Characterization of the low-lying electronic states of tin monohydride cation including the spin-orbit coupling effect: A theoretical perspective

Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 227 (2020) 117667

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Characterization of the low-lying electronic states of tin monohydride cation including the spin-orbit coupling effect: A theoretical perspective Song Li a, *, Nian Lu a, Ning Wang a, Ming-Jie Wan b, Yuan-Yuan Jin a, Wei-Bin Zhang a, Chuan-Zhao Zhang a, Shan-Jun Chen a a b

School of Physics and Optoelectronic Engineering, Yangtze University, Jingzhou, China Computational Physics Key Laboratory of Sichuan Province, Yibin University, Yibin, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 24 June 2019 Received in revised form 11 October 2019 Accepted 15 October 2019 Available online 19 October 2019

High-level ab initio computations have been performed on SnHþ. The potential energy curves and spectroscopic constants of the low-lying L-S electronic states, as well as their associated U states, are derived at the icMRCI þ Q level employing basis sets of quintuple-z quality. The transition dipole moments, Einstein coefficients, radiative lifetimes and Franck-Condon factors of three spin-forbidden 1 þ 1 þ 3 1 þ transition bands (13 P1  X1 Sþ 0þ , 1 P0  X S0þ and 1 P1  X S0þ ) are determined. Comparisons between our predictions and available experimental results indicate reasonable agreement. The spin-orbit coupling effect has been proved to affect these low-lying electronic states significantly. © 2019 Elsevier B.V. All rights reserved.

Keywords: SnHþ ab initio calculation Electronic structure Spectroscopic constant Spin-orbit coupling effect

1. Introduction The IVA-group monohydride cations have long been the research topic of both experimentalists and theorists due to their importance in combustion processes, astrophysics, atmospheric chemistry and plasma chemistry. Extensive researches have been carried out for CHþ, SiHþ and GeHþ for several decades. From the 1940s, both theorists and experimentalists have dedicated their studies to the chemical and physical characterization of CHþ. From astronomical observations, the presence of CHþ in varies of interstellar materials has also been identified. Extensive studies of this species have derived fruitful information on its properties in molecular collisions, spectroscopy, dynamics, etc. The physical and chemical properties, such as molecular stabilities, potential energy curves, spectroscopic properties, were unambiguously determined. In 1970, the emission spectrum of the A1 P  X 1 Sþ band of SiHþ was firstly detected in the laboratory with the hollow-cathode discharge technique in the viseUV region by Douglas and Lutz

* Corresponding author. School of Physics and Optoelectronic Engineering, Yangtze University, Nanhuan Road 1, Jingzhou, China. E-mail address: [email protected] (S. Li). https://doi.org/10.1016/j.saa.2019.117667 1386-1425/© 2019 Elsevier B.V. All rights reserved.

[1]. Spectra of this species were also investigated by techniques of high-frequency deflection [2], flowing afterglow reactor [3] and electron collision [4] for the A1 P  X 1 Sþ band, and by the velocity modulation method for the fundamental band [5]. Recently,
nech et al. performed the first measurement of the J ¼ 1)0 Dome pure rotational transition with a difference frequency laser spectrometer coupled with a hollow-cathode discharge [6]. Based on their high-resolution spectra lines, accurate spectroscopic parameters were then derived. Theoretically, several groups have devoted to their investigations on electronic structures and molecular constants of SiHþ [7e19]. Potential energy curves, Franck-Condon factors, oscillator strengths and transition frequencies were studied for the ground X 1 Sþ and the first excited A1 P state by the configuration interaction (CI) [12,15], many-body perturbation theory (MBPT) [13], multireference configuration interaction (MRCI) [13,18,19], coupled-cluster methods including all single, double, and (perturbatively) triple excitations [CCSD(T)] [14], multireference single and double-excitation configuration interaction method (MRDCI) [17] methodologies respectively. In addition, the Mosnier group has recently carried out combined investigations of both spectroscopic detections and ab initio configuration interaction calculations of SiHþ [20,21]. The photoionization spectrum of SiHþ in the L-shell region was recorded and analyzed.

