Transition dipole moments and probabilities of the CCl radicals

Journal of Quantitative Spectroscopy & Radiative Transfer 237 (2019) 106634

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Transition dipole moments and probabilities of the CCl radicals Yuan Yin, Deheng Shi∗, Jinfeng Sun College of Physics, Henan Normal University, Xinxiang 453007, China

a r t i c l e

i n f o

Article history: Received 4 June 2019 Revised 2 September 2019 Accepted 2 September 2019 Available online 3 September 2019 Keywords: Potential energy curve Spectroscopic parameter Franck–Condon factor Transition dipole moment Transition probability Spin–orbit coupling effect

a b s t r a c t This work studies the transition dipole moments and properties of 12 electronic states. These states are X2 , A2 , B2  + , C2 , 12  − , 22  − , a4  − , b4 , 14  + , 14 , 24 , and 24  − ; they originate from the first dissociation limit of the carbon monochloride radical. The potential energy curves were calculated using the complete active space self-consistent field method, followed by the valence internally contracted multireference configuration interaction approach. The B2  + state has a double well and C2  a single barrier. The radiative lifetimes of the vibrational levels are in the order of 10−7 s for the A2  state, and 10−7 and 10−5 s for the first and second wells of the B2  + state, respectively, suggesting that the spontaneous emissions originated from the two states can easily occur. The radiative lifetimes are long for C2 , b4 , 14 , 14  + , and 24  states and the Einstein A coefficients are small for the emissions originated from these states, indicating that the spontaneous emissions generated from these states are difficult to measure through spectroscopy. The 12  − , 22  − , and 24  − states are repulsive. Furthermore, the spectroscopic parameters and vibrational levels were evaluated. For the A2  – X2  and B2  + – X2  systems, the Einstein A coefficients of the vibronic emissions are large, indicating that the emissions from the two systems can be easily detected by spectroscopy. The spectral range of the spontaneous emissions was evaluated for certain transitions. © 2019 Elsevier Ltd. All rights reserved.

1. Introduction The carbon monochloride (CCl) radical is a pollutant in the upper atmosphere. In addition, it has certain astrophysical significance and is present in high-energy media containing halo–carbon [1]. This radical has been found to be an important intermediate due to the reaction of carbon insertion into the carbon chloride bond in chloromethane [2]. Furthermore, halocarbon plasmas are important in the etching process of semiconductor materials, because they can be regarded as the valuable radical probes to determine both the temperature and chemistry of halocarbon plasmas [1,2]. For the detection of this radical in these environments, spectroscopic information is required. For this reason, several experiments [1,3–19] have been made to study its transition properties. However, only a few theoretical spectroscopic properties, especially transition properties, of the CCl radical are currently available [2,21–23]. In 1937, the first experimental results were published by Asundi and Karim [3], who photographed the emission spectra of the CCl radical. In 1939, Horie [4] recorded the emission bands of this rad-

∗

Corresponding author. E-mail address: [email protected] (D. Shi).

https://doi.org/10.1016/j.jqsrt.2019.106634 0022-4073/© 2019 Elsevier Ltd. All rights reserved.

ical and tentatively assigned them to the B2  + – X2  transition. In 1950, Venkateswarlu [5] summarized the previously reported emission bands, detected some new bands, and also tentatively assigned them to the B2  + – X2  transition. In 1953, Barrow et al. [6] measured several emission bands and tried to assign them to the B2  + – X2  transition. Verma and Mulliken [7] in 1961 reported the 0–0 and 0–1 bands and made the rotational analysis in ˚ They confirmed that these bands bethe region of 2750–2800 A. long to the A2  – X2  transition [7], including all emissions reported previously [3–6]. The spin–orbit coupling (SOC) splitting energy of the X2  state were determined to be approximately 134.92 cm−1 . In 1970, Tyerman [8] observed a new absorption system and tentatively assigned it to the B2  + – X2  transition. In 1979, Huber and Herzberg [20] summarized certain accurate spectroscopic parameters and molecular constants available as of that time. Prior to 1979, only the properties of the X2  and A2  states had been studied, as summarized by Huber and Herzberg [20]. Subsequently, Yamada et al. [9] detected the vibration–rotation transitions of the fundamental band in the X2 1/2 and X2 3/2 states and evaluated certain spectroscopic parameters and transition properties. In 1982, Larsson et al. [10] detected the A2  – X2  transition, investigated the predissociation of the A2  state, and measured the predissociation lifetimes of its υ = 0, 1, and 2 vibrational levels. Gottscho et al. [11] measured the radiative lifetimes of the υ = 0

2

Y. Yin, D. Shi and J. Sun / Journal of Quantitative Spectroscopy & Radiative Transfer 237 (2019) 106634

level of the A2  state as approximately 105 ± 3 ns. Endo et al. [12] recorded the rotational transitions in the X2 1/2 and X2 3/2 states. The ground-state internuclear equilibrium separation was ˚ accurately determined as 1.6452 A. In 1983, Mélen et al. [13] reinvestigated the A2  – X2  transition and considerably extended the rotational analysis to obtain the accurate molecular constants. They also observed the B2  + – X2  transition for the first time in the ranges of 34,130 – 34,272 and 35,151–35,294 cm−1 [13]. Because of the poor intensity, the results of the B2  + – X2  transition obtained were of low significance. In 1986, Sharpe and Johnson [14] detected the 1 – 0 and 2 – 0 bands of the A2  – X2  transition in the ranges of ˚ respectively, and evaluated the 2711 – 2715 and 2652 – 2655 A, spectroscopic parameters of the A2  state. In 1988, Burkholder et al. [15] measured the 1–0 band of the X2 3/2 – X2 1/2 transition. In 1991, Robie et al. [16] measured the laser-induced fluorescence spectra of the A2  – X2  transition and assigned the 2782–A˚ peak to the 0 – 0 P1 band head. Remy et al. [17] recorded the absorption spectra of the 1 – 0, 2 – 0, and 3 – 0 vibronic bands of the B2  + – X2  transition and confirmed the existence of the B2  + state. They also measured the absorption spectra of the CCl radical in the range of 60 0–150 0 A˚ [18]. In 1996, Reid [1] detected the collision–excitation spectra of this radical. In 1997, Jin et al. [19] identified the 1 – 0, 3 – 2, 4 – 3, and 5 – 4 bands of the X2  state. Several spectroscopic parameters of the X2  state were obtained. In summary, only the emissions of A2  – X2  and B2  + – X2  systems have been experimentally observed so far. Theoretically, at least five research groups [2,10,21–23] calculated some of the potential energy curves (PECs) of this radical. A number of spectroscopic parameters were evaluated using these PECs, including the excitation term Te from the ground state, dissociation energy De , equilibrium separation Re , harmonic frequency ωe , rotational constant Be , first– and second–order anharmonic constants ωe xe and ωe уe , and vibration coupling constant α e . In 1976, Bialski and Grein [21] performed the first ab initio calculations of this radical with a minimal basis set, with few spectroscopic parameters obtained. In 1982, Larsson et al. [10] computed the PECs of the X2 , A2 , and several other states using the complete active space self-consistent field (CASSCF) and contracted configuration interaction (CI) approaches. They evaluated several spectroscopic parameters of the X2  and A2  states using these PECs, and determined the predissociation lifetimes of υ = 0, 1, and 2 levels of the A2  state [10]. In 1986, Karna and Grein [22] calculated the PECs of several states using the CI method. They evaluated a number of spectroscopic parameters using these PECs. In 1991, Gutsev and Ziegler [23] determined the Te and Re values of the X2  and a4  − states using the density functional theory within the local density approximation. In 2001, Li and Francisco [2] computed the PECs of only four states with the CASSCF method, followed by the internally contracted multi-configuration reference CI (icMRCI) approach with the aug-cc-pVTZ, with the evaluation of certain spectroscopic parameters. However, they did not calculate the transition properties, such as transition dipole moments (TDMs), vibrational energies, radiative lifetimes, FranckCondon (FC) factors, and Einstein A coefficients, except for electronic dipole moments of only several electronic states. Summarizing the experimental results reported previously, only the X2 , A2 , and B2  + states have been studied and only the A2 –X2  and B2  + –X2  transitions have been measured. In addition, the emissions of the A2  – X2  system are easy to detect; while those of the B2  + –X2  system are difficult to measure. This raises a question: is the A2  – X2  transition sufficiently strong or is the B2  + – X2  transition very weak? In addition to the A2  – X2  and B2  + – X2  transitions, a further question is whether spontaneous emissions originating from other states, such

