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High-Resolution Spectroscopy of TaS in the Visible and Near-Infrared Regions
JOURNAL OF MOLECULAR SPECTROSCOPY ARTICLE NO.
192, 368 –377 (1998)
MS987716
High-Resolution Spectroscopy of TaS in the Visible and Near-Infrared Regions S. Wallin, G. Edvinsson, and A. G. Taklif Department of Physics, Stockholm University, Box 6730, S-11385 Stockholm, Sweden Received July 1, 1998; in revised form August 5, 1998
The spectrum of TaS between 4000 and 20 000 cm21 has been recorded in emission from a microwave discharge with a resolution between 0.011 and 0.025 cm21. Seventeen electronic transitions have been rotationally analyzed. Fifteen of these have the ground state, 2D, as the lower state and two of them are transitions between excited states. The ground state has been fitted to a Hund’s case (a) Hamiltonian. Effective molecular constants have been determined for the excited states, which are mainly described as Hund’s case (c). Perturbations that have been found in the excited states are discussed. Transitions between states that are connected neither to the ground state nor to any of the other 14 electronic states of this work have been found. No analysis is presented for these transitions, but some of their characteristic features are described. © 1998 Academic Press INTRODUCTION
The spectra of transition metal (TM) diatomic oxides and sulfides have been widely studied for a long time and a large amount of spectroscopic data (1) has been collected for these molecules. Detailed knowledge of the spectra and structure of these molecules is of great astrophysical interest since many of them have been found or proposed to be present in the spectra from M- and S-type stars (2). During recent years the molecular physics group at the Physics Department, Stockholm University has studied several sulfide spectra in high resolution. Analyses of these spectra have made it possible to identify the molecules ZrS and TiS in star spectra (3, 4). Diatomic molecules containing TM elements are simple systems where the role of d electrons in chemical bonding can be studied. For the first two elements La and Hf in the 5d transition period the spectra of LaO, HfO, and HfS are well known, and the ground state and the low-lying excited states of these molecules can be classified and derived from a simple scheme of molecular orbitals (5, 6). In Ref. (6), Launila et al. were able to classify and successfully describe the ground state and the low-lying excited states of the rather heavy molecule HfS according to coupling case (a). One of the motives for the present study of TaS was to investigate if this case (a) description could be extended for sulfides further into the 5d transition period. The TaS molecule has also been proposed to be present in S-type star spectra (2) and therefore a detailed knowledge of this molecule is of astrophysical interest. Except for the TaO molecule, very little high-resolution spectroscopy has been done on diatomic molecules containing the Ta atom. In 1967, Cheetham and Barrow (7) gave an Supplementary data for this article may be found on the journal home page (hhtp://www.apnet.com/www//journal/ms.htm://www.europe.apnet.com/www/ journal/ms.htm).
extensive rotational analysis of TaO and identified the ground state of this molecule to be a 2D state. The spectrum of TaO was recently reinvestigated by Al-Khalili et al. (8). This is the first time to the best of our knowledge that the TaS spectrum has been studied in high resolution. Preliminary results for the ground state have been published as a note (9). EXPERIMENTAL PROCEDURE
The emission spectrum of TaS was produced by a 2450-MHz microwave excitation. The same experimental setup of the light source has successfully been used before (10, 11). In this experiment a few grams of TaCl5 was put between pieces of crystalline sulfur inside a 50-cm-long quartz tube. The sulfur and TaCl5 were mixed by heating the tube with a Bunsen flame at low (;1022 Torr) pressure as described in Ref. (11). Argon was used as carrier gas. With optimal conditions in the light source the TaS spectrum could be maintained for 30 min up to 1 h. The spectrum was recorded in the region 4000 –20 000 cm21. The recording was done using a BOMEM DA 3.002 Fourier transform spectrophotometer at resolutions between 0.011 and 0.025 cm21. Both InSb and Si detectors were used. When recording in the infrared region, the interferometer was evacuated and the region between the King Furnace and the interferometer was purged with N2 to avoid heavy absorption from water vapor. A few bands were recorded in high resolution with a 5-m grating spectrograph using photographic plates with Th atomic lines as references. These bands could not be seen in the BOMEM recordings due to noise from nearby strong atomic lines. Recordings of the TaO spectrum made later by Al-Khalili et al. used mainly the same experimental procedure (8). This spectrum contained very strong TaS bands since sulfur was
368 0022-2852/98 $25.00 Copyright © 1998 by Academic Press All rights of reproduction in any form reserved.
HIGH-RESOLUTION SPECTROSCOPY OF TaS
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FIG. 1. A low-resolution plot of the 6000 –9800 cm21 region of the TaS spectrum. The spectrum is very dense and many transitions overlap each other. Only (0, 0) bands have been marked in the figure. The band at ;6200 cm21 is the unanalyzed band with resolved hyperfine splitting.
also necessary to obtain TaO. Many TaS bands, mainly in the visible region, were stronger in the TaO recordings and these have therefore been included in our data. An overview of the region 6000 –9800 cm21 is shown in Fig. 1. Argon atomic lines were used for calibration of the spectrum as well as HCl lines and H2O absorption lines from residual water vapor in the evacuated interferometer. The wavenumber accuracy of unblended lines is believed to be better than 0.003 cm21. The linewidth of isolated lines is typically 0.025 cm21. Complete listings of rotational lines can be received upon request from the authors or from the journal. ANALYSIS
1. Picking Out and Numbering of Branches The picking out of branches was performed by means of Loomis–Wood methods on a PC as well as on a UNIX workstation. The first step of the analysis was to find the absolute J numbering. This was done using the Q branch of the very strong J–X1 transition (where X1 is the lower component, X2D3/2, of the ground state). An unperturbed Q branch can be given an absolute numbering by a least-squares fit to the expression n(J) 5 n0 1 DBJ(J 1 1) 2 DDJ2(J 1 1)2. The J numbering with the least RMS error in this fit is the correct one. Assuming that there is no V-type doubling, we found that the first combination differences from the R and Q branches could be matched to first combination
differences from the Q and P branches hence giving an absolute numbering of the entire band. Once having numbered these branches, numbering of all other branches in transitions to the same lower state, X1, was made by matching to first or second combination differences. The same procedure, with R, Q, and P branches from the I–X2 transition (where X2 is the upper component, X2D5/2, of the ground state), was used to find the correct numbering for all transitions to the X2 state. Fourteen electronically excited states involved in 17 transitions (Table 1) were found. At least one other electronic state is indicated by perturbations and up to six electronic states can be involved in three transitions that have not yet been possible to analyze. Our efforts to classify the excited states according to case (a) and electronic configurations have so far been in vain. They have, however, been classified according to case (c) (see Fig. 2). 2. Energy Level Expressions About 37 400 lines from 138 bands in 17 electronic transitions were picked out and numbered. The entire line material was fitted to a 2D Hamiltonian for the ground state. Despite the expected strong case (c) character of a heavy molecule like TaS, the ground state can be well described by a Hamiltonian written in case (a) basis. A Hamiltonian, using so-called N2 formalism according to Brown et al. (12) with the following definitions of parameters (N 5 J 2 S) was used:
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TABLE 1 Listing of All Electronic States That have Been Identified and All Transitions Involving These States
a
Calculated from the molecular constants.