2

S. Li et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 227 (2020) 117667

þ Spectra of the a3 P0þ ;1  X 1 Sþ have been 0þ bands of GeH investigated by Tsuji et al. with their flowing afterglow apparatus in the visible spectral region [22,23]. Nine bands were observed and rotationally analyzed. A re-examination of these bands in the 490 nme720 nm region with more sensitive apparatus by the same group yielded higher resolution spectra lines and improved rotational constants [24]. Besides, eleven bands of GeDþ were observed for the first time, and four bands of the a3 P0þ  X 1 Sþ 0þ transition and (0,0) band of a3 P1  X 1 Sþ 0þ were rotationally analyzed. The Franck-Condon factors and the vibrational population associated with the a3 P0þ state of both GeHþ and GeDþ have also been determined. By using laser photofragment spectroscopy, Gibbon et al. recorded high-resolution photodissociation spectra of the A1 P  X 1 Sþ band in the visible region [25]. Molecular constants correlated with these two states were derived and compared with those obtained from other researches. Binning and Curtiss [26] carried out MP4 calculation on the ground X 1 Sþ state of GeHþ. Their theoretically determined equilibrium geometry and harmonic frequency agreed well with those obtained by Tsuji et al. [22,23]. Systematical calculations on low-lying electronic states associated with the first four dissociation limits were performed by Das and Balasubramanian [27,28]. Potential energy curves, as well as their corresponding spectroscopic constants, were obtained by the configuration interactions method. In 2014, Li et al. have also performed high-level configuration interaction calculations to study the low-lying electronic states of GeHþ [29]. They mainly focused on 23 U states under the effect of spin-orbit coupling. Transition properties, such as the transition dipole moments, Franck-Condon factors and radiative lifetimes, associated with transitions from several lowlying excited states to the ground one were deduced and compared with available experimental results. As for SnHþ, the first experimental detection was carried out by Yamaguchi et al. with the flowing-afterglow apparatus [30]. Three new bands in the 550e650 nm region were observed and assigned to the (0,0) and (0,1) bands of the a3 P0þ  X 1 Sþ 0þ transition and (0,0) band of a3 P1  X 1 Sþ 0þ . Moreover, the group has reinvestigated the species with a higher resolution and the spectral range extended from 530 nm to 750 nm [31]. More bands attributed to SnHþ were observed in the visible region and eleven bands þ originated from a3 P0þ ;1  X 1 Sþ 0þ of SnD have also been detected and rotationally analyzed. A set of spectroscopic constants of both SnHþ and SnDþ were then determined by fitting the observed spectra. However, to the best of our knowledge, no theoretical investigation was performed for SnHþ. Molecular properties of electronic states other than the ground X 1 Sþ and the first excited 3 P one still remain unknown. In the present paper, we report a systematic investigation of SnHþ from a theoretical perspective. Information associated with potential energy curves (PECs), spectroscopic constants and vibrational energy levels for the ten low-lying L-S states as well as their respective twenty-six U states are presented and analyzed. The transition dipole moments (TDMs), Einstein emission coefficients, radiative lifetimes and the Franck-Condon factors (FCFs) for selected transitions are also determined and discussed. It is anticipated that the results and data derived from this work will shed some light on our understanding of the physical and chemical characteristics of this species.

2. Computational details The low-lying electronic states correlating with the first three dissociation limits are characterized by the ab initio method. The first dissociation channel, derived from the ground atomic states of 2 Sg for H and 2 Pu for Snþ, correlates with the singlet and triplet states of Sþ and P. The second dissociation limit is Hð2 Sg Þ þ Snþ ð4 Pg Þ, correlating to triplet and quintet S and P states. Two

Pþ þ states of 1 and 3 S correspond to the dissociation asymptote of Hð2 Sg Þ þ Snþ ð2 Sg Þ. The basis sets aug-cc-pV5Z for H [32] and aug-cc-pwCV5Z-PP for Sn [33] are utilized to construct the molecular orbitals of SnHþ. The basis set used for Sn includes a relativistic pseudo-potential ECP28MDF, where electrons from 1s to 3d orbitals are replaced by an energy consistent pseudo-potential. The 4s4p electrons of Sn are not optimized in the energy computations. The closed orbitals contain ten 4d electrons of Sn. Electrons associated with the 5s5p6s orbitals of Sn and 1s of H are included in the active space. In order to take into account the electron correlation effect sufficiently, the energy computations are carried out with the internal contraction multireference configuration interaction (icMRCI) methodology [34,35], based on optimized molecular orbitals derived from the state-averaged complete active space selfconsistent field (SA-CASSCF) method [36,37]. The Davidson correction (þQ) has been used to minimize the size nonconsistency errors. The number of external orbitals is 330, including 117a1, 81b1, 81b2 and 51a2 symmetry molecular orbitals. The spin-orbit coupling (SOC) effect is included in the PEC calculations by the state interacting method with the Breit-Pauli Hamiltonian [38] on the MRCI þ Q level. The SOC effect is considered across the entire PEC of each state with the same active space and basis sets that have been used in the determinations of single-point energies. All our calculations have been performed with average atomic masses with the aid of the MOLPRO 2015.1 package [39]. According to our testing calculations, complicated crossings and avoided crossings are present among our interested states, except the 1 P, 3 P and X 1 Sþ ones correlating with the first dissociation limit. To obtain an unambiguous characterization of avoided crossings of the U states under the spin-orbit coupling effect, several states with respect to higher dissociation asymptotes should also be considered in our overall energy calculations. Therefore, ten electronic states correlating with the first three þ dissociation limits, with the inclusion of two additional 1 S and þ two 3 S states correlating with the higher dissociation channel are incorporated into our final state-averaged calculations. It should be noted that these additional states will not be analyzed or discussed unless where is necessary. The Murrell-Sorbie potential energy function [40] is used to fit the calculated energy points. This fitting process has been successfully utilized to deduce the PECs of several species by our group [41e45]. This potential energy function is given by the following expression,

VðrÞ ¼  De 1 þ

n X

! ai ri expð  a1 rÞ

(1)

i¼1

where r ¼ R  Re . R and Re are the internuclear distance and the equilibrium internuclear distances, respectively. De is the dissociation energy. In this work, all parameters are floated in our fittings with n ¼ 12. With the aid of the LEVEL 8.5 program package [46], the vibrational energy levels, rotational and centrifugal distortion constants for the vibrational levels of the interested low-lying electronic states of SnHþ are obtained by numerically solving the € dinger equation of nuclear motion. The one-dimensional Schro Franck-Condon factors, Einstein coefficients and radiative lifetimes have also been determined.