as the C2 , b4 , 14 , 14  + , and 24  are observable in a spectroscopy experiment. As a summary of the theoretical results in the literature, only the spectroscopic parameters of several states are currently available and very few transition properties have been calculated, as stated above. For this reason, in this study, we aim to determine the transition probabilities of spontaneous emissions between all states generated from the first dissociation limit of this radical. On one hand, we use the larger basis sets to perform the ab initio calculations. On the other hand, we include the extrapolation of potential energies to the compete basis set (CBS) limit, and core-valence correlation and scalar relativistic corrections into the present work so as to improve the accuracy of the ab initio results as accurately as possible.

2. Methodology The ground state of a C atom is 3 Pg , and the ground state of a Cl atom is 2 Pu . Thus, the first dissociation limit of the CCl radical is C(3 Pg ) + Cl(2 Pu ). According to molecular group theory, there are 12 states arising from the first dissociation channel, which are the 12  (X2 ), 12  (A2 ), 12  + (B2  + ), 22  (C2 ), 12  − , 22  − , 14  − (a4  − ), 14  (b4 ), 14  + , 14 , 24 , and 24  − states. Because of historical reasons, we still consider the 12 , 12  + , and 22  states as the A2 , B2  + , and C2  states, although the 12 , 12  + , and 22  states are the third, first, and second excited doublet states, respectively, with respect to the Te values calculated in this paper. The PECs were calculated using the CASSCF method, which was followed by the valence icMRCI approach with the Davidson correction (icMRCI + Q) [24]. The basis sets used in this work were the aug-cc-pV5Z (AV5Z) and aug-cc-pV6Z (AV6Z). The point spacing interval was 0.5 A˚ for each state. To obtain more information of each PEC, the point spacing was 0.05 A˚ around the internuclear equilibrium separations of all bound states. Note that these point spacing intervals stated here were also used to calculate the core–valence correlation and scalar relativistic corrections, SOC effect, and TDMs. All PECs and TDMs were calculated in the C2 v point group in the 2010.1 package of MOLPRO program [25]. The molecular orbitals (MOs) used for the icMRCI calculations were obtained from the CASSCF results. Each state had the same weight factor of 1/12. In the calculations, the nine outermost MOs (5a1 , 2b1 , and 2b2 ) were placed in the active space, corresponding to the 5–9σ , 2π , and 3π MOs in the radical. The 11 valence electrons were distributed into the nine valence MOs. Therefore, this active space is referred to as the CAS (11, 9). The remaining 12 inner electrons were placed into the six lowest MOs (4a1 , 1b1 , and 1b2 ), corresponding to the 1–4σ and 1π MOs in the radical. It should be noted that these active spaces were also used to calculate the core–valence correlation and scalar relativistic corrections, TDMs, and SOC effect. For the icMRCI calculations using the AV6Z basis set, the total number of the external orbitals was 367, including 125a1 , 90b1 , 90b2 , and 62a2 . In the CASSCF calculations using the AV6Z basis set, the A1 , B2 , B1 , and A2 symmetries corresponding to the doublet states had 1568, 1512, 1512, and 1456 configuration-state functions (CSFs), and those corresponding to the quartet states had 884, 950, 950, 956 CSFs, respectively. In the icMRCI calculations using the AV6Z basis set, the total number of contracted configurations corresponding to the A1 , B2 , B1 , and A2 symmetries of the doublet states were approximately 3.97 × 106 , 3.96 × 106 , 3.96 × 106 , and 5.34 × 106 ; and those of the quartet states were approximately 3.70 × 106 , 3.72 × 106 , 3.72 × 106 , and 5.10 × 106 , respectively. When the core–valence correlation calculations were performed, the two electrons in the 1 s closed shell of the C atom and the eight electrons in the 2s2p closed shell of the Cl atom were used as the core electrons.

Y. Yin, D. Shi and J. Sun / Journal of Quantitative Spectroscopy & Radiative Transfer 237 (2019) 106634

re f EXre f = E∞ + Are f X α ,

(1)

corr EXcorr = E∞ + Acorr X β .

(2) re f

re f

corr in Eqs. (1) and The definitions of EX , EXcorr , E∞ , and E∞ (2) were introduced in [26]. The extrapolation parameters α and β were set as 3.4 and 2.4 for the reference and correlation energies [26], respectively. Here, the PEC obtained by the CBS extrapolation using the AV5Z and AV6Z basis sets is denoted as “56” for the description. Core–valence correlation correction was included in the PECs using the cc-pCV5Z basis set [27,28]. The potential energies were calculated using the all-electron cc-pCV5Z basis set and the ccpCV5Z basis set without all-electron correlations. The difference between the two energies is the contribution of the core–valence correlation correction to the total energy, which is denoted as “CV” in this work. The scalar relativistic correction was calculated using the cc-pV5Z-DK basis set. Specifically, the cc-pV5Z-DK basis set with the third–order Douglas–Kroll–Hess (DKH3) approximation and cc-pV5Z basis set with no DKH3 approximation were used to calculate the potential energies [29,30]. The difference between the two energies is the contribution of the scalar relativistic correction to the total energy, which is denoted as “DK”. The spin-oribit coupling (SOC) effect was calculated by the state interaction method with the Breit–Pauli operator [31] at the level of icMRCI theory using the all–electron cc-pCV5Z basis set. The all–electron cc-pCV5Z basis set with and without the Breit–Pauli operator was used to calculate the potential energies. The difference between the two energies is the SOC splitting energy. For example, when a PEC is obtained by the CBS extrapolation using the AV5Z and AV6Z basis sets, as well as the core–valence correlation and scalar relativistic corrections, we describe this approach as “icMRCI/56 + CV + DK” or “icMRCI + Q/56 + CV + DK”. For the spontaneous emissions between two electronic states, where the upper and lower vibrational levels are υ  and υ   , respectively, the total transition probability for a certain upper–level υ  is determined by summing the Einstein A coefficients of emissions from this level to all lower levels. The radiative lifetime of a certain upper level can be obtained by the following equations [32]:

