Laser induced fluorescence spectroscopy of jet-cooled ThO

Journal of Molecular Spectroscopy 360 (2019) 39–43

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Laser induced fluorescence spectroscopy of jet-cooled ThO Joel R. Schmitz, Leonid A. Kaledin, Michael C. Heaven ⇑ Department of Chemistry, Emory University, Atlanta, GA 30322, United States

a r t i c l e

i n f o

Article history: Received 10 February 2019 In revised form 23 April 2019 Accepted 27 April 2019 Available online 29 April 2019

a b s t r a c t Non-equilibrium ThO(X) that was vibrationally hot but rotationally cold was produced by pulsed laser vaporization followed by supersonic expansion. This source was ideal for spectroscopic investigations of vibrationally excited levels of both the ground and electronically excited states. Laser induced fluorescence spectroscopy has been used to characterize vibrationally excited levels of the X, C, D, E, F and I states. Data for the ground state have been used to determine the potential energy curve for the energy range 0–13000 cm
1. In addition, transitions to newly identified states O0 (0+) and L0 (1) are tentatively assigned. The results are found to be in reasonable agreement with the predictions of ligand field theory models. Ó 2019 Elsevier Inc. All rights reserved.

1. Introduction Diatomic ThO is one of the most extensively studied actinide species by means of gas phase spectroscopy [1–22]. Electronic transitions have been investigated using emission and laser excitation techniques. A significant fraction of these data was obtained by Edvinsson and co-workers [1–9,15,16] who used a microwave discharge to excite ThO emission. High-resolution laser induced fluorescence (LIF) spectroscopy was used to determine the dipole moments of the ground and selected excited states by means of the Stark effect [17,19], and magnetic g-factors from the Zeeman effect [19,23], while 2-dimensional LIF measurements have been used to determine fluorescence branching ratios [18]. Microwave spectroscopy has been used to examine the pure rotational transiP tions of the X1 + ground state for vibrational levels in the range of 00 v = 0–15 [14,21,22]. Over the past decade a number of studies were motivated by the possibility of using the lowest energy electronically excited state of ThO, H3D1, for determination of the electron electric dipole moment (eEDM) [20,23–29]. The current lower bound of <1.1  10
29 e cm was obtained using the C-X, CAH and IX transitions for state preparation and read-out [20]. The spectroscopic properties of ThO have also been used to evaluate the capabilities of relativistic electronic structure models [28,30–37]. Excited state properties have been predicted using ab initio [32,37] and ligand field theory (LFT) approaches [13,38– 41]. These studies have shown that the electronic states of ThO below 5 eV can be understood in terms of the states of the Th2+ ion perturbed by the closed-shell O2
ligand. Kaledin et al. [39] have recently developed a configuration interaction LFT (CI-LFT) ⇑ Corresponding author. E-mail address: [email protected] (M.C. Heaven). https://doi.org/10.1016/j.jms.2019.04.010 0022-2852/Ó 2019 Elsevier Inc. All rights reserved.

model for ThO that has been used to identify previously unreported states using unassigned data from the Vatican Atlas listings for ThO [12]. The present study of ThO was motivated by three primary considerations. The first was practical. We have been investigating a range of ThX species using pulsed laser vaporization as the means to obtain gas phase samples of refractory materials. Despite considerable efforts to suppress oxide production, ThO is always present in our LIF and emission spectroscopy measurements (note that Edvinsson et al. [1–6,8,9] obtained their emission spectra using a discharge in ThI4 vapor, with no deliberately added source of oxygen). In our LIF studies of expansion-cooled ThX species we found that many of the accompanying ThO bands had not been reported previously. This was not particularly surprising given that the conditions for our LIF measurements were dramatically different from those of the earlier emission spectroscopy experiments. An interesting property of the laser ablation – jet cooling source is that the internal degrees of freedom for a molecule will often exhibit different effective temperatures for different kinds of motion. Rotational relaxation is easily achieved but the rates for vibrational and electronic relaxation are more dependent on the energy intervals between states. Consequently, these degrees of freedom may exhibit temperatures that are much higher than the rotational temperature. Long et al. [14] used laser ablation with jet expansion cooling in their study of the microwave spectrum of ThO(X). A low rotational temperature was achieved, but vibrational levels up to v00 = 15 were significantly populated (roughly consistent with a vibrational temperature of 2500 K). The implication for our LIF detection of ThO is that many of the bands that had not been reported may originate from these highly excited vibrational levels. Prior to the present work, only the v00 = 0–3 levels of ThO(X) had been observed by electronic spectroscopy. So, to

