Laser spectroscopy of VS: hyperfine and rotational structure of the C4Σ−–X4Σ− transition

Journal of Molecular Spectroscopy 220 (2003) 87–106 www.elsevier.com/locate/jms

Laser spectroscopy of VS: hyperfine and rotational structure of the C 4R
–X 4R
transition Qin Ran,a W.S. Tam,b A.S.-C. Cheung,b,* and A.J. Mererc a

c

Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui, PR China b Department of Chemistry, The University of Hong Kong, Pokfulam Road, Hong Kong Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, BC, Canada V6T 1Z1 Received 22 January 2003

Abstract The (0,0) and (0,1) bands of the C 4 R
–X 4 R
electronic transition of VS (near 809 and 846 nm, respectively) have been recorded at high resolution by laser-induced fluorescence, following the reaction of laser-ablated vanadium atoms with CS2 under supersonic free-jet conditions. A least squares fit to the resolved hyperfine components of the rotational lines gives the rotational constants and
; X 4 R
: B0 ¼ 0:203684  0:000025 cm
1 , r0 ¼ 2:0526 A
. The bond lengths as C 4 R
: B0 ¼ 0:188898  0:000027 cm
1 , r0 ¼ 2:1315 A electron spin parameters for the two states show that there are some similarities between the states of VS and those of VO, but the hyperfine parameters show that the compositions of the partly filled molecular orbitals are by no means the same. The ground state Fermi contact parameter of VS, bðX 4 R
Þ, is only 58% of that of the ground state of VO, which implies that the r orbital of the ground rd2 electron configuration has less than 50% vanadium 4s character. Similarly, the excited state Fermi contact parameter, bðC 4 R
Þ, is very much smaller than that of VO. No local rotational perturbations have been found in the C 4 R
state of VS, though an internal hyperfine perturbation between the F2 and F3 electron components at low N confuses the hyperfine structure and induces some forbidden (DJ ¼ 2) rotational branches. Ó 2003 Elsevier Science (USA). All rights reserved.

1. Introduction The electronic band systems of transition metal sulfides are important in astrophysics, since several of them have been observed in the spectra of Mira-type variable stars. So far the sulfides TiS, YS, and ZrS have been detected [1–3], but as yet VS has not been identified, [4] although the corresponding oxide, VO, gives rise to some of the strongest band systems in the spectra of cool stars, second only to TiO. One of the obvious reasons why VS has not been identified is that the wavelengths of its characteristic bandheads are not known, since the electronic spectrum has not yet been mapped in detail. In the present paper we report the first experimental investigation of the electronic spectrum of VS; it is hoped that the data we offer will encourage astronomers to search for the presence of VS in the atmospheres of cool stars. * Corresponding author. Fax: +852-2857-1586. E-mail address: [email protected] (A.S.-C. Cheung).

Two theoretical studies of the electronic structure of VS have been carried out. Bauschlicher and Langhoff [5], using a coupled-pair functional (CPF) approach, calculated the properties of its low-lying electronic states and showed that the ground state should be a 4 R
state. Later, Bauschlicher and Maitre [6] using complete active space self-consistent field (CASSCF) methods, confirmed that the ground state is a 4 R
state and also concluded that the bonding mechanism in transition metal sulfides and oxides is very similar. The bands whose analysis is reported in this paper are the (0,0) and (0,1) bands of the C 4 R
–X 4 R
electronic transition of VS, near 800 nm. They were recorded by laser-induced fluorescence, following the reaction of laser-ablated vanadium with carbon disulfide under supersonic jet-cooled conditions [7]. The linewidth in our experiments is limited to about 250 MHz, but this is sufficient for most of the hyperfine structure to be resolved. Accurate values for the rotational, electron spin, and nuclear hyperfine constants have been obtained for both states.

0022-2852/03/$ - see front matter Ó 2003 Elsevier Science (USA). All rights reserved. doi:10.1016/S0022-2852(03)00095-X

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2. Experimental details

3. Appearance of the spectrum and its analysis

VS molecules have been prepared by the reaction of laser-ablated vanadium atoms with carbon disulfide under supersonic free jet conditions, and their spectra recorded by laser-induced fluorescence. The experimental procedures have been described in a previous paper [8], so that only a brief outline will be given here. A pulsed molecular beam valve (General Valve Series 9) released a mixture of about 4% CS2 in argon (from a backing pressure of 5 atm.) towards a 6 mm diameter vanadium rod (Goodfellow, 99.9%) approximately 15 mm away. The output (5–6 mJ, 10 ns) of the second harmonic of a Nd:YAG laser (532 nm) was focused onto the vanadium rod, producing a metal plasma near the surface of the rod; the rod was rotated and translated so as to expose a fresh part of the surface to each laser pulse. The timing of the gas pulse relative to the vaporization laser pulse was adjusted so that the maximum pressure of gas over the vanadium rod occurred at the same time as the plasma was formed. The VS molecules formed by reaction of the metal atoms and the CS2 expanded supersonically, through a small channel 22 mm long and 2 mm in diameter, into the vacuum of the apparatus, cooling in the process. The flow of gas was orthogonal to both the axes of rotation of the rod and the propagation of the Nd:YAG laser beam. The various pulses were synchronized by a four-channel digital time delay/pulse generator (Stanford Research Systems model DG535). The timing sequence for the experiment was initiated by the opening of the pulsed valve; this typically remained open for 240 ls, though the Nd:YAG ablation laser was triggered 200 ls after the valve was opened. The repetition rate for the experiment was 10 Hz. The VS molecules were excited by an argon ionpumped Ti:sapphire ring laser (Coherent Inc. model CR899-21), whose output was passed through the gas mixture, at right angles to its direction of flow, about 5 cm downstream from the nozzle. The laser-induced fluorescence signal was detected through a lens system and a sharp-cut red filter by a Hamamatsu R636-10 photomultiplier tube. The signal was averaged by a boxcar integrator (Stanford Research Systems, model SR250). The spectrum was recorded as overlapping 0:8 cm
1 segments, each taking about 9 min to record. The widths of the VS lines were measured to be about 250 MHz. The wavelength of the Ti:sapphire laser was measured by a wavemeter (Burleigh, model WA-1500) with a repetition rate of 1 Hz and an accuracy of 1 part in 107 . The absolute calibration of the wavemeter was checked against I2 absorption lines, which are estimated to be accurate to about 0:003 cm
1 in the near IR region [9].

The rotational analysis of the new spectrum was carried out by the standard method of picking out branches and looking for combination difference relations between them. It soon became clear that each band consisted of two red-degraded sub-bands about 8 cm
1 apart and that, since the widths of the hyperfine patterns at the highest N values were in the ratio 3:1:)1:)3, one or both the combining states was a 4 R state near case (b) coupling [10]. Since only two sub-bands are present the other state had to be another 4 R state, or possibly a 2 P state. In the end the details of the rotational level patterns established that both states were 4 R states, and by analogy with VO, the transition could be assigned as C 4 R
–X 4 R
. No perturbations by other electronic states were found, but the great number of branches, many with rapidly varying hyperfine widths and unexpected degradation, proved a challenge; an example is the R2 branch of Fig. 1, which forms no head and opens out to the low frequency side right from its first line (J 00 ¼ 0:5), in the manner expected for a P branch. Comparison of corresponding branches in the (0,0) and (0,1) bands was useful, as it allowed us to obtain the approximate Nnumberings of lines still to be assigned. In the end all 24 branches expected for a 4 R
–4 R
transition were identified. An energy level diagram for a transition of this type is given in Fig. 2. The bands of the C 4 R
–X 4 R
transition of VS are somewhat different in appearance from those of the corresponding transition of VO [10], although the electron spin parameters of the two states are quite similar in the two molecules. The reason is that the rotational constants of VS are less than half of those of VO, which means that the electron spin coupling in the ground state of VS is much closer to HundÕs case (a) than it is in VO. This has two effects. Since the C 4 R
state is very close to case (b) coupling in both molecules, the change of coupling case in the electronic transition enhances the satellite branches in the C–X system of VS, so that all of them are observable. The other effect is that the internal hyperfine perturbations between the F2 and F3 electron spin components of the ground state, which are a major complication in the VO spectrum, are shifted to much higher N values, beyond the range that we observe in our spectra. The ground states of VO and VS come from the configuration rd2 , where the r orbital is derived from the vanadium 4s atomic orbital. They therefore have large Fermi contact parameters and wide hyperfine structure in their F1 and F4 electron spin components. The upper states have narrow hyperfine structure, since the 4s electron has been promoted to the vanadium 3dr molecular orbital, where the Fermi contact interaction is much smaller. Figs. 1 and 3 illustrate two regions of the (0,0) band of the C 4 R
–X 4 R
system of VS. 51 V has a nuclear spin

Q. Ran et al. / Journal of Molecular Spectroscopy 220 (2003) 87–106

89

Fig. 1. The region near the most prominent head (formed by the R1 branch) in the (0,0) band of the C 4 R
–X 4 R
electronic transition of VS.

Fig. 2. Energy level diagram for a 4 R
–4 R
transition, illustrating the origins of the 24 branches allowed by the selection rules DJ ¼ 0, 1.