Aυ  =

τυ  =

 υ 

Aυ  υ 

1 Aυ 

(3)

(4)

Here, Aυ  υ  is the Einstein A coefficient of the transition from level υ  to level υ   ; Aυ  is the total transition probability of υ  ; and τυ  is the radiative lifetime of this level υ  . Occasionally, several systems contribute to the total Einstein A coefficient of a certain upper level. When several spontaneous systems (i = 1, 2, …) originate from a certain upper state, the total Einstein A coefficient of an upper–level υ  is

Aυ  =



Ai,υ 

(5)

i

Where, Ai,υ  is the total Einstein A coefficient of the emissions from an upper–level υ  for the ith system.

60000

8

4

-1

9

Potential energy /cm

The potential energy calculated by the icMRCI + Q approach is composed of two parts. One part is the reference energy and the other is the correlation energy. To obtain a more accurate PEC for a certain state, the reference energy and the correlation energy were separately extrapolated to the CBS limit, because their convergence speed is different. The extrapolation scheme is as follows [26]:

3

12 10 11

5 45000

6 7 3

30000 2 15000

0

1 1.5

2.0

2.5

3.0

3.5

4.0

Internuclear separation / Å Fig. 1. PECs of the 12 states of CCl radical. 1-X2 ; 2-a4  − ; 3-B2  + ; 4-b4 ; 5-C2 ; 6–12  − ; 7-A2 ; 8–24 ; 9–14  + ; 10– 14 ; 11–24  − ; 12–22  − .

3. Results and discussion Fig. 3 shows the PECs of all 12 electronic states that are generated from the first dissociation asymptote of the CCl radical. These PECs are calculated by the icMRCI + Q/56 + CV + DK calculations. To clearly reveal more information on each PEC, we demonstrate them over a small range of internuclear separations as well. According to Fig. 1, four important conclusions can be drawn. The first one is that the 12  − , 22  − , and 24  − states are repulsive. The second conclusion is that only the X2 , A2 , and a4  − states have a deep well and the C2 , b4 , 14  + , 14 , and 24  states are very weakly-bound states. These five states look like the repulsive ones. The third conclusion is that the A2  state has a single barrier and the potential energy at the top of this barrier is considerably higher than that at the dissociation asymptote. The fourth conclusion is that the B2  + state has a double well. All transitions between these states are 12 pairs, which TDMs were calculated by the icMRCI/AV6Z approach. As the MOLPRO 2010.1 program arbitrarily assigns a sign of the wavefunction to calculate the TDM at each point, the TDMs obtained in this study occasionally appear as "jumps" from the positive to the negative or from the negative to the positive value as the internuclear separation is increasing. Therefore, the correct choice of the sign for the TDMs is required considering the wavefunctions of the upper and lower states. After careful analysis, the final curves of TDM as a function of the internuclear separation obtained in this work are shown in Figs. 2 and 3. To reveal more details of each TDM curve, we display them over only a small internuclear separation range. In addition, we list the TDM values of these seven-pair transition systems at some internuclear separations in Tables S1 and S2 as supplementary material. For the better understanding of the transition properties between different doublet or quartet states, we computed the electronic configurations of each state using the icMRCI approach and AV6Z basis set. Table 1 lists the main valence configurations of each bound state near the internuclear equilibrium separations. For the sake of brevity, in Table 1 the configurations with CSF–squared coefficients smaller than 0.08 are ignored. From Table 1, we confirm that only the A2 , B2  + , b4 , and 24  states have obvious multireference characters around the equilibrium separations.

4

Y. Yin, D. Shi and J. Sun / Journal of Quantitative Spectroscopy & Radiative Transfer 237 (2019) 106634 Table 1 Leading valence configurations of nine states near the equilibrium positions. State

Leading valence configuration

B 2 + 1st well 2nd well

5σ 2 6σ 2 2π 4 7σ 1 3π 2 8σ 0 9σ 0 5σ 2 6σ 2 2π 4 7σ 1 3π 0 8σ 2 9σ 0 5σ 2 6σ 2 2π 3 7σ 2 3π 1 8σ 1 9σ 0 5σ 2 6σ 2 2π 3 7σ 2 3π 1 8σ 1 9σ 0 5σ 2 6σ 2 2π 3 7σ 2 3π 2 8σ 0 9σ 0 5σ 2 6σ 2 2π 3 7σ 2 3π 2 8σ 0 9σ 0 5σ 2 6σ 2 2π 4 7σ 1 3π 1 8σ 1 9σ 0

1 4 + X2  b4  a

Leading valence configuration 5σ 2 6σ 2 2π 4 7σ 2 3π 0 8σ 1 9σ 0 5σ 2 6σ 2 2π 4 7σ 1 3π 2 8σ 0 9σ 0 5σ 2 6σ 2 2π 4 7σ 1 3π 2 8σ 0 9σ 0 5σ 2 6σ 2 2π 3 7σ 2 3π 2 8σ 0 9σ 0 5σ 2 6σ 2 2π 3 7σ 2 3π 1 8σ 1 9σ 0 5σ 2 6σ 2 2π 3 7σ 2 3π 2 8σ 0 9σ 0 5σ 2 6σ 2 2π 4 7σ 1 3π 1 8σ 1 9σ 0

A2  (0.864). (0.757); (0.230). (0.889). (0.823). (0.758); (0.126).

a 4 − C2  14  24 

(0.647); (0.131). (0.861). (0.823). (0.891). (0.555); (0.334).

Values in parentheses are the coefficients squared of CSF associated with the electronic configuration.

Table 2 Effect of core-valence correlation and scalar relativistic corrections on the De , Re , and ωe of the X2  and A2  states at the icMRCI theoretical level and the AV6Z basis set. X2  De /cm−1

Re /nm

ωe /cm−1

De /cm−1

Re /nm

ωe /cm−1

33,432.58 −361.38 216.92 −102.47

1.6435 0.0034 −0.0138 −0.0103

915.62 −4.42 −27.85 −30.43

8920.37 −261.68 59.57 −202.11

1.6373 0.0002 −0.0129 −0.0123

913.96 2.38 −18.38 −15.99

3

0.2

Transition diple mement / a.u.

Transition dipole moment / a.u.