H 5 T e 1 v e~ y 1 12 ! 2 v ex e~ y 1 12 ! 2 1 v ey e~ y 1 12 ! 3 1 ~B e 2 a e~ y 1 12 ! 1 d e~ y 1 12 ! 2!N 2 2 ~D e 1 b e~ y 1 12 !!N 4 1 12 @A e 1 A y~ y 1 12 ! 1 1 ~ A De 1 A Dy~ y 1 2 !!N 2, L zS z] 1.
The notation [ x, y] 1 stands for the anticommutator xy 1 yx. From this fit, a set of molecular constants for the ground state (Table 2) and term values for the excited states were obtained. Effective molecular constants have also been determined separately for the X 2 D 3/ 2 and X 2 D 5/ 2 substates. These constants are also given in Table 2. The term values for the excited states were used to obtain effective molecular constants for these states (Tables 3, 4, and 5). Attempts to describe the excited states by a case (a) Hamiltonian have been made, however, without success. A case (c) description has therefore been chosen and the excited states have only been classified according to their V values. Effective molecular constants have been determined for these states; i.e., the term values have been fitted to the following expression: 1 1 1 T~ y , J! 5 T e 1 v e~ y 1 2 ! 2 v e x e~ y 1 2 ! 2 1 v ey e~ y 1 2 ! 3
1 ~B e 2 a e~ y 1 12 ! 1 d e~ y 1 12 ! 2!J~ J 1 1! 2 ~D e 1 b e~ y 1 2 !!~ J~ J 1 1!! 2 1 H~ J~ J 1 1!! 3 1
The V-type doubling in the V 5 21 state is treated by adding a term 6 21 p( J 1 21 ). V-type doubling in V 5 23 states is treated by adding a term 6 21 q( J 1 21 ) 3 . 3. Classification of the States According to Their V Values and Description of the Bands The first key to the V-value classification is provided by the F–X 1 transition. The F state has a large V-type doubling proportional to J, thus giving V 5 21 (since the V-type doubling should be proportional to J 2V ). Since the F–X 1 transition has R, Q, and P branches, the V value of the lower ground state component, X 1 , is 23. The B–X 1 transition has single R and P branches so B must be an V 5 23 state. The (0, 0) band is relatively strong and unperturbed, but bands originating from transitions from y 5 1, 2, and 3 show large perturbations (Fig. 3). At the perturbation, the B state has a measurable V-type doubling. The (0, 0) band of the F–B transition, that confirms the analysis, has also been found. The R and P branches were used in the numbering of all branches in this band, but are weak and blended. Therefore only the Q branches have been included in the fit. Since transitions between two excited states cannot be handled by the term value program, the B (y 5 0) level in this transition was technically treated as a ground state level with its own effective molecular constants. Therefore this transition does not contribute to the B state statistics. It does, however, increase the J number region of the F state. Q branches of the (1, 1) and (2, 2)
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HIGH-RESOLUTION SPECTROSCOPY OF TaS
FIG. 2. Term scheme of the observed electronic states and transitions of TaS. The excited states have been classified according to case (c). The V values of the dashed states are uncertain. These states may also have V 5 27.
bands of the F–B transition can be seen but have not been included in the global fit since no numbering can be determined for double Q branches when no R and P branches can be seen. However, the zero gap positions can be estimated and this gives vibrational constants ve 5 498 6 1 cm21 and ve xe 5 1.4 6 0.3 cm21 for the F (V 5 21) state. The C–X 1 , H–X 1 , and J–X 1 transitions have R, Q, and P branches, so DV 5 1. No V-type doubling is seen so the C, H, and J states have V 5 25. If the V value was 21, a large V-type doubling would be expected. The D–X 1 , G–X 1 , and K–X 1 transitions have single R and P branches and therefore the D, G, and K states have V 5 23. The K–X 1 transition is the strongest of all transitions in our measurements. The second key to the V-value classification is provided by the E–A transition, which also has a small resolved V-type doubling. This doubling is small and proportional to J 3 , which would be expected in an V 5 23 state. A must be the doubled state since no V-type doubling at all can be measured in the E–X 2 transition. Since the E–A transition has Q branches, DV 5 1. However, since no V-type doubling can be seen in the E–X 2 transition, E has V 5 25. For the same reason as in F–B, the A state has technically been treated as a ground state level with its own effective molecular constants. The E–X 2 transition has single R and P branches. This confirms that the lower state of this transition has V 5 25 and that it is in fact the upper ground state component, X 2 . The I–X 2 and M–X 2 transitions have R, Q, and P branches but no V-type doubling so I and M can have V 5 23 or V 5 27. Since no large V-type doubling would be expected in either case, other means must be used to determine the V value of the I and M states. The linestrengths can give us a hint. Due to
TABLE 2 Molecular Constants (cm21) for the Ground State, X2D, in TaS
a b
371
1s error bounds. The energy difference between X 2 D 5/ 2 J 5 2.5 and X 2 D 3/ 2 J 5 1.5 is 3412.089 cm21.
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TABLE 3 Effective Molecular Constants (cm21) for All Excited States Except J (V 5 25) and K (V 5 23) (see Table 4)
1s error bounds. For technical reasons this state has been treated as a part of the ground state (although with its own effective Hamiltonian). The state has an V-type doubling that has been treated separately for each vibrational level, giving uq 0 u 5 1.77(4) z 10 28 cm21 and uq 1 u 5 1.47(3) z 10 28 cm21. c Limited to the unperturbed J-regions: y 5 0 unperturbed, y 5 1 J , 94.5 and J . 190.5, y 5 2 J , 80.5 and J . 203.5, y 5 3 J , 55.5 and J . 182.5. d Limited to the unperturbed J-regions by removing 19 termvalues that deviated more than 0.04 cm21 in a first fit. e Only y 5 0 has been rotationally analysed in the F (V 5 21 ) state. Therefore v e and v e x e are approximate values. The B and D values given are B 0 and D 0 values respectively. f Observe that only y 5 0 2 1 have been found in these states. Therefore these values are DG 1/ 2 values. g The V-type doubling of this state has been treated separately for each vibrational level, giving uq 0 u 5 3.87(3) z 10 27 cm21 and uq 1 u 5 3.99(5) z 10 27 cm21. a b
large overlaps in both bands, it is difficult to find unblended lines that show their true intensity. The R and P branches seem to be equally strong, a fact indicating that the V values of the I and M states are 23 rather than 27. This is, however, to be considered uncertain. The L–X 2 transition has double R, Q, and P branches. The V-type doubling is proportional to J 3 so L has V 5 23. The N–X 2 transition has single R and P branches so N has V 5 25. Four transitions determine the spin– orbit splitting in the X2D state. A very weak Q branch from the (0, 0) band in the K–X2 transition confirms that the K state has V 5 23. We already know that the H state has V 5 25. This is confirmed by the H–X2 transition, a weak transition with single R and P branches. These two transitions together with the K–X1 and H–X1 transitions determine the spin– orbit splitting in the ground state. The very weak K–X2 and H–X2 transitions would never have been found without the Loomis–Wood method.
