Journal of Molecular Spectroscopy 234 (2005) 34–40
www.elsevier.com/locate/jms
Velocity modulation spectroscopy of molecular ions I:
The pure rotational spectrum of TiCl+ (X3Ur)
D.T. Halfen, L.M. Ziurys *
Departments of Chemistry and Astronomy, Arizona Radio Observatory, and Steward Observatory, University of Arizona, 933 N.
Cherry Avenue, Tucson, AZ 85721, USA
Received 14 May 2005; in revised form 22 July 2005
Available online 26 September 2005
Abstract
The pure rotational spectrum of the TiCl+ ion in its X3Ur ground state has been measured in the frequency range 323–424 GHz,
using a combination of direct absorption and velocity modulation techniques. The ion was created in an AC discharge of TiCl4 and
argon. Ten, eleven, and nine rotational transitions were recorded for the 48Ti35Cl+, 48Ti37Cl+, and 46Ti35Cl+ isotopomers, respectively; fine structure splittings were resolved in every transition. The rotational fine structure pattern was irregular with the X = 4
component lying in between the X = 2 and 3 lines. This result is consistent with the presence of a nearby 3Dr state, which perturbs the
X = 2 and 3 sub-levels, shifting their energies relative to the X = 4 component. The data for each isotopomer were analyzed in a
global fit, and rotational and fine structure parameters were determined. The value of the spin–spin constant was comparable to
that of the spin–orbit parameter, indicating a large second-order spin–orbit contribution to this interaction. The bond length established for TiCl+, r0 = 2.18879 (7) Å, is significantly shorter than that of TiCl, which has r0 = 2.26749 (4) Å. The shorter bond length
likely results from a Ti2+Cl structure in the ion relative to the neutral, which is thought to be represented by a Ti+Cl configuration. The higher charge on the titanium atom shortens the bond.
2005 Elsevier Inc. All rights reserved.
Keywords: Spectroscopy; Ions; Rotational
1. Introduction
The technique of velocity modulation (VM) has traditionally been used only in optical and infrared ion spectroscopy (i.e., 600–17 000 cm1) [1,2]. However, it is not
limited to these spectral regions and has recently been
shown to work at much longer wavelengths. Stephenson
and Saykally [3] have demonstrated that velocity modulation can be applied at terahertz frequencies, and Savage, Apponi, and Ziurys [4,5] extended the scope of
VM to the millimeter/sub-millimeter regime. At the
longer wavelengths, the VM technique is not quite as
powerful as in the infrared, for example, because the
lines are somewhat undermodulated [3,4]. Nevertheless,
*
Corresponding author. Fax: +1 520 621 1532.
E-mail address: [email protected] (L.M. Ziurys).
0022-2852/$ - see front matter 2005 Elsevier Inc. All rights reserved.
doi:10.1016/j.jms.2005.08.004
the ion selectivity of this method is still a major advantage in eliminating neutral signals [4].
The first molecule studied with the mm/sub-mm VM
instrument in the Ziurys group was SH+ [5]. The measurement of the pure rotational spectrum of this openshell ion demonstrated the potential of the spectrometer
system to preferentially detect such species. Naturally
obtaining the rotational spectrum of other ionic species
using this instrument is of interest, in particular metalcontaining compounds. One such ion is TiCl+.
Titanium chloride cation has been the subject of various studies over the past 15 years. It was observed initially by Balfour and Chandrasekhar [6] in 1990, who
measured P-branch bandheads from 559 to 564 nm
and assigned the spectrum as a 3P–X3D transition. Following this work, Kaledin et al. [7] used ligand field theory (LFT) to calculate the electronic states of TiCl+.