AV6Z +DK +CV +DK + CV

A2 

5 0.1 0.0

4

-0.1 -0.2 2 1

-0.3 1.5

2.0

2.5

3.0

3.5

4.0

Internuclear separation / Å Fig. 2. Curves of TDM versus internuclear separation for the five-pair states 1: C2 –X2 ; 2: A2 –X2 ; 3: B2  + –X2 ; 4: C2 –A2 ; 5: C2 –B2  + .

From these configurations, it can be seen instantly which electronic transitions occur between two doublet or quartet states. Table 2 lists the effect of core-valence correlation and scalar relativistic corrections on the De , Re , and ωe of the X2  and A2  states at the icMRCI theoretical level and the AV6Z basis set. As can be seen in Table 2, the two corrections has great effect on the De , wheres only the core-valence correlation correction has great effect on the Re and ωe value. As a conclusion, Table 2 demonstrates that the effect of DK and CV vorrections on the spectroscopic properties ia latgely additive fot this system, and so subsequently calculations are done by combining results from separate DK and CV runs. Using the PECs determined via icMRCI + Q/56 + CV + DK calculations, we evaluated the spectroscopic parameters and vibrational levels of all nine attractive electronic states with the LEVEL program [33]. Each PEC is fitted to an analytical form using a cubic spline. Within the framework of the Born–Oppenheimer approximation, the rovibrational constants are first calculated from the analytic potential by solving the rovibrational Schrödinger equa-

7 0.4

2 5 6

0.2 3 0.0

-0.2

4

1 1.5

2.0

2.5

3.0

3.5

4.0

Internuclear separation / Å Fig. 3. Curves of TDM versus internuclear separation for the seven-pair states 1: 14  + –b4 ; 2: 14 –b4 ; 3: 14 –24 ; 4: 24 –a4  − ; 5: b4 –a4  − ; 6: 14  + – 24 ; 7: 24 –b4 .

tion, and then the spectroscopic parameters are evaluated by fitting the vibrational levels. The spectroscopic parameters are listed in Table 3. As a summary, the available theoretical [2,10,21–23] and experimental [1,9,12,14,18–20] spectroscopic parameters are listed in Table 3 as well. For the convenient discussion of the spectroscopic parameters and transition properties, the 9 bound states of CCl radical are divided into two groups with respect to spin multiplicity. The first group contains the four bound doublet states and the second group contains the five bound quartet states. 3.1. Spectroscopic parameters and transition properties of the doublet states For the X2  state, the Re value obtained in the present work is ˚ The three groups of experimental Re results are 1.645 A˚ 1.6375 A. [1], 1.645 A˚ [9], and 1.6452 A˚ [12]. A good agreement exists between the experimental [1,9,12] and the theoretical results. The ωe

Y. Yin, D. Shi and J. Sun / Journal of Quantitative Spectroscopy & Radiative Transfer 237 (2019) 106634

5

Table 3 Spectroscopic parameters and their comparison with available experimental and other theoretical spectroscopic results of the CCl radical.

X2  Exp. [1] Exp. [9] Exp. [12] Exp. [19] Exp. [20] Cal. [2] Cal. [10] Cal. [21] Cal. [23] a 4 − Cal. [21] Cal.[23] B 2 + 1stwell Exp. [1,18] Cal. [2] Cal. [22] 2nd well b4  C2  24  1 4 + 14  A2  Exp. [1] Exp. [14] Exp. [20] Cal. [2] Cal. [10] Cal. [22]

De /cm−1

Te /cm−1

Re /nm

ωe /cm−1

ωe xe /cm−1

ωe уe /cm−1

Be /cm−1

102 α e /cm−1

33228.54 – – – – – – 25567.76b , c 27745.46b , d 23500 — 14210.68 8900 –

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 19746.35 14,000 21938.27

1.6375 1.645 1.645 1.6452 – 1.645 1.665a 1.704c 1.649d 1.79 1.642 1.6751 1.85 1.648

881.04

7.501

0.735

0.7035

0.801

876.75 876.74 876.90 866.72 844a 807.02c 814.75d ∼1000

5.33 5.330 5.447 6.2 – 6.73c 3.96d

– – 0.026 – –

0.680 0.677 0.685 0.672

–

0.6975 – 0.69714 0.6936 0.6771 0.646c 0.659d

864.25 ∼1100

5.486

0.859

0.6965

0.885

1388.11 – – – 1600.20 626.68 351.66 346.01 141.95 204.06 8704.76 – – – – – –

36322.31 34117.24 – – 32443.18 33539.67 33829.82 33907.73 33961.07 33992.89 36340.83 35811.00 36,005.0 ± 0.6 – – – –

1.6599 1.505 – 1.524 2.1288 2.8097 3.2564 4.0054 4.1440 4.0068 1.6194 1.634 — 1.6346 – 1.672 1.624

469e 1453.05 420.28 86.40 59.40

– 3.527 3.694 5.747

– 0.844 0.041 0.686

0.8120 0.4062 0.2390 0.1754

−0.307 0.320 1.195 0.750

895.06

12.69

0.6538

0.7196

1.044

876.2 ± 0.3 848.10 845e 736 1209.80

12.05 ± 0.3 –

–

0.7062

22 –

– –

0.672 0.7155

−0.230

Notes: a obtained by the MRCI/aug-cc-pVTZ method with the (11, 9) active space; b D0 value; c obtained by the CASSCF method; d obtained by the CI method; e obtained by the MRCI/aug-cc-pVTZ method with the (11, 10) active space.

value calculated in this work is 881.04 cm−1 and the corresponding experimental values are 876.75 cm−1 [9], 876.74 cm−1 [12], and 876.90 cm−1 [19]. The greatest difference between the present result and the experimental ones [9,12,19] is 4.30 cm−1 . By careful comparison, we confirm that the ωe xe , Be , and α e values obtained in this work also agree well with the corresponding experimental values [9,12,19]. In 1964, Miller and Palmer [34] determined the D0 value to be approximately 26938.9 cm−1 by investigating flame reactions. As summarized in Table 3, the De result calculated in this work is 33228.54 cm−1 , which is significantly higher than the experimental value [34]. However, as noted in Ref. [34], this experimental D0 value is less accurate. By analyzing the photolysis process of the CCl4 molecule, Tyerman [8] suggested that the ground–state D0 value was higher than 35,970 cm−1 . Using an estimation, Tyerman [8] determined the ground–state D0 value of the CCl radical as approximately 32,262.14 ± 4032.77 cm−1 . Overall, considering the comparison above, the spectroscopic parameters obtained in this study are accurate. Several theoretical research groups [2,10,21,23] reported the ground-state spectroscopic parameters. By careful comparison, we confirm that no theoretical Re , ωe , and Be values are closer to those of the measurements [1,9,12,19] than the values presented in this work. The main reason for this is that the calculations performed in this study include various corrections, namely, Davidson correction, core–valence correlation and scalar relativistic corrections, as well as extrapolation of the PECs to the CBS limit, whereas those in the previous theoretical studies did not consider these.