I ¼ 7=2, so that every line (except those at the lowest J values) has eight hyperfine components which follow the selection rule DF ¼ DJ . The strong hyperfine-resolved R1 head at 12366:7 cm
1 , shown in Fig. 1, is the most characteristic feature of the band. To the blue side of this head (not shown) are three simple-looking T-form branches with widely spaced hyperfine structure, of

which the two T R branches are the most prominent. To the red side the most obvious features are some strong sharp lines belonging to the R2 branch; as can be seen in Fig. 1, the R2 branch continues on both sides of the sharp features, but the lines break up into partly resolved hyperfine structure. Strong sharp lines of this type occur at those J values where the upper and lower state hyperfine

90

Q. Ran et al. / Journal of Molecular Spectroscopy 220 (2003) 87–106

Fig. 3. Central portion of the VS, C 4 R
–X 4 R
, (0,0) band, showing the wide hyperfine structure of the P1 branch, and the ‘‘spikes’’ formed by the P2 and R3 branches.

widths are the same; all eight hyperfine components lie at the same frequency and a narrow ‘‘spike’’ results. Other examples can be seen in Fig. 3, where the ‘‘spikes’’ in the P2 and R3 branches are prominent. The hyperfine widths are small in the C 4 R
state but the F2 and F3 electron spin components of the ground state have much larger hyperfine widths which change quite rapidly with J and happen to pass through zero at J ¼ 5:5 and 8.5, respectively. The narrowest ‘‘spike’’ in the R2 branch (shown in Fig. 1) occurs at J ¼ 7:5. The hyperfine width in the F4 spin component of the ground state passes through zero near J ¼ 3:5 but, since the branches involving this component are not very strong, the ‘‘spikes’’ are not so obvious (see Fig. 3). A few hyperfine satellite lines, of the type DF 6¼ DJ , can be picked out in the lowest-J rotational lines such as P1 ð1:5Þ and R2 ð0:5Þ, but in general these are not prominent, and their assignments were mostly made after the initial least squares fitting had been done. The hyperfine widths are very small in the low J levels of the F30 and F40 electron spin components, so that the first lines of the branches going to them show just the ground state hyperfine patterns, with each component slightly broadened to indicate the presence of unresolved upper state hyperfine splittings. For example, a line such as R Q43 ð1:5Þ consists of four hyperfine components representing the ground state splitting pattern, but these are noticeably broader than the instrumental linewidth. Although Fig. 2 shows that only 24 rotational branches are expected for a 4 R
–4 R
transition, we have actually identified 27 branches. The reason is that an internal hyperfine perturbation in the C 4 R
upper state,

at the very lowest N values, allows us to assign a few lines of the rotationally forbidden N O34 , P O32 and T S21 branches. Internal hyperfine perturbations arise when two electron spin components of a state near case (b) coupling accidentally lie at the same energy for a given N value, but differ by one unit in J; matrix elements of the hyperfine Hamiltonian, of the type DN ¼ 0, DJ ¼ 1, DF ¼ 0, then cause avoided crossings in the hyperfine structures of the interacting electron spin components, and induce extra branches. Such perturbations are an important feature of the VO, C–X system [10], where they occur in both electronic states but, in contrast, there are no internal hyperfine perturbations at low N values in the ground state of VS. Even though the spin–spin parameter k is almost identical in the two molecules, the smaller B value in VS prevents the middle two spin components, F2 and F3 (J ¼ N þ 1=2 and J ¼ N
1=2, respectively), from crossing through each other until about N ¼ 30, far beyond what we observe in our supersonic jet-cooled spectra. The most obvious of these rotationally forbidden hyperfine-induced branches is the N O34 branch. Its first line, with J 00 ¼ 3:5, has two of its four hyperfine components clearly visible at 12355.2765 and 12355:2868 cm
1 (F 0 ¼ 5 and 4, respectively), while the six hyperfine components of its second line (J 00 ¼ 4:5) form a prominent ‘‘spike’’ at 12354:3935 cm
1 . The next line (J 00 ¼ 5:5) is quite weak, and its hyperfine structure is not resolved. This branch had been a puzzle in the early stages of the analysis, but its assignment became clear when the spin structure of the upper state was better understood.

Q. Ran et al. / Journal of Molecular Spectroscopy 220 (2003) 87–106

Two other rotationally forbidden branches of this type could be identified from calculations of their line positions. For the T S21 branch, two hyperfine components of the J 00 ¼ 1:5 line can be seen among the components of the allowed T R31 ð1:5Þ line, but the components of the P O32 branch are weak and unresolved. No features corresponding to the fourth branch of this type, R S23 , have been found. No lines belonging to the less abundant isotopomer, 51 34 V S (4% natural abundance) have been identified.

4. Results The Hamiltonian used for the least squares fitting of the C 4 R

X 4 R
transition of VS was assumed to have the form [11]
 H ¼ BN ðN þ 1Þ þ ð2=3Þk 3Sz2
S2 þ cN S 
  2
DN 2 ðN þ 1Þ þ ð1=3ÞkD 3Sz2
S2 ; N2 þ þ ð1=2ÞcD ½N S; N2 þ þ 10cS T 3 ðL2 ; JÞ T 3 ðS; S; SÞ hpffiffiffi i = 6hKjT02 ðL2 ÞjKi þ bI S þ cIz Sz pffiffiffiffiffi þ 5 14bS T 1 ðIÞ T 1 fT 2 ðL2 Þ; T 3 ðS; S; SÞg   ð1Þ = 3hKjT02 ðL2 ÞjKi þ cI N I; where N ¼ J
S, and ½x; yþ denotes the anti-commutator, xy þ yx. The various terms can be identified by the parameter names. In addition to the rotation (B), we have the electron spin–spin (k) and spin–rotation (c) interactions and their centrifugal corrections (D, kD , and cD ), together with the third order spin–orbit distortion of the spin–rotation interaction ðcS ). For the hyperfine structure of the ground state we needed only the Fermi contact interaction (b) and the nuclear spin-electron spin dipolar interaction (c) but, for the upper state, we also varied the third order spin–orbit distortion of the Fermi contact interaction (bS ) and the nuclear spin–rotation interaction (cI ). The third order spin–orbit distortion terms allow the effective spin–rotation and Fermi contact parameters to be different in the X ¼ 1=2 and 3/2 components of a 4 R state in case (a) coupling, as will happen when spin–orbit interaction mixes them in different ways with distant electronic states. The strangelooking numerical factors appearing in the operators for these third order spin–orbit distortions have been chosen so that the final matrix elements should have coefficients that are as similar as possible to those of the spin–rotation and Fermi contact interactions [11]; their effect is to cancel the various factors that arise in the calculation of the matrix elements of the compound tensor operators. No attempt was made to determine the quadrupole parameters, e2 Qq0 , because in our experience with VO [10,12] this requires higher resolution than is available in the present experiments. Matrix elements

91

of the operators in Eq. (1), in a case (ab ) basis, can be found in [11]. As might be expected with a complicated scheme of energy levels, it was not always easy to match the eigenvalues of the Hamiltonian matrices to the observed levels. In particular, the identification of the F2 and F4 electron spin components depends on the details of the eigenvectors in a way that is not simple to predict, though allowances could be made once the problem had been recognized. To obtain the rotational and hyperfine constants of the two states, we fitted just the resolved hyperfine components and the sharpest of the ‘‘spikes’’ by least squares. We found that the quality of the hyperfine fit was degraded if we included those rotational lines where the hyperfine structure was not resolved, presumably because it is not possible to determine exactly where in the line profile a particular hyperfine component lies. Although this has meant that some of the data were thrown away, the final fit has a much lower standard deviation. Various least squares fits were carried out. It was found immediately that, with the data only providing rotational combination differences up to N ¼ 12, the centrifugal distortion parameters D are not well determined. In particular the value of D00 in the ground state is higher than expected according to the Kratzer relation [13], De ¼ 4B3e =x2e :

ð2Þ

Assuming this equation can be applied to the zero-point level, with Be taken as B0 and xe as DG1=2 , the calculated value is D000 ¼ 1:15  10
7 cm
1 . A fit to all the available ground state combination differences for v00 ¼ 0 gave D000 ¼ ð3:2  1:3Þ  10
7 cm
1 , while if D000 was fixed at the Kratzer value, the r.m.s. error became slightly larger. It seems that the problem has arisen from some minor Table 1 Rotational constants for the C 4 R
, v ¼ 0 and X 4 R
, v ¼ 0 and 1 levels of VS

T0 B 107 D k c cS kD 104 cD b c bS cI

C 4 R
, v ¼ 0

X 4 R
, v ¼ 0

X 4 R
, v ¼ 1

12361.3438 (4) 0.188898 (27) 0.47 (156) 0.38609 (27) 0.02589 (8) )0.000414 (25) )0.000491 (5) 0.128 (9) )0.00025 (7) )0.0039 (5) )0.00048 (6) 0.0010 (5)

0.0 (fixed) 0.203684 (25) 3.21 (131) 2.11506 (20) 0.02195 (14) 0.000028 (27) 0.000018 (5) 0.005 (9) 0.01583 (11) )0.0026 (4) 0.0 (fixed) 0.0 (fixed)

542.1353 (7) 0.202683 (39) 4.13 (292) 2.12700 (20) 0.02224 (13) 0.0 (fixed) 0.0 (fixed) )0.013 (13) 0.01561 (14) )0.0025 (4) 0.0 (fixed) 0.0 (fixed)

Values in cm
1 . Error limits are 3r, in units of the last significant figure; r.m.s. error ¼ 0:00119 cm
1 . Bond lengths in the zero-point levels: r0 ðC 4 R
Þ ¼
; r0 ðX 4 R
Þ ¼ 2:0526 A
. Equilibrium parameters for X 4 R
: 2:1315 A
. Be ¼ 0:204185 cm
1 ; ae ¼ 0:001001 cm
1 ; re ¼ 2:0501 A

