( 2,lZ) L5( 2,131 l?( 2,lQ) 16( 2114) lb( 2,151 td( 2,161 i9( 2,171 13( 2,171 13f 2,191 2lI L,19) 21( 2.23) 23( 2.23) L5( .?,24) -
2( Z( 3 i 1 3 2 3( 3( 5( 5( 7( 7( 3( 6( 9( 9( lO( iP( ll( ll( 12( 12( ;4( L4( 15( 15( 17( l'( 16( ld( 20( 2C( zst 2&f
35199.467 35199.467 35179.406 35114.73C 35199.185 35199.406 35193.730 4b932.490 L5932.490 70376.202 70396.202 93663.162 93663.16: 105595.354 105595.354 117327.263 117327.283 123OF6.903 123056.903 140790.236 1~0755.236 152521.187 152521.107 175962.211 175961.869 1677i2.078 167711.613 211170.356 211169.663 222696.77r 222697.986 246353.941 ZC6352.927 2932'7.013 293255.315
35199.462( 35199.459( -0.060( G.276I -0.278( -O.OSO( 0.276( 46932.485( 46932.479( 7G398.169( 7G396.1451 936b3.132( 93603.125( 105595.367( 105595.236( 117327.523( 117327.1691 129056.954( i29958.8 ,b( 140790.331~ 14073O.lC8( 152521.312( 152521.067( 175982.216( :75931.639( 137712.053( 167711.596( 21117C.356( 2111b9.706( 222698.769( 222698.003( 246353.971( 246352.936( 293257.1?7( 293255.361(
3( 3,--b 4 3
45936.463 ub338.358
2
46936.356
46938.517( -0.081( 0.251( -0.209(
,( 3,--D F = 5F= 4F= 3-
2, 41 2, 1)
2, 11 2, 2) 2, 31 2, 41 21 5) 2, 6) 2, b$ 2, 71 2, 6) 2, 8) 2, 6) it 9) 2, 9) Z,lO) Z*lO$ 2,lll 2,121 2,131 2,131 2,:4) 2115) 2116) 2116) 2rl7) 2,161 2,191 2,221 2,231
46936.726
NOTE
H.F.
3) 3) 31 41 41 4) 4)
5) 5) 51 5) 7) 7) 12) 141 11 1) lb) 17) 17) lb) 17) 2) 2) 3) 31 3) 3) 41 41 5) 1) 4) 4) 4) 4) 41 41
51 31 51 5) 61 ~1 7) 71 9) 9) lb) lb)
O.OG2 -0.0TP -0.017 -0.OC6 0.2G6 -0.051 0.011 0.913 0.025 t.tc3 0.011 -0.bL5 o.oc2 0.237 0.033 o.oc5 O.OC8
0.015 0.012 0.033 0.057 cf.000 0.057 -0.013 0.066 -0.2L3 0.09L -0.051 O.CY7 -t.G65 0.128 -0.125 0.120 -0.0?5 0.u30 0.0%5 O.Cl8 -0.OC2 -0.OL3 G.OL5 -0.017 -t.OJO -0.099 -0.094 -t.051
2) -0.034 20) 201 21)
r n n r r*A
n A N
r n t!
U.A
n
M,A h9A r*B M,B 42.857 29.630 20.0CJ 3.754 3.7ci 1.9 M,B H*B r.0 r*a MsB MtB r*a P,A,Ij ktA*fl k,AIH k,A,?1 hl,A,d
k,AlB M,A*B k,A,H r M n p: c n If k )r k U*A k9A
r co.741 31.250 i3.8iO
194
YAMADA
ET AL.
TABLE I-Continued TRANSITION UPPER LOHEF :TATE STATE 3( 3*--b b( 3,--b d( 3,--B lit
3,--J
-
Ll( ;zt 13( 1rt 15( 1k.t 1st lY( i5t
3,--b 3,--D 4,--j 3,--l 3,--b 3,--j 3,--B 3,--b .3,--b
-
bl *,--I jt L(*--) i2( ,,--) -
5( 7( 8( 91 lot il( 12t :3t lL( 1st :7t let 1+(
1,21 1*21) 1.22) 1,23) 1.24) i,25)
-
27(
1.25)
-
iJ( Zj( jg( 3it 32( 3k( 35( 214 37( 35( 33( -J( *it -f3( G+( -51
,,27) 1,2d) l,L')) 1,301 1.31) 1,331 1,341 &,55) 1,3b) i.37) r.3)) 1,33) ',+J) 1,-+2) i,43) 1.44) -
FIR 'it 12( 13( I*( 19t 2G( z;t 22t 2-t
CALCULATED + O-C H.F. SHIFTS (STANDARD 0EV.I
3,--B 3,--j 3,--j 3,--j 3,--B 3,--b 3,--j 3,--b 3,--b 3,--I 3,--b 3,--j 3,--b
7osc7.19* 930'5.187 1056C b.684 137342.300 12907 5.416 1408C8.278 1525kO.735 lb4272.845 1:6OL +.518 167735.877 211197.01~ 222926.034 293253.478
70407.206( 93875.211( ld5608.886( 117342.3Ccl 129075.438( 140808.256( [email protected]( 16*272.844( 176004.553( 117735.835t 211197.oc2t 222926.831t 293293.438(
3) 4) 4) 4) 4) 5) 5) 5) 5) 5) 7) 8) Z3)
-0.012 -0.024 -0.002 -0.OC4 -0.020 0.020 -0.001 0.061 -0.035 0.042 0;012 0.093 O.Orl
51 *,--I 6( 4*--b
70397.583 115594.57c 148789.217 1642F;D.716 175900.040 ;077:~.572 2ill68.649
70397.644t 105594.57ot 1*37d9.222( 164250.5831 175980.138( 187710.572l 211168.664t
5) 71 7) 6) 6) 7) 10)
-0.055 o.otc -e.oc4 0.035 0.010 -0.000 -0.015
8737.7981
3) 3) 3) *I 4) 4) 4) 4) 4) 4) 41 4) 4) 4) 4) 4) 4) 4) 4) 5) 6) 7) 8)
0.008 a.a:5 0.0c0 0.012 0.009 O.OLl 0.005 O.OO2 -0.0O4 0.052 -0.OC6 -0.002 -0.017 -0.0(12 -o.aie -0.OC6 -o.osi -0.036 0.024 0.025 -0.oco -0.020 0.034
17) 17) 17) 17) 17) 17) 17) 17) 17) 17) 17)
-0.022 -0.orj7 -0.010 0.007 0.010 -0.OlO -0.OC9 o.oc3 0.008 -0.025 0.019
iI.t
TL( *,--I 13( 15( *,--) - 14( ,b( u,--1 - ;5( Id( *,--I - i7(
2L( LZ( 23( L*l :st LD(
OEISERYED
*p--b
h,--) et--1 9,--b *s--1
211 1.21) 22( 1.22) 23( 1,231 2&l i.24) 25( 1,25) 2b( 1,26) 27( 1,271 2R( _,28) Z9( 1,23) 30( 1130) 3:t 1131) 32( 1132) 3rt 1,341 35( 1,351 36( 1,361 37( 1,37) 38( 1.38) 39t 1139) -ill l,UUI +l( '1411 +3( 1143) 4lr( 1,441 -5( 1,45)
TRAYSITI3NS 1,1&j - lot Itlit) - il( i,13) - 12( 1,141 - i3t 111)) - 18( 1,23) - :9t 1,211 - 2L( 1,2?) - Lit lr2rrl - 23f .?b( 1,211) - 25( 271 i,27) - 26(
O,lO) Orll) Oll2) 0113) J,18) 0,191 2123) G,21) Cl231 C,25) @,26)
8737.806 9569.36G 10438.605 11345.519 1229i.079 13212.31 14292.093 15344.510 164‘:-,.506 175T7.076 197k7.180 199r*.cu7 224f2.562 238'2.63Y 2316C.131 26555.06 2798'. 33 234E7.00 30964.06 325C8.37 357C b.76 373h4.83 330rtJ.15 ! 7.73 48.13 Lb.51 ‘8.91 F0.82 FL.18 51.56 51.95 52.71 53.43 F3.85
9569.3551 10438.597( 113L5.507( 1223O.C70( 13272.270t 1429E.C80( 15349.508( 16444.5101 17577.076( 10747.186~ 19954.819( 22482.569( 238C2.641( 251bO.149t 26555.066t 27937.3714 29457.O36t 36964.036( 32508.365t 35708.780( 37364.850( 39058.116( s7.752t 48.137l r.3.520( 48.903l >0.810( 51.190( 51.569( 51.947( C2.7J3t 53.455( 53.831(
NOTE
M
n II
w M M
n n Ii t!