D.T. Halfen, L.M. Ziurys / Journal of Molecular Spectroscopy 234 (2005) 34–40
Their computations indicated that a 3Ur term was the
ground state, and therefore these authors suggested that
the transition observed by Balfour and Chandrasekhar
was the [17.9]3Dr–X3Ur system. Kaledin and Heaven [8]
subsequently confirmed this assignment experimentally
using direct laser absorption methods, and determined
preliminary spectroscopic constants for the 3D and
ground 3U states, as well. At the same time, Focsa
et al. [9] used laser absorption/velocity modulation techniques to also measure the [17.9]3Dr–X3Ur band of TiCl+
with 0.005 cm1 resolution, establishing effective rotational, spin–orbit, and spin–spin parameters for both
states. These authors also suggested that the X = 4
spin–orbit component in the X3Ur state was perturbed
relative to the other two X components. Kaledin and
Heaven [10] then conducted further measurements of
the [17.9]3Dr–X3Ur and [17.9]3Dr–(1)3Dr transitions with
associated LFT calculations, which predicted nearby
3
R and 3P states. The most recent work is by Focsa
et al. [11,12] and Focsa and Pinchemel [13]. In the Focsa
et al. [11] study, the [17.9]3Dr–X3Ur (v = 0 and 1) and the
[17.9]3Dr–A3Dr systems were measured. Here, the X = 2
and 3 ladders of TiCl+ in its X3Ur (v = 0 and 1) and
A3Dr (v = 0) states were found to interact with each
other, while the X = 4 sub-level (X3Ur) remained free
of any perturbations [11]. An analysis combining the
data of the X3Ur (v = 0 and 1) and A3Dr (v = 0) states
was then performed to establish ‘‘deperturbed’’ spectroscopic constants for these states [11]. Focsa et al. [12]
additionally performed density functional theory
(DFT) and LFT calculations on TiCl and TiCl+, and
determined that the ionization potential of titanium
chloride was 7.06 eV.
In this study, we report the first measurement of the
pure rotational spectrum of TiCl+ in its X3Ur (v = 0)
state. The ion was synthesized in an AC discharge of
TiCl4. All three spin components were observed for
the isotopomers 48Ti35Cl+, 48Ti37Cl+, and 46Ti35Cl+.
This study was conducted using a combination of velocity modulation (for ion selectivity) and direct absorption
(for sensitivity in scanning). Here, we present our results, spectral analysis, and a discussion of the data.
2. Experimental
The pure rotational spectrum of TiCl+ was measured
using the velocity modulation spectrometer of the Ziurys
group, which has been described in detail elsewhere [4].
Briefly, the instrument consists of a radiation source, gas
cell, and detector. Gunn oscillators/Schottky diode multipliers are used to generate frequencies between 65 and
650 GHz. The reaction chamber is a single-pass glass
cell containing ring discharge electrodes, and a cooling
jacket chilled to 65 C by methanol. The radiation is
launched from a scalar feedhorn and is propagated
35
through the system quasi-optically using a series of Teflon lenses, two of which seal off the ends of the gas cell.
The detector is an InSb hot electron bolometer, and the
system is under computer control.
Titanium chloride cation was created in an AC discharge of gas-phase TiCl4 and argon. The strongest signals of TiCl+ occurred using 20 mTorr of Ar and less
than 1 mTorr of TiCl4; this mixture produced a bright
blue–white plasma that dominated the normal purple
discharge glow from the argon. The discharge was modulated at a rate of 20 kHz with a power level of 200 W at
600 X.
Signals arising from TiCl+ were initially found by
recording scans 100 MHz in coverage. First, scans were
taken in source modulation mode with 2f detection for a
higher signal-to-noise ratio. If lines were present, the
data were then retaken in velocity modulation mode to
select those signals arising from ions. Precise rest frequencies were obtained by averaging scans 5 MHz wide,
taken in increasing and decreasing frequency, using
source modulation. Typically, 1–4 scan pairs were needed to obtain a sufficient signal-to-noise ratio. Gaussian
profiles were fit to the line shapes to obtain the center
frequency and line width, which varied from 1.0 to
1.4 MHz from 323 to 424 GHz. The experimental accuracy is estimated to be ±40 kHz.
3. Results and analysis
The transitions frequencies of 48Ti35Cl+ and
Ti37Cl+ were initially predicted using the effective rotational parameters of Focsa et al. [9,11]. These constants
were sufficiently accurate that signals from these ions
were found within 100 MHz of the predictions. Previous
estimates of rotational constants for 46Ti35Cl+ did not
exist, so these were obtained from the 48Ti isotopomer
by scaling by molecular mass.