4. Description of Unanalyzed Bands Three bands, which have so far been impossible to analyze, have been found. None of these transitions have common states with any of the already identified transitions. The first band is found at ;6203 cm21. There is a large hyperfine splitting in this band, but all eight hyperfine components, which are expected since the nuclear spin of Ta is 27, are not entirely resolved. The line splitting is about 0.2 cm21 between the outer components and does not seem to be J dependent. Due to the large number of lines, the Loomis–Wood pattern is hard to identify. Two relatively strong branches are found. These are probably two R branches. Since no P branch can be found, the branches cannot be given a unique numbering. The second band that is so far unanalyzed is found at ;10 381 cm21. This band has a nonresolved broadening of about 0.2 cm21. Five branches can be found. There are double R, Q, and P branches but one of the P branches is too weak to be seen. Therefore no unique numbering can be found.
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TABLE 4 Effective Molecular Constants (cm21) for Individual Vibrational Levels of the J (V 5 25) and K (V 5 23) States
a
1s error bounds.
The third unanalyzed band is found at ;15 320 cm21. Five branches can be found in this band too and the structure looks very much like the band at ;10 381 cm21. There is no or very small hyperfine broadening. DISCUSSION
1. Electronic Configurations of Low-Lying States For the three first TM sulfide molecules MS (where M is La, Hf, or Ta) in the 5d transition period, a simple scheme of molecular orbitals involved in the bonding of these molecules can be constructed. These orbitals are in order of increasing energy: 17 s (M 5d s 1 S3p s), 9 p (M 5d p 1 S3p p), 18 s (M 6s s), 4 d (S5d d), 10 p *(M 5d p 1 S3p p), and 19 s *(M 5d s 1 S3p s). The same scheme of molecular orbitals is expected for the oxides where instead of S3p we have O2p . For all low-lying electronic states of LaS, HfS, and TaS, the TABLE 5 Vibrational Constants (cm21) Calculated from the Ty Values of Individual Vibrational Levels of the J (V 5 25) and K (V 5 23) States
1s error bounds. The levels y 5 5– 8 are too perturbed to make a reasonable fit. a b
17s and 9p orbitals are fully occupied. The ground state and the low-lying excited doublet states in LaS can be derived from the following configurations using the scheme of molecular orbitals given above: X2S(9p418s), 2D(9p44d), 2P(9p410p*), and 2S(9p419s*). The same types of states from similar configurations are also true for LaO (1, 5). In recent years the HfS spectrum has been thoroughly investigated by Jonsson et al. (11) and Launila et al. (6) and the term scheme for low-lying singlet and triplet electronic states is well established. The low-lying states in order of energy can be derived from electron configurations as follows: X 1 S(9 p 4 18 s 2 ), 3 D, 1 D(9 p 4 18 s 4 d ), and 3P, 1P(9p410p*). The TaS molecule has one electron more than HfS and the prediction of the energy order of low-lying electronic states of different multiplicity from the simple molecular orbital scheme is not as straight forward as for HfS. By comparison with TaO (7, 8), the ground state of TaS is expected to be a regular 2D state, the only electronic state that can be derived from the configuration (9p418s24d). Another expected low-lying state is a 2P state derived from the configuration (9p418s210p*). The A state with V 5 23 is a candidate for the 2P3/2 component of this 2P state. Other expected excited low-lying states are 4 2 2 2 S , S , and 2G(9p418s4d2). It is known that VO and NbO have 4S2 as ground state (1) and the same is probably true for VS and NbS. According to the present analysis, when going from NbS to TaS, the ground state changes from the higher spin state 4S2 to a lower spin state 2D. The same type of change is known to take place in the group TiO, ZrO, HfO, and ThO, where TiO has 3D as ground state and the other three have 1S state as ground state. No ab initio calculations are available for TaO or TaS and the energy difference between the ground state X 2 D and the 4S2 state is unknown. The
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FIG. 3. Perturbed term values of the B (V 5 23 ) state. In each vibrational level, the amount B y J( J 1 1) 2 D y J 2 ( J 1 1) 2 has been subtracted from the term values.
B (V 5 23 ) state in TaS is perturbed by a so far unknown state with its y 5 0 level between the y 5 0 and y 5 1 levels of the B state. This perturbing state may be one of those that can be derived from the configuration 9p418s4d2. In an experimental and theoretical paper Launila et al. (13) give a detailed analysis and characterization of the doublet states of NbO together with ab initio calculations. The energy difference between the ground state X 4 S 2 and the lowest 2D state is determined with spectroscopic accuracy in very good agreement with the calculated value. The excited states were classified by a fruitful combination of theory and experiment. Recently, Fagerli et al. (14) have continued to successfully treat NbS in the same way. We hope that the present experimental work on TaS will initiate ab initio calculations on this molecule, and that by combination of experimental and theoretical results it will be possible to classify the excited states and to give their configurational origin. The relative position between the ground state X 2 D and the expected low-lying 4S2 state is of special interest. 2. Spin–Orbit Splitting of the Ground State A semiempirical calculation of the spin–orbit splitting of a 2D state from atomic parameters according to Ref. (15) confirms the classification and the orbital configuration of the ground state. The spin– orbit parameter for the Ta atom z 5d 5 1699 cm21 (12) can be used to estimate the molecular spin– orbit param-
eter aˆ . Assuming that a single unpaired 5d d electron is responsible for the spin– orbit interaction, the energy splitting can be written ^ da uSaˆ i l iz s iz u da & 5 aˆ ls 5 aˆ , where aˆ is the oneelectron spin– orbit parameter for the d electron. If the 5d d orbital is not appreciably changed when the bond is formed, this parameter equals the atomic spin– orbit parameter, thus z 5d 5 aˆ . The energy splitting can also be written in terms of the spin– orbit coupling constant A as ^ 2 D 5/ 2 uHSOu 2 D 5/ 2 & 5 ALS 5 A. Thus A 5 aˆ 5 z 5d 5 1699 cm21. This agrees extremely well with the experimental value of 1706 cm21. 3. Case (a) or Case (c)? The applicability of case (a) representations for transition metal (TM) molecules was discussed by Launila et al. (6). They noticed that many late 3d TM molecules require case (c) descriptions while case (a) representations seem to be applicable for many early 3d and 4d TM molecules, indicating that the applicability of case (a) descriptions may not only be a matter of molecular weight. They found that the relatively heavy early 5d TM molecule HfS, which they studied, could be consistently described by case (a) Hamiltonians. The analysis of the spectrum of TaS, which is also an early 5d TM molecule, shows, however, that a case (c) description actually does work better in this case. The ground state can be well described by a case (a) 2D Hamiltonian but attempts to uniquely assign the excited states to a case (a) description have
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HIGH-RESOLUTION SPECTROSCOPY OF TaS
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FIG. 4. Reduced term values in the perturbation region of the D (V 5 23 ) state. The D y 5 0 and 1 levels are shown with stars and the y 5 2 and 3 levels of the C (V 5 25 ) state with a solid line. The horizontal straight lines correspond to the T y of the D vibrational levels. The dots are the term values of the D state reproduced in the perturbation calculation.
failed. Thus, only effective molecular constants for all excited states have been determined and these constants are given in Tables 3, 4, and 5.