n u fi,A
h
n w w n u M P h M R
n n M
r M
n II
u n M
I? Y I I I I I I I ItC 1.0 1.0 I.0
SPECTROSCOPIC TABLE TRANSITION UPPER LOHER STATE STATE 1.28) lr23) 1.31) 1.32) 1.34) 1.35)
33( 32( 34( 35( 3ut 1,3bl 37( i.37) 3U( 1,361 LB1
231
5( 5( a( al
27( Zd( 29( 31( 33( 34( 35( 36( 37(
0,271 0,281 0129) J,3lJ C,33) 3934) 0135) 11,3bJ C,J7l
CONSTANTS
195
OF HNCS
I-Continued
OBSERVED
'4.23 S-,.61 5S.98 55.72 T6.41 56.85 57.22 f7.54 F7.91
CALCULATED l O-C W.F. SliIFTS (STANOARO OEV.) 54.2136( 54.58at 54.95ct 55.699( 56.443( jb.BlS( 57.104( 57.5F3( 57.922(
17) 0.02s 17) c.a3c 17) 0.026 171 a.021 17) -0.033 17) C.036 17) 0.036 17) -0.013 17) -0.012
118.785( 118.772( 119.972 ( 119.937( 120.369( 120.323( 120.707( 129.710( 121.165( 121.09bl i21.564( 121.&81( 121.964( 121.8bbt 122.365( i22.25Jt 125.188( 125.59'+( 125.3G3t 12b.OCl( 125.682( 12b.4.91 12b.G60( 126,817( 126.438( 127.226( 126.015( 12?.635( 127.192( 128.046( 127.568( 128.457( 127.9U+(
2, 3) 2, 4) 2, ,s) 2, 7) j( 2, 7) 1t 2, b) _ li)( 2, 0) *O( 2, 9) lit 2s 9) 11( 2,101 iZ( 2.10) 12( c?,lll 13( 2,111 ;3t Z,iZ) 1-t 2,12) 1-f 2.11) Ll( 2.19) 2L( 2,201 22f 2.21) L3( 2,211 23t 2,22) Zi( 2,22) 2it 2,23) Z5( 2,21) 25( 2.24) .?b( 2,2+1 2bt Z,25) 27( 21.25) 27( 2.25) 28( 2.26) ?a( 2.27) i)( 2,271 Zj( 2,281 3J( 2,281 30( 2.29) 3;( 2129) 31( 2,331 32( 2,3fB 3+( 2.32) 35( 2.33) 30( 2,34) 3b( 2.35) 37( 2.35) -
4( 1, 4) 4( 1, 3) 7( 1, 7) 7( 1, 6) b( :, 8) (I( 1, 7) 9t 1, 9) 3( 1, 81 lot l,lJ) ict 1, 91 tit l,ll) ll( l,lOl iZ( 1*12) 12( lsll) 13( 1,13) ;3t 1,121 2G( lt20) Ll( 1921) 21t 1.20) 2Z( 1122) 221 1.21) 23( ir23) 231 1,221 2*( lr2+) 2r( 1,231 25( 1,251 25( 112,) 26( 1,26) 2bt 1,251 27( 1.27) L7( 1,261 28( 1.28) 2e.t 1,271 29( 1,29) Zc)( itee, 3ot 1,301 3C( 1,29) 31t 1.30) 33L 1,331 3*( 1,341 35( 1,351 35( 1.34) 3b( 1,351
118.83 lib.83 X9.96 1;9.9a ltr.36 12i.36 120.73 125.73 121.13 121.13 lZl.55 121.55 121.91 121.91 122.33 122.33 125.26 125.62 125.26 126.05 125.62 126.43 St.05 126.81 126.43 127.20 126.81 127.59 127.20 128.01 lZi.59 126.38 128.01 128.81 128.38 129.20 120.81 129.20 130.39 130.90 131.53 13u.39 130.90
14) 0.015 14) G.050 1C) a.G78 14) c .a&4 14) -0.0:9 14) a.037 l&l -G .037 :4) 0.020 14) -0.035 1C) 6.034 14) -0.014 14) G.Cb3 14) -0.054 141 O.GW lb) -0.035 lb) a.080 lkt 0.072 :41 O.C26 ;(o -0.0-3 14) 0.049 141 -0.G62 14) 0.021 1cr1 -0.010 14) -a. 057 14) -o.or,.s i4) -0.026 lh) -0 .a05 14) -0.045 1U) C.Oi;B 14) -0.036 1u) 0.022 14) -0.ci77 14) II.066 128.868 ( 14) -0.058 128.319( 14) a.ofl 129.281( 14) -0.m 128.694( 14) 0.117 129.067( 14) 0.133 130.522( 14) -0.132 130.937( 14) -9.037 131.353( 141 0.177 1313.557( 14) -G.Ib7 130.928 1 14) -G.O28
51 3*--j G( 3.--l -
4( 2,--j 5( 2,--t
179.12 179.+9
179.124( 179.516(
141 -0.0&s 24) -0.026
NOTE
I*0 I*0 119 I*0 190 I*0 X,0 IIC,O I,0 I,R I*R 194 116 116 I.5 198 190 I*R 198 196 I,& 199 ISa ISa
198 I*0 ::," I,0 I-0 ItD I*U 190 190 I*D 1.0 I*0 I*0 Iv0 I,0 I,0 I,0 Is0 I*0 Iv0 I*A10 IrAt 1sA.U I,0 IsArCs 1.A
:
196
YAMADA TABLE TRANSITION LJPPEH LOWER STAft STalc 71 3*--I 31 3.--l 31 3,--J 1c I 3,--l 111 31--l
-
L2( 3,--j 13( 3,--l 1-g S.--l ;5t 3,--l l>( J,--I Lif 3,--l 221 J.--l :3t 3,--l L+( 3,--l 251 3,--l L7( a,--) 27( 31--J L.J( 3,--l 2j( 3r261 Ejt 3.27) 3ci 3.27) 33( 3128) 3:( 3,23J 3;t 3.2'31 3lz( 3.29) 3L( 3.39) 33( 3930) 3st 3,31) 5-t 3,3;1 3rt 3,321 35( 3.32) 5,( 3133) 30( 3.33) 36( 3,3*) 57f 3.35) 37( 3,3,) 51
41-l
at 7t j( 3(
-+1--b 2,--l *,--) *1--b
6( 2,--l I( 2,--l 9( 2,--l Y( 2,--l Lli( 2,--l 11( 2,--l itt 2,--l f3( 2,--D ;4( 2,--l 15I 2,--l 2C( 2,--l 21( 2,--j 22( 2,--l 23( 2,--l 2*( 2,--l 2I,( 2,--l 2b(
2,--j 2.27) 2,261 2128) 2,271 2,291 2,ZAl 2.30) 2,29t 2,311 2,301 2,321 i,3:1 2,33) 2,321 2,341 2,331 3b( 2,341 36( 2,351
L( 5t 6( 7( dt 3f - 121 -
-
t*t .*--1 ij( 4*--l ltJ( it,--) ;?( .(,--1 ld( .+,--) 13( *,--I LJ( *,--) Lit *,--I 2zt 4,--l 23( v,--) -
2,--l
27t 20( 2al 29( 2Yt 30( 3G( 3Lt J:f JZf 321 33( 33( 3rt 3+( 35( 35(
12t 13( 14( :5t 16t 17( 18( iY( 2u( 21( 22t
3,--b 3,--J 3,--j 3,--l 3,--l 3,--l 3,--l 3,--l 3,--l 3,--l 3,--j 3,--j 3,--l 3,") 3,--l 3,--l 3,--j 3,--l
ET AL.
I-Continued
OBSERVED
179.90 180.29 38C.69 161.37 181.48 181.85 18 2.26 192.66 163.03 18 3.r3 185.39 185.79 186.17 186.55 186.94 187.34 107.74 108.14 108.51 180.51 108.92 160.92 189.31 189.32 189.72 18Y.72 19c.14 19t.14 190.55 lY6.55 19c.94 190.94 191.34 19i.34 191.70 191.70 23G.41 233.83 231.18 231.58 232.02 232.40 232.77 ZT3.16 233.55 233.97 234.30 234.74 235.15 235.45 235.84 23b.29 236.70 237.04 237.45
CALCULATED + O-C H.F. SHIFTS (STANDARD DEV.) 179.931)( lBO.299( 160.691( iRl.083( ia1.475( 181.0671 182.259( id2.551( 183.043( 183.435( 195.396( 185.786( 186.180( 166.572( ia7.357t 187.750( 188.142( 188.5351 198.534( 188.927( 186.927( 189.32Ut 189.319( 189.712( i83.711( 19O.li5( 190.104( 190.497( UO.496( 190.890( 130.889( 191.283( 131.281( 191.674( 191.675(
141 141 141 141 14) lrl 1~) 1st II0 141 141 ilo irl 141 14) 141 141 141 14) lrl :4) 141 1~) 141 i41 14) i4) 141 141 141 141 141 1~) 141 141 i41
-O.OGb -0.009 -0.OCl -0.013 0.0?5 -0.017 O.OCl o.oc9 -0.013 -0.095 -0.OC6 0.002 -0.010 -0.022 -0.025 -0.017 -0.010 -0.OC2 -9.025 -0.024 -0,OCT -U.OC? -O.OlG -0.009 o.oco 0.009 0.035 0.036 O.G53 0.054 c.050 0.051 o.c57 0.059 0.026 0.025
23G.4251 230.8:6l 231.237i 231.598( 231.989( 232.380( 232.77ll 233.162( 233.552( 233.9*3( 234.333i 234.724( 235.114( 235.505( 235.895t 236.285( 236.675( 237.0651 237.455t
13) 131 i3) 13) 13) 13) 13) 131 131 131 131 131 131 131 131 13) 13) 13) 131
-0.015 0.014 -0.027 -0.018 0.031 0.020 -O.OCl -0.0'12 -0.002 0.027 -0.033 0.016 0.036 -0.055 -0.055 o.ot5 0.025 -0.025 -0.005
186.965i
NOTE
I
I I
I I*B ItB
ISa
1,B 118 Iti3
I,a I*B
I,8 118 1,s 118 I.9 I.6 I*8 118 ItI3 I,B
I I
SPECTROSCOPIC TABLE TKANSITION
UPPER STATE 2-t 2c(
27( LB{
*.--I 4,--b
--a 4,--l 9,
$bt
4,--l 49-j
-
OBSERVED
23( ?E( 26( 27( zat 3ot 31( 321 33I 34( 35( 361
3,--l 3,--j 3,--j 3,--I 3,--j 3,--l 3,--b 3,--l 3,--j 3,--l 3,--j 3,--l
197
OF HNCS
I-Continued CALCULATE0
+
o-c
NOTE
0.015
I
N.F. SHIFTS (WINOAR NV.)