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connect back to our first motivation, the fact that the LIF spectra for jet-cooled ThO contain many unassigned bands complicates the analyses of spectra for mixed ThX/ThO samples. Mapping the ThO bands will facilitate the recognition of these features in future studies. The expected presence of vibrationally hot ThO in the expansion source provides the second motivation for our study. The energies of the excited vibrational levels, taken in combination with the rotational constants provided by the microwave study, permits the determination of an accurate RKR potential energy curve for the ground state. A compact representation of these results can then be obtained by fitting the point-wise RKR data to a suitably flexible and realistic potential energy function. Transitions from vibrationally excited ThO(X) typically access vibrationally excited levels of the upper electronic states, permitting extensions of some previously characterized band systems. For example, we observed transitions to the v0 = 2–7 levels of the D(X = 1) state for the first time. The third motivation was provided by the CI-LFT model of Kaledin et al. [39] While it is established that semi-empirical methods can yield good agreement with the energies of known electronic states, it is important to assess whether the model has predictive capabilities. Two previously unreported electronic states were observed in this study, with term energies close enough to the LFT results for configurational assignment.

was 9 atm. ThO was cooled by expanding the gas flow into vacuum via a 2 mm diameter orifice. The beam from a tunable dye laser (Lambda Physik FL3002E, pumped by an EMG201 excimer laser) crossed the expanding gas at a distance of approximately 25 mm from the orifice. The dye laser beam was propagated along an axis that was perpendicular to the direction of the jet expansion. LIF was collected along an axis that was orthogonal to both the dye laser beam and the expansion axis. The fluorescence was focused onto the cathode of a photomultiplier tube. Long pass filters, positioned in front of the photomultiplier tube, were used to reduce the interference from scatted laser light. The dye laser could be operated using just a diffraction grating for wavelength selection, with a linewidth of approximately 0.3 cm
1. A linewidth of 0.06 cm
1 could be achieved by adding an intra-cavity etalon to the system. Absolute wavelength calibration of the dye laser was established by the simultaneous recording of standard reference spectra. For wavelengths longer than 500 nm the spectrum of the B-X transition of I2 was used, with the line positions taken from the atlas of Salami and Ross [43]. For wavelengths below 500 nm the spectrum of 130Te2 was used for calibration. The tellurium was contained in a sealed quartz cell that was heated to 650 °C to produce an adequate vapor pressure. The Te2 A-X and B-X line positions were taken from the atlas of Cariou and Luc [44].

2. Experiment

3. Results and analyses

The apparatus used for these measurements has been described previously [42]. ThO was obtained by pulsed laser ablation of a Th metal rod. The fundamental output from a Nd/YAG laser at 1064 nm was used for ablation. It was attenuated to powers in the range of 3–10 mJ/pulse and focused onto the rod by a 50 cm focal length lens. The rod was rotated and translated to reduce the shot-to-shot fluctuations in the ablation process. The ablation plume was entrained in a flow of pure He delivered by a pulsed valve (Parker-Hannifin General Valve, Series 9). ThO was readily formed, without the addition of oxygen-containing reagents in the carrier gas flow. The total source pressure, prior to expansion,

Low resolution LIF survey spectra for ThO were recorded over the range from 16700 to 21200 cm
1. Within this range, 55 bands were of sufficient intensity for investigation using the higher resoP lution of the etalon-narrowed dye laser. Fig. 1 shows the D(1 +)1P+ X 2–0 band as an example. The rotational temperatures observed in these experiments were very sensitive to the operating conditions of the pulsed valve. While Fig. 1 is consistent with a rotational temperature of approximately 80 K, bands recorded on different days sometimes showed temperatures that were somewhat lower. Rotational temperatures around 80–90 K proved to be optimal, as the spectral congestion was not too great, and the

Fig. 1. Rotationally resolved spectrum of the D1P-X1R+ 2–0 transition. The downward-going trace is a simulation with a rotational temperature of 80 K.