T 1~ J! 2 T 2~ J! 2 7
4. Perturbations The B (V 5 y 5 0 vibrational level is perfectly regular and lines originating from this level show no sign of resolved V-type doubling or broadening. The B (V 5 23 ) y 5 1–3 levels show local perturbations. The V-type doubling increases near the perturbation maximum (Fig. 3) due to the interaction with the perturbing state. The B state is crossed by an V doubled state with larger B and v values, from below the y 5 1 level. It can be seen in the figure that one of the symmetry components of B is more strongly perturbed than the other. The D (V 5 23 ) state shows local perturbations in the y 5 0 and 1 levels. No perturbations have been found in the higher vibrational levels, because these levels cannot be followed to high enough J. These perturbations are due to interaction with the y 5 2 and 3 levels of the C (V 5 25 ) state (Fig. 4). The perturbations cannot be observed in the C state since no branches of the C–X 1 transitions can be followed to high enough J. The perturbations have been treated as a two-level heterogeneous perturbation with J-dependent matrix element H 0 =J( J 1 1) 2 V(V 1 1) (15). The observed term values have been fed into a nonlinear least-squares fit to the expression 3 ) 2
T~ J! 5
Î
~T 1~ J! 2 T 2~ J!! 2 1 H 20~ J~ J 1 1! 2 V~V 1 1!!, 4
where T 1 ( J) 5 T 01 ( J) 1 B 01 J( J 1 1) 2 DJ 2 ( J 1 1) 2 and T 2 ( J) 5 T 02 ( J) 1 B 02 J( J 1 1) 2 DJ 2 ( J 1 1) 2 . Index 1 refers to the D (V 5 23 ) level and index 2 refers to the C (V 5 25 ) level. The result of this fit is found in Table 6 and Fig. 4. The J (V 5 25 ) and K (V 5 23 ) states also appear to be perturbed. It is not possible to find a good fit with a reasonable set of equilibrium parameters. Therefore effective molecular constants including an H y term have been determined for the individual vibrational levels (Table 4). A vibrational analysis has been made on all the T y values for the J (V 5 25 ) state and on y 5 0 – 4 for the K (V 5 23 ) state (Table 5). The good fit in the vibrational analysis of the J (V 5 25 ) state indicates that this state is unperturbed at low J. The density of states in this region is so high that perturbations are expected. 5. V-type Doublings The V-type doublings in the A (V 5 23 ) and F (V 5 21 ) states show a regular behavior, the doubling being proportional to ;J 2V . The A (V 5 23 ) molecular constants have been
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TABLE 6 Molecular Constants (cm21) from a Fit to the Perturbation between the D (V 5 23) and C (V 5 25) States
a
1s error bounds.
determined in two steps. Only the averages of, respectively, the two R, Q, and P branches were entered into the global fit for the ground state and equilibrium constants were determined. Then the Q branches of the E–A (0, 0) and (1, 1) transitions were used to calculate the V doubled term values of the A state from the term values of the E state determined in the global fit to the ground state. These term values were used in a fit to each vibrational level separately, giving uq 0 u 5 1.77(4) z 10 28 and uq 1 u 5 1.47(3) z 10 28 cm21. The V-type doubling of the L (V 5 23 ) state is proportional to ;J 3 for J less than about 100. The doubling is a little larger at high J, indicating that there is some kind of perturbation (Fig. 5). For the determination of molecular constants, an average of the V-type doubling components was used for each vibrational level. A new fit to each vibrational level including the V-type doubling gave uq 0 u 5 3.87(3) z 10 27 and
FIG. 5.
uq 1 u 5 3.99(5) z 10 27 cm21. The J number regions were limited to J , 100 for y 5 0 and J , 110 for y 5 1. SUMMARY
A rotational analysis of 17 transitions of the TaS molecules in the IR and visible regions has been presented. Molecular constants for the ground state, described by a case (a) 2D Hamiltonian, have been derived. The excited states have been treated as case (c) and effective molecular constants have been derived. The character of three unanalyzed bands has been described and perturbations in four excited states have been discussed. No quantum chemical calculations on TaS are available. It is our hope that this experimental study of the molecule will stimulate theoretical studies of the electronic structure of this molecule.
V-type doubling in the L (V 5 23 ) y 5 0 and 1 levels. The regions inside the boxes have been used for calculation of the q y values.
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HIGH-RESOLUTION SPECTROSCOPY OF TaS
ACKNOWLEDGMENTS The authors are grateful to Drs. Ulf Sassenberg and Olli Launila for fruitful discussions and to Dr. Launila for his skillful assistance with the Fourier transform spectrometer part of the experiment.
REFERENCES 1. K. P. Huber and G. Herzberg, “Molecular Spectra and Molecular Structure, IV. Constants of Diatomic Molecules,” Van Nostrand, New York, 1979. 2. A. J. Sauval, Astron. Astrophys. 62, 295–298 (1978). 3. J. Jonsson, O. Launila, and B. Lindgren, Mon. Not. R. Astron. Soc. 258, 49 –51 (1992). 4. J. Jonsson and B. Lindgren, J. Mol. Spectrosc. 169, 30 –37 (1995). 5. J. Schamps, M. Bencheikh, J-C. Barthelat, and R. Field, J. Chem. Phys. 103, 8004 – 8013 (1995).
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6. O. Launila, J. Jonsson, G. Edvinsson, and A. G. Taklif, J. Mol. Spectrosc. 177, 221–231 (1996). 7. C. J. Cheetham and R. F. Barrow, Trans. Farad. Soc. 63, 1835–1845 (1967). 8. A. Al-Khalili, U. Ha¨llsten, and O. Launila, to be published. 9. S. Wallin, G. Edvinsson, and A. G. Taklif, J. Mol. Spectrosc. 184, 466 – 467 (1997). 10. J. Jonsson, B. Lindgren, and A. G. Taklif, Astron. Astrophys. 246, L67– L68 (1991). 11. J. Jonsson, G. Edvinsson, and A. G. Taklif, Physica Scripta. 50, 661–665 (1994). 12. J. M. Brown, E. A. Colbourn, J. K. G. Watson, and F. D. Wayne, J. Mol. Spectrosc. 74, 294 –318 (1979). 13. O. Launila, B. Schimmelpfennig, H. Fagerli, O. Gropen, A. G. Taklif, and U. Wahlgren, J. Mol. Spectrosc. 186, 131–143 (1997). 14. H. Fagerli, B. Schimmelpfennig, O. Launila, O. Gropen, A. G. Taklif, and U. Wahlgren, to be published. 15. H. Lefebvre-Brion and R. W. Field, in “Perturbations in the Spectra of Diatomic Molecules,” Academic Press, New York, 1986.