The X2  state has a well depth of 33,228.54 cm−1 with 53 vibrational levels. Because high vibrational states are difficult to populate in experiment, we list them only the first 20 levels in Table 4. Unfortunately, there have not been any experimental or other theoretical levels in the literature. As reported in [9,12,15,19], certain rovibrational transitions from the X2 3/2 state to the X2 1/2 state have been observed experimentally. These properties between the X2 3/2 state and the X2 1/2 state are expected to be calculated in the near future. Employing the icMRCI + Q/56 + CV + DK approach, we determined the SOC splitting energy of the X2  state as 134.98 cm−1 . Several experimental research groups obtained the ground-state SOC splitting energy. Sharpe and Johnson [14] determined it as 134.72 cm−1 and Jin et al. [19] obtained it as 135.65 cm−1 . The ground-state SOC splitting energy calculated in this study agrees well with these measurements [14,19]. The 12  state is the third excited doublet state, and its Te value is higher than those of the B2  + and C2  states. Historically, this state is regarded as the A2  state. To comply with historical evolution, we also regard the 12  state as the A2  state in this paper. No experimental De result has been reported to date. The Te result calculated in this study is 36340.83 cm−1 . The experimental Te values are 35811.00 cm−1 [1] and 36005.0 ± 0.6 cm−1 [14]. The deviations of the present Te value from the experimental ones are 529.83 cm−1 [1] and 335.83 cm−1 [14]. To a certain extent, only general agreement exists between the theoretical and the experimental values. The available experimental Re values are 1.634 A˚

6

Y. Yin, D. Shi and J. Sun / Journal of Quantitative Spectroscopy & Radiative Transfer 237 (2019) 106634 Table 4 Gυ (cm−1 ) of the X2 , A2 , B2  + , C2 , a4  − , b4 , 24 , 14  + , and 14  states.

ϒ

X2 

A2 

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

438.74 1307.17 2167.21 3017.21 3856.94 4686.69 5506.54 6316.55 7116.81 7907.40 8688.39 9459.89 10221.94 10974.63 11718.01 12452.13 13177.06 13892.82 14599.49 15297.18

444.02 1309.57 2141.85 2944.40 3717.50 4458.13 5163.83 5830.33 6453.11 7026.07 7026.07 7542.44 8008.60 8461.28

B2  + 1st well

2nd well

807.55

196.15 606.63 1003.46 1381.87

[1] and 1.6346 A˚ [20]. The Re result computed in this work is ˚ which is smaller than the experimental values by 0.0146 A˚ 1.6194 A, [1] and 0.0152 A˚ [20]. The ωe value calculated in this study is 895.06 cm−1 , which deviates from the recent experimental result [14] by 18.86 cm−1 . By careful comparison, we can confirm that no other theoretical Re or ωe results [2,10,22] are closer to the corresponding experimental values [1,14,20] than the present results in this study. The A2  state has a single barrier, which is formed by the avoided crossing of this state with the 22  state. The barrier ˚ The potential energy at the top of is at approximately 2.28 A. this barrier is higher than that at the dissociation asymptote by 11043.03 cm−1 . Therefore, the dissociation energy and the well depth of this state are relative to the barrier. The barrier has been reported by Li and Francisco [2] and by Larsson et al. [10]. They determined that the barrier was at the internuclear separation of ˚ The A2  state has a well depth of 8704.76 approximately 2.3 A. cm−1 with 13 vibrational levels, as listed in Table 4. Because of spin and symmetry limitations, the A2  state spontaneously decays only to X2  and C2  states. Considering the dominant valence configurations summarized in Table 1, the dominant transitions from the A2  state to the X2  state are the 7σ 1 – 2π 3 7σ 2 electronic promotions while those from the A2  state to the C2  state are the 2π 4 7σ 1 –2π 3 7σ 2 electronic promotions. On one hand, as listed in Table 3, the Re value of the A2  state is close to that of the X2  state, and both states have several vibrational levels. On the other hand, as shown in Fig. 1, the TDMs of the A2  – X2  transition are large near the equilibrium separations of the X2  and A2  states. Based on these considerations, the FC principle suggests that the A2  – X2  transitions are strong. Similarly, as shown in Fig. 1, the TDMs of the A2  – C2  transition are very small over a wide internuclear separation range. By contrast with the A2  –X2  transitions, the A2  – C2  transitions need to be very weak. The results obtained in this work confirm the expectations from the FC principle. Using the PECs and TDMs computed in this study, we calculated the band origins, FC factors, and Einstein A coefficients of all spontaneous emissions from the A2  – X2  and A2  – C2  systems using the LEVEL program [33]. Based on the present calculations, for the A2  – X2  system, there are 8, 43, and 71 emissions, whose Einstein A coefficients are approximately 106 , 105 , and 104 s−1 , respectively. Therefore, the A2 –X2  tran-

C2 

a4  −

b4 

24 

14  +

14 

28.73 79.36 132.02 197.52

430.86 1286.93 2139.76 2978.98 3803.54 4611.74 5402.51 6174.93 6928.13 7661.17 8372.86 9061.75 9726.09 10363.74 10972.15 11548.75 12090.63 12591.24 13042.20 13438.74

42.31 121.45 193.58 258.61 315.47 364.78 437.98

58.81 152.83

66.62

65.24

sition is intense. We give a selection of relatively large Einstein A coefficients of spontaneous emissions with their corresponding FC factors in Table 5. A complete list of the Einstein A coefficients and FC factors is included in Table S3-S6 of the Supplementary Material. Because the band origins can be easily calculated considering the vibrational levels, we omit them in Table 5. The spectra of the A2 –X2  transition extend from the ultraviolet (UV) region to the infrared region. The strong emissions are in the UV range. For the A2  –C2  transition, the largest Einstein A coefficients are approximately 10° s−1 ; therefore, the intensity of the A2  – C2  transition is very low. Thus, we do not collect them in this paper. Owing to this reason, the A2  – X2  transition could be detected via spectroscopy in previous experiments; whereas the A2  – C2  transition has not been measured so far. Both the A2  – X2  and A2  – C2  transitions contribute to the radiative lifetimes of the vibrational levels of the A2  states. By applying the Einstein A coefficients determined in this study, given by Eqs. (3)–(5), we calculated the radiative lifetimes of all vibrational levels of the A2  state. The results are listed in Table 6. For comparison, the experimental radiative lifetime for the υ = 0 vibrational level of the A2  state is also listed in Table 6 [11]. Good agreement can be found between the present result and the only experimental value [11]. The radiative lifetime calculated here is slightly larger than the experimental one [11], because the experimental result includes the pure rotational transitions occurring within the A2  state, whereas the results calculated in this work not consider these. In terms of the radiative lifetimes presented in Table 6, the spontaneous emissions originating from the A2  state can easily occur. The combination of the radiative lifetimes with the Einstein A coefficients reported here, implies that the emissions of the A2  – X2  system can be easily measured via spectroscopy. This conclusion has been proven by a number of experiments performed previously [3–8,10,11,13,14,16]. Many spectroscopic observations of the A2  – X2  transition have been reported [3–8,10,11,13,14, 16]. The observations prior to 1961 were assigned to the B2  + – X2  system; however, they belong to the A2  – X2  transition. Verma and Mulliken [7] measured two sub–bands for the 0 – 0 band of the A2  ˚ they – X2  system, whose wavelengths were 2777 and 2788 A; also detected two sub–bands for the 0 – 1 band, whose wave˚ Considering the results calculated lengths were 2866 and 2856 A. in this study, the 0 – 0 and 0 – 1 band origins are 2765.0 A˚