LOWEF. STATE
L9( 4*--l 311 4,--l 32( 4, --I 33( 4.--l 34( 4,--l 3L?( *,--I 37(
CONSTANTS
237.06 238.61 239.02 239.45 239.83 246.56 240.97 241.40 241.66 242.i4 242.52 242.90
237.8&5( 238.625(
13) 131 239.01b4 131 239.404( 131 239.794( 13) 24C.573( 13) 240.962( 13) 2.+1.352( 13) 2r1.740( 13) 242.129( 13) 2r2.5161 131 242.937t 13)
-0.015
I
0.006 0.046 0.03b -0.013 O.OC8 0.049 -0.080 0.011 0.012 -0.037
I I I I I I I I I I
a) The entries in the last column (note) have the following meaning: i-l: Microwave measurements in the present work. The numbers are frequencies in WHz. The weight factors of these lines used in the fit are 1.0 unless other specifications are qiven. I: Far infrared measurements listed in Table VI of Ref. (5). The numbers of wavenumbers in cm-'. The weight factors of these lines used in the fit are 4.45x10-"
unless any
other specifications are given. A: Not used in the fit. 5: Components of the K-doublets are not resolved. The weight factors for each component have been reduced by a factor of two. c: Obvious misprints in the transition wavenumbers in Table VI of Ref.(6) - have been corrected. 0: The J quantum numbers for these lines have been reassigned in the present work, which seem to be misprinted in Ref. (2). Numbers: For hyperfine components, the relative intensities are given in this column in %.
fit the observational data, because of the large centrifugal distortion effects in this molecule. Such effects have been observed for several light molecules including HNCO, DNCO (9), DNCS (5), H,O and D,O (10, I1 ). Several higher order correction terms were therefore added to the Hamiltonian. The Hamiltonian
198
YAMADA
ET AL.
used is X = {A - ‘/z(B + C)} .f: + ‘/(B
+ C)sfz + 1/(B
- c)(j2+ + 35)
where j* = 1, ? ij,. The total angular momentum operator is], and its components along the principal axes are ja, lb, and jc in the above expression. For the sextic and the higher order corrections only those terms were used which contribute as diagonal matrix elements in the symmetric rotor basis to the rotational energy. This Hamiltonian is equivalent to the Hamiltonian used in the analysis of DNCS (5) except for the d2 term and the sign convention for the L and T terms. In the case of DNCS the d, term was defined as 2d2[2(j$ - j:) - I4 + 2j2.?z - jz] whereas in the present analysis this term is defined as d2(.?4+ + .f4_). The difference between the two formulations is -d2(4s2 + 103:) and results in a small contribution to the rotational constants A and (B + C) of about the order of d, itself which is much less than the standard deviation of the adjusted parameters. The rotational energy has been obtained by numerical diagonalization of the Hamiltonian energy matrix. The matrix elements of the Hamiltonian were calculated on the basis of Wang’s linear combinations of the symmetric rotor wavefunctions. For each J value (2J + 1) functions were used. However, it was found unnecessary to use the complete set of basis functions in the present analysis, due to the fact that energy levels of high K, were not needed and the effect of inertial asymmetry is negligibly small for this type of molecule in high K, states. The basis functions used were limited by setting an upper limit for the K, quantum number, for example K, < 6. The parameters appearing in the Hamiltonian were adjusted to the observed frequencies by a least squares procedure. For the lines which show hyperfme splittings, the unsplit frequency positions were calculated as described in the next section and used in the fit. The mw and mmw data were sufficient to determine the parameters associated with j or J+ and J_, which are B, C, D,, D,, dl, d2, HJK, HKJ, LKJI and SKJ. However, the parameters purely associated with j,, that is DK, HK, LK, SK, and TK, were not determinable from the mw and mmw data, because no b-type transitions could be measured. Thus the fir data reported in Table VI of Ref. (6) were included to determine the remaining important parameters. For the combined analysis of the mw, mmw, and fir data, a weighted least squares analysis was applied. The statistical weight of the value of an observational quantity was set proportional to the inverse of the squared experimental uncertainty of the measurement: the uncertainty of a mw or mmw measurement was estimated to be 10 kHz and of a fir measurement 0.05 cm-‘, which results in the ratio of relative weights for (mw or mmw)/(fir) = l/(4.45 X 10-l’). The wavenumbers of the transitions for the ‘QK branches were not used in the final fit because the measurements of these line positions were not sufficiently
SPECTROSCOPIC
199
CONSTANTS OF HNCS
accurate. The wavenumbers for ‘P, transitions listed in Table VI in Ref. (6) show small but systematic deviations from the calculated frequencies, and were therefore rejected from the final fit; they are not listed in Table I. Several obvious misprints in Table VI of Ref. (6) were also corrected as indicated in Table 1. Transition frequencies and wavenumbers which deviated more than 100 kHz and 0.1 cm-‘, respectively, were rejected from the final fit. In cases where the components of the K, doublets were not resolved, the weighting factors of each component were reduced by a factor of two. If the calculated frequencies of a K, doublet show a splitting of less than 1 kHz for a mw or mmw transition or 0.001 cm-’ for an fir transition. respectively, the transition is listed in Table I as a single line ignoring the K, quantum number. From the combined mw, mmw, and iir data set the spectroscopic constants A, Dh., Hti, and LR were determined in addition to the parameters determinable from the mw and mmw data alone. The parameters thus obtained are listed in Table II, under the column of Fit 1. For this fit the basis functions used for the energy calculation were limited to K, < 6. The reason for this choice of the limit is discussed in the final section of this paper. The calculated frequencies and wavenumbers using the adjusted parameters of Fit 1 are listed in Table I for TABLE II Rotational Parameters of HNCS” Parameter
Fit 1
Fit 2
Unit
A B e D, DJK DK d, & HJ HJK
1357.25(70) 5883.4627(3) 5845.6113(3) 1.19393(37) - 1.02537(28) 5 1.57(25) - 13.7808(30) -4.59(19) O.O(fixed) 1.019(72) -185.40(11) 4.002(28) O.O(fixed) - 16.597(13) 119.7( 10) O.O(fixed) -0.53263(45) O.O(fixed) O.O(fixed) 22.1
1361.53(81) 5883.4628(3) 5845.6114(3) 1.19419(41) - 1.02532(31) 57.52(33) - 13.7808(33) -4.59(20) O.O(fixed) 0.919(79) -18X28( 12) 6.038(52) O.O(fixed) - 16.569(14) 363.2(36) O.O(fixed) -0.53128(49) 10.43(11) 0.1113(13) 24.3
GHz MHz MHz kHz MHz GHz Hz Hz
H XI
HK L.lK LKJ LK S .Jx SXd SK TX I+
Hz kHz GHz kHz MHz kHz MHz MHz kHz
a Parameters are defined in the Hamiltonian, Eq. (1). The numbers in parentheses are one standard deviation in the unit of the last digit. b Standard deviation of the fit. Fit 1: Derived from transitions in Table I; Fit 2: In addition to transitions in Tabie I the positions of the ‘Q4 and rQ5 branches were used.
200
YAMADA
ET AL.
comparison with the observed line positions. The observed-calculated quite small, resulting in a standard deviation of the fit of 22.1 kHz. IV. QUADRUPOLE
COUPLING
values are
CONSTANTS
Nuclear quadrupole hyperfine structure due to the 14N nucleus was observed in the 10,1-%0, 2,~ lo,192,,,-- 11,0,21,Z- 11,1,3,-22, and 4,-3, transitions, as listed in Table I. The analysis of the hyperfine structure was carried out by fitting the frequencies of the individual hyperfine components by a least squares method. First order theory was applied in the analysis using the rigid rotor basis for the calculations. The three parameters which were adjusted for each transition were the coupling constants xaa, &,-XCCr and the unsplit frequency. When a line frequency was assigned to a single component, this line was given the weight of unity in the fit. When the frequency of a blended line was assigned to two (or more) components, each component was weighted proportional to its relative intensity requiring the sum of the weights of the two (or more) components to be unity. The rotational constants obtained from the centrifugal distortion analysis were used in the hyperfine analysis. On the other hand the unsplit line frequencies obtained from the hyperflne analysis were necessary for the centrifugal distortion analysis. Therefore, the two procedures have been carried out iteratively. The obtained coupling constants are listed in Table III. The constant xaa has been determined well because the observed hyperfine splittings are mainly dependent upon this constant. On the contrary, the present data do not allow xb* - xCCto be determined precisely as shown in Table III. However, it can be concluded that the Vahe Xbb - xec is less than 0.23 MHz, which is twice the derived standard deviation. V. DISCUSSION
The parameters A, DK, HK, and LK obtained from Fit 1 must be considered as pure fitting parameters and therefore have limited physical significance. These parameters are sufficient to reproduce the K, rotational energies up to K, = 4 which were included in the fit. However, the energy levels for K, > 4 calculated using these parameters are completely unreliable. For example, the energy for the K, = 6 sublevel is calculated to be negative, which obviously is wrong. This arises from the fact that the power series expansion in the energy matrix elements is not converging with respect to the K, quantum number. Therefore, it is reasonable to truncate the basis wavefunctions with K, < 6 in Fit 1 as mentioned before. TABLE
III
Nuclear Quadrupole Coupling Constants for ‘
XIII7 Xbb - Xcc a Numbers in parentheses
are one standard
deviation
in units of last digit.