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MS987716
High-Resolution Spectroscopy of TaS in the Visible and Near-Infrared Regions S. Wallin, G. Edvinsson, and A. G. Taklif Department of Physics, Stockholm University, Box 6730, S-11385 Stockholm, Sweden Received July 1, 1998; in revised form August 5, 1998
The spectrum of TaS between 4000 and 20 000 cm21 has been recorded in emission from a microwave discharge with a resolution between 0.011 and 0.025 cm21. Seventeen electronic transitions have been rotationally analyzed. Fifteen of these have the ground state, 2D, as the lower state and two of them are transitions between excited states. The ground state has been fitted to a Hund’s case (a) Hamiltonian. Effective molecular constants have been determined for the excited states, which are mainly described as Hund’s case (c). Perturbations that have been found in the excited states are discussed. Transitions between states that are connected neither to the ground state nor to any of the other 14 electronic states of this work have been found. No analysis is presented for these transitions, but some of their characteristic features are described. © 1998 Academic Press INTRODUCTION
The spectra of transition metal (TM) diatomic oxides and sulfides have been widely studied for a long time and a large amount of spectroscopic data (1) has been collected for these molecules. Detailed knowledge of the spectra and structure of these molecules is of great astrophysical interest since many of them have been found or proposed to be present in the spectra from M- and S-type stars (2). During recent years the molecular physics group at the Physics Department, Stockholm University has studied several sulfide spectra in high resolution. Analyses of these spectra have made it possible to identify the molecules ZrS and TiS in star spectra (3, 4). Diatomic molecules containing TM elements are simple systems where the role of d electrons in chemical bonding can be studied. For the first two elements La and Hf in the 5d transition period the spectra of LaO, HfO, and HfS are well known, and the ground state and the low-lying excited states of these molecules can be classified and derived from a simple scheme of molecular orbitals (5, 6). In Ref. (6), Launila et al. were able to classify and successfully describe the ground state and the low-lying excited states of the rather heavy molecule HfS according to coupling case (a). One of the motives for the present study of TaS was to investigate if this case (a) description could be extended for sulfides further into the 5d transition period. The TaS molecule has also been proposed to be present in S-type star spectra (2) and therefore a detailed knowledge of this molecule is of astrophysical interest. Except for the TaO molecule, very little high-resolution spectroscopy has been done on diatomic molecules containing the Ta atom. In 1967, Cheetham and Barrow (7) gave an Supplementary data for this article may be found on the journal home page (hhtp://www.apnet.com/www//journal/ms.htm://www.europe.apnet.com/www/ journal/ms.htm).
extensive rotational analysis of TaO and identified the ground state of this molecule to be a 2D state. The spectrum of TaO was recently reinvestigated by Al-Khalili et al. (8). This is the first time to the best of our knowledge that the TaS spectrum has been studied in high resolution. Preliminary results for the ground state have been published as a note (9). EXPERIMENTAL PROCEDURE
The emission spectrum of TaS was produced by a 2450-MHz microwave excitation. The same experimental setup of the light source has successfully been used before (10, 11). In this experiment a few grams of TaCl5 was put between pieces of crystalline sulfur inside a 50-cm-long quartz tube. The sulfur and TaCl5 were mixed by heating the tube with a Bunsen flame at low (;1022 Torr) pressure as described in Ref. (11). Argon was used as carrier gas. With optimal conditions in the light source the TaS spectrum could be maintained for 30 min up to 1 h. The spectrum was recorded in the region 4000 –20 000 cm21. The recording was done using a BOMEM DA 3.002 Fourier transform spectrophotometer at resolutions between 0.011 and 0.025 cm21. Both InSb and Si detectors were used. When recording in the infrared region, the interferometer was evacuated and the region between the King Furnace and the interferometer was purged with N2 to avoid heavy absorption from water vapor. A few bands were recorded in high resolution with a 5-m grating spectrograph using photographic plates with Th atomic lines as references. These bands could not be seen in the BOMEM recordings due to noise from nearby strong atomic lines. Recordings of the TaO spectrum made later by Al-Khalili et al. used mainly the same experimental procedure (8). This spectrum contained very strong TaS bands since sulfur was
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FIG. 1. A low-resolution plot of the 6000 –9800 cm21 region of the TaS spectrum. The spectrum is very dense and many transitions overlap each other. Only (0, 0) bands have been marked in the figure. The band at ;6200 cm21 is the unanalyzed band with resolved hyperfine splitting.
also necessary to obtain TaO. Many TaS bands, mainly in the visible region, were stronger in the TaO recordings and these have therefore been included in our data. An overview of the region 6000 –9800 cm21 is shown in Fig. 1. Argon atomic lines were used for calibration of the spectrum as well as HCl lines and H2O absorption lines from residual water vapor in the evacuated interferometer. The wavenumber accuracy of unblended lines is believed to be better than 0.003 cm21. The linewidth of isolated lines is typically 0.025 cm21. Complete listings of rotational lines can be received upon request from the authors or from the journal. ANALYSIS
1. Picking Out and Numbering of Branches The picking out of branches was performed by means of Loomis–Wood methods on a PC as well as on a UNIX workstation. The first step of the analysis was to find the absolute J numbering. This was done using the Q branch of the very strong J–X1 transition (where X1 is the lower component, X2D3/2, of the ground state). An unperturbed Q branch can be given an absolute numbering by a least-squares fit to the expression n(J) 5 n0 1 DBJ(J 1 1) 2 DDJ2(J 1 1)2. The J numbering with the least RMS error in this fit is the correct one. Assuming that there is no V-type doubling, we found that the first combination differences from the R and Q branches could be matched to first combination
differences from the Q and P branches hence giving an absolute numbering of the entire band. Once having numbered these branches, numbering of all other branches in transitions to the same lower state, X1, was made by matching to first or second combination differences. The same procedure, with R, Q, and P branches from the I–X2 transition (where X2 is the upper component, X2D5/2, of the ground state), was used to find the correct numbering for all transitions to the X2 state. Fourteen electronically excited states involved in 17 transitions (Table 1) were found. At least one other electronic state is indicated by perturbations and up to six electronic states can be involved in three transitions that have not yet been possible to analyze. Our efforts to classify the excited states according to case (a) and electronic configurations have so far been in vain. They have, however, been classified according to case (c) (see Fig. 2). 2. Energy Level Expressions About 37 400 lines from 138 bands in 17 electronic transitions were picked out and numbered. The entire line material was fitted to a 2D Hamiltonian for the ground state. Despite the expected strong case (c) character of a heavy molecule like TaS, the ground state can be well described by a Hamiltonian written in case (a) basis. A Hamiltonian, using so-called N2 formalism according to Brown et al. (12) with the following definitions of parameters (N 5 J 2 S) was used:
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TABLE 1 Listing of All Electronic States That have Been Identified and All Transitions Involving These States
a
Calculated from the molecular constants.