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Q. Ran et al. / Journal of Molecular Spectroscopy 220 (2003) 87–106

Table 2 Energy levels of the X 4 R
and C 4 R
, v ¼ 0 states of VS, up to J ¼ 4:5, calculated from the final least squares parameters of Table 1 J

Fmax

Energy levels of the X 4 R
, v00 ¼ 0 state )3.8338 0.5 F1 F2 )3.1336

Fmin )3.9356 )3.0677

1.5

F1 F2 F3 F4

)3.6386 )2.1911 4.8842 4.8912

)3.6924 )2.1584 4.8490 4.8573

)3.7320 )2.1334 4.8209 4.8305

)3.7606 )2.1152 4.8000 4.8107

2.5

F1 F2 F3 F4

)3.0608 )0.8721 5.9481 5.9776

)3.1026 )0.8495 5.9339 5.9660

)3.1362 )0.8314 5.9217 5.9563

)3.1626 )0.8172 5.9116 5.9484

)3.1820 )0.8068 5.9039 5.9425

)3.1948 )0.8000 5.8987 5.9386

3.5

F1 F2 F3 F4

)2.0948 0.8154 7.4428 7.5177

)2.1315 0.8320 7.4364 7.5153

)2.1624 0.8457 7.4306 7.5132

)2.1877 0.8569 7.4255 7.5116

)2.2078 0.8656 7.4213 7.5104

)2.2227 0.8720 7.4180 7.5095

)2.2326 0.8763 7.4158 7.5089

)2.2375 0.8784 7.4147 7.5086

4.5

F1 F2 F3 F4

)0.7373 2.8677 9.3626 9.5109

)0.7712 2.8798 9.3602 9.5141

)0.8006 2.8900 9.3578 9.5171

)0.8254 2.8985 9.3555 9.5197

)0.8460 2.9054 9.3535 9.5220

)0.8623 2.9109 9.3518 9.5239

)0.8745 2.9149 9.3504 9.5253

)0.8826 2.9176 9.3495 9.5263

Energy levels of the C 4 R
, v0 ¼ 0 state 123 0.5 F1 60.8941 F2 61.5934

60.8820 61.5942

1.5

F1 F2 F3 F4

123

60.9428 62.0358 62.7922 63.1045

60.9411 62.0448 62.8011 63.1099

60.9397 62.0520 62.8092 63.1142

60.9387 62.0574 62.8163 63.1175

2.5

F1 F2 F3 F4

123

61.3662 62.8171 63.9094 64.5669

61.3657 62.8258 63.9129 64.5687

61.3652 62.8320 63.9162 64.5701

61.3649 62.8359 63.9192 64.5713

61.3646 62.8380 63.9216 64.5722

61.3644 62.8387 63.9232 64.5728

3.5

F1 F2 F3 F4

123

62.1667 63.9674 65.4029 66.4140

62.1665 63.9738 65.4045 66.4148

62.1663 63.9785 65.4060 66.4156

62.1662 63.9819 65.4076 66.4162

62.1661 63.9844 65.4089 66.4167

62.1660 63.9860 65.4099 66.4171

62.1660 63.9870 65.4107 66.4173

62.1659 63.9875 65.4111 66.4174

4.5

F1 F2 F3 F4

123

63.3453 65.4917 67.2731 68.6415

63.3452 65.4968 67.2737 68.6420

63.3452 65.5008 67.2744 68.6424

63.3451 65.5039 67.2752 68.6428

63.3451 65.5062 67.2760 68.6431

63.3451 65.5080 67.2766 68.6434

63.3450 65.5092 67.2771 68.6436

63.3450 65.5100 67.2775 68.6437

Values in cm
1 .

calibration shifts between different parts of the (0,0) band, which we have not been able to resolve without rerecording the whole band. For the upper state the Kratzer value lies within the 3r error limits on D0 . The final fit was carried out using the complete data set of resolved hyperfine lines and ‘‘spikes’’ from the (0,0) and (0,1) bands, and gave the parameters listed in Table 1. The energy levels calculated from the final least squares parameters are given, for the low J rotational levels of the v ¼ 0 vibrational levels of both states, in Table 2; it is hoped that these will assist in future microwave studies of VS, and in the determination of the dipole moments by optical means. A list of the assigned lines is given in the Appendices A and B.

5. Discussion Figs. 4 and 5 illustrate the spin structures of the C 4 R
and X 4 R
states. In these figures the total energy, less BN ðN þ 1Þ, is shown plotted against N. A point has been plotted for every hyperfine level but, since the hyperfine splittings are small on the scale of the electron spin structure, the individual hyperfine components mostly blend with each other in the figures. The ground state pattern (Fig. 5) is typical for a 4 R
state where k is much larger than B; at low N values the levels group into two pairs corresponding to X ¼ 1=2 and 3/2 in case (a) coupling, but with increasing rotation the levels rearrange into pairs corresponding to jJ
N j ¼ 1=2 and 3/2. On

Q. Ran et al. / Journal of Molecular Spectroscopy 220 (2003) 87–106

the other hand the C 4 R
pattern (Fig. 4) is typical for a state very close to case (b) coupling, where the rearrangement of the levels (caused by spin-uncoupling) occurs at very low N, and the four electron spin components form a ‘‘fan’’ where the energies are given by cðJ
N Þ. The electron spin parameters for the X 4 R
state of VS are remarkably similar to those of VO [10]. For instance the ground state spin–spin parameter k for VO is a mere 4% smaller than that of VS, while the spin–rotation parameter c is 3% larger. The value of k is related to the energy sep-

93

aration of the 2 Rþ and 4 R
states from the configuration rd2 , and is given to second order by the equation [14] k ¼ 2a2d =3DEð2 Rþ ; 4 R
Þ:

ð3Þ

Since the spin–orbit parameter ad will not change much between VO and VS (because the unpaired electrons are based on the vanadium atom rather than the ligand), the implication is that the rd2 2 Rþ state of VS must lie at roughly the same energy as in VO, that is near 10; 000 cm
1 . The spin–rotation parameter c is related to the positions

Fig. 4. Electron spin and hyperfine structure of the C 4 R
, v ¼ 0 state of VS. The total energy of each hyperfine component, less T0 þ BNðN þ 1Þ, is plotted against N. The hyperfine splittings are very small in this state, so that the points representing the hyperfine components of an (N, J) rotational level are mostly overlapped at this scale.

Fig. 5. Electron spin and hyperfine structure of the X 4 R
, v ¼ 0 state of VS. The total energy of each hyperfine component, less BN ðN þ 1Þ, is plotted against N. The points representing the individual hyperfine components run into each other at this scale, forming a bar whose length gives the hyperfine width of a rotational level.

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Q. Ran et al. / Journal of Molecular Spectroscopy 220 (2003) 87–106

of distant 4 P states, and in the single perturber (‘‘pure precession’’) approximation is given by the equation c ¼ 2h4 PjALþ j4 R
ih4 PjBLþ j4 R
i=DEPR :

ð4Þ

Assuming again that the matrix elements of ALþ are the same in VO and VS, the implication is that the distant 4 P state (or states) in VS that are responsible for the value of c lie at much lower energy than they do in VO; specifically, the energies should be in the ratio of the rotational constants, which is 0.37. The spin–rotation parameter c for the C 4 R
state has the opposite sign in VS, compared to VO; since nothing is known about the energies of the higher 4 P states of VS, there is no information to be obtained from its value. The similarity between the spin parameters of VS and VO does not extend to the hyperfine structure. For instance the Fermi contact parameter in the ground state of VS is only 58% of that for VO. Now Adam et al. [15] have shown that the contact parameter in the ground state of VO is 86% of the value expected for the electron configuration 4sr3dd2 , based on the atomic hyperfine parameters for the 3d 4 4s configuration, [16] implying that the 4sr molecular orbital (m.o.) has 86% V 4s character. The implication for VS is that the 4sr m.o. has only 49% 4s character. A simple explanation for this difference can be given in terms of the ionization potentials (IP) of O and S. In the standard way of constructing the m.o. diagram for metal-containing diatomic molecules (see for example [17]), the three important r m.o.s for the low-lying electronic states of VO are made up from a linear combination of V 4sr, V 3dr and ligand npr atomic orbitals, where the shapes of the m.o.s are not unduly changed from the orbitals of the free atoms. Since the IP of S is lower than that of O, and the principal quantum number is higher, the 3p orbital of S lies closer in energy to the V 4s orbital than does the 2p orbital of O. This means that when the m.o.s are formed, other things being equal, the half-filled r m.o. in the ground state of VS (corresponding to ‘‘4sr’’ in VO) will contain more ligand npr character and less V 4sr character, which will result in a smaller contact parameter. Consistent with this, the Fermi contact parameter, b, for the C 4 R
state of VS (
0:00025 cm
1 ) is much smaller than that for the C 4 R
state of VO (
0:00881 cm
1 ). To be exact, it is less negative. The C 4 R
states of these molecules come from the electron configuration 3dd2 3dr, where spin polarization in the vanadium 3d orbital is responsible for the comparatively large negative value. In VS the ‘‘ 3dr’’ m.o. has more ligand npr character than in VO because of the mixing described in the previous paragraph, and therefore the contact parameter for the C state will be less negative. The hyperfine parameters for VS have not been determined in the present work to the accuracy with which the VO parameters are known, because microwave data [18] are available for VO, while this paper reports the first measurements for VS, performed by optical spectros-