SPECTROSCOPIC
CONSTANTS OF HNCS
201
We have tried an alternative fit by introducing the ‘Q4 and ‘Q5 fir transitions which were not used in Fit 1. These two unresolved sets of transitions were observed with peak positions at 273.9 and 313.7 cm-’ (6), respectively. These wavenumbers were assumed to mark the positions of the & + 5,,, and 6,,, + 6,,, transitions of the Q branches, respectively. Using these two transitions in addition to those used in Fit 1, a new fit called Fit 2 has been carried out, the results of which are also listed in Table II. Since two more K, sublevels were included in the fit, two more parameters were required, SK and T *. The basis functions are limited by K, c 7 and therefore compose a minimal basis set. The parameter A and the Kdependent distortion constants such as Dh. were found to be rather different from those of Fit 1. However, it is reassuring that the other parameters remain stable, especially the B and C rotational and the quartic centrifugal distortion constants. Small changes in HJK, LKJ, and SKJ may therefore compensate for the effect of the change in basis truncation. Though the rotational constant A and the centrifugal distortion constant D, are well determined as fitting parameters, they are not reliable enough to be applicable for a precise molecular geometry calculation or a force field analysis. They depend strongly on the model used in the fit, as shown by the difference between Fit 1 and Fit 2. By using the Fit 2 parameters the K, rotational sublevels can be predicted up to K, = 6 but the predicted position of the J rotational levels is still only useful up to K, = 4. The convergence of the DJK, HKJ, LKJ, SxJ series is not good enough to predict the line positions with sufficient accuracy that they could be located. However, it is one of the important purposes of scientific research to predict the values of physical quantities by extrapolation. From such a point of view, the results of the present study are unfortunately poor, because the range of prediction of the HNCS spectrum outside the measured range is very limited. Recently, one of the four atomic quasi-linear molecules, HCNO, has been analyzed by using a semirigid bender model by Bunker et al. (12), and its spectra could be explained well with a small number of adjusted parameters. It seems to be a promising direction of further studies of HNCS to apply a similar physical model, though the problem is much more complicated in HNCS than in HCNO, because the two skeletal bending modes must be taken into account in addition to the HNC bending mode. VI. ACKNOWLEDGMENTS This work was supported in part by the Deutsche Forschungsgemeinschaft, the National Research Council of Canada, and the North Atlantic Treaty Organization. The authors would like to thank Dr. Brenda P. Winnewisser for commenting on the manuscript. RECEIVED:
December
11, 1978 REFERENCES
1. L. H. JONES, J. N. SHOOLERY,R. G. SHULMAN, AND D. M. YOSTJ. Chem. Phys. l&990-991 (1950). 2. C. I. BEARD AND B. P. DAILEY, J. Chem. Phys. 18, 1437-1441 (1950) and J. Chem. Phys. 19, 975 (1951).
202
YAMADA
ET AL.
3. G. C. DOUSMANIS,T. M. SANDERS, C. H. TOWNES, AND H. J. ZEIGER,J. Chem. Phys. 21, 1416-1417 (1953). 4. R. KEWLEY, K. V. L. N. SASTRY,AND M. WINNEWISSER,J.Mol. Spectrosc. 10,418-441(1%3). 5. L. B. SZALANSKI, M. C. L. GERRY, G. WINNEWISSER,K. YAMADA, AND M. WINNEWISSER, Canad. J. phys. 56, 1297-1307 (1978). 6. B. KRAKOW, R. C. LORD, AND G. 0. NEELY, .I. Mol. Spectrosc. 27, 148-176 (1%8). 7. K. YAMADA AND M. WINNEWISSER,J. Mol. Spectrosc. 72, 484-501 (1978). 8. J. K. G. WATSON, “Vibrational Spectra and Structures” (J. R. Durig, Ed.), Vol. 16, Chap. 1, Elsevier, ASP, Amsterdam, 1977. 9. W. H. HOCKING,M. C. L. GERRY,AND G. WINNEWISSER,Canad. J. Phys. 53,1869-1901(1975). IO. F. C. DELUCIA, P. HELMINGER,AND W. H. KIRCHHOFF,.I. Phys. Chem. Ref Data 3, 211-219 (1974). Il. G. STEENBECKELIERS AND J. BELLET,J. Mol. Spectrosc. 45, lo-34 (1973). 12. P. R. BUNKER,B. M. LANDSBERG,AND B. P. WINNEWISSER, J. Mol. Spectrosc.
74,9-25
(1979).
OF MOLECULAR
Ground
SPECTROSCOPY
78, 189-202 (1979)
State Spectroscopic Constants of lsothiocyanic HNCS, from Its Microwave and Millimeter Wave Spectra Combined With Far Infrared Data KOICHI
YAMADA
Physikalisch-Chemisches Heinrich-Buff-Ring
AND MANFRED
Acid,
WINNEWISSER
Institut, Justus Liebig-Universitiit Giessen. 58, D-6300 Giessen, West Germany
GISBERT WINNEWISSER Max-Planck-lnstitut
fiir Radioastronomie, Auf dem Hiigel69, D-5300 Bonn. West Germany AND
L. B. Department
SZALANSKI
AND M.
C. L. GERRY
of Chemistry, The University of British Vancouver, B.C.. V6T I W5, Canada
Columbia,
The microwave and millimeter wave spectra of isothiocyanic acid, HNCS, in the ground vibrational state have been investigated in the frequency region 8-300 GHz. The a-type R-branch transitions have been assigned up to J = 25 and K, = 4, and the a-type “Q, branch transitions up to J = 45. No b-type transitions could be identified in the frequency region covered. The far infrared data reported by Krakow, Lord, and Neely [J. Mol. Spectrosc. 27, 148 (1%8)] were combined with our millimeter wave data in order to determine reliable spectroscopic constants. The rotational Hamiltonian, Watson’s formalism with S reduction, has been extended empirically to higher order to facilitate the fitting of the large centrifugal distortion effects. The obtained constants are: A = 1357.3 GHz; D, = 1.19393 kHz; d, = -13.781 Hz:
B = 5883.4627 MHz: DJx = -1025.37 kHz; d, = -4.59 Hz.
C = 5845.6113 MHz; Dx = 51.57 GHz;
The 14N quadrupole coupling constant has also been determined:
xaa = 1.114 MHz.
I. INTRODUCTION
The rotational spectra of isothiocyanic acid, HNCS, and all singly substituted isotopic species, have been investigated extensively in the present series of studies by microwave (mw) and millimeter wave (mmw) spectroscopy. The precision of the transition frequencies for QRKbranches measured earlier (I -4) has been improved and the frequency range of observations has been extended. The u-type Q branch “QI has been measured for the first time for each of these molecules except for HNC34S. Recently the part of the present investigation concerning DNCS was reported (5). The present paper concerns our measurements of the mw 189
0022-2852/79/120189-14$02.00/O Copyright
0 1979 by Academic
AU rights of reproduction
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Inc.
in any form reserved.
190
YAMADA
ET AL.
and mmw spectra of the parent isotopic species, H14N12C32S,and the centrifugal distortion analysis of the observed spectra. The analysis and the results of the spectra for the isotopic species H15NCS, HN13CS, and HNC34S will be published in a separate paper together with a new evaluation of the rs structure of this molecule in the light of recent ab initio calculations indicating a bent chain of the heavy atoms. The measured a-type spectra supply us with precise information about the J-dependent terms in the rotational Hamiltonian of the molecule. However, the terms which depend purely upon the K, quantum number could not be determined from our spectra, due to lack of b-type rotational transitions. As mentioned in the previous paper (5), in DNCS the b-type transitions for K, = 1 t 0 have been identified, but it was not possible to locate the corresponding transitions for the H species. In the frequency range of our spectrometers, the Boltzmann factor is unfavorable and it is difficult to predict the line positions forJ values as high as 100, which fall in the measurable frequency range. To date, no b-type transition has been identified for HNCS by microwave techniques, though the far infrared (fir) spectrum shows strong b-type transitions (6). We used the fir data reported by Krakow et al. (6) as complementary information in order to determine the spectroscopic parameters which will reproduce all of the observed rotational spectrum and allow the calculation of the rotational energy levels of the molecule. As the earlier work established (4, 6), the K, rotational energy, i.e., the energy of rotation about the axis of least moment of inertia, is quite anomalous in the sense that high order terms in the Hamiltonian are needed to reproduce them and similarly the K, dependence of the a-type R-branch transitions is anomalous. The centrifugal distortion effect is very large and terms up to PI2 in the Hamiltonian are required to fit the observed frequencies to the conventional power series expansion in the K, quantum number. II. OBSERVED
SPECTRA
AND ASSIGNMENT
The method for preparing the HNCS samples and the procedure of measuring the mw and mmw spectra have been explained in detail in our earlier papers (5, 7). The frequency ranges covered for this molecule in our laboratories extend from 8 to 50 GHz and from 70 to 300 GHz. The u-type R-branch transitions, aR,, were easily assigned for K, = 0, 1,2, and 3, because they are the strongest of the lines which compose the band structure for eachJ. The assignment could be confirmed in the mw region by the Stark effect, the hyperfine structure due to the 14N nucleus, and the limited number of K, components for each J transition due to J > K,. The lines arising from levels with K, = 4, @R4, were rather difficult to identify because the lines are weak, with comparable intensity to that of some of the vibrational satellites as can be deduced from Fig. 1. Since our spectrometers do not reach the frequency region where J = 5 t 4 transitions appear, the hyperhne structure of the aR4 (4) transition has not been observed, but it should be resolvable. Therefore, none of the criteria for assigning the lines as mentioned above was applicable to this branch of transitions. In addition, the prediction of the line frequencies for the *R4 transitions from the data for lower K, transitions was impossible because the large
SPECTROSCOPIC
CONSTANTS OF HNCS
191
E/cm-’ 800 Z--i i
1
1-z 3-i
o-* b-Cm
1-t’
40104
MHz
a
b
V5~ 1
“6; 1
C Vlb State “4; 1
J 1-i
0
o-’
K, GS
rovrb panty for even _I
FIG. 1. Energy level diagram showing the K, rotational levels in the ground vibrational state and in the three bending excited vibrational states, labeled according to Ref. (7). The rovibrational parity for even J levels is indicated by + and -. The network of local resonances has been discussed in Ref. (7).