H 5 T e 1 v e~ y 1 12 ! 2 v ex e~ y 1 12 ! 2 1 v ey e~ y 1 12 ! 3 1 ~B e 2 a e~ y 1 12 ! 1 d e~ y 1 12 ! 2!N 2 2 ~D e 1 b e~ y 1 12 !!N 4 1 12 @A e 1 A y~ y 1 12 ! 1 1 ~ A De 1 A Dy~ y 1 2 !!N 2, L zS z] 1.
The notation [ x, y] 1 stands for the anticommutator xy 1 yx. From this fit, a set of molecular constants for the ground state (Table 2) and term values for the excited states were obtained. Effective molecular constants have also been determined separately for the X 2 D 3/ 2 and X 2 D 5/ 2 substates. These constants are also given in Table 2. The term values for the excited states were used to obtain effective molecular constants for these states (Tables 3, 4, and 5). Attempts to describe the excited states by a case (a) Hamiltonian have been made, however, without success. A case (c) description has therefore been chosen and the excited states have only been classified according to their V values. Effective molecular constants have been determined for these states; i.e., the term values have been fitted to the following expression: 1 1 1 T~ y , J! 5 T e 1 v e~ y 1 2 ! 2 v e x e~ y 1 2 ! 2 1 v ey e~ y 1 2 ! 3
1 ~B e 2 a e~ y 1 12 ! 1 d e~ y 1 12 ! 2!J~ J 1 1! 2 ~D e 1 b e~ y 1 2 !!~ J~ J 1 1!! 2 1 H~ J~ J 1 1!! 3 1
The V-type doubling in the V 5 21 state is treated by adding a term 6 21 p( J 1 21 ). V-type doubling in V 5 23 states is treated by adding a term 6 21 q( J 1 21 ) 3 . 3. Classification of the States According to Their V Values and Description of the Bands The first key to the V-value classification is provided by the F–X 1 transition. The F state has a large V-type doubling proportional to J, thus giving V 5 21 (since the V-type doubling should be proportional to J 2V ). Since the F–X 1 transition has R, Q, and P branches, the V value of the lower ground state component, X 1 , is 23. The B–X 1 transition has single R and P branches so B must be an V 5 23 state. The (0, 0) band is relatively strong and unperturbed, but bands originating from transitions from y 5 1, 2, and 3 show large perturbations (Fig. 3). At the perturbation, the B state has a measurable V-type doubling. The (0, 0) band of the F–B transition, that confirms the analysis, has also been found. The R and P branches were used in the numbering of all branches in this band, but are weak and blended. Therefore only the Q branches have been included in the fit. Since transitions between two excited states cannot be handled by the term value program, the B (y 5 0) level in this transition was technically treated as a ground state level with its own effective molecular constants. Therefore this transition does not contribute to the B state statistics. It does, however, increase the J number region of the F state. Q branches of the (1, 1) and (2, 2)
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HIGH-RESOLUTION SPECTROSCOPY OF TaS
FIG. 2. Term scheme of the observed electronic states and transitions of TaS. The excited states have been classified according to case (c). The V values of the dashed states are uncertain. These states may also have V 5 27.
bands of the F–B transition can be seen but have not been included in the global fit since no numbering can be determined for double Q branches when no R and P branches can be seen. However, the zero gap positions can be estimated and this gives vibrational constants ve 5 498 6 1 cm21 and ve xe 5 1.4 6 0.3 cm21 for the F (V 5 21) state. The C–X 1 , H–X 1 , and J–X 1 transitions have R, Q, and P branches, so DV 5 1. No V-type doubling is seen so the C, H, and J states have V 5 25. If the V value was 21, a large V-type doubling would be expected. The D–X 1 , G–X 1 , and K–X 1 transitions have single R and P branches and therefore the D, G, and K states have V 5 23. The K–X 1 transition is the strongest of all transitions in our measurements. The second key to the V-value classification is provided by the E–A transition, which also has a small resolved V-type doubling. This doubling is small and proportional to J 3 , which would be expected in an V 5 23 state. A must be the doubled state since no V-type doubling at all can be measured in the E–X 2 transition. Since the E–A transition has Q branches, DV 5 1. However, since no V-type doubling can be seen in the E–X 2 transition, E has V 5 25. For the same reason as in F–B, the A state has technically been treated as a ground state level with its own effective molecular constants. The E–X 2 transition has single R and P branches. This confirms that the lower state of this transition has V 5 25 and that it is in fact the upper ground state component, X 2 . The I–X 2 and M–X 2 transitions have R, Q, and P branches but no V-type doubling so I and M can have V 5 23 or V 5 27. Since no large V-type doubling would be expected in either case, other means must be used to determine the V value of the I and M states. The linestrengths can give us a hint. Due to
TABLE 2 Molecular Constants (cm21) for the Ground State, X2D, in TaS
a b
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1s error bounds. The energy difference between X 2 D 5/ 2 J 5 2.5 and X 2 D 3/ 2 J 5 1.5 is 3412.089 cm21.
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TABLE 3 Effective Molecular Constants (cm21) for All Excited States Except J (V 5 25) and K (V 5 23) (see Table 4)
1s error bounds. For technical reasons this state has been treated as a part of the ground state (although with its own effective Hamiltonian). The state has an V-type doubling that has been treated separately for each vibrational level, giving uq 0 u 5 1.77(4) z 10 28 cm21 and uq 1 u 5 1.47(3) z 10 28 cm21. c Limited to the unperturbed J-regions: y 5 0 unperturbed, y 5 1 J , 94.5 and J . 190.5, y 5 2 J , 80.5 and J . 203.5, y 5 3 J , 55.5 and J . 182.5. d Limited to the unperturbed J-regions by removing 19 termvalues that deviated more than 0.04 cm21 in a first fit. e Only y 5 0 has been rotationally analysed in the F (V 5 21 ) state. Therefore v e and v e x e are approximate values. The B and D values given are B 0 and D 0 values respectively. f Observe that only y 5 0 2 1 have been found in these states. Therefore these values are DG 1/ 2 values. g The V-type doubling of this state has been treated separately for each vibrational level, giving uq 0 u 5 3.87(3) z 10 27 cm21 and uq 1 u 5 3.99(5) z 10 27 cm21. a b
large overlaps in both bands, it is difficult to find unblended lines that show their true intensity. The R and P branches seem to be equally strong, a fact indicating that the V values of the I and M states are 23 rather than 27. This is, however, to be considered uncertain. The L–X 2 transition has double R, Q, and P branches. The V-type doubling is proportional to J 3 so L has V 5 23. The N–X 2 transition has single R and P branches so N has V 5 25. Four transitions determine the spin– orbit splitting in the X2D state. A very weak Q branch from the (0, 0) band in the K–X2 transition confirms that the K state has V 5 23. We already know that the H state has V 5 25. This is confirmed by the H–X2 transition, a weak transition with single R and P branches. These two transitions together with the K–X1 and H–X1 transitions determine the spin– orbit splitting in the ground state. The very weak K–X2 and H–X2 transitions would never have been found without the Loomis–Wood method.