copy. It is therefore less easy to make comparisons for the smaller hyperfine parameters, such as the dipolar parameter, c. For the X 4 R
states of VS and VO the c parameters are in roughly the same ratio as the contact parameters, but for the C 4 R
states the c parameter of VS is about three times that of VO. In principle the dipolar parameter is related to the expectation values of the quantities ð3 cos2 h
1Þ=r3 for the p and d electrons, but where there is no dominant atomic orbital in the composition of an m.o., this becomes more difficult to interpret. A surprising result is the size of the parameter for the third order spin–orbit distortion of the Fermi contact interaction, bS , for the C 4 R
state of VS, which is 10 times that found in the C 4 R
state of VO, and well determined. The parameter bS is a complicated function of the spin–orbit and hyperfine matrix elements between the state of interest and distant states [19], which again is hard to quantify if the compositions of the orbitals are not known. In a 4 R state which is very close to case (b) coupling, such as the C state of VS, its effect is to make the apparent Fermi contact parameter different in the F1 and F4 electron spin components compared to the F2 and F3 components [10]. Since the spin–orbit matrix elements will be much the same in VO and VS (because the unpaired electrons are based on the vanadium atom in both molecules), the larger value of the bS parameter in VS is telling us that the energy denominators in the perturbation theory expressions are smaller than in VO, or in other words that the density of interacting electronic states is greater. This is consistent with the lowering in energy of the C 4 R
state in VS, compared to VO, and with the conclusions about the positions of the 4 P states given by the spin–rotation parameters (described above). In view of the higher density of electronic states implied by the various spin parameters, it is interesting that no local rotational perturbations have been found in the C 4 R
, v ¼ 0 state of VS; this is in contrast to the C 4 R
, v ¼ 0 state of VO, [10,20] where quite a number have been observed. This may be to some extent accidental, and reflect the limited J range of our spectra, because preliminary examination of data we have taken for the VS, C 4 R
, v ¼ 1–3 levels indicates that the spin constants change considerably with vibrational excitation, which in turn suggests the presence of nearby electronic states. Acknowledgments The work described in this paper was supported by grants from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKU 503/96P) and the Committee on Research and Conference Grants of the University of Hong Kong. AJM thanks the Natural Sciences and Engineering Council of Canada for financial support, and the University of Hong Kong for travel funds which enabled him to assist with the analysis at Hong Kong.

Appendix A Rotational lines assigned in the (0,0) band of the C 4 R
–X 4 R
transition of VS J 00

N ¼
1

R1 R Q21

0.5 0.5

N ¼0

R1 P1 T R31 R P31 R2 R Q32

1.5 1.5 1.5 1.5 0.5 0.5

N ¼1

R1 P1 T R31 T Q41 R P31 R2 P Q12

2.5 2.5 2.5 2.5 2.5 1.5 1.5

R1 P1 T R31 T Q41 R P31 R2 P2 T R42 P Q12 R3 R Q43

3.5 3.5 3.5 3.5 3.5 2.5 2.5 2.5 2.5 1.5 1.5

12365.5886

R1 P1 T R31 T Q41 R P31 R2 P2 T R42 P Q12 R3 R Q43 R4

4.5 4.5 4.5 4.5 4.5 3.5 3.5 3.5 3.5 2.5 2.5 1.5

12365.7891 363.0539 370.4045 369.5171* 366.2896*

365.7773 363.0415 370.3941 369.5122* 366.2729

361.2754

367.7643 361.2818*

R1 P1 T R31

5.5 5.5 5.5

12365.9701 362.4785 371.2758

N ¼2

N ¼3

N ¼4

F ¼ J
7=2

F ¼ J
5=2

F ¼ J
3=2

F ¼ J
1=2

F ¼ J þ 1=2

12365.1260 364.6469 367.6785 365.7472* 365.1130

12368.6204*

12368.6105 365.9178

369.5171* 366.1286*

365.5770 365.5982 369.5122* 368.6536 366.1191

362.1722

365.9602 362.4685 371.2651

12365.3612 364.1326 368.6014* 367.7682* 365.9081*

12365.0982 364.6161 367.6478 365.7358 365.1196

F ¼ J þ 5=2

F ¼ J þ 7=2

12364.8772 365.5328*

12364.7774 365.4293

365.0589 364.5758 367.6049 365.7093 365.1797 365.1260*

365.0065 364.5335 367.5469 365.6806 365.1870 365.1713

365.3293 364.1032 368.5680 367.7307 365.8784 364.9529 363.0745*

365.3026 364.0786 368.5422* 367.7036 365.8556* 364.9679 363.0808*

365.2702 364.0368 368.5058* 367.6685 365.8341 364.9914 363.0910*

365.2281 364.0046 368.4628 367.6256 365.8123 365.0174 363.1000*

367.2139 362.1834

365.5525 365.5733 369.4813 368.6204* 366.0839 364.7947 362.8600 367.2211 362.1981

365.5328* 365.5531 369.4610 368.6014* 366.0606 364.8021 362.8712 367.2307 362.2165 359.1212 358.3162

365.5078 365.5285 369.4342 368.5742 366.0322 364.8122 362.8839 367.2448 362.2424* 359.0974 358.2935

365.4766 365.4979 369.4030 368.5422* 366.0034 364.8260 362.8964 367.2627 362.2581* 359.0649 358.2592

365.4403 365.4621* 369.3649 368.5058* 365.9701* 364.8411 362.9057* 367.2848 362.2772* 359.0263 358.2217

365.7640 363.0265 370.3828 369.4986 366.2587* 364.6274 361.9659 367.7682* 361.2918 359.5136 358.6740

365.7472 363.0128 370.3659 369.4867 366.2500 364.6382 361.9718 367.7742 361.3009 359.5059 358.6687

365.7276 362.9923 370.3456 369.4641 366.2292 364.6469 361.9811 367.7828 361.3075 359.4971 358.6594 359.7620

365.7025 362.9677 370.3203 369.4392 366.2055 364.6573 361.9863 367.7947 361.3215 359.4852 358.6485 359.7400

365.6731 362.9379 370.2918 369.4096 366.1785 364.6666 361.9951 367.8087 361.3357 359.4713 358.6367* 359.7115

365.6390 362.9057* 370.2575 369.3761 366.1531 364.6783 362.0021 367.8253 361.3519 359.4549 358.6217* 359.6753

365.9463 362.4549 371.2505

365.9291 362.4381 371.2341

365.9081 362.4166 371.2135

365.8840 362.3917 371.1888

365.8556 362.3635 371.1599

365.8233 362.3306 371.1282

365.5674 365.5883 369.4977 368.6376 366.1045 364.7891

12365.3493 364.1209 368.5885 367.7515 365.8929

F ¼ J þ 3=2

Q. Ran et al. / Journal of Molecular Spectroscopy 220 (2003) 87–106

Assignment

95

96

Appendix A (continued) Assignment

N ¼6

F ¼ J
7=2

R2 P2 T R42 R P42 P Q12 R3 P3 R Q43 P Q23 R4

4.5 4.5 4.5 4.5 4.5 3.5 3.5 3.5 3.5 2.5

R1 P1 T R31 R2 P2 T R42 R P42 P Q12 R3 P3 R Q43 P Q23 N P13 P R13 R4 P Q34 N P24 N Q14

6.5 6.5 6.5 5.5 5.5 5.5 5.5 5.5 4.5 4.5 4.5 4.5 4.5 4.5 3.5 3.5 3.5 3.5

12366.1403* 361.8893 372.1301

R1 P1 T R31 R2 P2 T R42 R P42 P Q12 R3 P3 R Q43 P Q23 N P13 P R13 R4 P4 P Q34 P R24

7.5 7.5 7.5 6.5 6.5 6.5 6.5 6.5 5.5 5.5 5.5 5.5 5.5 5.5 4.5 4.5 4.5 4.5

12366.2896 361.2818 372.9612

F ¼ J
5=2

12368.3319

F ¼ J
3=2

F ¼ J
1=2

F ¼ J þ 1=2

F ¼ J þ 3=2

F ¼ J þ 5=2

F ¼ J þ 7=2

12364.4957

12364.5006 361.0724 368.3411 363.5114 360.4366* 359.8567

360.4778

12364.5090 361.0768* 368.3475 363.5173 360.4466* 359.8496* 356.4929 358.9894 356.5632 360.4670

12364.5172 361.0818* 368.3560 363.5285* 360.4574* 359.8447 356.4789 358.9841 356.5487 360.4574

12364.5241 361.0876* 368.3669 363.5355 360.4670* 359.8375 356.4759 358.9787 356.5402 360.4466

12364.5335 361.1009 368.3788 363.5501 360.4778* 359.8305 356.4656 358.9719 356.5250 360.4366 365.9914 361.7393* 371.9811 364.3843 360.2088 368.9491 363.3604 359.6201 360.1615 356.0541 359.2790* 356.1272 352.8093 355.5461* 361.0768* 357.9070 355.2765 354.6508* 366.1403* 361.1297 372.8112 364.2570 359.3256* 369.5331 363.1878 358.7771 360.4417* 355.5711* 359.5475* 355.7041 351.6401* 355.1333* 361.7251 356.8967 357.7643 357.8841*