centrifugal distortion effects prevent any meaningful extrapolation of the line position. Therefore, the vibrational satellites of the lowest three bending excited states were examined first [see Fig. 1 and Ref. (7)], since the K, = 0 and 1 lines for each excited state were about as intense as the K, = 4 lines in the ground vibrational state. The lines in these excited vibrational states have now been identified successfully up to K, = 2 (7). The relatively intense lines which were still left unassigned have been consequently identified as the qR4branch by the method of elimination. The ‘JQ1transitions have been assigned by using the predicted frequencies based on the assigned qR,transitions. The assignment was confirmed by the unresolved and very slow Stark lobes. The hyperfine splitting due to the 14N nucleus could not be observed for these transitions. Similarly it was also not observed in the qQl transitions of DNCS. The measured transition frequencies and their assignments are given in Table I. The observed hyperfine components for the low frequency transitions of the IiRRK branches are also listed. The table also contains the fir transitions reported by Krakow et al. (6) which have been used in the present work for determining the spectroscopic parameters. III. CENTRIFUGAL
DISTORTION ANALYSIS
The rotational transitions measured were analyzed by using Watson’s Hamiltonian for an asymmetric rotor in the S reduction (8). However, the Hamiltonian given by Watson includes only terms up to the sixth order and is not sufficient to
192
YAMADA ET AL. TABLE I Rotational Transitions of HNCS TSANSIILON JPPEH LOHEF: STATE STATi. :IrlANO Mnll TRANSITIONS ;t U, 1J - u( c, 01 F= iI F= l1 F= ci 2i G, 2) - 1( 01 11 F= 32 F= Z1 F= lC F= Z2 F= i1 3( u, 31 - zt ;, 2) -( 3, 4) - 3( ;, 3J o( j, 5) - C( c, 5J a( 3, 9) - 7( ?, 7) 3( s* 3) - 81 L, 8) iTl( U,lJJ - Y( i, 9) 11( ,l,ilJ - iC( Lti*J 1:t J,l') - ll( 3,llJ ;Jl U,l3J - i2( li,lZJ 1-i 2,141 - 13( 1.13) i5( $915) - :ht C,14J ic,( O,lbJ - iSI G,15) ;J( 0,18J - 171 S*lTJ IV1 11,13J - 181 Ctl8J L',( b.22) - 2cc i,2Gl 2-t L,24J - ?3( C,23J i5( L.25) - ZL( :,2*1 2( 1, 1) F= 3F= 2iF= F= LF= :Z( 1, 2) F= 3F= 2F;F= 2F= I3( 1, 2) J( 1, 31 -( i, 31 -( 1, 4) c,( 1, 5) Ct I, b) b( 1, 7J b( 1, 0) 3( 1, 6) ?( 1, '3) LJI 1, 9) lJ( l,LOJ iit 1,111 12( isilJ lL( 1.121 i3( lrlll -
it 2 2 C 2 1 11 2 1 c 2 i 2( 24 3( 3( 5t II
7( 7t 8( 8( 9( 9( lG( ll( ll( i2(
1, 0)
1, 1)
1, 1, 1, 1, is
11 2) 2) 31 4) 1, 5) 1, 6) 1, 7J 1, 7) 1, 8) I, 81 it 9) iriO) IrlOJ l*llJ l*Ll)
OBSERVE0
CALCULATE0 + H.F. SHIFTS (STANDARO
liT24.066 11724.018 117;,.347 li72b.500 23458.108 23458.099 23458.099 23458.421 2345e.r25 23457.533 zg;'o';; . 76373.366 9383C.05G lL555fl.074 117285.805 12dG13.249 1+071ro.375 152467.130 i64193.525 175929.509 187b45.017 211094.597 222810.626 2+626r.989 261429.903 293149.911 23499.377 23499.352 23*99.651 23496.947 23499.352 23494.352 23423.691 23423.649 23423.972 23423.285 23u23.b49 23423.649 352-9.001; 35135.440 4i.998.52i
468k7.190 7C4')7.25@ 702:0.15& a3995.194 93692.459 lk5743.8b4 ltiJ*03.258 117492.254 i17113.84O 12w32r.141 140968.131 14C53r(.lC8 152735.541
OEV.
1172Y.C69( -0.056( G.278( -0.557( 23r58.149( -O.OZC( G.OOOt G.278( G.334( [email protected]( 351BT.O89( 46915.981( 70373.341l 93830.071( 105556.077( 1172d5.816( 129Oi3.260( 1407*0.379( 152467.144( 164133.524( 175919.491(' 197645.014( 21IO~l4.614( 222818.631( 246264.951( 281429.7Urt 293149.91Ot 23499.385(
-C.G67( L.270( -0.425( G.lU2( 0.015( 23423.6831 -G.C6U( 6.278( -0.4101 0.121t -0.015( 352i9.t%l 35135.4534 46998.536( 4b847.137( 70497.22ot 70275.135t 93995.21;3( 93692.4&8( 1057r3.859( 105403.276t 117492.252( 117113.9*7( 128824.133( 140988.132~ 14rJ534.135( 152735.561(
O-C
NOd
B
1) 16) 18) 19) 1) 161 16) 18) 19) 19) 21 2J 3) 3) 4) 4J 41 41 4) 4J 5) 5) bJ 61 8) 131 lb)
-0.073
1) 171 181 21) 22) -0) 1) i7J 18) 21) 22) *O) 11 1J 2) 2) 2) 2) 3J 3J 3) 31 3) 3J 3J 3) 31 31
-0.008
,!5.556 33.333 11.111 -0 .OCl
o.a21 0.019 -0.015 -0.021 -0.063 -0.011 -0.011 -0.0"4 -O.C14 0.001 o.oc9 O.OG3 -0eOi7 -0.005 0.038 0.199 0.011
k
46.667 25.000 11.111 8.333 0.333 n P J4 M n r
r n w r r n
M M M HlA H*A w 4b.667
25.OCO 11.111 8.333 a.333 O.OC8
-0.0:4 -O.OiS -;.;'I; . 0.030 O.Gl5 -0.OC9 0.011 0.005 -0.018 c.oc3 -0.oc7 O.O(Ib -O.O@l 0.053 -0.02G
M
46.667 25.000 11.111 8.333 8.333 n n n c r n Ii I M M n H r n n w
193
SPECTROSCOPIC CONSTANTS OF HNCS TABLE TRANSITION LOWEF UPPER STATE STATE
I-Continued
OBSERVED
CALCULATED + O-C SliIFTS (STANOARO OEV.)
:3( 1.13) isi 1,131 ib( irllc) 1st l,lSJ l~( 1ri.j) 1k.t 1*15) ibl l,lb) IY( 1,17) 18( 1.16) 19( lrl6) 13( 1.1)) 21( 1.20~ 21( 1121) 2S( 1,241 25( 1,2*) -
12( 1.12) i3( lsl2) 13( 1,131 iY( 1.13) 14( i,iC~ 15f 1,141 L51 1,151 17( 1,161 17( 1,171 16I Irl?J 26( 1,161 2C( 1,19) 2(r( 1,201 23( 1,231 2~1 1123)
1522+3.736 164u62.601 163952.976 176229.245 175662.056 187975.403 167376.293 211456.441 210765.770 223211.144 222492.731 2C669 0.226 2459CS.016 2610L9.127 293666.779
152243.735( 164482.610( 163952.993( 176229.251( 175661.652( 167975.45uf 16737G.2621 211466.426( 210765.7~5( 223211.141( 222492.720( 246698.873( 245905.014( 231018.690( 293666.7kbt
3( Zr 1) 3( 2, 2) F: 4F= 3F: ZFJF= L-( 2, 2) -?( 2, 31 6( 2, 4) 6( 2, 5) fit 2, 5) %( 2, 71 1( 2, 71 3( 2, d) lO( 2, 01 10( 2, 9) 111 2, 9) iit 2~10) 12( 2,131 12( 2111) 13( L.11) 13( 2,lZ) L5( 2,131 l?( 2,lQ) 16( 2114) lb( 2,151 td( 2,161 i9( 2,171 13( 2,171 13f 2,191 2lI L,19) 21( 2.23) 23( 2.23) L5( .?,24) -
2( Z( 3 i 1 3 2 3( 3( 5( 5( 7( 7( 3( 6( 9( 9( lO( iP( ll( ll( 12( 12( ;4( L4( 15( 15( 17( l'( 16( ld( 20( 2C( zst 2&f
35199.467 35199.467 35179.406 35114.73C 35199.185 35199.406 35193.730 4b932.490 L5932.490 70376.202 70396.202 93663.162 93663.16: 105595.354 105595.354 117327.263 117327.283 123OF6.903 123056.903 140790.236 1~0755.236 152521.187 152521.107 175962.211 175961.869 1677i2.078 167711.613 211170.356 211169.663 222696.77r 222697.986 246353.941 ZC6352.927 2932'7.013 293255.315
35199.462( 35199.459( -0.060( G.276I -0.278( -O.OSO( 0.276( 46932.485( 46932.479( 7G398.169( 7G396.1451 936b3.132( 93603.125( 105595.367( 105595.236( 117327.523( 117327.1691 129056.954( i29958.8 ,b( 140790.331~ 14073O.lC8( 152521.312( 152521.067( 175982.216( :75931.639( 137712.053( 167711.596( 21117C.356( 2111b9.706( 222698.769( 222698.003( 246353.971( 246352.936( 293257.1?7( 293255.361(
3( 3,--b 4 3
45936.463 ub338.358
2
46936.356
46938.517( -0.081( 0.251( -0.209(
,( 3,--D F = 5F= 4F= 3-
2, 41 2, 1)
2, 11 2, 2) 2, 31 2, 41 21 5) 2, 6) 2, b$ 2, 71 2, 6) 2, 8) 2, 6) it 9) 2, 9) Z,lO) Z*lO$ 2,lll 2,121 2,131 2,131 2,:4) 2115) 2116) 2116) 2rl7) 2,161 2,191 2,221 2,231
46936.726
NOTE
H.F.
3) 3) 31 41 41 4) 4)
5) 5) 51 5) 7) 7) 12) 141 11 1) lb) 17) 17) lb) 17) 2) 2) 3) 31 3) 3) 41 41 5) 1) 4) 4) 4) 4) 41 41
51 31 51 5) 61 ~1 7) 71 9) 9) lb) lb)
O.OG2 -0.0TP -0.017 -0.OC6 0.2G6 -0.051 0.011 0.913 0.025 t.tc3 0.011 -0.bL5 o.oc2 0.237 0.033 o.oc5 O.OC8
0.015 0.012 0.033 0.057 cf.000 0.057 -0.013 0.066 -0.2L3 0.09L -0.051 O.CY7 -t.G65 0.128 -0.125 0.120 -0.0?5 0.u30 0.0%5 O.Cl8 -0.OC2 -0.OL3 G.OL5 -0.017 -t.OJO -0.099 -0.094 -t.051
2) -0.034 20) 201 21)
r n n r r*A
n A N
r n t!