3. Results and discussions 3.1. Equilibrium parameters and PECs of the L-S states In Fig. 1, we have illustrated the PECs of ten L-S electronic states associated with the first three dissociation channels. Extra states

S. Li et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 227 (2020) 117667

Fig. 1. The PECs of the L-S states.

corresponding to the fourth dissociation limit are also plotted in the figure. þ The two additional 3 S states both cross with the 15 P state around 2.0 Å. Multiple PEC avoided crossings and crossings can be þ verified for the two extra 1 S states with those correlating with the second and the third dissociation limits. Such a complex pattern of PECs will definitely result in a great challenge for interpreting their U states. Atomic and molecular states, and energies differences (in cm1) at the dissociation limit for the L-S states of SnHþ are presented in Table 1. Notice that at this limit the second dissociation channel is located at 46398 cm1 higher than the first channel, a result in good accord with the experimental value of 45951 cm1 [47]. Among these four states, only 13 Sþ interacts with other higher ones; the other three states can be identified quite straightforward since no PEC crossing or avoided crossing occurs. On the contrary, states correlating with the higher two dissociation limits are densely distributed in the absolute energy range from 52000 cm1 to 77000 cm1. A double-well character is observed for the 21 Sþ state, þ which experiences an avoided crossing with a higher 1 S one. þ Except for the 13 S and 15 P states, eight L-S states calculated for the first time in this work are found to be bound states, although several of them pose quite shallow well-depths. Table 2 collects our derived spectroscopic constants, such as the equilibrium internuclear distances (Re), dissociation energies (De), rotational constants (Be), vibrational frequencies (ue), first anharmonicities (uece), centrifugal distortion constants (Drot) and excitation energy terms (Te) of the L-S states, as well as those of the only experimental investigation available so far. It is found that our theoretical results excellently reproduce the experimental ones Table 1 Atomic and molecular states, and energies differences (in cm-1) at the dissociation limita for the L-S states of SnHþ. Atomic states Hð2 Sg Þ þ Snþ ð2 Pu Þ Hð2 Sg Þ þ

Exp [47].

This workb

0

0

13 S , 15 S 23 P, 15 P

46398

45951

21 Sþ , 23 Sþ

56886

56343

Molecular states X

1

Sþ , 13 Sþ 11 P,

1 P 3

þ 4

Sn ð Pg Þ Hð2 Sg Þ þ þ 2

Sn ð Pg Þ a b

Weighted average over the multiplets. Calculated at R ¼ 50 Å.

3

[31], where the emission bands of SnHþ were observed in the helium-afterglow reactions of SnH4. For the ground state, deviations in the values of Re , Be , ue , between the two studies are ~0.1%, ~0.1% and ~0.5% respectively. To some extent, this consistency indicates that our approach of utilizing the MRCI þ Q method coupled with basis sets up to quintet-z quality are of high quality, and our derived data are expected to be reliable. In Table 3, we have collected the sets of spectroscopic parameters of CHþ [48e51], SiHþ [1,2,18,19], GeHþ [23,25,29] and SnHþ [31]. It should be noted that just selected experimental and theoretical results are presented for the first three cations. As expected, the spectroscopic constants of the ground X1 Sþ , the first excited 13 P and the second excited 11 P states exhibit regular trends. The equilibrium bond lengths Re of the X1 Sþ state shows an increasing trend from 1.1309 Å in CHþ [50], 1.5041 Å in SiHþ [1], 1.579(1) Å in GeHþ [25] to 1.748(2) Å in SnHþ [31], while opposite trends can be noticed for both dissociation energies De and harmonic vibrational frequencies ue . As for the first and second excited states, the situation is similar to the ground one. In general, the two atoms in CHþ are more tightly bound at its equilibrium bond length than to that of the other three cations. The dissociation energies of the two excited states of GeHþ and SnHþ, as well as the 11 P of SiHþ, are all smaller than 1 eV, which indicate the weak bond nature of these electronic states. For SnHþ, the Re values increasing substantially compared with those of CHþ, with bond length increases by ~55%, ~114% and ~62% for the X1 Sþ , 13 P and 11 P states respectively. The contributions of the electronic configuration state functions (CSFs) at Re for ten electronic states are listed in Table 4 with 1s22s21p43s24s22p45s26s23p41d47s24p48s29s210s2 as the core electron configuration. It should be noted that we have omitted CSFs with weights smaller than 3%. The ground state X1 Sþ is mainly represented by the configuration of 5pabab11sab12sab2dabab with a coefficient of 86.06% at its equilibrium internuclear distance position. For the first excited state 13 P, 5pabab11sab12sa6pay2dabab is the dominant configuration with a weight factor of 89.93%, and it corresponds to the electron removal from the 12s orbital to the 6p one. The 13 S state is found to be multi-configurational, as it has three configurations with weights between 3% and 6%, except the main configuration of 5pabab11sab6paxay2dabab. All four configurations are generated with the electron excitation from the 11s and/ or 12s orbital to the 6p one. 3.2. Equilibrium parameters and PECs of the U states To investigate the changes in the overall pattern of PECs introduced by the SOC effect, we have also performed energy computations by the state interaction method with the Breit-Pauli Hamiltonian on the MRCI þ Q level. As has been mentioned in þ þ Section 2, four electronic states, two 1 S and two 3 S , with respect to a higher dissociation asymptote, are included in the energy calculations for the unambiguous descriptions of the U states. Under the effect of the SOC coupling, ten L-S states associated with the first three dissociation limits split into twenty-six U states, which associate with six asymptotes, as illustrated in Fig. 2 for each of the U values. Atomic and molecular states, and energies differences (in cm1) at the dissociation limit for the U states of SnHþ are presented in Table 5. Our calculated energy separations of higher dissociation limits to that of the first one agree quite well with experimental results [47]. The spectroscopic constants of the U states are listed in Table 6. For the ground state, excellent data consistency is noticeable between our theoretical predictions and experimental determinations [31]. As to the excitation energies of the first and second excited states to that of the ground one, where experimental values are available, deviations of ~2% are verified for both states.