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number of clearly observable spectral lines was sufficient to define the rotational constants with reasonable accuracy. The downward going trace in Fig. 1 shows a simulation of the spectrum produced using the POGPHER analysis and simulation program [45]. Many vibronic transitions were observed that involved upper and/or lower levels that had not been characterized previously. The method used to analyze and assign these bands was as follows. First, the rotational structure of each band was assigned and fitted using the PGOPHER program [45]. This provided the transition band origin, upper and lower state rotational constants and the P P P electronic transition type (invariably 1 -1 or 1P-1 in terms of Hund’s case (a) labels). The band origins were then compared with the predictions for the known electronic transitions. For example, the term energy and vibrational constants for the D-X system were used to calculate all transitions for v‘‘ = 0–10, v0 = 0– 10. These predictions were close enough to provide reliable assignments in several instances. It is well-known that electronic spectra provide accurate values for the difference between upper and lower state rotational constants, but the absolute values of the constants are of lower accuracy due to cross correlation. This problem can be mitigated if one constant is known with good accuracy. Hence, once the assignments had been made, we re-fit our data with the ground state rotational constants held fixed at the values determined by microwave spectroscopy [14]. Of the 55 bands investigated, 34 involved upper and/ or lower state vibronic levels that had not been identified previously. Tables 1 and 2 list the molecular constants for these bands. Twenty-six members of this set could be assigned to known electronic transi-

Table 1 Band origins and rotational constants for newly observed vibronic states of ThO.

Table 2 Molecular constants of unassigned ThO bands. Transition type P 1 P- 1 1 1P P1P 1P -

m0 (cm
1)

B’ (cm
1)

B‘‘ (cm
1)

20762.3 19754.0 18944.5

0.320(2) 0.320 0.323

0.324(2) 0.332 0.331

tions, 5 were ascribed to previously unreported electronic states and 3 were unassigned. The band origin data for the known states was combined with the results from previous studies to obtain improved values for the vibrational constants (listed in Table 3). In discussing this part of the analysis, we begin by considering the ground state where the effects of perturbations are expected to be minimal. Data from the D-X and E-X transitions provided combination differences that defined the energies of the v00 = 0–4 levels (the D-X 7–5 band was observed, but there was no other transition observed from v00 = 5 that could be used to link to the lower energy vibrational states). The energies of the v00 = 0–2 levels were taken from ref. [9]. Fitting to the vibrational energies defined the vibrational constants xe and xexe. The inclusion of the xeye constant did not improve the fit and the value obtained was statistically insignificant. A pointwise RKR potential energy curve [46] was generated from the vibrational constants given in Table 3 and the rotational constants from the microwave study of Long et al. [14] The rotational constants, vibrational energies and turning points from this calculation are listed in Table 4. To provide a continuous potential energy curve we fit an Expanded Morse Oscillator (EMO) function to the RKR points using the program betaFIT [47]. The specific EMO model used here was defined by the equation

V ðRÞ ¼ De ð1
Expð
bðRÞðR
Re ÞÞÞ2

Transition

v0 -v00

m0 (cm
1)

B0 (cm
1)

L0 -X L0 -X

0–4 1–5

20769.0 20711.9

0.325(1) 0.318(2)

O0 -X O0 -X O0 -X

2–0 0–1 0–2

20985.5 18390.8 17504.6

0.3212(4) 0.3253(4) 0.3252(4)

bðRÞ ¼

F-X F-X F-X F-X

3–0 2–1 2–2 2–3

20618.4 19013.3 18127.3 17245.2

0.3252(4) 0.3232(4) 0.3229(4) 0.3229(4)

I-X I-X I-X I-X

3–2 4–3 3–3 4–4

20147.0 20055.8 19265.6 19179.1

0.3251(7) 0.3258(8) 0.3253(4) 0.3245(4)

E-X E-X E-X E-X E-X E-X E-X E-X E-X

4–1 5–2 6–3 2–0 4–2 5–3 6–4 4–3 5–4

18700.4 18620.4 18540.6 17965.1 17814.2 17739.1 17663.9 16932.8 16862.3

0.3173(4) 0.3168(4) 0.3146(4) 0.3198(4) 0.3173(4) 0.3152(4) 0.3143(4) 0.3176(4) 0.3149(4)