U.A
n
M,A h9A r*B M,B 42.857 29.630 20.0CJ 3.754 3.7ci 1.9 M,B H*B r.0 r*a MsB MtB r*a P,A,Ij ktA*fl k,AIH k,A,?1 hl,A,d
k,AlB M,A*B k,A,H r M n p: c n If k )r k U*A k9A
r co.741 31.250 i3.8iO
194
YAMADA
ET AL.
TABLE I-Continued TRANSITION UPPER LOHEF :TATE STATE 3( 3*--b b( 3,--b d( 3,--B lit
3,--J
-
Ll( ;zt 13( 1rt 15( 1k.t 1st lY( i5t
3,--b 3,--D 4,--j 3,--l 3,--b 3,--j 3,--B 3,--b .3,--b
-
bl *,--I jt L(*--) i2( ,,--) -
5( 7( 8( 91 lot il( 12t :3t lL( 1st :7t let 1+(
1,21 1*21) 1.22) 1,23) 1.24) i,25)
-
27(
1.25)
-
iJ( Zj( jg( 3it 32( 3k( 35( 214 37( 35( 33( -J( *it -f3( G+( -51
,,27) 1,2d) l,L')) 1,301 1.31) 1,331 1,341 &,55) 1,3b) i.37) r.3)) 1,33) ',+J) 1,-+2) i,43) 1.44) -
FIR 'it 12( 13( I*( 19t 2G( z;t 22t 2-t
CALCULATED + O-C H.F. SHIFTS (STANDARD 0EV.I
3,--B 3,--j 3,--j 3,--j 3,--B 3,--b 3,--j 3,--b 3,--b 3,--I 3,--b 3,--j 3,--b
7osc7.19* 930'5.187 1056C b.684 137342.300 12907 5.416 1408C8.278 1525kO.735 lb4272.845 1:6OL +.518 167735.877 211197.01~ 222926.034 293253.478
70407.206( 93875.211( ld5608.886( 117342.3Ccl 129075.438( 140808.256( [email protected]( 16*272.844( 176004.553( 117735.835t 211197.oc2t 222926.831t 293293.438(
3) 4) 4) 4) 4) 5) 5) 5) 5) 5) 7) 8) Z3)
-0.012 -0.024 -0.002 -0.OC4 -0.020 0.020 -0.001 0.061 -0.035 0.042 0;012 0.093 O.Orl
51 *,--I 6( 4*--b
70397.583 115594.57c 148789.217 1642F;D.716 175900.040 ;077:~.572 2ill68.649
70397.644t 105594.57ot 1*37d9.222( 164250.5831 175980.138( 187710.572l 211168.664t
5) 71 7) 6) 6) 7) 10)
-0.055 o.otc -e.oc4 0.035 0.010 -0.000 -0.015
8737.7981
3) 3) 3) *I 4) 4) 4) 4) 4) 4) 41 4) 4) 4) 4) 4) 4) 4) 4) 5) 6) 7) 8)
0.008 a.a:5 0.0c0 0.012 0.009 O.OLl 0.005 O.OO2 -0.0O4 0.052 -0.OC6 -0.002 -0.017 -0.0(12 -o.aie -0.OC6 -o.osi -0.036 0.024 0.025 -0.oco -0.020 0.034
17) 17) 17) 17) 17) 17) 17) 17) 17) 17) 17)
-0.022 -0.orj7 -0.010 0.007 0.010 -0.OlO -0.OC9 o.oc3 0.008 -0.025 0.019
iI.t
TL( *,--I 13( 15( *,--) - 14( ,b( u,--1 - ;5( Id( *,--I - i7(
2L( LZ( 23( L*l :st LD(
OEISERYED
*p--b
h,--) et--1 9,--b *s--1
211 1.21) 22( 1.22) 23( 1,231 2&l i.24) 25( 1,25) 2b( 1,26) 27( 1,271 2R( _,28) Z9( 1,23) 30( 1130) 3:t 1131) 32( 1132) 3rt 1,341 35( 1,351 36( 1,361 37( 1,37) 38( 1.38) 39t 1139) -ill l,UUI +l( '1411 +3( 1143) 4lr( 1,441 -5( 1,45)
TRAYSITI3NS 1,1&j - lot Itlit) - il( i,13) - 12( 1,141 - i3t 111)) - 18( 1,23) - :9t 1,211 - 2L( 1,2?) - Lit lr2rrl - 23f .?b( 1,211) - 25( 271 i,27) - 26(
O,lO) Orll) Oll2) 0113) J,18) 0,191 2123) G,21) Cl231 C,25) @,26)
8737.806 9569.36G 10438.605 11345.519 1229i.079 13212.31 14292.093 15344.510 164‘:-,.506 175T7.076 197k7.180 199r*.cu7 224f2.562 238'2.63Y 2316C.131 26555.06 2798'. 33 234E7.00 30964.06 325C8.37 357C b.76 373h4.83 330rtJ.15 ! 7.73 48.13 Lb.51 ‘8.91 F0.82 FL.18 51.56 51.95 52.71 53.43 F3.85
9569.3551 10438.597( 113L5.507( 1223O.C70( 13272.270t 1429E.C80( 15349.508( 16444.5101 17577.076( 10747.186~ 19954.819( 22482.569( 238C2.641( 251bO.149t 26555.066t 27937.3714 29457.O36t 36964.036( 32508.365t 35708.780( 37364.850( 39058.116( s7.752t 48.137l r.3.520( 48.903l >0.810( 51.190( 51.569( 51.947( C2.7J3t 53.455( 53.831(
NOTE
M
n II
w M M
n n Ii t!
n u fi,A
h
n w w n u M P h M R
n n M
r M
n II
u n M
I? Y I I I I I I I ItC 1.0 1.0 I.0
SPECTROSCOPIC TABLE TRANSITION UPPER LOHER STATE STATE 1.28) lr23) 1.31) 1.32) 1.34) 1.35)
33( 32( 34( 35( 3ut 1,3bl 37( i.37) 3U( 1,361 LB1
231
5( 5( a( al
27( Zd( 29( 31( 33( 34( 35( 36( 37(
0,271 0,281 0129) J,3lJ C,33) 3934) 0135) 11,3bJ C,J7l
CONSTANTS
195
OF HNCS
I-Continued
OBSERVED
'4.23 S-,.61 5S.98 55.72 T6.41 56.85 57.22 f7.54 F7.91
CALCULATED l O-C W.F. SliIFTS (STANOARO OEV.) 54.2136( 54.58at 54.95ct 55.699( 56.443( jb.BlS( 57.104( 57.5F3( 57.922(
17) 0.02s 17) c.a3c 17) 0.026 171 a.021 17) -0.033 17) C.036 17) 0.036 17) -0.013 17) -0.012
118.785( 118.772( 119.972 ( 119.937( 120.369( 120.323( 120.707( 129.710( 121.165( 121.09bl i21.564( 121.&81( 121.964( 121.8bbt 122.365( i22.25Jt 125.188( 125.59'+( 125.3G3t 12b.OCl( 125.682( 12b.4.91 12b.G60( 126,817( 126.438( 127.226( 126.015( 12?.635( 127.192( 128.046( 127.568( 128.457( 127.9U+(
2, 3) 2, 4) 2, ,s) 2, 7) j( 2, 7) 1t 2, b) _ li)( 2, 0) *O( 2, 9) lit 2s 9) 11( 2,101 iZ( 2.10) 12( c?,lll 13( 2,111 ;3t Z,iZ) 1-t 2,12) 1-f 2.11) Ll( 2.19) 2L( 2,201 22f 2.21) L3( 2,211 23t 2,22) Zi( 2,22) 2it 2,23) Z5( 2,21) 25( 2.24) .?b( 2,2+1 2bt Z,25) 27( 21.25) 27( 2.25) 28( 2.26) ?a( 2.27) i)( 2,271 Zj( 2,281 3J( 2,281 30( 2.29) 3;( 2129) 31( 2,331 32( 2,3fB 3+( 2.32) 35( 2.33) 30( 2,34) 3b( 2.35) 37( 2.35) -
4( 1, 4) 4( 1, 3) 7( 1, 7) 7( 1, 6) b( :, 8) (I( 1, 7) 9t 1, 9) 3( 1, 81 lot l,lJ) ict 1, 91 tit l,ll) ll( l,lOl iZ( 1*12) 12( lsll) 13( 1,13) ;3t 1,121 2G( lt20) Ll( 1921) 21t 1.20) 2Z( 1122) 221 1.21) 23( ir23) 231 1,221 2*( lr2+) 2r( 1,231 25( 1,251 25( 112,) 26( 1,26) 2bt 1,251 27( 1.27) L7( 1,261 28( 1.28) 2e.t 1,271 29( 1,29) Zc)( itee, 3ot 1,301 3C( 1,29) 31t 1.30) 33L 1,331 3*( 1,341 35( 1,351 35( 1.34) 3b( 1,351
118.83 lib.83 X9.96 1;9.9a ltr.36 12i.36 120.73 125.73 121.13 121.13 lZl.55 121.55 121.91 121.91 122.33 122.33 125.26 125.62 125.26 126.05 125.62 126.43 St.05 126.81 126.43 127.20 126.81 127.59 127.20 128.01 lZi.59 126.38 128.01 128.81 128.38 129.20 120.81 129.20 130.39 130.90 131.53 13u.39 130.90