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S. Li et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 227 (2020) 117667

Table 2 The spectroscopic constants of the L-S states. Re /Å

De /eV

Be /cm1

ae /cm1

ue /cm1

13 P

1.7492 1.748(2)a 1.8442

2.792 e 0.486

5.512 5.519(11)a 4.959

0.137 0.141(11)a 0.468

1831.9 1822(10)a 1080.6

11 P

2.6416

0.149

2.417

0.201

285.7

13 S 

1.7567

1.966

5.465

0.188

1563.6

23 P

2.0536

1.609

3.999

0.087

1409.2

27.7

1.29

55348.85

21 Sþ -left

1.7273

0.935

5.653

0.177

1694.2

38.3

2.52

59723.88

21 Sþ -right

2.8103

1.307

2.136

0.017

726.2

8.4

0.74

65766.12

15 S 

2.3100

0.350

3.161

0.200

687.6

36.7

2.67

65520.11

23 S þ

1.9324

0.415

4.516

0.339

934.8

44.5

4.22

72961.07

L-S states X1 S þ

a

ue ce /cm1

104 Drot /cm1

Te /cm1

28.0 30(10)a 107.4

2.00 e 4.18

0 e 18785.89

22.7

6.92

21899.71

33.9

2.67

52467.23

Ref. [31], the uncertainties denote two standard deviations.

Table 3 Molecular parameters of the IVA group monohydride cations. L-S states

Re /Å

Be /cm1 CH

X

1

Sþ

13 P 11 P

De /eV

ue /cm1

Te /cm1

þ

Exp [50].a Exp [49].b Cal [48].c Cal [51].d Cal [51].d

1.1308843(30) e 1.1284625(58) 1.1295 1.1352

14.177461(75) 14.17878(6) e 14.2084 14.0706

4.77(43) e 4.26044(4) 4.26959 3.04230

2857.561(22) 2857.792(31) e 2858.6 2685.8

0 0 0 0 9899

Exp [50].a

1.235053(37)

11.88677(72)

1.79(44)

1864.402(22)

24118.726(14)

Exp [49].b Cal [48].c Cal [51].d

e 1.235896(14) 1.2388

11.88651 e 11.8623

e 1.27750(4) 1.25620

1857.656 e 1852.3

24120.8095 e 24305

e e 3.41 e 1.10 e e e 0.19 e

2157.15 2157.10 2177.91 2154.3 1635.16 1721.8 448.39 468.60 409.32 405.8

0 0 0 0 18631.40 18609 25878.52 25025.20 25971.04 25883

SiHþ X Sþ 1

13 P 11 P

e

Exp [2]. Exp [1].f Cal [18].g Cal [19].h Cal [18].g Cal [19].h Exp [2].e Exp [1].f Cal [18].g Cal [19].h

e 1.5041 1.5002 1.504 1.5412 1.545 e 1.8782 1.8719 1.888

7.6576 7.6603 7.6984 7.6609 7.3097 7.2597 5.003 4.9125 4.7222 4.8615 GeHþ

X1 S þ

13 P 11 P

i

Exp [23]. Exp [25].j Cal [29].k Cal [29].k

e 1.579(1) 1.5682 1.6529

e 6.80(1) 6.8958 6.2167

e e 3.09 0.68

2015.2(10) e 2040.20 1149.20

0 0 0 19530

Exp [25].j Cal [29].k

2.229(2) 2.3639

3.413(5) 3.0605

e 0.13

422.3(2) 347.46

24115(3) 23934

SnHþ X1 S þ 13 P

This work Exp [31].l This work

1.7492 1.748(2) 1.8442

5.512 5.519(11) 4.959

2.792 e 0.486

1831.9 1822(10) 1080.6

0 0 21900

11 P

This work

2.6416

2.417

0.149

285.7

22457

a

Ref. [50]. The numbers in parentheses indicate one standard deviation in the last digits shown. b Ref. [49]. The numbers in parentheses indicate one standard deviation in the last digits shown. c Ref. [48]. Result of a global analysis with the inclusion of all available “conventional” spectroscopic data and two types of photodissociation data. The numbers in parentheses indicate one standard deviation in the last digits shown. d Ref. [51]. e Ref. [2]. f Ref. [1]. g Ref. [18]. h Ref. [19]. i Ref. [23]. Uncertainties in parentheses are two standard deviations. j Ref. [25]. Values in parentheses are 3s in the last quoted number. k Ref. [29]. l Ref. [31].