The observed rotational transitions of the three TiCl+
isotopomers are listed in Table 1. Ten, eleven, and nine
transitions were measured for 48Ti35Cl+, 48Ti37Cl+, and
46 35 +
Ti Cl , respectively. As shown in the table, each rotational transition is split into three fine structure components due to spin–orbit/spin–spin coupling and is
labeled by the quantum number X. As is also evident
in Table 1, the pattern of the spin–orbit splittings deviates considerably from a typical case (a) coupling
scheme. For a given rotational transition, the X = 2
and 3 components are both shifted to significantly higher frequency as compared to the X = 4 line, such that the
ordering of these features in increasing frequency is
X = 2, 4, and 3, not X = 2, 3, and 4 as in a ‘‘normal’’
Ur state. This pattern can be seen in Fig. 1, which displays spectra of the J = 37 fi 38 transition of 48Ti35Cl+
near 395 GHz (top panel), and the J = 36 fi 37 transition of 46Ti35Cl+ near 392 GHz (bottom panel). These
48
36
D.T. Halfen, L.M. Ziurys / Journal of Molecular Spectroscopy 234 (2005) 34–40
Table 1
Observed rotational transitions of
J00 fi J 0
X
30 fi 31
2
3
4
2
3
4
2
3
4
2
3
4
2
3
4
2
3
4
2
3
4
2
3
4
2
3
4
2
3
4
2
3
4
2
3
4
31 fi 32
32 fi 33
33 fi 34
34 fi 35
35 fi 36
36 fi 37
37 fi 38
38 fi 39
39 fi 40
40 fi 41
41 fi 42
a
b
48
Ti35Cl+,
48
Ti37Cl+, and
46
Ti35Cl+ (X3Ur: v = 0)a
48
Ti35Cl+
48
Ti37Cl+
mobs
mobsmcalc
322927.414
323297.905
323156.037
333322.960
333705.663
333561.278
343716.434
344111.266
343964.669
354107.777
354514.788
354366.190
364496.962
364916.143
364765.753
374883.903
375315.282
375163.298
385268.555
385712.131
385558.767
395650.832
396106.617
395952.103
406030.676
406498.708
406343.266
416408.036
416888.324
416732.131
0.032
0.068
0.085
0.005
0.038
0.037
0.015
0.020
0.011
0.004
0.017
0.031
0.007
0.007
0.058
0.003
0.005
0.066
0.010
0.001
0.056
0.005
0.014
0.027
0.006
0.009
0.004
0.012
0.001
0.104
46
Ti35Cl+
mobsmcalc
mobs
322953.671
323314.057
323171.257
333024.570
333396.685
333251.156
343093.350
343476.429
343329.329
353160.158
353554.693
353405.545
363224.870
363630.856
363479.909
373287.393
373704.867
373552.337
383347.712
383776.673
383622.750
393405.736
393846.223
393691.112
403461.443
403913.422
403757.295
413514.731
413978.255
413821.346
423565.431
424040.610
423883.213
0.037
0.105
—b
0.043
—b
0.111
0.014
0.047
0.005
0.002
0.031
0.004
0.014
0.027
0.022
0.002
0.025
0.053
0.005
0.018
0.063
0.007
0.002
0.071
0.003
0.001
0.002
0.007
0.024
0.043
—b
0.019
0.061
mobsmcalc
mobsmcalc
328815.478
329199.173
329056.267
339400.167
339796.364
339651.042
349982.690
350391.441
350244.185
360562.942
360984.439
360835.220
371141.161
371575.125
371424.259
381716.920
382163.551
382011.184
392290.326
392749.576
392596.013
402861.286
403333.176
403178.597
413429.697
413914.287
413758.893
0.017
0.043
0.051
0.013
0.003
—b
0.003
0.043
0.016
—b
0.005
0.021
0.016
0.020
0.038
0.008
0.001
0.009
0.000
0.007
0.011
0.011
0.001
0.046
0.012
0.020
—b
In MHz.
