Journal of Molecular Spectroscopy 264 (2010) 50–54
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Journal of Molecular Spectroscopy
journal homepage: www.elsevier.com/locate/jms
The pure rotational spectrum of TiS (X3Dr) at submillimeter wavelengths
R.L. Pulliam 1, L.N. Zack, L.M. Ziurys ⇑
Department of Chemistry, University of Arizona, Tucson, AZ 85721, USA
Department of Astronomy, Steward Observatory, University of Arizona, 933 N. Cherry Ave., Tucson, AZ 85721, USA
a r t i c l e
i n f o
Article history:
Received 17 August 2010
In revised form 3 September 2010
Available online 16 September 2010
Keywords:
Titanium sulfide (TiS (X3Dr))
Rotational spectra
Millimeter/sub-millimeter directabsorption spectroscopy
a b s t r a c t
The pure rotational spectrum of TiS in its X3Dr ground state has been measured using millimeter–wave
direct-absorption techniques in the frequency range of 313–425 GHz. This free radical was created by the
reaction of titanium vapor, produced in a high-temperature Broida-type oven, with H2S. Eight to ten rotational transitions were recorded for the main titanium isotopologue, 48TiS, in the v = 0 and v = 1 levels, as
well as for the v = 0 state of 46TiS, observed in natural abundance (48Ti:46Ti = 74:8). All three X components were observed in almost every recorded transition, with no evidence for lambda-doubling. The data
were fit with a Hund’s case(a) Hamiltonian, and rotational, spin–orbit, and spin–spin constants were
determined, as well as equilibrium parameters for 48TiS. Relatively few fine structure parameters were
needed for the analysis of TiS (A, AD, and k), unlike other 3d metal species. The rotational pattern of
the three fine structure components suggests the presence of a nearby excited 1D state, lying
3000 cm1 higher in energy. From the equilibrium parameters, the dissociation energy for TiS was estimated to be 5.1 eV, in reasonable agreement with past thermochemical data.
Ó 2010 Elsevier Inc. All rights reserved.
1. Introduction
Titanium sulfide plays a significant role in a variety of scientific
areas. The disulfide form, TiS2, is an excellent high-temperature lubricant, primarily because of its layered structure, where titanium
cations occupy octahedral sites between layers of sulfide anions
[1]. The lubricating properties arise from the weak van der Waals
interaction between the layers. TiS2 is also a semiconductor material, and is widely used as the active cathode component in lithium
batteries [2]. Titanium sulfide complexes have been shown to activate H2 [3], and TiS clusters have been created with interesting
geometries, stabilized by bridging oxygen atoms [4]. TiS has also
been observed in the gas-phase in the atmospheres of S-type stars
via its A–X and E–X electronic transitions near 1 lm [5], suggesting
it may be detectable in circumstellar ejecta. Clearly, it is important
to understand TiS at the most fundamental (monomer) level [6]. If
simple properties of this species are understood, they can be generalized to more complex, bulk systems.
For several decades, various optical transitions of TiS have been
measured, starting in 1968, when Clements and Barrow recorded
the C3Dr–X3Dr band of this radical in the infrared [7]. These authors
⇑ Corresponding author at: Department of Chemistry, Steward Observatory,
University of Arizona, 933 N. Cherry Ave., Tucson, AZ 85721, USA. Fax: +1 520 621
5554.
E-mail address: [email protected] (L.M. Ziurys).
1
Present address: National Radio Astronomy Observatory, 520 Edgemont Rd.,
Charlottesville, VA 22903, USA.
0022-2852/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved.
doi:10.1016/j.jms.2010.09.005
were the first to identify the ground state term of TiS as X3Dr,
obtaining spectra for all three spin components and performing a
rotational analysis. The molecule was then further characterized
using Fourier-transform infrared methods by Jonsson and Launila,
who measured the A3U–X3D, E3P–X3D, and C3D–X3D bands in the
regions 6000–8600 and 10000–12600 cm1 [8]. Laser induced fluorescence studies of TiS were subsequently conducted by the Cheung group, who employed a supersonic jet/laser ablation source;
Ran et al. measured the lower J transitions of the C3D–X3D band
in the 743–863 nm region [9], while Cheung et al. found twentyone sub-bands which were assigned to the b1P–X3D, B3P0-X3D1,
and C3D–X3D transitions [10]. From their data, Cheung et al. determined that the v = 0, 1, and 2 levels of the C3D1 sub-band were
highly perturbed by the close-lying b1P state.