4. Description of Unanalyzed Bands Three bands, which have so far been impossible to analyze, have been found. None of these transitions have common states with any of the already identified transitions. The first band is found at ;6203 cm21. There is a large hyperfine splitting in this band, but all eight hyperfine components, which are expected since the nuclear spin of Ta is 27, are not entirely resolved. The line splitting is about 0.2 cm21 between the outer components and does not seem to be J dependent. Due to the large number of lines, the Loomis–Wood pattern is hard to identify. Two relatively strong branches are found. These are probably two R branches. Since no P branch can be found, the branches cannot be given a unique numbering. The second band that is so far unanalyzed is found at ;10 381 cm21. This band has a nonresolved broadening of about 0.2 cm21. Five branches can be found. There are double R, Q, and P branches but one of the P branches is too weak to be seen. Therefore no unique numbering can be found.
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TABLE 4 Effective Molecular Constants (cm21) for Individual Vibrational Levels of the J (V 5 25) and K (V 5 23) States
a
1s error bounds.
The third unanalyzed band is found at ;15 320 cm21. Five branches can be found in this band too and the structure looks very much like the band at ;10 381 cm21. There is no or very small hyperfine broadening. DISCUSSION
1. Electronic Configurations of Low-Lying States For the three first TM sulfide molecules MS (where M is La, Hf, or Ta) in the 5d transition period, a simple scheme of molecular orbitals involved in the bonding of these molecules can be constructed. These orbitals are in order of increasing energy: 17 s (M 5d s 1 S3p s), 9 p (M 5d p 1 S3p p), 18 s (M 6s s), 4 d (S5d d), 10 p *(M 5d p 1 S3p p), and 19 s *(M 5d s 1 S3p s). The same scheme of molecular orbitals is expected for the oxides where instead of S3p we have O2p . For all low-lying electronic states of LaS, HfS, and TaS, the TABLE 5 Vibrational Constants (cm21) Calculated from the Ty Values of Individual Vibrational Levels of the J (V 5 25) and K (V 5 23) States
1s error bounds. The levels y 5 5– 8 are too perturbed to make a reasonable fit. a b
17s and 9p orbitals are fully occupied. The ground state and the low-lying excited doublet states in LaS can be derived from the following configurations using the scheme of molecular orbitals given above: X2S(9p418s), 2D(9p44d), 2P(9p410p*), and 2S(9p419s*). The same types of states from similar configurations are also true for LaO (1, 5). In recent years the HfS spectrum has been thoroughly investigated by Jonsson et al. (11) and Launila et al. (6) and the term scheme for low-lying singlet and triplet electronic states is well established. The low-lying states in order of energy can be derived from electron configurations as follows: X 1 S(9 p 4 18 s 2 ), 3 D, 1 D(9 p 4 18 s 4 d ), and 3P, 1P(9p410p*). The TaS molecule has one electron more than HfS and the prediction of the energy order of low-lying electronic states of different multiplicity from the simple molecular orbital scheme is not as straight forward as for HfS. By comparison with TaO (7, 8), the ground state of TaS is expected to be a regular 2D state, the only electronic state that can be derived from the configuration (9p418s24d). Another expected low-lying state is a 2P state derived from the configuration (9p418s210p*). The A state with V 5 23 is a candidate for the 2P3/2 component of this 2P state. Other expected excited low-lying states are 4 2 2 2 S , S , and 2G(9p418s4d2). It is known that VO and NbO have 4S2 as ground state (1) and the same is probably true for VS and NbS. According to the present analysis, when going from NbS to TaS, the ground state changes from the higher spin state 4S2 to a lower spin state 2D. The same type of change is known to take place in the group TiO, ZrO, HfO, and ThO, where TiO has 3D as ground state and the other three have 1S state as ground state. No ab initio calculations are available for TaO or TaS and the energy difference between the ground state X 2 D and the 4S2 state is unknown. The
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FIG. 3. Perturbed term values of the B (V 5 23 ) state. In each vibrational level, the amount B y J( J 1 1) 2 D y J 2 ( J 1 1) 2 has been subtracted from the term values.
B (V 5 23 ) state in TaS is perturbed by a so far unknown state with its y 5 0 level between the y 5 0 and y 5 1 levels of the B state. This perturbing state may be one of those that can be derived from the configuration 9p418s4d2. In an experimental and theoretical paper Launila et al. (13) give a detailed analysis and characterization of the doublet states of NbO together with ab initio calculations. The energy difference between the ground state X 4 S 2 and the lowest 2D state is determined with spectroscopic accuracy in very good agreement with the calculated value. The excited states were classified by a fruitful combination of theory and experiment. Recently, Fagerli et al. (14) have continued to successfully treat NbS in the same way. We hope that the present experimental work on TaS will initiate ab initio calculations on this molecule, and that by combination of experimental and theoretical results it will be possible to classify the excited states and to give their configurational origin. The relative position between the ground state X 2 D and the expected low-lying 4S2 state is of special interest. 2. Spin–Orbit Splitting of the Ground State A semiempirical calculation of the spin–orbit splitting of a 2D state from atomic parameters according to Ref. (15) confirms the classification and the orbital configuration of the ground state. The spin– orbit parameter for the Ta atom z 5d 5 1699 cm21 (12) can be used to estimate the molecular spin– orbit param-
eter aˆ . Assuming that a single unpaired 5d d electron is responsible for the spin– orbit interaction, the energy splitting can be written ^ da uSaˆ i l iz s iz u da & 5 aˆ ls 5 aˆ , where aˆ is the oneelectron spin– orbit parameter for the d electron. If the 5d d orbital is not appreciably changed when the bond is formed, this parameter equals the atomic spin– orbit parameter, thus z 5d 5 aˆ . The energy splitting can also be written in terms of the spin– orbit coupling constant A as ^ 2 D 5/ 2 uHSOu 2 D 5/ 2 & 5 ALS 5 A. Thus A 5 aˆ 5 z 5d 5 1699 cm21. This agrees extremely well with the experimental value of 1706 cm21. 3. Case (a) or Case (c)? The applicability of case (a) representations for transition metal (TM) molecules was discussed by Launila et al. (6). They noticed that many late 3d TM molecules require case (c) descriptions while case (a) representations seem to be applicable for many early 3d and 4d TM molecules, indicating that the applicability of case (a) descriptions may not only be a matter of molecular weight. They found that the relatively heavy early 5d TM molecule HfS, which they studied, could be consistently described by case (a) Hamiltonians. The analysis of the spectrum of TaS, which is also an early 5d TM molecule, shows, however, that a case (c) description actually does work better in this case. The ground state can be well described by a case (a) 2D Hamiltonian but attempts to uniquely assign the excited states to a case (a) description have
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HIGH-RESOLUTION SPECTROSCOPY OF TaS
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FIG. 4. Reduced term values in the perturbation region of the D (V 5 23 ) state. The D y 5 0 and 1 levels are shown with stars and the y 5 2 and 3 levels of the C (V 5 25 ) state with a solid line. The horizontal straight lines correspond to the T y of the D vibrational levels. The dots are the term values of the D state reproduced in the perturbation calculation.
failed. Thus, only effective molecular constants for all excited states have been determined and these constants are given in Tables 3, 4, and 5.