368.3356 363.5039 360.4300

359.0002

358.9950

366.1286 361.8775 372.1173

366.1132 361.8621 372.1021

366.0957 361.8443 372.0844 364.3679

366.0742 361.8225 372.0639 364.3722

368.9124

368.9168

359.5839

359.5873

368.9216 363.3255 359.5927

368.9271 363.3340 359.5978

366.0490 361.7994 372.0391 364.3750 360.1926 368.9321 363.3451 359.6052

355.3250

355.3178

355.3085

355.2966 354.6469*

366.0217 361.7712 372.0121 364.3792 360.1991 368.9402 363.3509 359.6126 360.1656 356.0450 359.2847 356.1379 352.8044 355.5360* 361.0818* 357.9002 355.2868 354.6508*

356.1560

356.1476

366.2729 361.2693 372.9489

366.2587 361.2538 372.9336

366.2404 361.2346 372.9145

366.2215 361.2126 372.8919

359.3256*

359.3256* 369.5122*

359.3256* 369.5171*

359.3256* 369.5202 363.1674

360.4417* 355.5711* 359.5475*

360.4417* 355.5711* 359.5475*

360.4417* 355.5711* 359.5475*

360.4417* 355.5711* 359.5475*

360.4417* 355.5711* 359.5475*

366.1970 361.1875 372.8690 364.2531 359.3256* 369.5218 363.1736 358.7669 360.4417* 355.5711* 359.5475*

366.1709 361.1602 372.8413 364.2549 359.3256* 369.5261 363.1779 358.7724 360.4417* 355.5711* 359.5475*

351.6401* 355.1333*

351.6401* 355.1333*

351.6401* 355.1333*

351.6401* 355.1333*

351.6401* 355.1333*

351.6401* 355.1333* 361.7393*

357.8841*

357.8841*

357.8841*

357.8841*

351.6401* 355.1333* 361.7337 356.9035 357.7562 357.8841*

361.0876*

Q. Ran et al. / Journal of Molecular Spectroscopy 220 (2003) 87–106

N ¼5

J 00

Appendix A (continued) F ¼ J
7=2

F ¼ J
5=2

F ¼ J
3=2

F ¼ J
1=2

F ¼ J þ 1=2

F ¼ J þ 3=2

F ¼ J þ 5=2

F ¼ J þ 7=2

P24 Q14

4.5 4.5

12354.4586*

12354.4586*

12354.4586*

12354.4586*

12354.4586*

12354.4586* 353.8210*

12354.4586* 353.8284

12354.4586* 353.8339

R1 P1 T R31 R2 P2 T R42 R P42 P Q12 R3 P3 R Q43 P Q23 N P13 P R13 R4 P4 P Q34 P R24 N P24 N Q14

8.5 8.5 8.5 7.5 7.5 7.5 7.5 7.5 6.5 6.5 6.5 6.5 6.5 6.5 5.5 5.5 5.5 5.5 5.5 5.5

12366.4184 360.6532 373.7699 364.1444* 358.4644*

366.4066* 360.6389 373.7558 364.1444* 358.4644*

366.3878 360.6220 373.7396 364.1444* 358.4644*

366.3709 360.6026 373.7200 364.1444* 358.4644*

366.3483 360.5805 373.6984 364.1444* 358.4644*

366.3245 360.5565 373.6750 364.1444* 358.4644*

363.0128

363.0162

366.2973 360.5299 373.6482 364.1444* 358.4644* 370.1279 363.0210 357.9373 360.6769* 355.0528* 359.7620* 355.2056 350.4341* 354.7103* 362.2697 356.6752 357.5558 357.6990 353.5232 352.9369

366.2674 360.5004 373.6203 364.1444* 358.4644* 370.1280 363.0265 357.9490 360.6769* 355.0528* 359.7679 355.2104 350.4341* 354.7103* 362.2772 356.6821 357.5642 357.7079 353.5300 352.9445

R1 P1 T R31 R2 P2 T R42 R P42 R3 P3 R Q43 P Q23 N P13 P R13 R4 P4 P Q34 P R24 N P24 N Q14

9.5 9.5 9.5 8.5 8.5 8.5 8.5 7.5 7.5 7.5 7.5 7.5 7.5 6.5 6.5 6.5 6.5 6.5 6.5

12366.5242 360.0042 374.5531

366.3772 359.8496 374.4007 364.0453 357.6095 370.7349* 362.8757* 360.8816 354.5014 359.9592 354.6827* 349.1908 354.2007* 362.7309 356.3915 357.2890 357.4658 352.5331 351.9810

R1 P1 T R31 R2

10.5 10.5 10.5 9.5

366.4649 359.1774 375.1590 363.9493

N N

N ¼7

N ¼8

N ¼9

360.6769*

360.6769* 355.0528*

360.6769* 355.0528*

360.6769* 355.0528*

360.6769* 355.0528*

350.4341*

350.4341*

357.5191

362.2424* 356.6540 357.5296

362.2499 356.6588 357.5379

350.4341* 354.7103* 362.2581 356.6637 357.5447

350.4341* 354.7103* 362.2636 356.6692 357.5503

352.9064

352.9117

352.9165

352.9224

353.5170* 352.9293

366.5177 359.9888 374.5389

366.4960* 359.9710 374.5218

366.4796 359.9509 374.5019

366.4578 359.9296 374.4804

370.7349* 362.8757*

370.7349* 362.8757*

370.7349* 362.8757*

370.7349* 362.8757* 360.8705

366.4333 359.9049 374.4577 364.0368 357.6018 370.7349* 362.8757* 360.8745

354.6827*

354.6827*

354.6827*

354.6827*

362.6871 356.3407* 357.2248

362.6920 356.3472 357.2368 357.4402

362.7001 356.3553 357.2461 357.4468

351.9222

351.9308

351.9341

351.9456

362.7056 356.3629* 357.2576 357.4501 352.5008 351.9521

354.2007* 362.7131 356.3715 357.2690 357.4576 352.5091 351.9610

366.4066* 359.8784 374.4300 364.0417 357.6061 370.7349* 362.8757* 360.8778 354.4958 359.9509* 354.6827* 349.1979 354.2007* 362.7223 356.3816* 357.2795 357.4626 352.5203 351.9717

12366.6197 359.3256* 375.3133

366.6087 359.3163 375.2975

366.6017 359.2982 375.2802

366.5782 359.2790 375.2595

366.5596 359.2560 375.2380 363.9342

366.5334 359.2319 375.2146 363.9397

366.4960* 359.2062 375.1879 363.9448

370.7349* 362.8757*

360.6769*

Q. Ran et al. / Journal of Molecular Spectroscopy 220 (2003) 87–106

J 00

Assignment

97

98

Appendix A (continued) Assignment

N ¼ 11

F ¼ J
7=2

P2 T R42 R P42 R3 P3 R Q43 P Q23 N P13 P R13 R4 P4 P Q34 P R24 N P24

9.5 9.5 9.5 8.5 8.5 8.5 8.5 8.5 8.5 7.5 7.5 7.5 7.5 7.5

R1 P1 T R31 R2 P2 T R42 R P42 R3 P3 P Q23 N P13 P R13 R4 P4 P Q34 P R24 N P24

11.5 11.5 11.5 10.5 10.5 10.5 10.5 9.5 9.5 9.5 9.5 9.5 8.5 8.5 8.5 8.5 8.5

12366.6850 358.6367 376.0454

R1 P1 T R31 R2 P2 T R42 R P42 P3 P Q23 N P13 R4 P4 P Q34 P R24 N P24

12.5 12.5 12.5 11.5 11.5 11.5 11.5 10.5 10.5 10.5 9.5 9.5 9.5 9.5 9.5

12366.7582 357.9241 376.7524

F ¼ J
5=2

F ¼ J
3=2

F ¼ J
1=2

F ¼ J þ 1=2

F ¼ J þ 3=2

F ¼ J þ 5=2

F ¼ J þ 7=2

12371.3500*

12371.3500*

12356.7561 371.3500*

361.0206

361.0243

361.0301

12356.7449 371.3500* 362.7414 361.0339

354.1154*

354.1154*

354.1154*

354.1154*

354.1154* 347.9189

363.0745 355.9668* 356.8617 357.1117 351.4147

363.0808 355.9758* 356.8670 357.1195 351.4212

363.0910 355.9837* 356.8791 357.1284* 351.4276

363.1000* 355.9942* 356.8967* 357.1395 351.4361

363.1123 356.0060* 356.9125 357.1489* 351.4448

12356.7391 371.3500* 362.7358 361.0375 353.8958 360.1049 354.1154* 347.9151 353.6893 363.1248 356.0174 356.9301 357.1574 351.4547

12356.7344 371.3500* 362.7337 361.0425 353.9102 360.0948 354.1154* 347.9089 353.6795 363.1359 356.0305 356.9429 357.1661 351.4635

366.6702 358.6217 376.0292

366.6563* 358.6045 376.0104

366.6378 358.5854 375.9912

366.6087* 358.5624 375.9693 363.8257 355.8871

366.5859 358.5388 375.9454 363.8350 355.8917

361.1463

366.5661 358.5127 375.9195 363.8431 355.8985 371.9694 362.5992 361.1602* 353.2714 353.5170* 346.5961 353.1314* 363.4621* 355.5852 356.4928* 356.7229 350.3117

366.5442 358.4844 375.8917 363.8504 355.9054 371.9629 362.5885 361.1670 353.2818 353.5170* 346.5860 353.1230 363.4776 355.6006* 356.5135 356.7344 350.3240

366.6320 357.7962 376.6251 363.7375 355.0464 372.5780 362.4549* 352.6056 352.8746* 345.2515 363.7537* 355.0905 355.9942* 356.2911* 349.1045