S. Li et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 227 (2020) 117667 Table 4 Main CSFs of the L-S states around the equilibrium positions. Main CSFs at Re (%)a

L-S states

5pabab11sab12sab2dabab(86.06%)

X1 Sþ

5pabab11sab12sa6pay2dabab(89.93%)

13 P

5pabab11sab12sa6pbx2dabab(83.13%) 5pabab11sa12sab6pbx2dabab(5.58%) 5pabab11sab6paxay2dabab(76.80%) 5pabab11sa12sa6pbxay2dabab(5.25%) 5pabab11sa12sb6paxay2dabab(3.94%) 5pabab12sab6paxay2dabab(3.61%) 5pabab11sa12sab6pay2dabab(62.18%) 5pabab11sab13sa6pay2dabab(22.18%) abab 5pabab11sab6pab (42.56%) x 2d abab 5pabab11sab6pab (42.56%) y 2d abab a a aa abab 5p 11s 12s 6pxy2d (93.09%)

11 P 13 S

23 P 21 Sþ 15 S

5pabab11sab12sa14sa2dabab(85.72%)

23 Sþ a

Values in parentheses are the coefficient squared of CSF of each electronic configuration. Those CSFs with weights smaller than 3% are not listed.

5

The SOC effect perturbs the ground state just slightly, as the parameters of X1 Sþ listed in Table 1 and those of X1 Sþ 0þ in Table 6 present slight variations. The first excited L-S state 13 P split into four components with increasing energy from 13 P0 , 13 P0þ , 13 P1 to 13 P2 , which is identical with the energy sequence of CHþ [51] and SiHþ [18], and different with the order of U ¼ 0þ ; 0 ; 1; 2 for GeHþ [29]. The 13 P0 and 13 P1 states of SnHþ correlate with the first dissociation limit Hð2 S1=2 Þ þ Snþ ð2 P1=2 Þ, while the other two corresponding to the second channel of Hð2 S1=2 Þ þ Snþ ð2 P3=2 Þ. For 11 P and its corresponding U state 11 P1 , parameter variations can be noticed by comparing values in Table 1 and 6 For example, Re decreases ~11% from 2.6416 Å for 11 P to 2.3754 Å for 11 P1 , and ue increases ~27% from 285.7 cm1 to 394.3 cm1. Similar variations can also be found for the analogue GeHþ cation, with a decrease of ~4% for Re and an increment of ~15% for ue [29]. However, just minor changes of ~1% and ~0.1% for ue for SiHþ [18] and CHþ [51] respectively are inspected, and the Re values derived

Fig. 2. The PECs of the U states.

Table 5 Atomic and molecular states, and energies differences (in cm1) at the dissociation limit for the U states of SnHþ.

U state

Atomic states

Relative energy Exp [47].

This worka

1,0þ,0-

0.0

0.0

Hð S1=2 Þ þ Sn ð P3=2 Þ

2,1,1,0þ,0-

4251

4067

Hð2 S1=2 Þ þ Snþ ð4 P1=2 Þ

1,0þ,0-

46464

45951

Hð2 S1=2 Þ þ Snþ ð4 P3=2 Þ

2,1,1,0þ,0-

48368

47640

Hð2 S1=2 Þ þ Snþ ð4 P5=2 Þ

3,2,2,1,1,0þ,0-

50730

49636

Hð2 S1=2 Þ þ Snþ ð2 P1=2 Þ

1,0þ,0-

56886

56343

Hð2 S1=2 Þ þ Snþ ð2 P1=2 Þ 2

a

þ 2

Calculated at R ¼ 50 Å.

with or without the SOC effect are kept unchanged for both species [18,51]. This regular changing trend indicates the SOC effect influences the structures of these XHþ (X ¼ C, Si, Ge and Sn) cations more and more significantly with the increase of the atomic number of the X atom. The energy splitting of the 13 P0þ and 13 P1 increases from 23(7) 1 cm of CHþ [52], 80.6 cm1 of SiHþ [18], 499 cm1 of GeHþ [24], to 735 cm1 of SnHþ [31], which is another evidence of the fact that the heavier the XHþ cation is, the stronger the SOC effect act on the species. As has been expected, multiple PEC crossings and avoided crossings can be seen in Fig. 2, especially for the U ¼ 1 and U ¼ 0þ components, which indicates the character of the PECs of these U states will not be clearly presented without the inclusion of additional states in the overall SOC computations. For instance, the (5) 0þ state interacts with (4)0þ at ~1.79 Å and ~3.09 Å, and with the