Here we present the first measurement of the pure rotational
spectrum of TiS in the X3Dr ground state. Rotational transitions
in all three spin components of the v = 0 and v = 1 vibrational levels
were recorded for 48TiS using millimeter-wave direct-absorption
techniques, as well as lines arising from the v = 0 state of 46TiS.
From these data, the spectroscopic constants have been refined,
including equilibrium parameters. Here we present our data, its
analysis, and interpretation of the constants in terms of the nearby
excited electronic states.
2. Experimental
The spectrum of TiS was measured utilizing one of the quasioptical millimeter/sub-millimeter spectrometers of the Ziurys
group. The details of the instrument are described elsewhere [11].
The instrument consists of a radiation source, a free-space gas cell,
and a detector. The radiation sources are phase-locked Gunn-oscillator/varacter multiplier combinations, which cover the frequency
range 65–850 GHz. Using a polarizing grid and two offset ellipsoidal mirrors, the radiation is quasi-optically directed into the
double-pass, steel reaction cell and then to the detector, a helium-cooled, InSb hot-electron bolometer. A pathlength modulator,
placed at the beam waist between the two mirrors, is employed to
improve baseline stability.
The TiS radical was created from the reaction of titanium vapor
and H2S. To produce the metal vapor, small titanium rods about 100
long (ESPI: 99.9%) were melted in a Broida-type oven, modified to
withstand higher temperatures (m.p. (Ti) = 1668 °C). Modifications
included the use of boron nitride crucibles in place of the usual alumina ones, as well as employing molybdenum rods for the oven
electrodes, instead of ones constructed of stainless steel. The oven
also had to be packed with alumina pieces and the crucible
wrapped with zirconia felt, in order to contain the heat. Such adaptations were previously used in the study of TiF [12]. About 1–
3 mTorr of H2S, added over the top of the oven, produced the best
TiS signals. Five mTorr of argon carrier gas was also added underneath the oven, which helped to control the melting rate of the
titanium.
Final measurements of the rotational transitions were made
from an average of one scan in increasing frequency, and the other
in decreasing frequency, covering the same 5 MHz range. Gaussian
curves were then fit to the line profiles to obtain the center frequency. Typical line widths were 0.7–1.6 MHz over the frequency
range of 313–425 GHz. The instrumental accuracy is estimated to
be ±50 kHz.
3. Results and analysis
The initial search for TiS was conducted by continuously scanning the entire range 380–420 GHz, based on frequency estimates
using the constants of Cheung et al. [10]. In these data, a pattern of
four repeating lines was readily found. Three of these features were
attributed to the spin components of a 3D pattern, while the fourth
line was identified as arising from the X = 1 component of the v = 1
level of TiS. Based on this pattern, the X = 2 and X = 3 components
of the v = 1 state of TiS were quickly identified. Some remaining
weaker features had a similar triplet structure, and were found
to be due to 46TiS, in the natural abundance of titanium
(48Ti:46Ti = 74:8). Sufficient signal-to-noise could not be achieved
to locate the 47TiS or 49TiS isotopologues, which would have provided valuable hyperfine information. There was no discernable
lambda-doubling splitting in any of the spectral data.
Once the spectrum of TiS was identified, additional transitions
were located and measured. For 48TiS, 10 rotational J + 1
J transitions were recorded in the v = 0 state and nine for the v = 1 excited level, while eight transitions were measured for the 46Ti
isotopologue (v = 0), as listed in Table 1. All three spin components
were observed for the majority of transitions. In total, 77 lines
were measured over the range 310–425 GHz.
Fig. 1 displays a stick diagram of the J = 34
33 transition near
414 GHz for the v = 0 and v = 1 states of 48TiS and the v = 0 state of
46
TiS. The relative intensities are also indicated, which were clearly
useful in identifying the X quantum numbers. As shown in the figure, the splitting between the three spin components was found to
be fairly regular. The X = 1 and X = 2 components are separated by
1.8 GHz for the J = 34
33 transition, while the separation between the X = 2 and X = 3 components is 1.6 GHz. For the
J = 29
28 transition, the splittings are 1.5 and 1.3 GHz.