D-X D-X D-X D-X D-X D-X D-X

3–1 4–2 5–3 6–4 7–5 2–1 3–2

17543.9 17477.8 17411.7 17345.6 17279.4 16719.1 16657.7

0.3170(4) 0.3157(4) 0.3142(4) 0.3124(4) 0.3112(4) 0.3182(4) 0.3169(4)

where De is the dissociation energy and Re is the equilibrium bond length. The Morse range parameter (bðRÞ) is defined by a radially dependent polynomial in the reduced variable yRpe ðRÞ. The number of terms included in the polynomial is indicated by N + 1. Following the recommendations of ref. [47], p was set to a value of 3 and De was fixed at the value obtained by fitting to the standard Morse Oscillator (N = 0, De = 80500 cm
1). Fitting to the N = 0, 1, and 2 and 3 models yielded standard deviations of 10.6, 7.3, 2.7, and 0.24 cm
1. For N > 3 the improvement in the fit was slight and the statistical significance of the expansion coefficients was questionable. Rotational constants and vibrational energies, recovered from the N = 3 potential energy curve using the Level 8.0 program [48], were in good agreement with the input data. The parameters of this potential are given in Table 5, where the systematic rounding option of the betaFIT program [47] was used to optimize the number of significant figures needed for the definition of each

C P-X C1P-X 1

4–1 5–2

16894.2 16820.9

with

bi yRpe ðRÞi

and

i¼0

yRpe ðRÞ

 p  R
Rpe   ¼ p R þ Rpe

Table 3 Vibrational constants for ThO. Electronic State

xe (cm
1)

xexe (cm
1)

X R C1P D1P E1R+ I1Pa

895.72(21) 834.65(30) 839.08(11) 829.28(10) 800.70(11)

2.388(39) 2.176(6) 2.383(13) 2.309(4) 1.44(1)

1

0.3159(5) 0.3164(5)

Ground state rotational constants were held fixed at the values from the microwave study of Long et al. [14] The values are listed in Table 2. Fitting with both the upper and lower state rotational constants as free parameters was carried out when the lower vibrational state assignment was uncertain.

N X

a

+

The v0 = 4 level was not included in this fit as it appears to be perturbed.

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J.R. Schmitz et al. / Journal of Molecular Spectroscopy 360 (2019) 39–43

Table 4 RKR potential energy curve data for ThO(X). v

Bv

G(v)

DGv+1/2

Rmin

Rmax

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0.332040 0.330737 0.329434 0.328130 0.031211 0.325522 0.324218 0.322914 0.321609 0.320304 0.318998 0.317692 0.316386 0.315080 0.313773 0.312466

447.28 1338.21 2224.37 3105.79 3982.44 4854.34 5721.48 6583.87 7441.50 8294.37 9142.49 9985.85 10824.46 11658.31 12487.40 13311.74

890.92 886.17 881.41 876.66 871.90 867.14 862.39 857.63 852.87 848.12 843.36 838.61 833.85 829.09 824.34 819.58

1.7919 1.7587 1.7369 1.7198 1.7054 1.6928 1.6816 1.6714 1.6621 1.6535 1.6454 1.6379 1.6308 1.6240 1.6176 1.6116

1.8923 1.9330 1.9625 1.9873 2.0093 2.0296 2.0486 2.0666 2.0837 2.1002 2.1162 2.1317 2.1468 2.1616 2.1761 2.1903

The rotational constants and vibrational energies are in cm
1 units. The turning points are given in Å units.