Y. Yin, D. Shi and J. Sun / Journal of Quantitative Spectroscopy & Radiative Transfer 237 (2019) 106634

7

Table 5 Some Einstein A coefficients (s− 1 , 2nd line) of emissions together with the FC factors for the A 2  – X 2 , B 2  + – X 2 , and C 2  – X 2  systems.

υ  –υ 

υ  –υ 

FC

A 2 – X 2 0–0

0.9672 0–1 6.01 × 106 2–2 0.9018 2–3 5.32 × 106 4–4 0.9269 4–5 5.06 × 106 6–8 0.0535 7–5 1.75 × 105 8–7 0.1067 8–8 7.80 × 105 1st well of the B 2 + – X 2  0–0 0.8803 0–1 3.45 × 106 2 + 2 2nd well of the B  – X  0–8 0.0134 0–9 1.51 × 103 0–14 0.1402 1–15 5.74 × 103 1–7 0.0256 1–8 3.79 × 103 1–13 0.0251 1–16 1.29 × 103 1–21 0.0624 2–4 2.35 × 103 C 2 – X 2 2–37 0.0005 2–38 1.33 × 101

FC

υ  –υ 

FC

υ  –υ 

FC

υ  – υ 

FC

υ  –υ 

FC

0.0306 2.19 × 105 0.0383 3.25 × 105 0.0100 1.59 × 105 0.0324 1.94 × 105 0.5947 2.77 × 106

1–0

0.0327 1.71 × 105 0.0495 2.04 × 105 0.9394 4.91 × 106 0.0183 2.20 × 105 0.1379 3.33 × 105

1–1

0.9189 5.58 × 106 0.9085 5.17 × 106 0.3353 1.29 × 105 0.8117 3.89 × 106 0.2744 1.61 × 106

1–2

0.0424 3.26 × 105 0.0256 2.60 × 105 0.0212 1.50 × 105 0.0878 2.45 × 105 0.2922 1.39 × 106

2–1

0.0495 2.33 × 105 0.0367 1.21 × 105 0.9151 4.57 × 106 0.0336 1.60 × 105 0.0853 1.16 × 105

3–2 5–5 7–6 8–10

3–3 5–7 7–7 9–8

3–4 6–4 7–9 9–9

4–3 6–6 8–6 9–10

0.1017 7.24 × 105

0–2

0.0061 5.79 × 104

0–3

0.0043 8.59 × 103

0–4

0.0049 2.26 × 104

0–5

0.0013 8.49 × 103

0.0280 2.65 × 103 0.1321 4.61 × 103 0.0481 5.92 × 103 0.0409 1.35 × 103 0.0046 1.34 × 104

0–10

0.0505 4.01 × 103 0.1103 3.30 × 103 0.0738 7.59 × 103 0.0814 2.30 × 103 0.0135 3.23 × 103

0–11

0.0794 5.31 × 103 0.0818 2.10 × 103 0.0912 7.86 × 103 0.1074 2.61 × 103 0.0309 6.05 × 103

0–12

0.1091 6.18 × 103 0.0540 1.19 × 103 0.0881 6.39 × 103 0.1086 2.28 × 103 0.0549 8.86 × 103

0–13

0.1317 6.33 × 103 0.0111 1.99 × 103 0.0616 3.77 × 103 0.0897 1.64 × 103 0.0749 1.00 × 103

0.0011 1.99 × 101

0–16 1–9 1–17 2–5

2–39

0.0020 2.82 × 101

0–17 1–10 1–18 2–6

3–34

0.002 1.41 × 101

0–18 1–11 1–19 2–7

3–35

0.0005 2.30 × 101

1–6 1–12 1–20 2–8

3–36

0.0010 3.59 × 101

Table 6 Radiative lifetimes (ns) of the A2  state of the CCl radical and comparison with the experimental result.

This work Exp. [11]

υ

τ

υ

τ

υ

τ

υ

τ

υ

τ

υ

τ

0

160.13 107 ± 3 203.34 346.68

1

163.61

2

168.28

3

174.60

4

182.38

5

191.77

7 13

218.04 361.75

8

237.22

9

263.22

10

299.25

11

333.45

6 12

(36166.23 cm−1 ) and 2833.1 A˚ (35296.40 cm−1 ), respectively. Thus, good agreement exists between the observations [7] and the values in this study. Larsson et al. [10] confirmed that the strong transition around 2820 A˚ correspond to the 2 – 0 band. However, according to the analyses mentioned above, this transition should correspond to the 0 – 1 band. Sharpe and Johnson [14] determined the 1 – 0 and 2 – 0 band origins to be approximately 36850 cm−1 ˚ and 37,678 cm−1 (2654.0 A), ˚ respectively. In terms of the (2713.7 A) results obtained in this work, these band origins were calculated ˚ and 37868.64 cm−1 (2640.7 A), ˚ respecas 37035.3 cm−1 (2700.1 A) tively. In conclusion, the present results agree well with the experimental values [14]. In addition, this work determined the Einstein A coefficients to be approximately 6.01 × 106 , 2.19 × 105 , 1.71 × 105 , and 1.30 × 103 s−1 for the 0 – 0, 0 – 1, 1 – 0, and 2 – 0 bands, respectively. With respect to these Einstein A coefficients, the emissions observed in the previous experiments can be considered to be almost strong. The B2  + state has a double well and possesses a single barrier. As the depths of the double well are very shallow, they cannot be shown distinctly in Fig. 1, especially for the first well. The first ˚ which well is located at the internuclear separation of 1.6599 A, has a well depth of approximately 1338.11 cm−1 . The second well ˚ which has a is located at the internuclear separation of 2.1288 A, well depth of approximately 1600.20 cm−1 . The vibrational levels of the double well are listed in Table 4. The barrier is located at ˚ Accurate calthe internuclear separation of approximately 1.68 A. culations show that the potential energy at the top of this barrier is 2541.22 cm−1 higher than that at the dissociation asymptote. As a consequence, the well depth and dissociation energy of the first