Blended lines, not included in fit.
two isotopomers were observed in natural abundance of
titanium (48Ti:46Ti = 73.7:7.4). There are two frequency
breaks in each spectrum of about 300 and 150 MHz,
respectively. The ratio of relative intensities of the
spin–orbit components is X = 2:3:4 = 5:2.2:1, indicating
Tspin–orbit=Tso 355 K. No hyperfine splittings arising
from the chlorine nuclear spin of I = 3/2 are visible in
these spectra, a general result for the whole data set.
These lines persisted in velocity modulation mode, as
demonstrated in Figs. 2 and 3, which distinguished them
from neutral species, in particular TiCl. In Fig. 2, the exact same transition from Fig. 1 is shown, but in velocity
modulation mode. The features now display a first
derivative line shape, and the signal-to-noise ratio has
decreased by about a factor of 4. The velocity-modulated lines are also narrower than those generated by
source modulation by about a factor of 1.5. The de-
crease in intensity and line width is due to undermodulation of the spectral lines. The loss in signal-to-noise,
however, is countered by effective neutral suppression,
as demonstrated in Fig. 3. These data display the
X = 2 component in the J = 38 fi 39 transition of
46 35 +
Ti Cl in source modulation (top panel) and velocity
modulation (bottom panel) modes. In the source modulation spectrum, there are seven features, all within the
estimated frequency range of the respective component
of TiCl+. The same data taken using velocity modulation show only one feature, the TiCl+ transition in
question.
No lines originating in excited vibrational states of
TiCl+ were observed in this work, as opposed to other
chloride molecules studied in our group, such as CoCl
[14] and MnCl [15], where several vibrational states were
found. This result is probably because the VM cell,
D.T. Halfen, L.M. Ziurys / Journal of Molecular Spectroscopy 234 (2005) 34–40
48
Ω=2
Ti35Cl+ (X3Φr): J = 37
48
38
Ω=2
37
Ti35Cl+ (X3Φr): J = 37
38
Velocity Modulation
Ω=4
Ω=3
Ω=3
Ω=4
395.640
395.660
395.945
395.965
46
*
Ω=2
396.095
Ti Cl (X Φr): J = 36
35
+
3
*
392.300
392.585
37
Ω=3
Ω=4
392.280
396.115
*
392.605 392.735
*
392.755
Frequency (GHz)
Fig. 1. Laboratory spectra of the J = 37 fi 38 transition of 48Ti35Cl+
(X3Ur) near 395 GHz and the J = 36 fi 35 transition of 46Ti35Cl+ near
392 GHz recorded in source modulation mode. There are two
frequency breaks in each spectrum to display the three spin–orbit
components, which are plotted on the same intensity scale. The spin–
orbit spacing is irregular with the X = 4 component lying between the
X = 2 and 3 lines. Unknown features in the spectra are marked with an
asterisk. The spectra were created from a composite of three single
110 MHz wide scans, each acquired in 70 s, and then cropped to each
display a 40 MHz frequency range.
which is methanol-cooled, produces colder molecules
than those that were made using a Broida-type oven.
For TiCl+, Tso 355 K, for example, while Tso
480 K for CoCl [14]. Also, the vibrational separation
of TiCl+ is 700 K (485 cm1) [11], making population
of higher vibrational levels difficult.
The spectrum of TiCl+ was analyzed using an effective HundÕs case (a) Hamiltonian, including rotation,
spin–orbit, and spin–spin constants and their respective
centrifugal distortion corrections:
^ eff ¼ H
^ rot þ H
^ so þ H
^ ss .
H
ð1Þ
For each isotopomer, all rotational data from the three
spin–orbit components were analyzed simultaneously in
a global fit. To fit these data, the spin–orbit constant A
395.640
395.660
395.945
395.965
Frequency (GHz)
396.095
396.115
Fig. 2. Spectrum of the J = 37 fi 38 transition of 48Ti35Cl+ near
395 GHz taken in velocity modulation mode. There are two frequency
breaks in the spectra to accommodate the three spin–orbit components, which are plotted on the same scale. These data have the firstderivative line profile characteristic of velocity modulation spectra.