Table 5 Expanded morse oscillator potential energy parameters for ThO(X). Parameter

Value

Error

De Re b0 b1 b2 b3

80,500 1.8420327 1.4871657
1.090E
02 8.702E
02 5.08E
02

Fixed 2.3E
06 2.1E
05 1.9E
04 4.5E
04 3.1E
03

All values are in Å
1 units, with the exception of Re which is given in Å units and De which is given in cm
1 units. Fig. 2. Schematic energy level diagram for the F-X and O0 -X band systems (not to scale).

coefficient. Note that the dissociation energy is not accurately defined by this procedure and should be regarded as no more than a fitting parameter. The data obtained for the C-X, D-X and E-X transitions extended the range of upper state vibrational levels, adding v0 = 4, 5 for the C state, v0 = 4–6 for the E state and v0 = 2–7 for the D state. These results, combined with published data for lower vibrational levels [2,9], were fitted to define new vibrational constants (given in Table 3). The vibrational manifolds for all three upper states appeared to be free from perturbation at the level of accuracy of the present band origin determinations (±0.11 cm
1). For the I1P-X transition, previously known from the 0–0 and 1–1 bands [1,19], we observed the v0 = 2, 3, and 4 levels via the 2–2, 3–3, 4– 4, 4–3, 3–2 and 2–1 bands. The excited state vibrational intervals were recovered from these data by using the ground state intervals derived from the E-X and D-X systems. The I state vibrational intervals were consistent with the simple Morse expression, DGv þ1=2 ¼ xe
2xe xe ðv þ 1Þ, for v0 = 0–3. The 4–3 interval was 1.9 cm
1 lower than the extrapolated value, indicating the presence of a local perturbation. P The 0–0 and 1–1 bands of the F1 +-X transition were reported by Edvinsson et al. [9] The assignment of these bands to a common electronic transition was tentative due to the anomalously small excited state vibrational interval implied by the 1–1 assignment. In the present work we found bands that appear to be part of the F-X system, terminating on the v0 = 2 and 3 levels. The energy level scheme for this group of bands is shown in Fig. 2. With the assignment scheme shown here the vibrational intervals for the F state are DG1=2 = 757.4, DG3=2 = 809.4, and DG5=2 = 714.1 cm
1. If we assume that the v0 = 2 level is strongly perturbed (pushed up by approximately 48 cm
1), the average vibrational interval is 760 cm
1. In the same energy range we found transitions to two vibronic levels that do not belong to any of the know electronic

states. These are labeled as O0 (0+) v0 = 0 and 2 in Fig. 2 and Table 1, and both have 0+ symmetry. This tentative assignment is suggested as the term energy of the lower energy band (19281 cm
1) is consistent with the v0 = 0 level of the O0 (0+) state, predicted by the CILFT model [39] to be at 18922 cm
1 and tentatively located at 19271 cm
1 by assigning the bands listed in the Vatican Atlas [12]. Assignment of the band at 20985.5 cm
1 to the v0 = 2 level of O0 yields a reasonable average value for the vibration constant of 852 cm
1, but we did not observe bands that could be assigned to v0 = 1. Another pair of bands that could not be assigned to known electronic states was found in the 20700–20770 cm
1 range. The rotaP tional structures were consistent with (X = 1)-X1 + transitions. The lower state rotational constants indicated that they originated from relatively high vibrational levels of the ground state. By comparison with the CI-LFT predictions [39] it was found that the most likely assignment for the 20769.0 cm
1 band was L0 (1)-X, 0–4. This would yield a term energy for L0 (1), v0 = 0 of 24304.2 cm
1, in reasonable agreement with the CI-LFT prediction (23008 cm
1) and the value derived from an analysis of the Vatican Atlas data (24325 cm
1). There are two nearby bands that are close to the expected energy of the 1–5 sequence band. Assignment to the lower energy of the two, 20711.9 cm
1, yields an excited state vibrational interval (DG1=2 = 814.8 cm
1) that is typical of unperturbed excited states in this energy range [2]. Our spectra included transitions that originated from the ground state v00 = 5 level, which is 4407.0 cm
1 above v00 = 0. As the first electronically excited state (H3D1) has a term energy of 5316.6 cm
1 [3,4], we considered the possibility that unassigned transitions of Table 2 may have originated from this state. However, scans over the regions where the origin bands of the PAH