well is relative to the barrier, while those of the second well are relative to the dissociation limit. The existence of a double well has not been reported in any previous experiment and has not been analyzed theoretically so far. As listed in Table 3, the Te value for the first well is higher than those of the X2  and C2  states, whereas the Te value for the second well is higher than that of the X2  state only. Therefore, the first well spontaneously decays to the X2  and C2  states and the second well spontaneously decays exclusively to the X2  state. No experimental or other theoretical De results are currently available for the B2  + state. The experimental Te and Re values were de˚ respectively [1,18]. The termined to be 34,117.24 cm−1 and 1.505 A, comparison of the experimental results with those in this study, the measurements [1,18] belong to the first well. A general agreement exists between the experimental results [1,18] and the theoretical ones for the first well. As the first well has only one vibrational level, the ωe value cannot be evaluated in this work. Li and Francisco [2] clearly show the double well of the B2  + state, however, they did not discuss them. In addition, Bialski and Grein [22] clearly depicted the PEC of the first well. Because they displayed the PEC of the B2  + state over only a small range of internuclear separations, the second well was not shown. For the B2  + state, the first well has a single reference characteristics and the second well possesses obvious multireference characteristics around the respective internuclear equilibrium positions. The dominant transition from the first well to the C2  state is the 2π 4 7σ 1 –2π 3 7σ 2 electronic promotion; that from the first well to the X2  state is the 2π 4 7σ 1 –2π 3 7σ 2 electronic promotion; and that from the second well to the X2  state are the

8

Y. Yin, D. Shi and J. Sun / Journal of Quantitative Spectroscopy & Radiative Transfer 237 (2019) 106634 Table 7 Radiative lifetimes (μs) of the B2  + and C2  states of the CCl radical. state

υ

τ

υ

τ

υ

τ

υ

τ

B 2 + 1st well 2nd well C2 

0 0 0

2.34 × 10−1 2.21 × 101 2.18 × 105

1 1

1.91 × 101 5.11 × 104

2 2

1.67 × 101 1.23 × 104

3 3

1.49 × 101 3.19 × 103

3π 1 8σ 1 –3π 2 8σ 0 electronic promotion. On one hand, the TDMs of the B2  + –X2  system are large near the equilibrium separations of the X2  state and the first well, as shown in Fig. 1. On the other hand, the Re value of the first well is close to that of the X2  state. Having considering these factors, the spontaneous emissions between them are expected to be intense. The total number of emissions between them is only a few, because the first well has only one vibrational level. The TDMs of the B2  + –X2  system are small near the internuclear equilibrium separation of the second well. Overall, the spontaneous emissions from the second well to the X2  state are expected to be weaker than those from the first well to the X2  state according to the FC principle. Considering the results computed in this work, there are only one, one, two, and three spontaneous emissions generated from the first well to the X2  state, where the orders of magnitude of the Einstein A coefficients are 6, 5, 4, and 3, respectively. Strong emissions occur from the first well to the lower vibrational levels of the X2  state with the spectra extending from the UV region to the near–infrared region. The most intense emissions are in the UV region. There are 3 and 52 emissions generated from the second well to the X2  state, respectively, with Einstein A coefficients of approximately 104 and 103 s−1 . The spectral range extends from the UV region to the near–infrared region. Most of the emissions are in the UV and visible regions. The emissions in the near–infrared region are so weak that they are expected to be very difficult to measure via spectroscopy. For the emissions generated from the first well to the C2  state, the emissions are too weak to measure via spectroscopy. The emissions of this system have only four bands, because the first well has only one level and the C2  state has only four. Overall, the predictions of the FC principle are correct. Applying Eqs. (3)–(5) and using the PECs and TDMs, we calculated the radiative lifetimes for the vibrational levels of the double well. The results are listed in Table 7. According to Table 7, we confirm that the radiative lifetime for the υ = 0 vibrational level of the first well is in the order of 10−7 s, and for vibrational levels of the second well are in the order of 10−5 s. To a certain extent, the B2  + –X2  transitions are strong. However, the measurement of these emissions via spectroscopy has certain difficulties, because there are only a few of these strong emissions. As a consequence, the experimental results of the B2  + –X2  system are very limited in the literature. Mélen et al. [13] measured the emissions of two pairs of medium intensity violet in the regions of 34,272–34,130 and 35,294–35,151 cm−1 and assigned them to the B2  + –X2  transition. Comparing the experimental results with those in this study, we tentatively assign them to the 0–3 and/or 0–4 bands for the transition from the first well of the B2  + state to the X2  state, because the only bands in the regions of 34,272–34,130 and 35,294–35,151 cm−1 are 0 – 3 and/or 0 – 4. The Einstein A coefficients of the two bands are 8.59 × 103 and 2.26 × 104 s−1 , respectively. Thus, both bands have only medium intensity. In addition, no emissions fall into the two ranges mentioned above for the transitions from the second of the B2  + state to the X2  state. To date, no spectroscopic parameters or transition properties have been reported for the C2  state, neither experimentally nor theoretically. This state has a well depth of 351.66 cm−1 with four

levels, as listed in Table 4. According to the Te values listed in Table 3, the C2  state is the first excited state, which spontaneously decays to the X2  state and the second well of the B2  + state. According to Table 1, the leading electronic configuration of this state is the same as that of the X2  state, and the dominant transition from the C2  state to the second well are 3π 2 8σ 0 – 3π 1 8σ 1 promotion near the equilibrium separations. The emissions from the C2  state to the X2  state and from the C2  state to the second well are expected to be weak, as the Re value of the C2  state is significantly higher than those of the X2  state and the second well. Using the PECs and TDMs, we computed the band origins, FC factors, and Einstein A coefficients of the transitions from the C2  state to the X2  state and from the C2  state to the second well. Considering the results calculated in this work, for the C2 –X2  system, the largest Einstein A coefficients are approximately 10 s−1 , and for the transition from the C2  state to the second well, the largest Einstein A coefficients are in the order of 10−8 s−1 . In other words, the two groups of transitions are so weak that they can hardly be measured via spectroscopy. In addition, Table 7 shows that all levels of the C2  state have very long radiative lifetimes, indicating that the emissions originating from the C2  state hardly occur. As a consequence, the C2  state has not been measured experimentally until now. The conclusions of this section can be summarized as follows. (1) The A2 –X2  and B2  + –X2  transitions can be measured via spectroscopy, whereas the C2 –X2 , C2 –B2  + , and A2 –C2  transitions are very difficult to detect due to their low intensity. (2) Although certain transitions from the B2  + -X2  system are strong, they are still difficult to detect because there are only a few of these strong emissions. (3) The C2  state is weakly bound and has very few levels. From a spectroscopic viewpoint, the C2  state is insignificant. 3.2. Spectroscopic parameters and transition properties of the quartet states The a4  − state is the lowest–lying quartet state and has the second–deepest potential well among all states originating from the first dissociation limit. This state has a well depth of 14210.68 cm−1 with 23 vibrational levels, as listed in Table 4. No experimental spectroscopic parameters or other theoretical ones are currently available in the literature. No spontaneous emissions generated from the a4  − state, because it is the lowest–lying quartet state. The Re value of the a4  − state is close to that of the X2  state and the PECs of the X2  and a4  − states are similar; further, both states have some vibrational levels, as listed in Table 4. Considering these results, the rovibrational transitions from the a4  − state to the X2  state are expected to be intense. We endeavor to carefully investigate these rovibrational transitions in the near future. The b4  state is the second lowest–lying quartet state. This state has a well depth of is 626.68 cm−1 with seven vibrational levels, which are listed in Table 4. In contrast to the a4  − state, the b4  state has obvious multireference characters around the internuclear equilibrium separation. The dominant electronic transitions from the b4  state to the a4  − state are the 2π 3 7σ 2 –