The spectrum was created from a composite of three single 110 MHz
wide scans, each acquired in 70 s, and then cropped to display a
40 MHz frequency range. The signal-to-noise ratio is about a factor of
4 less than in source modulation mode (see Fig. 1).
was held fixed to the value of Focsa et al. [11], but
the spin–spin parameter k was allowed to vary. Higher-order spin–orbit and spin–spin terms (AD, AH, kD,
and kH) were found to be necessary to achieve a good
fit. Because the error was found to be comparable to
its value, kH was fixed in the final fit for all three species.
The resulting spectroscopic parameters are listed in Table 2. The rms of the fits ranged from 23 to 41 kHz. For
comparison, the constants determined by Focsa et al.
[9,11] are also listed in Table 2 for 48Ti35Cl+ and
48 37 +
Ti Cl . The rotational parameters for 48Ti35Cl+ from
Focsa et al. [11] are in good agreement with those established in this work, although k and the higher-order
spin–orbit and spin–spin constants are significantly different. However, the constants of Focsa et al. [11] were
determined from a deperturbation analysis. Thus, their
fine structure parameters are not directly comparable,
as the analysis here made no correction for perturbations. Furthermore, the mm wave analysis included the
additional higher-order terms AH and kH, which impacts
the fit as well. The rotational constants of Focsa et al. [9]
for 48Ti37Cl+ are also in reasonable agreement with
those established in this work. Again, there are some differences because Focsa et al. [9] only used the X = 2 and
3 components in their analysis, while here all three spin
sub-levels were considered.
A more direct comparison of the optical and mm
wave parameters is given in Table 3. Here, the effective
rotational constants from both the millimeter-wave
and the optical studies are listed. The agreement between the two sets of parameters is very good for both
chlorine isotopomers of TiCl+. Differences in the global
38
D.T. Halfen, L.M. Ziurys / Journal of Molecular Spectroscopy 234 (2005) 34–40
46
fits therefore must arise from variations in the individual
data sets, as previously described.
Ti35Cl+ (Ω = 2)
J = 38
39
4. Discussion
Source Modulation
Velocity Modulation
413.40
413.43
413.46
Frequency (GHz)
Fig. 3. Spectrum of the J = 38 fi 39, X = 2 transition of 46Ti35Cl+
near 413 GHz taken in source modulation mode (top panel: secondderivative spectrum) and velocity modulation mode (bottom panel:
first-derivative spectrum). The intensity scale of the VM spectrum is
four times less than that of the source modulation spectrum. The
source modulation spectrum displays various lines, which disappear in
the velocity modulation data. These features arise from unwanted
neutral species. The source modulation and velocity modulation data
are an average of two and twelve 100 MHz wide scans, respectively,
each 70 s in duration.
Table 2
Spectroscopic constants for
Parameter
B
D
A
AD
AH
k
kD
kH
rms
r0 (Å)
a
b
c
d
48
35
48
Ti35Cl+,
Ti Cl
48
Ti37Cl+, and
The r0 bond lengths were calculated from the rotational constants for all three isotopomers of TiCl+ and
are listed in Table 2. The bond lengths of the three isotopomers are very similar, illustrating that the molecule
closely follows the Born–Oppenheimer approximation.
The
average
bond
length
of
TiCl+
is
+
r0 = 2.18879 (7) Å. The bond length of TiCl is significantly shorter than that of neutral TiCl:
r0 = 2.26749 (4) Å [16]—a difference of 0.079 Å. This decrease is probably due to the additional electrostatic
attraction in the ion relative to the neutral species.
According to Focsa, Bencheikh, and Pettersson [12],
TiCl+ can be thought of as Ti2+Cl with an electron
configuration of (core) 5p11d1, as opposed to Ti+Cl0.