Representative spectra for 48TiS are shown in Fig. 2, which displays the three spin components of the J = 30
29 transition near
363 GHz. There are two frequency breaks in the figure in order to
show all three lines. Each component appears as a single feature,
with no evidence of lambda-doubling splittings. The relative intensities between the three spin components indicate a rotational
temperature near 500 K.
The data sets for the v = 0 and v = 1 states of 48TiS and 46TiS were
individually analyzed with the following Hund’s case(a) effective
Hamiltonian:
^ eff ¼ H
^ rot þ H
^ so þ H
^ ss
H
ð1Þ
The terms describe molecular frame rotation, spin–orbit coupling, and spin–spin interactions. The spectra were fit with an
non-linear least-squares routine, HUNDA, developed by Brown.
For each data set, rotational (B and D), spin–orbit (A and AD), and
spin–spin (k) constants were determined, and these results are
shown in Table 2. The rms values for the 48TiS fits are 12 and
16 kHz for the v = 0 and v = 1 states, respectively, and 28 kHz for
46
TiS. Surprisingly, kD and higher order centrifugal distortion terms
to the fine structure constants were not required to achieve these
rms values, unlike other 3d species such as NiCN or TiCl+ [13,14].
The rotational constants derived here are in excellent agreement
with those determined from optical measurements [8,10],
although previous fits held many of the spin parameter to fixed
values. Our fitted A value of 47.4 cm1 agrees well with that determined by Cheung et al. from effective B constants (48.9 cm1) [10].
The spin–spin parameter found in this work (1.11 cm1), on the
other hand, is about a factor of two less than that derived by Jonsson and Launila (2.68 cm1), who based their analysis on the A–X,
C–X, and E–X electronic transitions [8]. However, a direct comparison between the two analyses is not feasible because the spin–orbit parameter, A, was fixed at 50 cm1 in the Jonsson and Launila fit
[8], and they included the additional parameters kD, c, and cD, but
not AD.
Based on the v = 1 and v = 0 data for 48TiS, equilibrium parameters Be, De, ae, and be were calculated using a least-squares analysis,
from which an equilibrium bond length was also derived. These
parameters are also listed in Table 2. The harmonic vibrational frequency, xe, and anharmonic correction, xexe, were additionally
estimated using the Kratzer and Pekeris approximations, see
[15–17]. Finally, the dissociation energy was calculated from the
harmonic and anharmonic potential terms. The equilibrium
parameters and vibrational constants are in excellent agreement
with those of Jonsson and Launila [8], as shown in the table.
4. Discussion
The pure rotational spectra obtained in this work clearly support the TiS ground state assignment as X3
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R.L. Pulliam et al. / Journal of Molecular Spectroscopy 264 (2010) 50–54
Table 1
Rotational transition frequencies of TiS (X3Dr) in MHz.