Y. Yin, D. Shi and J. Sun / Journal of Quantitative Spectroscopy & Radiative Transfer 237 (2019) 106634

9

Table 8 Radiative lifetimes (s) for the vibrational levels of the b4 , 14 , 14  + , and 24  states of the CCl radical. State

υ

τ

υ

τ

υ

τ

υ

τ

υ

τ

υ

τ

b4 

0 6 0 0 0

1.55 × 102 4.60 × 10−1 9.66 × 103 1.30 × 102 2.65 × 102

1

1.96 × 101

2

6.37

3

3.11

4

1.85

5

1.43

1

4.05 × 101

14  1 4 + 24 

2π 4 7σ 1 and 3π 1 8σ 1 –3π 2 8σ 0 promotions. Similar to the case of the a4  − state, no spectroscopic parameters and transition properties of the b4  state have been reported so far, neither experimentally nor theoretically. On the one hand, the TDMs of the b4 –a4  − transition are very small for internuclear separations ˚ as shown in Fig. 2. On the other hand, as shown larger than 2 A, in Table 3, the Re value of the b4  state is significantly higher than that of the a4  − state. Considering these results, the emissions from the b4 –a4  − system are expected to be very weak. To calculate the band origins, FC factors, and Einstein A coefficients of the b4 –a4  − transition, we use the LEVEL program [33] with the PECs and TDMs. Considering the results calculated in this study, the largest Einstein A coefficients of the b4 –a4  − transition are in the orders of 10−2 s−1 . Thus, all emissions from the b4 –a4  − system are so weak that they can be hardly measured via spectroscopy. Using Eqs. (3) and (4), we computed the radiative lifetimes of all levels of the b4  state. The results calculated in this study are summarized in Table 8. From where, we confirm that the radiative lifetimes of the b4  state are very long. As a result of these long radiative lifetimes, the occurrence of the emissions originated from this state is inhibited. The potential wells of the 24  and 14  + states are very shallow: the 24  state has a well depth of only 346.01 cm−1 and that of the 14  + state is only 141.95 cm−1 . For this shallow well, the LEVEL program [33] determined that the 24  and 14  + states have 2 and 1 vibrational levels, respectively, as listed in Table 4. Their ωe values cannot be evaluated, because both states have vibrational levels of less than three. The 24  state spontaneously decays to the b4  state only, and the 14  + state decays at least to the b4  and 24  states. Considering the transition properties computed in this work, the largest Einstein A coefficients of the 24 –a4  − transition are approximately 10−4 s−1 ; and those of the 24  – b4  transition are approximately 10−2 s−1 . These Einstein A coefficients indicate that all emissions originating from the 24  state are rather weak. According to Table 8, the radiative lifetimes of the 24  state are in the range of 101 to 102 s, which is rather long. This result indicates that the occurrence of spontaneous emissions generated from the 24  state is nearly impossible. Considering the 14  + state, the largest Einstein A coefficients of the 14  + – b4  and 14  + – 24  transitions are in the order of 10−4 s−1 , and the radiative lifetime of the vibrational levels of the 14  + state is higher than 100 s. Considering these results, all spontaneous emissions generated from the 14  + state are expected to be too weak to measure via spectroscopy. Similar to the case of the C2 , b4 , 24 , and 14  + states, the 14  state is also a very–weakly bound state. The well depth of the 14  state is only 204.06 cm−1 . Accurate calculations show that the 14  state has only one vibrational level, as listed in Table 4. According to the Te values listed in Table 3, the 14  state spontaneously decays at least to the a4  and 24  states. Using the LEVEL program [33] with the PECs and TDMs, we determined that the emissions from the 14  – a4  and 14  – 24  systems are so weak that they are very difficult to measure via spectroscopy. In addition, it can be seen in Table 8, the lifetime of the vibrational

level is 9.66 × 103 s. This result indicates that the occurrence of all the emissions arising from the 14  state is nearly impossible. As a conclusion, the Einstein A coefficients are very small for the vibronic emissions generated from the b4 , 24 , 14  + , and 14  states, and the radiative lifetimes are too long for all vibrational levels of the b4 , 24 , 14  + , and 14  states. All emissions originated from these four states are very difficult to measure in a spectroscopy experiment due to too low intensity. 4. Conclusions This work computes the PECs and TDMs of the CCl radical using the icMRCI method with large correlation–consistent basis sets. Let us remark that the internally contracted method can have larger than errors for the PECs with barriers than without. The spectroscopic parameters and transition properties were evaluated using the MOLCAS 2010.1 program package and the LEVEL program. The ground-state SOC splitting energy is determined to be 134.98 cm−1 . Some necessary observations have been discussed and the results obtained in this study have been summarized below. (1) Individual vibronic emissions from the A2  – X2  and B2  + – X2  systems are intense. (2) The B2  + – X2  transition is difficult to be measured, not because the emissions from this system are not strong, but because there are only a few intense emissions from this system. (3) The radiative lifetimes are very long for the vibrational levels of the b4 , 24 , 14  + , and 14  states. Naturally, spontaneous emissions originating from these four states are very weak and therefore, very difficult to detect via spectroscopy. (4) Of these 12 states, the 12  − , 22  − , and 24  − states are determined to be repulsive; the b4 , C2 , 24 , 14  + , and 14  states are determined to be weakly bound, the C2  state has a single potential barrier, and the B2  + state has a double well and single potential barrier. Acknowledgments This work is sponsored by the National Natural Science Foundation of China under Grant no. 11274097. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.jqsrt.2019.106634. References [1] Reid CJ. Cationic and anionic states of CF, CCl, SiF and SiCl. Some new information derived using translational energy spectroscopy. Chem Phys 1996;210:501–11. [2] Li YM, Francisco JS. A complete active space self-consistent field multiconfiguration reference configuration interaction study of the potential energy curves of the ground and excited states of CCl. J Chem Phys 2001;114:2192–6. [3] Asundi RK, Karim SM. On the emission spectrum of CCl4 . Proc Indian Acad Sci 1937;6A:328–9. [4] Horie T. Vibratioal analysis of CCl bands. Phys Math Soc Jpn 1939;21:143–8. [5] Venkateswarlu P. On the emission bands of CC1. Phys Rev 1950;77:79–80.

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