TiCl is best represented as Ti+Cl with (core)11r11d15p1. The additional charge on the titanium
atom results in a stronger electrostatic attraction between the two atoms, shortening the internuclear distance. The difference is not likely to be a question of
covalent-type bonding because the valence 1d, 5p, and
11r orbitals are essentially nonbonding, arising from
the 3d electrons on titanium.
In addition to the TiCl+ ion, the neutral TiCl (X4Ur)
molecule was also observed in the AC discharge of
TiCl4. The relative intensity of the neutral compared
to the ion is shown in Fig. 4. Here, spectra of the
J = 38 fi 39 transition of TiCl+ (top panel) and the
J = 39.5 fi 40.5 transition of TiCl (bottom panel)
are displayed on the same intensity scale. There are frequency breaks in both spectra to include all of the
46
Ti35Cl+ (X3Ur: v = 0)a
+
48
Ti37Cl+
46
Ti35Cl+
mm wave
Opticalb
mm wave
Opticalc
mm wave
5216.6676 (21)
0.00256353 (78)
19 00 000d
2.7834 (89)
6.308 (36) · 105
44 04 278 (5000)
18.071 (46)
1.000 · 105d
0.037
2.1888077 (4)
5226.07 (54)
0.002728 (45)
19 04 570 (80)
0.489 (54)
5054.1115 (23)
0.00241142 (79)
19 00 000d
2.6012 (94)
5.647 (37) · 105
44 04 301 (5600)
16.993 (49)
5.992 · 106d
0.041
2.1887180 (5)
5056.12 (54)
0.00240 (11)
19 22 600 (90)
1.916 (18)
5311.9488 (17)
0.00265535 (69)
19 00 000d
2.8935 (70)
6.715 (35) · 105
44 04 291 (3900)
18.720 (37)
1.200 · 105d
0.023
2.1888587 (4)
11 030 (180)
0.507 (18)
In MHz; errors are 3r in the last quoted digits.
Deperturbed parameters from Focsa et al. [11].
From Focsa et al. [9]; based on X = 2 and 3 components only.
Held fixed (see text).
47 157 (90)
0d
D.T. Halfen, L.M. Ziurys / Journal of Molecular Spectroscopy 234 (2005) 34–40
39
Table 3
Effective rotational constants for the spin components of TiCl+a
48
Ti35Cl+
Parameter
Beff (X = 2)
Deff (X = 2)
Beff (X = 3)
Deff (X = 3)
Beff (X = 4)
Deff (X = 4)
a
b
c
48
Ti37Cl+
b
46
Ti35Cl+
c
mm wave
Optical
mm wave
Optical
mm wave
5213.6300 (43)
0.0026655 (17)
5219.5661 (43)
0.0026443 (17)
5216.7713 (43)
0.0023807 (17)
5213.75 (27)
0.002662 (54)
5219.72 (27)
0.002644 (45)
5217.26 (27)
0.002491 (54)
5051.2777 (43)
0.0025030 (16)
5056.8715 (42)
0.0024856 (14)
5054.1535 (43)
0.0022461 (15)
5050.27 (63)
0.002400 (90)
5056.09 (63)
0.002430 (90)
5053.7 (1.4)
0.00214 (45)
5308.7864 (52)
0.0027632 (20)
5314.9324 (50)
0.0027413 (20)
5312.0910 (67)
0.0024615 (27)
In MHz; errors are 3r in the last quoted digits.
From Focsa et al. [11].
From Focsa et al. [9].
1.0
Ti35Cl+ (X3Φr): J = 38
48
Intensity (mV)
Ω=2
0.5
Ω=4
39
Ω=3
*
0.0
-0.5
406.023
406.043
406.334 406.354
406.491
406.511
Ti35Cl (X4Φr): J = 39.5
40.5
1.0
Intensity (mV)
Ω = 3/2
48
Ω = 5/2
Ω = 7/2
0.5
Ω = 9/2
0.0
-0.5
391.298
392.375
393.456
394.554
Frequency (GHz)
Fig. 4. Spectrum of the J = 38 fi 39 transition of 48Ti35Cl+ near
406 GHz (top panel) and the spectrum of the J = 39.5 fi 40.5
transition of 48Ti35Cl near 391–394 GHz (bottom panel) taken in
source modulation mode. There are two frequency breaks in the TiCl+
spectrum and three in the TiCl data, such that all spin–orbit
components can be displayed. The data are plotted on the same scale
given in mV. An unknown feature in the TiCl+ spectra is marked with
an asterisk. The relative intensities of the ion and neutral species are
virtually identical, illustrating the efficient production of TiCl+ in an
AC discharge. Each of the spin component spectra is 40 MHz wide and
were each extracted from a single 110 MHz scan, acquired in 70 s in
source modulation mode.