J.R. Schmitz et al. / Journal of Molecular Spectroscopy 360 (2019) 39–43

and OAH transitions are expected [2] did not reveal these features. Hence, it seems that the population of the H state was too low for LIF detection. 4. Summary and conclusions The laser ablation/ jet expansion technique provides a source of ThO(X) that is rotationally cold but vibrationally very hot. This situation was first noted by Long et al. [14], who used microwave spectroscopy to observe significant populations in levels as high as v00 = 15. In this study we have exploited this dramatically nonequilibrium population distribution to extend the electronic spectroscopy of ThO(X). Using LIF detection we were able to observe transitions originating from vibrational levels up to v00 = 5. For the ground state, vibrational energies of the levels v00 = 3–5 were determined for the first time. These data, combined with the rotational constants from Long et al. [14] have been used to construct a potential energy curve. New vibrational levels of the C, D, E, and I states were observed and these data were used to define improved vibrational constants. Additional levels of the F(0+) state were observed, along with levels of a new state that was tentatively assigned as O0 (0+). Interactions between the these levels may be responsible for the erratic vibrational spacings of F(0+). Another pair of bands has been tentatively assigned to the L0 (1) state. These new state assignments were guided by the predictions of a CI-LFT calculation [39] and it seems that this semi-empirical theoretical method can be predictive with errors of around ±500 cm
1 for electronic state energies below 25000 cm
1. The range of vibronic transitions characterized for ThO has been increased, facilitating recognition of ThO features in spectroscopic studies that target other Th-containing species. Acknowledgements This research was support by the US Department of Energy under grant DE-FG02-01ER15153. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

G. Edvinsson, A.V. Bornstedt, P. Nylen, Arkiv foer Fysik 38 (1968) 193–218. G. Edvinsson, A. Lagerqvist, Phys. Scr. 30 (1984) 309–320. G. Edvinsson, A. Lagerqvist, Phys. Scr. 32 (1985) 602–610. G. Edvinsson, A. Lagerqvist, J. Molec. Spectrosc. 113 (1985) 93–104. G. Edvinsson, A. Lagerqvist, J. Molec. Spectrosc. 122 (1987) 428–439. G. Edvinsson, A. Lagerqvist, J. Molec. Spectrosc. 128 (1988) 117–125. G. Edvinsson, A. Lagerqvist, Phys. Scr. 41 (1990) 316–320. G. Edvinsson, L.E. Selin, Phys. Lett. 9 (1964) 238–239. G. Edvinsson, L.E. Selin, N. Aslund, Arkiv foer Fysik 30 (1965) 283–319. S.H. Behere, T. Wentink Jr., B.B. Laud, J. Indian, Phys., B 58B (1984) 52–56. S.H. Behere, T. Wentink Jr., B.B. Laud, Indian J. Phys., B 58B (1984) 15–22.