J+1
J
X
26
25
27
26
1
2
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
28
27
29
28
30
29
31
30
32
31
33
32
34
33
35
34
48
TiS,
48
v=0
TiS,
mobs
mobs–mcalc
313607.702
314957.038
0.002
0.029
327052.586
328294.019
337695.165
339146.070
340432.705
349735.915
351237.391
352569.081
361774.580
363326.501
364703.174
373811.082
375413.327
376834.918
385845.356
387497.804
388964.176
397877.306
399579.807
401090.912
409906.925
411659.296
413214.995
421934.077
423736.213
425336.400
0.007
0.015
0.001
0.012
0.035
0.003
0.004
<0.000
0.006
0.001
0.015
0.003
<0.000
0.003
0.002
0.017
0.002
0.020
0.002
0.011
0.001
0.008
0.008
0.003
0.004
0.007
46
v=1
TiS,
v=0
mobs
mobs–mcalc
mobs
mobs–mcalc
324185.578
325572.419
326801.411
336173.908
337610.993
338884.694
0.004
0.002
0.010
0.007
0.013
0.013
349647.394
350965.717
360144.429
361681.598
363044.465
372126.468
373713.472
375120.787
384106.299
385742.989
387194.664
396083.773
397770.043
399265.972
408058.884
409794.587
411334.688
420031.485
421816.483
423400.722
0.001
0.010
0.008
0.015
0.003
0.012
0.001
0.018
0.019
0.002
0.014
0.007
0.006
0.028
0.020
0.006
0.004
0.017
0.024
0.047
331273.558
332722.172
334007.059
343523.919
345024.860
346356.419
355772.169
357325.418
358703.632
368018.251
369623.682
371048.462
380262.156
381919.547
383390.768
392503.682
394213.028
395730.537
0.021
0.027
0.065
0.008
0.039
0.057
0.008
0.023
0.021
0.004
0.009
0.020
0.038
0.024
0.007
0.006
0.027
0.008
406503.937
408067.665
416979.544
418792.198
420402.063
0.035
0.001
0.034
0.002
0.019
spin–orbit coupling, resulting from perturbations with nearby excited states, i.e. k = kss + kso [20]. For heavier molecules, the second-order spin–orbit contribution dominates [21], and can
described by the following equation, based on second-order perturbation theory [22]:
kso ¼
30ð2S 2Þ! X X
ð2S þ 3Þ!
R n0 ;K0 ;R0
^ so jn; K; Rij2
½3R2 SðS þ 1Þjhn0 ; K0 ; R0 jH
En0 En
ð2Þ
The quantum numbers n0 , K0 , and R0 sum over nearby perturbing states. The a1D and X3D states in TiS can interact via the oneelectron spin–orbit operator, which follows the selection rules
DS = 0, ±1, DX = 0, DR = DK = 0, 1, and R± M R. Considering
the a1D state only, Eq. (2) simplifies to:
kSO ¼
Fig. 1. Stick spectrum of the J = 34
33 rotational transition of titanium sulfide
(X3Dr) near 414 GHz, showing the positions and relative intensities of the three fine
structure components originating in the v = 0 and v = 1 states of the main
isotopologue, 48TiS, as well as the ground vibrational state of 46TiS. The spacing
between the spin components is relatively equal, with a slight shift to higher
frequency in the X = 2 line relative to X = 1 and 3 features.
Heaven [19] predict that it exists with an energy of 3500 cm1,
significantly lower than any of the observed states. Furthermore,
the a1D and b1P states in TiO have been observed at 3444 and
14,717 cm1, respectively, above the X3D ground state [19]. Given
the similarities between TiO and TiS, the a1D state is probably the
closest perturber in titanium sulfide.
The energy of the a1D state in TiS can be estimated from the
spin–spin constant, k. This parameter is defined as a sum of the
pure microscopic electron spin–spin interactions and second-order
30ð2S 2Þ! ½3R2 SðS þ 1Þjha1 D2 jRai li si jX3 D2 ij2
ð2S þ 3Þ!
Eð1 DÞ EðX3 DÞ
ð3Þ
Here ai is the spin–orbit constant, and the summation is over
the unpaired electrons. Both the a1D and X3D states arise from a
11r11d1 electron configuration, and differ by a spin-flip. As discussed by Cheung et al. [10], the 11r orbital is chiefly 4s in character, while the 1d orbital is 3d. The Slater determinants of the X = 2
substates can be written as:
3 X D2 ¼ p1ffiffiffi jradþ b þ rbdþ aj
2
ð4Þ
and
1 a D2 ¼ p1ffiffiffi jradþ b rbdþ aj
2
ð5Þ
For the 3D2 level, S = 1 and R = 0, and considering that the state
can be created from both K = +2 and K = 2 values of angular
momentum, the above expression then becomes:
kso ¼
1 a2
4 DE
ð6Þ
Allowing kso = 33 340 MHz, the spin–spin constant derived from
the 48TiS fit, and assuming that a = 119 cm1, the atomic spin–orbit
constant of Ti2+ [19,20], then DE(1D 3D) 3190 cm1. This value
is quite close to the energy predicted for the a
54
R.L. Pulliam et al. / Journal of Molecular Spectroscopy 264 (2010) 50–54
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