6

S. Li et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 227 (2020) 117667

Table 6 The spectroscopic constants of the U states. Re /Å

De /eV

Be /cm1

ae /cm1

ue /cm1

ue ce /cm1

104 Drot /cm1

13 P0

1.7487 1.748(2)a 1.8489

2.500 e 0.318

5.515 5.519(11)a 4.934

0.138 0.141(11)a 0.502

1834.6 1822(10)a 1052.7

30.9 30(10)a 119.8

1.99 e 4.33

13 P0þ

1.8380

0.782 e

4.993 e

13 P1

e 1.8641

0.454 e

1098.1 1064

95.7 87

4.13 e

0.194

13 P2

1.8434

0.494

4.850

0.596

965.5

144.4

4.90

4.963

0.466

1086.0

107.5

4.15

11 P1

2.3754

13 S  0þ

1.7897

0.155

2.989

0.220

394.3

18.0

6.87

1.730

5.266

0.536

1149.7

86.7

4.42

13 S  1 23 P0

1.7593

1.814

5.449

0.349

1464.6

96.8

3.02

2.0019

1.678

4.209

0.095

1637.6

46.4

1.10

23 P1

2.0032

1.456

4.203

0.089

1633.0

46.6

1.11

23 P0þ

2.0448

1.361

4.034

0.073

1476.6

25.9

1.20

23 P2

2.0543

1.580

3.997

0.040

1442.9

13.6

1.23

21 S0þ

2.8090

1.307

2.138

0.032

703.3

9.1

0.79

15 S 0

2.3110

0.255

3.158

0.417

643.5

67.4

3.04

15 S 1

2.3333

0.260

3.098

0.204

645.4

31.9

2.85

15 S 2

2.3243

0.258

3.122

0.213

655.8

34.3

2.83

1.9333

0.414

4.512

0.331

942.6

48.1

4.14

1.9325

0.413

4.516

0.335

935.3

44.7

4.21

U states X Sþ 0þ 1

þ   

23 S þ 0 23 S þ 1 a

Ref. [31], the uncertainties denote two standard deviations.

higher (6)0þ one at ~1.54 Å, ~2.34 Å, and ~3.62 Å respectively. In contrast, for components with U ¼ 2, only one avoided crossing is  found at ~3.22 Å between 23 P2 and 15 S2 states. €dinger equation of nuclear motion, By solving the radial Schro we have derived the vibrational energy levels and their corresponding rotational constants for six bound states of SnHþ. Table 7 lists our calculated energy levels GðvÞ, rotational constants Bv and centrifugal distortion constants Dv , as well as available experimental results [31]. For the sake of simplicity, only states with the vibrational quantum number up to seven are presented in the table. Our calculated rotational and centrifugal distortion con3 3 þ stants for the first two energy levels of X1 Sþ 0þ , 1 P0 and 1 P1 states are all in reasonable agreement with available experimental values. To evaluate the strength of the SOC interactions, the spin-orbit matrix elements are calculated and analyzed. We use the notab BP jBD to present the spin-orbit matrix element between tion of CAj H SO

A and B states, which are listed in Table 8. Fig. 3 plots the SOC terms values versus the internuclear distance. Since term values associated with the x- and y-component of 1 P or 3 P states are identical, for instance, SO1 ¼ SO2 , SO3 ¼ SO4 , etc, the SOC curves corresponding to these states are overlapped. 1 Among the singlet-triplet bands, X Sþ  13 P(SO7 and SO8), 3 þ 3 1 1 1 P  1 S (SO1 and SO2), and 1 P  1 P (SO15 and SO16) present quite significant couplings in the Franck-Condon region, while 3 1 11 P  2 Sþ (SO3 and SO4), 11 P  23 P (SO13 and SO14) and X Sþ   3 1 S (SO17) exhibit weak interactions with SOC term values less than 300 cm1. For the triplet-triplet and triplet-quintet bands, þ interactions between the 3 P  3 S (SO23, SO24, SO25 and SO26) and 3 3 P  P (SO29 and SO30) bands, with coupling term values of no more than 150 cm1, are weaker than the others. Monotonic variation trends are observed for all spin-orbit matrix elements, except þ þ for the 11 P  23 S (SO3 and SO4), 13 S  13 P (SO23 and SO24) and 1 þ 3  1 X S  1 S (SO17) bands. The 1 P  13 P (SO15 and SO16) and

Table 7 Vibrational energy levels, rotational constants and centrifugal distortion constants of the U states. (in cm1). v

GðvÞ

Bv

104 Dv

GðvÞ

Bv

104 Dv

GðvÞ

13 P0þ 0 1 2 3 4 5 6 7

903.7 e 2674.5 e 4387.2 6040.7 7633.5 9163.5 10628.2 12024.2

a

514.5 1392.7 2086.8 2639.6 3082.2 3428.5 3684.0 3852.4

104 Dv

5.447 5.448(11)a

2.0 3.2(4)a

492.1 e

4.671 4.714(11)a

5.1 5.6(5)a

434.3 e

4.523 4.484(11)a

6.5 9.1(7)a

5.308 5.307(11)a 5.168 5.027 4.883 4.735 4.582 4.422

2.0 2.5(7)a 2.0 2.0 2.0 2.0 2.1 2.1

1304.0 e 1881.3 2234.3 2394.9 2492.2 e e

4.067 e 3.365 2.460 1.681 1.242 e e

7.2 e 10.9 21.3 16.0 20.0 e e

1077.3 e 1343.5 1434.0 1508.8 1549.5 e e

3.593 e 2.029 1.627 1.160 0.655 e e

15.8 e 39.5 13.2 23.1 37.9 e e

2.871 2.592 2.268 1.872 1.047 0.655 0.243 e

6.8 7.3 8.4 12.8 26.7 39.3 35.9 e

13 P2 0 1 2 3 4 5 6 7

Bv 13 P1

4.725 4.211 3.704 3.243 2.813 2.384 1.931 1.433

4.7 5.8 6.4 6.7 7.4 8.6 10.9 15.0

527.9 1440.9 2191.7 2840.6 3435.8 3999.7 4534.6 5030.8

Ref. [31], experimental results, the uncertainties denote two standard deviations.