366.6051 357.7643 376.5978 363.7537 355.0528* 372.5711 362.4381* 352.6144 352.8746* 345.2446 363.7860 355.1075 356.0060* 356.3064 349.1182

12361.0138

12354.1154*

355.9606 356.8446

355.8825

353.5170*

355.5171 356.4381 350.2574

355.0170* 355.9411 356.2150 349.0453

353.5170*

353.5170*

353.5170*

353.5170*

361.1522 353.2619 353.5170*

363.3983 355.5262 356.4471 356.6821* 350.2618

363.4083 355.5360 356.4561 356.6892 350.2713

363.4196 355.5461 356.4656 356.6965 350.2793

353.1428 363.4335 355.5576 356.4759 356.7036 350.2885

353.1373 363.4477 355.5711* 356.4789* 356.7130 350.2995

366.7417 357.9070 376.7356

366.7241 357.8841* 376.7158

366.7018 357.8675 376.6960

354.9912

355.0054

355.0170

366.6811 357.8449 376.6750 363.7153 355.0225

366.6563 357.8219 376.6506 363.7277 355.0339 372.5831

363.6685 355.0225* 355.9453 356.2283 349.0494

352.8746* 345.2744 363.6786 355.0339* 355.9548 356.2429 349.0574

352.5879 352.8746* 345.2672 363.6959 355.0464* 355.9668* 356.2550 349.0674

352.5935 352.8746* 345.2617 363.7107 355.0578 355.9758* 356.2650* 349.0765

352.5998 352.8746* 345.2552 363.7277* 355.0741 355.9837* 356.2788 349.0915

Q. Ran et al. / Journal of Molecular Spectroscopy 220 (2003) 87–106

N ¼ 10

J 00

Appendix A (continued) Assignment N ¼ 12

F ¼ J
7=2

F ¼ J
5=2

F ¼ J
3=2

F ¼ J
1=2

F ¼ J þ 1=2

F ¼ J þ 3=2

F ¼ J þ 5=2

F ¼ J þ 7=2

12357.1696 377.4151

12357.1489 377.3957 363.6022 354.1443

12357.1284 377.3745 363.6096 354.1520

351.8852

351.8907

12357.1056 377.3530 363.6147 354.1588 373.1856 351.8962

12357.0822 377.3278 363.6234 354.1664 373.1817 351.9019

363.8764 354.4630 355.3963 355.7153 347.7729

363.8944 354.4748 355.4059 355.7257 347.7845

363.9126 354.4894 355.4152 355.7375 347.7957

363.9283 354.5057 355.4313 355.7504 347.8089

363.9447 354.5200 355.4471 355.7650 347.8232

12357.0522 377.3021 363.6311 354.1766 373.1717 351.9081 352.2004 363.9624 354.5374 355.4638 355.7796 347.8380

12357.0272 377.2760 363.6399 354.1851 373.1645 351.9162 352.2037 363.9791 354.5569 355.4803* 355.7956 347.8551*

356.4022

356.3816*

356.3629*

351.1515

356.3407* 353.2619 373.7770 351.1559

356.3175 353.2714 373.7623 351.1622 351.4882 353.9102* 354.8640 355.1959 346.5007

356.2911 353.2818 373.7558 351.1735 351.4926 353.9293 354.8839 355.2107* 346.5191

356.2650 353.2919 373.7477 351.1786 351.4975 353.9481 354.9051 355.2290 346.5321

355.5077 352.3712 374.3366 350.4047 350.7600 353.2818* 354.6280 345.1440

355.4806 352.3629 374.3285 350.4131 350.7636 353.3034 354.6469 345.1625 354.6752 351.4147 349.6078 349.9965 352.5879

P1 T R31 R2 P2 T R42 P3 P Q23 R4 P4 P Q34 P R24 N P24

13.5 13.5 12.5 12.5 12.5 11.5 11.5 10.5 10.5 10.5 10.5 10.5

12357.1851 377.4313

P1 P2 T R42 P3 P Q23 P4 P Q34 P R24 N P24

14.5 13.5 13.5 12.5 12.5 11.5 11.5 11.5 11.5

12356.4204

P1 P2 T R42 P3 P Q23 P4 P R24 N P24

15.5 14.5 14.5 13.5 13.5 12.5 12.5 12.5

P1 P2 P3 P Q23 P4

363.8614 354.4526 355.3849 355.7041* 347.7646

353.8475* 354.7978 355.1411 346.4490

353.8617 354.8128 355.1533 346.4592

353.8719 354.8302* 355.1667 346.4730

353.8919 354.8470 355.1810 346.4860

12355.6361 352.4108

355.6187 352.4052

355.6006 352.3984 374.3628

355.5711* 352.3946 374.3568

355.5576 352.3871 374.3507

353.1708 354.5323 345.0554

353.1844 354.5454 345.0693

353.1992 354.5569* 345.0863

353.2158 354.5777 345.0955

353.2339 354.5941 345.1102

355.5360 352.3800 374.3425 350.3913 350.7545 353.2518 354.6108 345.1273

16.5 15.5 14.5 14.5 13.5

12354.8302*

354.8128* 351.4635

354.7918 351.4547

354.7709 351.4448

354.7482 351.4361

354.7245 351.4276

352.4636

352.4762

352.4900

352.5091*

349.9804 352.5248*

349.9831 352.5446

354.6996 351.4212 349.5988 349.9908 352.5643

P1 P2 P3 P4

17.5 16.5 15.5 14.5

12354.0001

353.9818 350.5687

351.7081

351.7232

353.9623 350.5569 348.7301 351.7399

353.9429 350.5485 348.7357 351.7576

353.9186 350.5416 348.7438 351.7764

353.8919 350.5334 348.7512 351.7954

353.8719 350.5233 348.7590 351.8174

353.8475 350.5124 348.7650 351.8381

N ¼ 17

P1 P2 P3 P4

18.5 17.5 16.5 15.5

12353.1497

350.9136

353.1314 349.6135 347.8551 350.9262

353.1128 349.6078 347.8634 350.9499

353.0917 349.5988 347.8683 350.9640

353.0697 349.5930 347.8742 350.9827

353.0464 349.5818 347.8816 351.0049

353.0214 349.5722 347.8886 351.0262

352.9950 349.5600 347.8964 351.0491

N ¼ 18

P1

19.5

12352.2790

352.2594

352.2417

352.2202

352.2004

352.1756

352.1504

352.1223

N ¼ 14

N ¼ 15

N ¼ 16

353.8284 354.7847 355.1333* 346.4371

Q. Ran et al. / Journal of Molecular Spectroscopy 220 (2003) 87–106

N ¼ 13

J 00

99

Assignment

J 00

100

Appendix A (continued) F ¼ J
7=2

F ¼ J
5=2

F ¼ J
3=2

F ¼ J
1=2

F ¼ J þ 1=2

F ¼ J þ 3=2

F ¼ J þ 5=2

F ¼ J þ 7=2

12348.6120 346.9587 350.1120

12348.6038 346.9632 350.1311

12348.5924 346.9693 350.1503

12348.5810 346.9758 350.1722

12348.5683 346.9839 350.1940

12348.5557 346.9916 350.2183

351.2559 347.5963 346.0406 349.3257

351.2351 347.5837 346.0562 349.3492

18.5 17.5 16.5

12348.6303 350.0782

12348.6221 346.9543 350.0939

P1 P2 P3 P4

20.5 19.5 18.5 17.5

12351.3848 347.6468

351.3669 347.6388

351.3474 347.6324

351.3257 347.6241

351.3040 347.6169

349.2100

349.2245

349.2417

349.2615

349.2820

351.2800 347.6048 346.0305 349.3053

N ¼ 20

P4

18.5

12348.2940

348.3174

348.3371

348.3528

348.3705

348.3948

348.4212

348.4400

N ¼ 21

P4

19.5

12347.3521

347.3703

347.3884

347.4084

347.4287

347.4496

347.4731

347.4963

N ¼ 19

Values in cm
1 . An asterisk (*) indicates a blended line.