T 1~ J! 2 T 2~ J! 2 7
4. Perturbations The B (V 5 y 5 0 vibrational level is perfectly regular and lines originating from this level show no sign of resolved V-type doubling or broadening. The B (V 5 23 ) y 5 1–3 levels show local perturbations. The V-type doubling increases near the perturbation maximum (Fig. 3) due to the interaction with the perturbing state. The B state is crossed by an V doubled state with larger B and v values, from below the y 5 1 level. It can be seen in the figure that one of the symmetry components of B is more strongly perturbed than the other. The D (V 5 23 ) state shows local perturbations in the y 5 0 and 1 levels. No perturbations have been found in the higher vibrational levels, because these levels cannot be followed to high enough J. These perturbations are due to interaction with the y 5 2 and 3 levels of the C (V 5 25 ) state (Fig. 4). The perturbations cannot be observed in the C state since no branches of the C–X 1 transitions can be followed to high enough J. The perturbations have been treated as a two-level heterogeneous perturbation with J-dependent matrix element H 0 =J( J 1 1) 2 V(V 1 1) (15). The observed term values have been fed into a nonlinear least-squares fit to the expression 3 ) 2
T~ J! 5
Î
~T 1~ J! 2 T 2~ J!! 2 1 H 20~ J~ J 1 1! 2 V~V 1 1!!, 4
where T 1 ( J) 5 T 01 ( J) 1 B 01 J( J 1 1) 2 DJ 2 ( J 1 1) 2 and T 2 ( J) 5 T 02 ( J) 1 B 02 J( J 1 1) 2 DJ 2 ( J 1 1) 2 . Index 1 refers to the D (V 5 23 ) level and index 2 refers to the C (V 5 25 ) level. The result of this fit is found in Table 6 and Fig. 4. The J (V 5 25 ) and K (V 5 23 ) states also appear to be perturbed. It is not possible to find a good fit with a reasonable set of equilibrium parameters. Therefore effective molecular constants including an H y term have been determined for the individual vibrational levels (Table 4). A vibrational analysis has been made on all the T y values for the J (V 5 25 ) state and on y 5 0 – 4 for the K (V 5 23 ) state (Table 5). The good fit in the vibrational analysis of the J (V 5 25 ) state indicates that this state is unperturbed at low J. The density of states in this region is so high that perturbations are expected. 5. V-type Doublings The V-type doublings in the A (V 5 23 ) and F (V 5 21 ) states show a regular behavior, the doubling being proportional to ;J 2V . The A (V 5 23 ) molecular constants have been
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TABLE 6 Molecular Constants (cm21) from a Fit to the Perturbation between the D (V 5 23) and C (V 5 25) States
a
1s error bounds.
determined in two steps. Only the averages of, respectively, the two R, Q, and P branches were entered into the global fit for the ground state and equilibrium constants were determined. Then the Q branches of the E–A (0, 0) and (1, 1) transitions were used to calculate the V doubled term values of the A state from the term values of the E state determined in the global fit to the ground state. These term values were used in a fit to each vibrational level separately, giving uq 0 u 5 1.77(4) z 10 28 and uq 1 u 5 1.47(3) z 10 28 cm21. The V-type doubling of the L (V 5 23 ) state is proportional to ;J 3 for J less than about 100. The doubling is a little larger at high J, indicating that there is some kind of perturbation (Fig. 5). For the determination of molecular constants, an average of the V-type doubling components was used for each vibrational level. A new fit to each vibrational level including the V-type doubling gave uq 0 u 5 3.87(3) z 10 27 and
FIG. 5.
uq 1 u 5 3.99(5) z 10 27 cm21. The J number regions were limited to J , 100 for y 5 0 and J , 110 for y 5 1. SUMMARY
A rotational analysis of 17 transitions of the TaS molecules in the IR and visible regions has been presented. Molecular constants for the ground state, described by a case (a) 2D Hamiltonian, have been derived. The excited states have been treated as case (c) and effective molecular constants have been derived. The character of three unanalyzed bands has been described and perturbations in four excited states have been discussed. No quantum chemical calculations on TaS are available. It is our hope that this experimental study of the molecule will stimulate theoretical studies of the electronic structure of this molecule.
V-type doubling in the L (V 5 23 ) y 5 0 and 1 levels. The regions inside the boxes have been used for calculation of the q y values.
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HIGH-RESOLUTION SPECTROSCOPY OF TaS
ACKNOWLEDGMENTS The authors are grateful to Drs. Ulf Sassenberg and Olli Launila for fruitful discussions and to Dr. Launila for his skillful assistance with the Fourier transform spectrometer part of the experiment.
REFERENCES 1. K. P. Huber and G. Herzberg, “Molecular Spectra and Molecular Structure, IV. Constants of Diatomic Molecules,” Van Nostrand, New York, 1979. 2. A. J. Sauval, Astron. Astrophys. 62, 295–298 (1978). 3. J. Jonsson, O. Launila, and B. Lindgren, Mon. Not. R. Astron. Soc. 258, 49 –51 (1992). 4. J. Jonsson and B. Lindgren, J. Mol. Spectrosc. 169, 30 –37 (1995). 5. J. Schamps, M. Bencheikh, J-C. Barthelat, and R. Field, J. Chem. Phys. 103, 8004 – 8013 (1995).
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6. O. Launila, J. Jonsson, G. Edvinsson, and A. G. Taklif, J. Mol. Spectrosc. 177, 221–231 (1996). 7. C. J. Cheetham and R. F. Barrow, Trans. Farad. Soc. 63, 1835–1845 (1967). 8. A. Al-Khalili, U. Ha¨llsten, and O. Launila, to be published. 9. S. Wallin, G. Edvinsson, and A. G. Taklif, J. Mol. Spectrosc. 184, 466 – 467 (1997). 10. J. Jonsson, B. Lindgren, and A. G. Taklif, Astron. Astrophys. 246, L67– L68 (1991). 11. J. Jonsson, G. Edvinsson, and A. G. Taklif, Physica Scripta. 50, 661–665 (1994). 12. J. M. Brown, E. A. Colbourn, J. K. G. Watson, and F. D. Wayne, J. Mol. Spectrosc. 74, 294 –318 (1979). 13. O. Launila, B. Schimmelpfennig, H. Fagerli, O. Gropen, A. G. Taklif, and U. Wahlgren, J. Mol. Spectrosc. 186, 131–143 (1997). 14. H. Fagerli, B. Schimmelpfennig, O. Launila, O. Gropen, A. G. Taklif, and U. Wahlgren, to be published. 15. H. Lefebvre-Brion and R. W. Field, in “Perturbations in the Spectra of Diatomic Molecules,” Academic Press, New York, 1986.
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