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[12] A. Gatterer, J. Junkes, E.W. Salpeter, B. Rosen, Molecular spectra of metallic oxides, Specola Vaticana (1957). [13] V. Goncharov, J. Han, L.A. Kaledin, M.C. Heaven, J. Chem. Phys. 122 (2005). 204311/204311-204311/204316. [14] B.E. Long, S.E. Novick, S.A. Cooke, J. Mol. Spectrosc. 302 (2014) 1–2. [15] A. Von Bornstedt, G. Edvinsson, Phys. Scr. 2 (1970) 205–210. [16] A. Von Bornstedt, G. Edvinsson, A. Lagerqvist, I. Renhorn, Phys. Scr. 20 (1979) 599–602. [17] F. Wang, A. Le, T.C. Steimle, M.C. Heaven, J. Chem. Phys. 134 (2011). 031102/ 031101-031102/031103. [18] D.L. Kokkin, T.C. Steimle, D. DeMille, Phys. Rev. A At., Mol. Opt. Phys. 90 (2014). 062503/062501-062503/062510. [19] D.L. Kokkin, T.C. Steimle, D. DeMille, Phys. Rev. A At. Mol. Opt. Phys. 91 (2015). 042508/042501-042508/042505. [20] V. Andreev, D.G. Ang, D. DeMille, J.M. Doyle, G. Gabrielse, J. Haefner, N.R. Hutzler, Z. Lasner, C. Meisenhelder, B.R. O’Leary, C.D. Panda, A.D. West, E.P. West, X. Wu, Nature 562 (2018) 355–360. [21] C.T. Dewberry, K.C. Etchison, S.A. Cooke, Phys. Chem. Chem. Phys. 9 (2007) 4895–4897. [22] C.T. Dewberry, K.C. Etchison, G.S. Grubbs, R.A. Powoski, M.M. Serafin, S.A. Peebles, S.A. Cooke, Phys. Chem. Chem. Phys. 9 (2007) 5897–5901. [23] A.C. Vutha, B. Spaun, Y.V. Gurevich, N.R. Hutzler, E. Kirilov, J.M. Doyle, G. Gabrielse, D. DeMille, Phys. Rev. A At., Mol., Opt. Phys. 84 (2011). 034502/ 034501-034502/034504. [24] J. Baron, W.C. Campbell, D. Demille, J.M. Doyle, G. Gabrielse, Y.V. Gurevich, P. W. Hess, N.R. Hutzler, E. Kirilov, I. Kozyryev, B.R. O’Leary, C.D. Panda, M.F. Parsons, B. Spaun, A.C. Vutha, A.D. West, E.P. West, New J. Phys. 19 (2017). 073029/073021-073029/073067. [25] M. Denis, T. Fleig, J. Chem. Phys. 145 (2016). 214307/214301-214307/214305. [26] A.N. Petrov, Phys. Rev. A At. Mol. Opt. Phys. 91 (2015). 062509/062501062509/062505. [27] A.N. Petrov, L.V. Skripnikov, A.V. Titov, N.R. Hutzler, P.W. Hess, B.R. O’Leary, B. Spaun, D. DeMille, G. Gabrielse, J.M. Doyle, Phys. Rev. A At. Mol. Opt. Phys. 89 (2014). 062505/062501-062505/062506. [28] L.V. Skripnikov, J. Chem. Phys. 145 (2016). 214301/214301-214301/214310. [29] E.R. Meyer, J.L. Bohn, Phys. Rev. A: At. Mol. Opt. Phys. 78 (2008). 010502/ 010501-010502/010504. [30] J. Paulovic, T. Nakajima, K. Hirao, R. Lindh, P.A. Malmqvist, J. Chem. Phys. 119 (2003) 798–805. [31] J. Paulovic, L. Gagliardi, J.M. Dyke, K. Hirao, J. Chem. Phys. 122 (2005) 144317. [32] R. Tyagi, Ab initio Studies of Systems Containing Actinides using Relativistic Effective Core Potentials, The Ohio State University, 2005. Ph.D. thesis (Advisor R. M, Pitzer). [33] A.A. Buchachenko, J. Chem. Phys. 133 (2010). 041102/041101-041102/041103. [34] T. Fleig, M.K. Nayak, J. Molec. Spectrosc. 300 (2014) 16–21. [35] L.V. Skripnikov, A.V. Titov, J. Chem. Phys. 142 (2015). 024301/024301-024301/ 024312. [36] C.M. Marian, U. Wahlgren, O. Gropen, P. Pyykko, Theochem 46 (1988) 339– 354. [37] W. Kuchle, M. Dolg, H. Stoll, H. Preuss, J. Chem. Phys. 100 (1994) 7535. [38] L.A. Kaledin, J.E. McCord, M.C. Heaven, J. Molec. Spectrosc. 164 (1994) 27–65. [39] L.A. Kaledin, A.L. Kaledin, M.C. Heaven, J. Comput. Chem. 40 (2019) 430–446. [40] R.W. Field, Ber. Bunsenges. Phys. Chem. 86 (1982) 771–779. [41] H. Schall, M. Dulick, R.W. Field, J. Chem. Phys. 87 (1987) 2898–2912. [42] J.T. Stewart, M.N. Sullivan, M.C. Heaven, J. Mol. Spectrosc. 322 (2016) 18–21. [43] H. Salami, A.J. Ross, J. Mol. Spectrosc. 233 (2005) 157–159. [44] J. Cariou, P. Luc, Atlas du Spectre d’Absorption de la Molecule de Tellure, CNRS, Paris, 1980. [45] C.M. Western, PGOPHER, J. Quant. Spectrosc. Radiat. Transfer 186 (2017) 221– 242. [46] R.J. Le Roy, J. Quant. Spectrosc. Radiat. Transfer 186 (2017) 158–166. [47] R.J. Le Roy, A. Pashov, J. Quant. Spectrosc. Radiat. Transfer 186 (2017) 210–220. [48] R.J. Le Roy, J. Quant. Spectrosc. Radiat. Transfer 186 (2017) 167–178.