11 P1 4.766 4.286 3.854 3.530 3.299 3.114 2.931 2.720

4.5 5.2 5.1 4.2 3.4 3.1 3.3 4.0

193.2 544.6 837.2 1064.3 1190.3 1233.3 1246.0 e

S. Li et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 227 (2020) 117667

7

Table 8 Notations of the spin-orbit matrix element of U states qv’v’’ .  BP  b 3 þ SO1 ¼ iC11 Py  H SO 1 S D

 BP  b 3 þ SO2 ¼  C11 Px  H SO 1 S Dy

 BP  b  3 þ SO3 ¼ iC11 Py  H SO 2 S Dx

 BP  b  3 þ SO4 ¼ C11 Px  H SO 2 S Dy

 BP  b  3  SO5 ¼ iC11 Px  H SO 1 S Dx

 BP  b  3  SO6 ¼ C11 Py  H SO 1 S Dy

 BP  b  3 1 SO7 ¼  iCX Sþ  H SO 1 Py Dx

 BP  b  3 SO8 ¼ CX1 Sþ  H SO 1 Px Dy

 BP  b  3 SO9 ¼  iC21 Sþ  H SO 1 Py Dx

 BP  b  3 SO10 ¼  C21 Sþ  H SO 1 Px Dy

 BP  b  3 SO11 ¼ iCX1 Sþ  H SO 2 Py Dx

 BP  b  3 SO12 ¼  CX1 Sþ  H SO 2 Px Dy

 BP  b  3 SO13 ¼ iC11 Py  H SO 2 Px Dz

 BP  b  3 SO14 ¼  iC11 Px  H SO 2 Py Dz

 BP  b  3 SO15 ¼ iC11 Py  H SO 1 Px Dz

 BP  b  3 SO16 ¼  iC11 Px  H SO 1 Py Dz

 BP  b  3  SO17 ¼ iCX1 Sþ  H SO 1 S Dz

 BP  b  3 SO18 ¼ iC13 Px  H SO 1 Py Dz

 BP  b  5  SO19 ¼ iC13 Px  H SO 1 S Dx

 BP  b  5  SO20 ¼ C13 Py  H SO 1 S Dy

 BP  b  3 SO21 ¼ iC13 S  H SO 1 Px Dx

 BP  b  3 SO22 ¼ C13 S  H SO 1 Py Dy

 BP  b  3 SO23 ¼  iC13 Sþ  H SO 1 Py Dx

 BP  b  3 SO24 ¼ C13 Sþ  H SO 1 Px Dy

 BP  b  3 SO25 ¼  iC23 Sþ  H SO 1 Py Dx

 BP  b  3 SO26 ¼ C23 Sþ  H SO 1 Px Dy

 BP  b  5 SO27 ¼ iC13 Py  H SO 1 Px Dz

 BP  b  5 SO28 ¼  iC13 Px  H SO 1 Py Dz

 BP  b  3 SO29 ¼  iC13 Px  H SO 2 Py Dz

 BP  b  3 SO30 ¼  iC13 Py  H SO 2 Px Dz

13 P  15 P (SO27 and SO28) bands are both found with values between 1250 cm1 and 1450 cm1, indicating these states are more strongly affected by the SOC effect than other states. Generally, the spin-orbit matrix element between two states both associated with the first dissociation limit shows relatively larger SOC term values of over 500 cm1 in the Franck-Condon þ region, such as X1 S  13 P (SO7 and SO8) and 11 P  13 P (SO15 and SO16). The matrix elements combined with states associated þ with different dissociation limits, for instance, 11 P  23 S (SO3 3 3 þ and SO4) and X S  2 P (SO11 and SO12), experienced relatively slight perturbation from the SOC effect and implicitly revealed the minor mixing of the wave functions of these two states.

tv’ ¼

X Av’v’’

!1 :

(3)

v’’

In Eq. (2) and Eq. (3), n is the transition frequency (in cm1), Jv’ and Jn’’ are normalized radial wave functions of the initial and final vibrational states respectively, TDM(R) is the transition dipole moment function (in Debye). The vibrational branching ratio (VBR) Rv’v’’ can be expressed as

A Rv’v’’ ¼ P v’v’’ ; Av’v’’

(4)

v’’

3.3. Transition properties The TDMs for several selected excited U states to the ground one as functions of R are illustrated in Fig. 4. In the Franck-Condon region, TDMs of the 11 P1  X1 Sþ 0þ band decrease from ~0.5 a.u. to nearly zero with the increasing of R from ~1.5 Å to ~3 Å. The 13 P1  X1 Sþ 0þ band presents a similar variation trend with quite smaller TDM. The 13 P0þ  X1 Sþ 0þ transition moment experiences an opposite monotonic tendency from almost zero to ~0.15 a.u. between ~1.5 Å to ~3 Å. Using the PECs and TDMs of these U states, the Einstein coefficients Av’v’’ , the Franck-Condon factors qv’v’’ and the radiative lifetimes tv’ are determined by the equations