Q. Ran et al. / Journal of Molecular Spectroscopy 220 (2003) 87–106

P2 P3 P4

Appendix B Rotational lines assigned in the (0,1) band of the C 4 R

X 4 R
transition of VS

N ¼
1 R1 R Q21

0.5 0.5

N ¼0

R1 P1 T R31 R P31 R2

1.5 1.5 1.5 1.5 0.5

N ¼1

R1 P1 T R31 T Q41 R P31 R2 P Q12

2.5 2.5 2.5 2.5 2.5 1.5 1.5

N ¼2

R1 P1 T R31 T Q41 R P31 R2 P2 T R42 P Q12 R3 R Q43 P R13

3.5 3.5 3.5 3.5 3.5 2.5 2.5 2.5 2.5 1.5 1.5 1.5

R1 P1 T R31 T Q41 R P31 R2 P2 T R42 P Q12 R Q32 R3 R Q43 N P13 P R13 R4

4.5 4.5 4.5 4.5 4.5 3.5 3.5 3.5 3.5 3.5 2.5 2.5 2.5 2.5 1.5

11823.6834 820.9478 828.3116 827.3936

N ¼3

F ¼ J
7=2

F ¼ J
5=2

F ¼ J
3=2

F ¼ J
1=2

11825.5781

F ¼ J þ 1=2

11823.0156 822.5580* 825.5409 823.6350 23.0085

F ¼ J þ 3=2

F ¼ J þ 5=2

F ¼ J þ 7=2

11822.7675 823.4219

11822.6669 823.3179

11822.9885 822.5165* 825.4982 823.6166 823.0206

822.9499 822.4775* 825.4409 823.5896 823.0641

822.8953 822.4419* 825.3947 823.5644 823.0740

11823.2573

11823.2515 822.0054* 826.4962 825.6422 823.8365*

823.2396 821.9967* 826.4804 825.6343 823.8227

823.2216 821.9697 826.4624 825.6154 823.8092 822.8522 820.9988

823.1956 821.9373 826.4329 825.5969 823.7919* 822.8681 821.0087

823.1623 821.8956 826.4000* 825.5625 823.7760 822.8839 821.0169

823.1204 821.8632 826.3565 825.5210 823.7453 822.9086 821.0350*

11823.4704

823.4610

827.4346 826.5195 824.0000

827.4278 826.5067 823.9920

823.4528 821.4833 827.4057 826.4962* 823.9823 822.6865 820.7653

820.0639

820.0710

823.4469 821.4666 827.3817 826.4804* 823.9668* 822.6964 820.7738 825.1228 820.0831

823.4219 821.4480 827.3593* 826.4624* 823.9575 822.7052 820.7807 825.1379 820.0970 816.9664 816.1603 814.4312*

823.4016 821.4241 827.3308 826.4409 823.9392* 822.7178 820.7882 825.1512 820.1158 816.9409 816.1353 814.4083*

823.3715 821.3939 827.3004 826.4243 823.9225 822.7282 820.8002 825.1691 820.1325* 816.9083 816.1036 814.3885*

823.3355 821.3576 827.2618 826.4000* 823.8997 822.7455 820.8130 825.1909 820.1470 816.8699 816.0668 814.3603

823.6754 820.9410 828.3044 827.3870

823.6647 820.9292 828.2845 827.3725

823.6478 820.9121 828.2661 827.3593*

822.5448

822.5487

822.5525 819.8695 825.6880

823.6273 820.8924 828.2467 827.3443 824.1511* 822.5580* 819.8775 825.6964 819.2164* 825.4900 817.3483 816.5240

823.6024 820.8680 828.2221 827.3239 824.1333 822.5676 819.8866 825.7070 819.2227* 825.4775 817.3360 816.5092

814.1013 817.6072

814.0908 817.5881

823.5739 820.8376* 828.1924 827.2946 824.1061 822.5766 819.8922 825.7211 819.2427 825.4645 817.3227 816.4958 812.9085* 814.0812 817.5584

823.5405 820.8050 828.1600 827.2707 824.0766 822.5872 819.9092 825.7387 819.2595 825.4419 817.3059 816.4835 812.9085* 814.0675 817.5224

825.6790 825.5346

825.5304

825.5165 817.3626

825.5035 817.3585 816.5321

814.1356

814.1210

814.1102

101

J 00

Q. Ran et al. / Journal of Molecular Spectroscopy 220 (2003) 87–106

Assignment

102

Appendix B (continued) J 00

F ¼ J
7=2

F ¼ J
5=2

F ¼ J
3=2

F ¼ J
1=2

F ¼ J þ 1=2

F ¼ J þ 3=2

F ¼ J þ 5=2

F ¼ J þ 7=2

N ¼4

R1 P1 T R31 R P31 R2 P2 T R42 R P42 P Q12 R Q32 R3 R Q43 N P13 P R13 R4 N Q14

5.5 5.5 5.5 5.5 4.5 4.5 4.5 4.5 4.5 4.5 3.5 3.5 3.5 3.5 2.5 2.5

11823.8778 820.3849 829.1994 824.3214

11823.8669 820.3743 829.1757 824.3132*

11823.8532 820.3620 829.1603 824.3064

11823.8365 820.3438 829.1436 824.2917

11823.8160 820.3244 829.1247 824.2840 822.4149

11823.7919 820.2998 829.0997 824.2741 822.4238 819.0025 826.2773 821.4346 818.3745 822.2744 817.7044 816.8447 812.8290*

11823.7638 820.2716 829.0707 824.2538 822.4338 819.0085 826.2875 821.4241* 818.3830 822.2563 817.6971 816.8369 812.8319* 813.7794 818.2995 813.2414*

11823.7318 820.2399 829.0395 824.2297 822.4419* 819.0149 826.2996 821.4106 818.3944 822.2374 817.6892 816.8291 812.8388* 813.7675 818.2859 813.2414*

R1 P1 T R31 R P31 R2 P2 T R42 R P42 P Q12 R Q32 R3 P3 R Q43 P Q23 N P13 P R13 R4 P4 P Q34 N P24 N Q14

6.5 6.5 6.5 6.5 5.5 5.5 5.5 5.5 5.5 5.5 4.5 4.5 4.5 4.5 4.5 4.5 3.5 3.5 3.5 3.5 3.5

11824.0552 819.8024 830.0609 824.4575

823.9392 819.6842 829.9281 824.3798 822.3050 818.1319 826.8692 821.2777 817.5478 822.1288 818.0338 813.9279* 817.1511* 814.0107 810.6791 813.4110 818.9893* 814.9161 815.7562* 813.1731 812.5581*

823.9078 819.6532 829.8984 824.3490 822.3122* 818.1365 826.8775 821.2564 817.5585* 822.1054 818.0314 813.9208* 817.1511* 814.0151 810.6831 813.4207 818.9893* 814.9202 815.7562* 813.1609 812.5581*

R1 P1 T R31 R2 P2 T R42 R P42 P Q12 R Q32

7.5 7.5 7.5 6.5 6.5 6.5 6.5 6.5 6.5

11824.2051 819.1996 830.8875

824.0997 819.0857 830.7693 822.1932* 817.2638* 827.4646 821.1127 816.7064 821.9967*

824.0695 819.0559 830.7402 822.1932* 817.2638* 827.4708 821.1042 816.7132 821.9840

N ¼5

N ¼6

826.2544

822.3684

822.2217

822.3557

824.0435 819.7894 830.0539 824.4547*

817.5118 822.2138

826.2628 821.4530 818.3619 822.3122* 817.7160 816.8572

826.2705 821.4452 818.3698 822.2961* 817.7088 816.8517

818.3324

818.3306* 813.2414*

818.3108 813.2414*

824.0304 819.7735 830.0341 824.4420

824.0129 819.7568 830.0037 824.4316

823.9920 819.7354 829.9816 824.4201

826.8426

826.8486

818.1237 826.8544

817.5186 822.2078

817.5255 822.1932*

823.9668 819.7118 829.9638 824.4001 822.2961* 818.1278 826.8622 821.2861 817.5397 822.1577 818.0386

818.3580 822.3319 817.7186 816.8643

817.5325 822.1771 818.0417

817.1617 814.0059

815.7562*

822.0925*

818.9893*

818.9893*

818.9893*

818.9893*

815.7562*

815.7562* 813.1962

815.7562* 813.1912

815.7562* 813.1860 812.5581*

815.7562* 813.1819 812.5581*

824.2016 819.1923 830.8753

824.1905 819.1748 830.8598 822.1932*

824.1715 819.1570 830.8415 822.1932*

824.1511 819.1366 830.8197 822.1932* 817.2638* 827.4510

824.1278 819.1116* 830.7964 822.1932* 817.2638* 827.4581 821.1246

822.0823

822.0668

822.0488

822.0352

822.0160

Q. Ran et al. / Journal of Molecular Spectroscopy 220 (2003) 87–106

Assignment

Appendix B (continued) F ¼ J
5=2

F ¼ J
3=2

F ¼ J
1=2

F ¼ J þ 1=2

F ¼ J þ 3=2

F ¼ J þ 5=2

F ¼ J þ 7=2

R3 P3 R Q43 P Q23 N P13 P R13 R4 P4 P Q34 P R24 N P24 N Q14

5.5 5.5 5.5 5.5 5.5 5.5 4.5 4.5 4.5 4.5 4.5 4.5

11818.3206* 813.4550* 817.4289*

11818.3206* 813.4550* 817.4289*

11818.3206* 813.4550* 817.4289*

11818.3206* 813.4550* 817.4289*

11818.3206* 813.4550* 817.4289*

11818.3206* 813.4550* 817.4289*

809.5253* 813.0192*

809.5253* 813.0192*

809.5253* 813.0192*

809.5253* 813.0192*

809.5253* 813.0192* 819.5961

809.5253* 813.0192* 819.5979

812.3354*

812.3354*

815.7479* 812.3354*

815.7479* 812.3354* 811.6958

11818.3206* 813.4550* 817.4289* 813.5733* 809.5253* 813.0192* 819.6002 814.7699 815.6298 815.7479* 812.3354* 811.7017

11818.3206* 813.4550* 817.4289* 813.5857 809.5253* 813.0192* 819.6033 814.7731 815.6345 815.7479* 812.3354* 811.7052

N ¼7

R1 P1 R2 P2 T R42 R P42 R3 P3 R Q43 P Q23 N P13 P R13 R4 P4 P Q34 P R24 N P24 N Q14

8.5 8.5 7.5 7.5 7.5 7.5 6.5 6.5 6.5 6.5 6.5 6.5 5.5 5.5 5.5 5.5 5.5 5.5

11824.3408 818.5893 822.0925* 816.4110*

824.3323 818.5749 822.0925* 816.4110*

824.3214* 818.5596 822.0925* 816.4110*

824.3064 818.5399 822.0925* 816.4110*

824.2917 818.5185 822.0925* 816.4110*

812.9517*

812.9517*

812.9517* 817.6654*

818.5705* 812.9517* 817.6654*

818.5705* 812.9517* 817.6654*

808.3333* 812.5848*

808.3333* 812.5848* 820.1325 814.5562 815.4254 815.5834

824.2683 818.4949 822.0925* 816.4110* 828.0701 820.9698* 818.5705* 812.9517* 817.6654* 813.1093* 808.3333* 812.5848* 820.1407 814.5605 815.4343 815.5877 811.4079 810.8662