14) 0.015 14) G.050 1C) a.G78 14) c .a&4 14) -0.0:9 14) a.037 l&l -G .037 :4) 0.020 14) -0.035 1C) 6.034 14) -0.014 14) G.Cb3 14) -0.054 141 O.GW lb) -0.035 lb) a.080 lkt 0.072 :41 O.C26 ;(o -0.0-3 14) 0.049 141 -0.G62 14) 0.021 1cr1 -0.010 14) -a. 057 14) -o.or,.s i4) -0.026 lh) -0 .a05 14) -0.045 1U) C.Oi;B 14) -0.036 1u) 0.022 14) -0.ci77 14) II.066 128.868 ( 14) -0.058 128.319( 14) a.ofl 129.281( 14) -0.m 128.694( 14) 0.117 129.067( 14) 0.133 130.522( 14) -0.132 130.937( 14) -9.037 131.353( 141 0.177 1313.557( 14) -G.Ib7 130.928 1 14) -G.O28
51 3*--j G( 3.--l -
4( 2,--j 5( 2,--t
179.12 179.+9
179.124( 179.516(
141 -0.0&s 24) -0.026
NOTE
I*0 I*0 119 I*0 190 I*0 X,0 IIC,O I,0 I,R I*R 194 116 116 I.5 198 190 I*R 198 196 I,& 199 ISa ISa
198 I*0 ::," I,0 I-0 ItD I*U 190 190 I*D 1.0 I*0 I*0 Iv0 I,0 I,0 I,0 Is0 I*0 Iv0 I*A10 IrAt 1sA.U I,0 IsArCs 1.A
:
196
YAMADA TABLE TRANSITION LJPPEH LOWER STAft STalc 71 3*--I 31 3.--l 31 3,--J 1c I 3,--l 111 31--l
-
L2( 3,--j 13( 3,--l 1-g S.--l ;5t 3,--l l>( J,--I Lif 3,--l 221 J.--l :3t 3,--l L+( 3,--l 251 3,--l L7( a,--) 27( 31--J L.J( 3,--l 2j( 3r261 Ejt 3.27) 3ci 3.27) 33( 3128) 3:( 3,23J 3;t 3.2'31 3lz( 3.29) 3L( 3.39) 33( 3930) 3st 3,31) 5-t 3,3;1 3rt 3,321 35( 3.32) 5,( 3133) 30( 3.33) 36( 3,3*) 57f 3.35) 37( 3,3,) 51
41-l
at 7t j( 3(
-+1--b 2,--l *,--) *1--b
6( 2,--l I( 2,--l 9( 2,--l Y( 2,--l Lli( 2,--l 11( 2,--l itt 2,--l f3( 2,--D ;4( 2,--l 15I 2,--l 2C( 2,--l 21( 2,--j 22( 2,--l 23( 2,--l 2*( 2,--l 2I,( 2,--l 2b(
2,--j 2.27) 2,261 2128) 2,271 2,291 2,ZAl 2.30) 2,29t 2,311 2,301 2,321 i,3:1 2,33) 2,321 2,341 2,331 3b( 2,341 36( 2,351
L( 5t 6( 7( dt 3f - 121 -
-
t*t .*--1 ij( 4*--l ltJ( it,--) ;?( .(,--1 ld( .+,--) 13( *,--I LJ( *,--) Lit *,--I 2zt 4,--l 23( v,--) -
2,--l
27t 20( 2al 29( 2Yt 30( 3G( 3Lt J:f JZf 321 33( 33( 3rt 3+( 35( 35(
12t 13( 14( :5t 16t 17( 18( iY( 2u( 21( 22t
3,--b 3,--J 3,--j 3,--l 3,--l 3,--l 3,--l 3,--l 3,--l 3,--l 3,--j 3,--j 3,--l 3,") 3,--l 3,--l 3,--j 3,--l
ET AL.
I-Continued
OBSERVED
179.90 180.29 38C.69 161.37 181.48 181.85 18 2.26 192.66 163.03 18 3.r3 185.39 185.79 186.17 186.55 186.94 187.34 107.74 108.14 108.51 180.51 108.92 160.92 189.31 189.32 189.72 18Y.72 19c.14 19t.14 190.55 lY6.55 19c.94 190.94 191.34 19i.34 191.70 191.70 23G.41 233.83 231.18 231.58 232.02 232.40 232.77 ZT3.16 233.55 233.97 234.30 234.74 235.15 235.45 235.84 23b.29 236.70 237.04 237.45
CALCULATED + O-C H.F. SHIFTS (STANDARD DEV.) 179.931)( lBO.299( 160.691( iRl.083( ia1.475( 181.0671 182.259( id2.551( 183.043( 183.435( 195.396( 185.786( 186.180( 166.572( ia7.357t 187.750( 188.142( 188.5351 198.534( 188.927( 186.927( 189.32Ut 189.319( 189.712( i83.711( 19O.li5( 190.104( 190.497( UO.496( 190.890( 130.889( 191.283( 131.281( 191.674( 191.675(
141 141 141 141 14) lrl 1~) 1st II0 141 141 ilo irl 141 14) 141 141 141 14) lrl :4) 141 1~) 141 i41 14) i4) 141 141 141 141 141 1~) 141 141 i41
-O.OGb -0.009 -0.OCl -0.013 0.0?5 -0.017 O.OCl o.oc9 -0.013 -0.095 -0.OC6 0.002 -0.010 -0.022 -0.025 -0.017 -0.010 -0.OC2 -9.025 -0.024 -0,OCT -U.OC? -O.OlG -0.009 o.oco 0.009 0.035 0.036 O.G53 0.054 c.050 0.051 o.c57 0.059 0.026 0.025
23G.4251 230.8:6l 231.237i 231.598( 231.989( 232.380( 232.77ll 233.162( 233.552( 233.9*3( 234.333i 234.724( 235.114( 235.505( 235.895t 236.285( 236.675( 237.0651 237.455t
13) 131 i3) 13) 13) 13) 13) 131 131 131 131 131 131 131 131 13) 13) 13) 131
-0.015 0.014 -0.027 -0.018 0.031 0.020 -O.OCl -0.0'12 -0.002 0.027 -0.033 0.016 0.036 -0.055 -0.055 o.ot5 0.025 -0.025 -0.005
186.965i
NOTE
I
I I
I I*B ItB
ISa
1,B 118 Iti3
I,a I*B
I,8 118 1,s 118 I.9 I.6 I*8 118 ItI3 I,B
I I
SPECTROSCOPIC TABLE TKANSITION
UPPER STATE 2-t 2c(
27( LB{
*.--I 4,--b
--a 4,--l 9,
$bt
4,--l 49-j
-
OBSERVED
23( ?E( 26( 27( zat 3ot 31( 321 33I 34( 35( 361
3,--l 3,--j 3,--j 3,--I 3,--j 3,--l 3,--b 3,--l 3,--j 3,--l 3,--j 3,--l
197
OF HNCS
I-Continued CALCULATE0
+
o-c
NOTE
0.015
I
N.F. SHIFTS (WINOAR NV.)
LOWEF. STATE
L9( 4*--l 311 4,--l 32( 4, --I 33( 4.--l 34( 4,--l 3L?( *,--I 37(
CONSTANTS
237.06 238.61 239.02 239.45 239.83 246.56 240.97 241.40 241.66 242.i4 242.52 242.90
237.8&5( 238.625(
13) 131 239.01b4 131 239.404( 131 239.794( 13) 24C.573( 13) 240.962( 13) 2.+1.352( 13) 2r1.740( 13) 242.129( 13) 2r2.5161 131 242.937t 13)
-0.015
I
0.006 0.046 0.03b -0.013 O.OC8 0.049 -0.080 0.011 0.012 -0.037
I I I I I I I I I I
a) The entries in the last column (note) have the following meaning: i-l: Microwave measurements in the present work. The numbers are frequencies in WHz. The weight factors of these lines used in the fit are 1.0 unless other specifications are qiven. I: Far infrared measurements listed in Table VI of Ref. (5). The numbers of wavenumbers in cm-'. The weight factors of these lines used in the fit are 4.45x10-"
unless any
other specifications are given. A: Not used in the fit. 5: Components of the K-doublets are not resolved. The weight factors for each component have been reduced by a factor of two. c: Obvious misprints in the transition wavenumbers in Table VI of Ref.(6) - have been corrected. 0: The J quantum numbers for these lines have been reassigned in the present work, which seem to be misprinted in Ref. (2). Numbers: For hyperfine components, the relative intensities are given in this column in %.
fit the observational data, because of the large centrifugal distortion effects in this molecule. Such effects have been observed for several light molecules including HNCO, DNCO (9), DNCS (5), H,O and D,O (10, I1 ). Several higher order correction terms were therefore added to the Hamiltonian. The Hamiltonian
198
YAMADA
ET AL.