spin–orbit components for both molecules. As can be
seen in the figure, the signal-to-noise ratio of TiCl+ is
comparable to that of TiCl. Accounting for the number
of spin–orbit components for both molecules, TiCl neutral is only 1.7 times stronger than the ion. This result
is relatively unusual since ions are thought to make up a
very small fraction of the species found in electrical discharges [4]. The relative strength of TiCl+ might be an
indication that TiCl4 easily breaks apart into ions as well
as neutral species in an AC discharge. Based on the relative intensities of the spin components, the spin–orbit
temperature observed for TiCl is Tso 440 K, as compared to Tso 355 K for TiCl+—roughly similar. This
result suggests that the neutral and the ion may both
be made directly from TiCl4, rather than from secondary
processes.
The fine structure pattern in TiCl+ deviates considerably from that of pure case (a) with rotational transitions of the highest energy spin component, X = 4,
appearing approximately midway in frequency between
those originating in the two lower spin sub-levels. This
rotational pattern is though to result from spin-electronic homogeneous perturbations, which follow the selection rules DX = 0, DK = DR = ±1, and DS = 0 [17].
As discussed by Focsa et al. [11], this perturbation is believed to arise from interactions with the nearby excited
A3Dr state. This state lies 400 cm1 in energy above the
X3Ur state and perturbs the X = 2 and 3 components,
lowering their energies relative to the X = 4 sub-level.
As a consequence, the regular case (a) spin–orbit pattern
in TiCl+ is distorted.
This perturbation manifests itself in the large value of
k, 44 04 278 MHz, generated in the fit. In fact, for TiCl+,
k > A, where A is the spin–orbit parameter. The k constant in part compensates for the shifting of the lower X
ladders. In contrast, the ‘‘deperturbed’’ k value, estimated by Focsa et al. [11], is 11 030 MHz—over two orders of magnitude smaller. A large value of k was also
found for the CoCl radical in its X3Ui state [14]. In this
species, the X = 3 ladder was perturbed such that the
spin–orbit components in a given rotational transition
did not follow a regular case (a) pattern. The rotational
data for CoCl, however, was easier to analyze because
the perturbation only occurred in the X = 3 sub-level
where k, but not A, is present in the diagonal matrix element. For TiCl+, the X = 2 level is additionally shifted,
and both A and k enter into the its diagonal matrix element as competing parameters.
40
D.T. Halfen, L.M. Ziurys / Journal of Molecular Spectroscopy 234 (2005) 34–40
5. Conclusion
References
The pure rotational spectrum of TiCl+ in its X3Ur
ground state has been recorded for the first time. The
study of this ion has been aided by using velocity modulation techniques, which have been extended to millimeter/
sub-millimeter wavelengths. Curiously, in an AC discharge, signals generated for TiCl+ are nearly equivalent
to those of the neutral TiCl, indicating that this ion production method can be very efficient for certain species.
Previous measurements of several electronic transitions
of TiCl+ have suggested the presence of perturbations in
the ground state, which are also observed in the pure rotational spectrum. The spin–spin constant k derived from
the spectroscopic analysis is quite large, indicating a substantial second-order spin–orbit contribution, which
likely arises from homogeneous spin-electronic perturbations. The measurement of the spectrum of TiCl+ suggests
that other metal ions can be studied using millimeter/submillimeter velocity modulation techniques.
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Acknowledgment
This research is supported by NSF Grant CHE0411551.