824.2419 818.4681 822.0925* 816.4110* 828.0747 820.9698* 818.5705* 812.9517* 817.6654* 813.1093* 808.3333* 812.5848* 820.1531 814.5664 815.4416 815.5925 811.4132 810.8770

824.2115 818.4390 822.0925* 816.4110* 828.0817 820.9698* 818.5705* 812.9517* 817.6654* 813.1093* 808.3333* 812.5848* 820.1627 814.5744 815.4513 815.5956 811.4206 810.8860

N ¼8

R1 P1 R2 P2 T R42 R P42 R3 P3 R Q43 P Q23 N P13 P R13 R4 P4 P Q34 P R24

9.5 9.5 8.5 8.5 8.5 8.5 7.5 7.5 7.5 7.5 7.5 7.5 6.5 6.5 6.5 6.5

11824.4607 817.9584

812.4146

824.3928 817.8621* 821.9967* 815.5691 828.6991* 820.8376* 818.7874 812.4134

824.3642 817.8352 822.0010 815.5660 828.6991* 820.8376* 818.7849 812.4111 817.8621* 812.5968* 807.1035

824.3358 817.8062 822.0054 815.5640 828.6991* 820.8376* 818.7824 812.4094 817.8700 812.5968* 807.1089 812.1151 820.6479 814.2978 815.1972 815.3716

814.5384

814.5423

814.5461

814.5504 815.4179

810.8554

828.6991* 820.8376*

814.2121

824.4547 817.9445

824.4470 817.9270

824.4391 817.9073

824.4158 817.8855

828.6991* 820.8376*

828.6991* 820.8376*

828.6991* 820.8376*

828.6991* 820.8376*

814.2198

812.5968*

812.5968*

812.5968*

812.5968*

820.6057 814.2299 815.1426 815.3340

820.6122 814.2407 815.1516 815.3379

820.6201 814.2528 815.1662 815.3448

820.6279 814.2649 815.1748 815.3530

820.6382 814.2792 815.1827* 815.3638

103

F ¼ J
7=2

Q. Ran et al. / Journal of Molecular Spectroscopy 220 (2003) 87–106

J 00

Assignment

104

Appendix B (continued) Assignment N

J 00

F ¼ J
7=2

6.5 6.5

R1 P1 R2 P2 T R42 R P42 R3 P3 R Q43 P Q23 N P13 R4 P4 P Q34 P R24 N P24

10.5 10.5 9.5 9.5 9.5 9.5 8.5 8.5 8.5 8.5 8.5 7.5 7.5 7.5 7.5 7.5

11824.5686 817.3001

N ¼ 10 R1 P1 R2 P2 T R42 R P42 R3 P3 P Q23 R4 P4 P Q34 P R24 N P24

11.5 11.5 10.5 10.5 10.5 10.5 9.5 9.5 9.5 8.5 8.5 8.5 8.5 8.5

11824.6390 816.6282

813.4717 814.3885 814.6414 808.2075

N ¼ 11 R1 P1 R2 T R42 R P42 P3 P Q23 P4 P R24 N P24

12.5 12.5 11.5 11.5 11.5 10.5 10.5 9.5 9.5 9.5

11824.7129 815.9351

N ¼ 12 R1 P1 R2 P3

13.5 13.5 12.5 11.5

11824.7494 815.2173

N ¼9

11824.5633 817.2887

F ¼ J
3=2

F ¼ J
1=2

F ¼ J þ 1=2

F ¼ J þ 3=2

F ¼ J þ 5=2

F ¼ J þ 7=2

11810.4152

11810.4222

11810.4284

11810.4340

11810.4445 809.8324

11810.4560 809.8490

824.5521 817.2706

824.5408 817.2514

824.5190 817.2288

829.3277* 820.7123*

829.3277* 820.7123*

829.3277* 820.7123*

812.0486*

812.0486* 805.8394*

812.0486* 805.8525

813.8753*

813.8812*

815.0195 809.3400

815.0238 809.3438

820.9988* 813.8890 814.8201 815.0306 809.3508

824.6334* 816.6120

824.6236 816.5941

812.0486*

811.8431 818.0314* 812.0486*

824.4974 817.2062 821.9117 814.7376 829.3277* 820.7123* 818.9699 811.8388 818.0338* 812.0486*

824.4719 817.1795 821.9173 814.7283 829.3277* 820.7123* 818.9661 811.8319 818.0386* 812.048

824.4420 817.1511* 821.9250 814.7188 829.3277* 820.7123* 818.9574 811.8290 818.0417* 812.0486*

821.0087 813.8956* 814.8304 815.0393 809.3581

821.0169 813.9113* 814.8425 815.0467 809.3661

821.0275 813.9279* 814.8529 815.0541 809.3738

821.0495 813.9432 814.8674 815.0627* 809.3827

821.0629 813.9569 814.8770 815.0707 809.3924

824.6074 816.5738

824.5951 816.5524 821.8256 813.9208

824.5802* 816.5278 821.8328 813.9113*

824.5272 816.4735 821.8467 813.8787 829.9573 820.5911 819.2061 811.2208* 811.4656* 821.3812 813.5513 814.4715 814.7095 808.2732

813.4778 814.4018 814.6474 808.2130

811.4656* 821.3290 813.4870 814.4083 814.6556 808.2231

811.4656* 821.3370 813.4996 814.4176 814.6652 808.2322

811.4656* 821.3466 813.5095 814.4312 814.6746 808.2393

811.4656* 821.3612 813.5218 814.4441* 814.6852 808.2510

824.5558 816.5017 821.8383 813.8956* 829.9638* 820.5844 819.2164 811.2311* 811.4656* 821.3701 813.5363 814.4577 814.6948 808.2611

824.7034 815.9172

824.6939* 815.8963

824.6806 815.8767 821.7302

824.6593 815.8566 821.7350

810.5916 810.8500* 813.0192* 814.2299* 807.0542

824.6334* 815.8325 821.7434 830.5936 820.4511 810.5863 810.8500* 813.0367 814.2528* 807.0658

824.6049 815.8109 821.7528 830.5886 820.4564 810.5800 810.8500* 813.0509 814.2686 807.0802

824.5802 815.7828 821.7593 830.5847 820.4649 810.5699 810.8500* 813.0671 814.2888 807.0936

824.6939* 815.1397 821.6257 809.9173

824.6684 815.1154 821.6354 809.9074

824.6488 815.0897 821.6498 809.8967

824.6283 815.0627* 821.6650 809.8854

813.9279

820.5788 819.2227

814.1854 807.0154

812.9887 814.2014 807.0229

812.9986 814.2121* 807.0330

813.0072 814.2198* 807.0436

824.7389 815.2007*

824.7298 815.1827*

824.7175 815.1611

Q. Ran et al. / Journal of Molecular Spectroscopy 220 (2003) 87–106

P24 Q14

N

F ¼ J
5=2

Appendix B (continued) Assignment P

J 00

F ¼ J
7=2

F ¼ J
5=2

F ¼ J
3=2

F ¼ J
1=2

F ¼ J þ 1=2

F ¼ J þ 3=2

F ¼ J þ 5=2

F ¼ J þ 7=2

11805.7656

11805.7751

11812.4519 805.7849

11812.4640 805.7984

11812.4777 805.8104

11810.2102 812.4907 805.8245

11809.2064 812.5053 805.8394*

11810.2025 812.5197 805.8525*

814.4623

11.5 10.5 10.5

N ¼ 13 P1 R2 P3 P Q23 P4

14.5 13.5 12.5 12.5 11.5

11814.4798

811.8534

811.8618

N ¼ 14 P1 P3 P4

15.5 13.5 12.5

11813.7233 811.2017

N ¼ 15 P1 P3 P4

16.5 14.5 13.5

11812.9222

N ¼ 16 P4

14.5

11809.4865

810.4648

814.4230

814.4018*

814.3796

814.3507

809.2059

809.1996

809.1923

809.1859

811.8678

811.8780

811.8913

811.9077

811.9248

814.3252 821.5692 809.1758 809.5253* 811.9410

813.7065

813.6886

811.2104

811.2208*

813.6687 808.4632 811.2311*

813.6455 808.4558 811.2466

813.6201 808.4478 811.2600

813.5984 808.4414 811.2727

813.5733 808.4326 811.2914

812.9085* 807.6883 810.4774

812.8942 807.6854 810.4866

812.8794 807.6802 810.4931

812.8638 807.6756 810.5133

812.8438 807.6686 810.5238

812.8177 807.6602 810.5362

812.7915 807.6532 810.5545

809.4958

809.5062

809.5198

809.5349

809.5456

809.5588

809.5775

Values in cm
1 . An asterisk (*) indicates a blended line.

814.4441*

Q. Ran et al. / Journal of Molecular Spectroscopy 220 (2003) 87–106

Q23 P4 N P24

105

106

Q. Ran et al. / Journal of Molecular Spectroscopy 220 (2003) 87–106

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