used is X = {A - ‘/z(B + C)} .f: + ‘/(B
+ C)sfz + 1/(B
- c)(j2+ + 35)
where j* = 1, ? ij,. The total angular momentum operator is], and its components along the principal axes are ja, lb, and jc in the above expression. For the sextic and the higher order corrections only those terms were used which contribute as diagonal matrix elements in the symmetric rotor basis to the rotational energy. This Hamiltonian is equivalent to the Hamiltonian used in the analysis of DNCS (5) except for the d2 term and the sign convention for the L and T terms. In the case of DNCS the d, term was defined as 2d2[2(j$ - j:) - I4 + 2j2.?z - jz] whereas in the present analysis this term is defined as d2(.?4+ + .f4_). The difference between the two formulations is -d2(4s2 + 103:) and results in a small contribution to the rotational constants A and (B + C) of about the order of d, itself which is much less than the standard deviation of the adjusted parameters. The rotational energy has been obtained by numerical diagonalization of the Hamiltonian energy matrix. The matrix elements of the Hamiltonian were calculated on the basis of Wang’s linear combinations of the symmetric rotor wavefunctions. For each J value (2J + 1) functions were used. However, it was found unnecessary to use the complete set of basis functions in the present analysis, due to the fact that energy levels of high K, were not needed and the effect of inertial asymmetry is negligibly small for this type of molecule in high K, states. The basis functions used were limited by setting an upper limit for the K, quantum number, for example K, < 6. The parameters appearing in the Hamiltonian were adjusted to the observed frequencies by a least squares procedure. For the lines which show hyperfme splittings, the unsplit frequency positions were calculated as described in the next section and used in the fit. The mw and mmw data were sufficient to determine the parameters associated with j or J+ and J_, which are B, C, D,, D,, dl, d2, HJK, HKJ, LKJI and SKJ. However, the parameters purely associated with j,, that is DK, HK, LK, SK, and TK, were not determinable from the mw and mmw data, because no b-type transitions could be measured. Thus the fir data reported in Table VI of Ref. (6) were included to determine the remaining important parameters. For the combined analysis of the mw, mmw, and fir data, a weighted least squares analysis was applied. The statistical weight of the value of an observational quantity was set proportional to the inverse of the squared experimental uncertainty of the measurement: the uncertainty of a mw or mmw measurement was estimated to be 10 kHz and of a fir measurement 0.05 cm-‘, which results in the ratio of relative weights for (mw or mmw)/(fir) = l/(4.45 X 10-l’). The wavenumbers of the transitions for the ‘QK branches were not used in the final fit because the measurements of these line positions were not sufficiently
SPECTROSCOPIC
199
CONSTANTS OF HNCS
accurate. The wavenumbers for ‘P, transitions listed in Table VI in Ref. (6) show small but systematic deviations from the calculated frequencies, and were therefore rejected from the final fit; they are not listed in Table I. Several obvious misprints in Table VI of Ref. (6) were also corrected as indicated in Table 1. Transition frequencies and wavenumbers which deviated more than 100 kHz and 0.1 cm-‘, respectively, were rejected from the final fit. In cases where the components of the K, doublets were not resolved, the weighting factors of each component were reduced by a factor of two. If the calculated frequencies of a K, doublet show a splitting of less than 1 kHz for a mw or mmw transition or 0.001 cm-’ for an fir transition. respectively, the transition is listed in Table I as a single line ignoring the K, quantum number. From the combined mw, mmw, and iir data set the spectroscopic constants A, Dh., Hti, and LR were determined in addition to the parameters determinable from the mw and mmw data alone. The parameters thus obtained are listed in Table II, under the column of Fit 1. For this fit the basis functions used for the energy calculation were limited to K, < 6. The reason for this choice of the limit is discussed in the final section of this paper. The calculated frequencies and wavenumbers using the adjusted parameters of Fit 1 are listed in Table I for TABLE II Rotational Parameters of HNCS” Parameter
Fit 1
Fit 2
Unit
A B e D, DJK DK d, & HJ HJK
1357.25(70) 5883.4627(3) 5845.6113(3) 1.19393(37) - 1.02537(28) 5 1.57(25) - 13.7808(30) -4.59(19) O.O(fixed) 1.019(72) -185.40(11) 4.002(28) O.O(fixed) - 16.597(13) 119.7( 10) O.O(fixed) -0.53263(45) O.O(fixed) O.O(fixed) 22.1
1361.53(81) 5883.4628(3) 5845.6114(3) 1.19419(41) - 1.02532(31) 57.52(33) - 13.7808(33) -4.59(20) O.O(fixed) 0.919(79) -18X28( 12) 6.038(52) O.O(fixed) - 16.569(14) 363.2(36) O.O(fixed) -0.53128(49) 10.43(11) 0.1113(13) 24.3
GHz MHz MHz kHz MHz GHz Hz Hz
H XI
HK L.lK LKJ LK S .Jx SXd SK TX I+
Hz kHz GHz kHz MHz kHz MHz MHz kHz
a Parameters are defined in the Hamiltonian, Eq. (1). The numbers in parentheses are one standard deviation in the unit of the last digit. b Standard deviation of the fit. Fit 1: Derived from transitions in Table I; Fit 2: In addition to transitions in Tabie I the positions of the ‘Q4 and rQ5 branches were used.
200
YAMADA
ET AL.
comparison with the observed line positions. The observed-calculated quite small, resulting in a standard deviation of the fit of 22.1 kHz. IV. QUADRUPOLE
COUPLING
values are
CONSTANTS
Nuclear quadrupole hyperfine structure due to the 14N nucleus was observed in the 10,1-%0, 2,~ lo,192,,,-- 11,0,21,Z- 11,1,3,-22, and 4,-3, transitions, as listed in Table I. The analysis of the hyperfine structure was carried out by fitting the frequencies of the individual hyperfine components by a least squares method. First order theory was applied in the analysis using the rigid rotor basis for the calculations. The three parameters which were adjusted for each transition were the coupling constants xaa, &,-XCCr and the unsplit frequency. When a line frequency was assigned to a single component, this line was given the weight of unity in the fit. When the frequency of a blended line was assigned to two (or more) components, each component was weighted proportional to its relative intensity requiring the sum of the weights of the two (or more) components to be unity. The rotational constants obtained from the centrifugal distortion analysis were used in the hyperfine analysis. On the other hand the unsplit line frequencies obtained from the hyperflne analysis were necessary for the centrifugal distortion analysis. Therefore, the two procedures have been carried out iteratively. The obtained coupling constants are listed in Table III. The constant xaa has been determined well because the observed hyperfine splittings are mainly dependent upon this constant. On the contrary, the present data do not allow xb* - xCCto be determined precisely as shown in Table III. However, it can be concluded that the Vahe Xbb - xec is less than 0.23 MHz, which is twice the derived standard deviation. V. DISCUSSION
The parameters A, DK, HK, and LK obtained from Fit 1 must be considered as pure fitting parameters and therefore have limited physical significance. These parameters are sufficient to reproduce the K, rotational energies up to K, = 4 which were included in the fit. However, the energy levels for K, > 4 calculated using these parameters are completely unreliable. For example, the energy for the K, = 6 sublevel is calculated to be negative, which obviously is wrong. This arises from the fact that the power series expansion in the energy matrix elements is not converging with respect to the K, quantum number. Therefore, it is reasonable to truncate the basis wavefunctions with K, < 6 in Fit 1 as mentioned before. TABLE
III
Nuclear Quadrupole Coupling Constants for ‘
XIII7 Xbb - Xcc a Numbers in parentheses
are one standard
deviation
in units of last digit.
SPECTROSCOPIC
CONSTANTS OF HNCS
201
We have tried an alternative fit by introducing the ‘Q4 and ‘Q5 fir transitions which were not used in Fit 1. These two unresolved sets of transitions were observed with peak positions at 273.9 and 313.7 cm-’ (6), respectively. These wavenumbers were assumed to mark the positions of the & + 5,,, and 6,,, + 6,,, transitions of the Q branches, respectively. Using these two transitions in addition to those used in Fit 1, a new fit called Fit 2 has been carried out, the results of which are also listed in Table II. Since two more K, sublevels were included in the fit, two more parameters were required, SK and T *. The basis functions are limited by K, c 7 and therefore compose a minimal basis set. The parameter A and the Kdependent distortion constants such as Dh. were found to be rather different from those of Fit 1. However, it is reassuring that the other parameters remain stable, especially the B and C rotational and the quartic centrifugal distortion constants. Small changes in HJK, LKJ, and SKJ may therefore compensate for the effect of the change in basis truncation. Though the rotational constant A and the centrifugal distortion constant D, are well determined as fitting parameters, they are not reliable enough to be applicable for a precise molecular geometry calculation or a force field analysis. They depend strongly on the model used in the fit, as shown by the difference between Fit 1 and Fit 2. By using the Fit 2 parameters the K, rotational sublevels can be predicted up to K, = 6 but the predicted position of the J rotational levels is still only useful up to K, = 4. The convergence of the DJK, HKJ, LKJ, SxJ series is not good enough to predict the line positions with sufficient accuracy that they could be located. However, it is one of the important purposes of scientific research to predict the values of physical quantities by extrapolation. From such a point of view, the results of the present study are unfortunately poor, because the range of prediction of the HNCS spectrum outside the measured range is very limited. Recently, one of the four atomic quasi-linear molecules, HCNO, has been analyzed by using a semirigid bender model by Bunker et al. (12), and its spectra could be explained well with a small number of adjusted parameters. It seems to be a promising direction of further studies of HNCS to apply a similar physical model, though the problem is much more complicated in HNCS than in HCNO, because the two skeletal bending modes must be taken into account in addition to the HNC bending mode. VI. ACKNOWLEDGMENTS This work was supported in part by the Deutsche Forschungsgemeinschaft, the National Research Council of Canada, and the North Atlantic Treaty Organization. The authors would like to thank Dr. Brenda P. Winnewisser for commenting on the manuscript. RECEIVED:
December
11, 1978 REFERENCES
1. L. H. JONES, J. N. SHOOLERY,R. G. SHULMAN, AND D. M. YOSTJ. Chem. Phys. l&990-991 (1950). 2. C. I. BEARD AND B. P. DAILEY, J. Chem. Phys. 18, 1437-1441 (1950) and J. Chem. Phys. 19, 975 (1951).
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YAMADA
ET AL.
3. G. C. DOUSMANIS,T. M. SANDERS, C. H. TOWNES, AND H. J. ZEIGER,J. Chem. Phys. 21, 1416-1417 (1953). 4. R. KEWLEY, K. V. L. N. SASTRY,AND M. WINNEWISSER,J.Mol. Spectrosc. 10,418-441(1%3). 5. L. B. SZALANSKI, M. C. L. GERRY, G. WINNEWISSER,K. YAMADA, AND M. WINNEWISSER, Canad. J. phys. 56, 1297-1307 (1978). 6. B. KRAKOW, R. C. LORD, AND G. 0. NEELY, .I. Mol. Spectrosc. 27, 148-176 (1%8). 7. K. YAMADA AND M. WINNEWISSER,J. Mol. Spectrosc. 72, 484-501 (1978). 8. J. K. G. WATSON, “Vibrational Spectra and Structures” (J. R. Durig, Ed.), Vol. 16, Chap. 1, Elsevier, ASP, Amsterdam, 1977. 9. W. H. HOCKING,M. C. L. GERRY,AND G. WINNEWISSER,Canad. J. Phys. 53,1869-1901(1975). IO. F. C. DELUCIA, P. HELMINGER,AND W. H. KIRCHHOFF,.I. Phys. Chem. Ref Data 3, 211-219 (1974). Il. G. STEENBECKELIERS AND J. BELLET,J. Mol. Spectrosc. 45, lo-34 (1973). 12. P. R. BUNKER,B. M. LANDSBERG,AND B. P. WINNEWISSER, J. Mol. Spectrosc.
74,9-25
(1979).