Av’v’’ ¼ and

16p3 v3 jCJv’ jTDMðRÞjJv’’ Dj2 3ε0 hc3

(2)

where Av’v’’ is the Einstein coefficient for the v’/v’’ transition. v’ and v’’ denotes the excited and lower vibrational levels respectively. The VBRs have a very sensitive dependence on the difference in the equilibrium bond length between the excited and ground state. We have tabulated the Einstein emission coefficients Av’v’’ , vibrational branching ratios Rv’v’’ and radiative lifetimes tv’ for the, 1 þ 1 13 P1  X1 Sþ 0þ and 1 P1  X S0þ bands from Table 9 to Table 11. It should be noted that we present the branching ratios following the excitations on the P(1) transitions. According to Eq. (2), transition frequencies and transition dipole moments are two main factors that influence the Einstein coefficients. As for transitions between low vibrational energy levels of two electronic states, it is anticipated that results derived from the Einstein A coefficients accord with those from the FCFs, especially for potential candidates for laser cooling, which should satisfy highly diagonal FCFs and the vibrational branching ratios [53,54]. However, it is found that our FCFs deviate from the VBRs slightly. The discrepancies may be attributed to: (1) the strong interaction of the 13 P state with its neighboring 11 P one, which is noticeable in

8

S. Li et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 227 (2020) 117667

the experimental studies of this system [31] and the analogue species GeHþ [24]; and (2) the anomaly energy sequence and significant 13 P1  13 P0þ energy separation (804 cm1 in this work and 735 cm1 in Ref. [31]), which is quite larger than that of the analogue GeHþ (493 cm1 [22]) and CHþ (23 cm1 [52]). Moreover, this anomaly of multiplet separation has also been found for the isoelectronic InH molecule with the 13 P1  13 P0þ energy separation of 663 cm1 [55]. The radiative lifetimes of v’ ¼ 0 vibrational levels for the 13 P0þ , 13 P1 and 11 P1 states are all on the order of tens of microseconds, which is similar to those of GeHþ [29]. Since the radiative lifetimes are determined by transition frequencies and transition dipole moments, it is found that although the 13 P1  X1 Sþ 0þ band poses a smaller Franck-Condon factor and a greater TDM value at Re than 3 that of 13 P0þ  X1 Sþ 0þ , the 1 P1 state still has a shorter radiative lifetime than 13 P0þ . The Franck-Condon factors qv’v’’ for these three bands, as listed in Table 12, are not highly diagonal, which is against one of the criteria of selecting candidate molecules and transitions for laser cooling [56]. Therefore, the present species is not an appropriate candidate for laser cooling. Furthermore, the changing trends of our calculated FCFs with v’ and v’’ are irregular, which was also observed in previous experimental [24] and theoretical [29] results of GeHþ. þ The 13 P0þ  X1 Sþ 0þ band of SnH is calculated to have an FCF of 0.7201 for the (0-0) transition, and this value is comparable with that of the theoretical prediction of GeHþ (0.737) [29] although it overestimates the experimental value of 0.664 [25]. As to CHþ and SiHþ, they both have highly diagonal FCF of 0.996 [51] and 0.9189 þ [18]. The FCF of the 13 P1  X1 Sþ 0þ band of SnH determined in this work is 0.5644 for the (0-0) transition. It is smaller than the analogue CHþ (0.996) [51], SiHþ (0.9186) [18] and GeHþ (0.728) [29]. The FCF of the (0-0) transition of 11 P1  X1 Sþ 0þ is quite small 1 (0.0061), since the difference of Re values of X1 Sþ 0þ and 1 P1 states is ~0.63 Å. The small FCFs are similar with those of GeHþ [29], which has a 0.002 FCF for the (0-0) transition of the same band. The maximum FCF of SnHþ is rather small (0.1563), and it is comparable with that of GeHþ [29] (0.152).

4. Conclusions Fig. 3. Spin-orbit matrix elements of (a) singlet-triplet, (b) triplet-triplet and tripletquintet L-S states.

In the present paper, we have investigated the ground and lowlying excited L-S and U states of SnHþ at the MRCI þ Q level with the quintuple-z basis sets. Potential energy curves, spectroscopic Table 9 Einstein emission coefficients Av’v’’ (in s1), vibrational branching ratios Rv’v’’ (in italics 3 and are given in %) and radiative lifetimes tv’ (in ms) for the X1 Sþ 0  1 P0 band. v’’

v’ ¼ 0

v’ ¼ 1

v’ ¼ 2

v’ ¼ 3

v’ ¼ 4

v’ ¼ 5

v’ ¼ 6

v’ ¼ 7

0

9605.7 50.1 6931.0 36.2 2016.6 10.5 499.1 2.6 90.5 0.5 14.4 0.1 1.8 0.0 0.2 0.0 0.0 0.0 52.19

984.4 4.4 2488.3 11.2 8661.7 39.1 6105.4 27.5 2790.6 12.6 883.3 4.0 218.3 1.0 40.0 0.2 5.3 0.0 45.09

0.0 0.0 3245.1 16.9 760.2 3.9 1623.4 8.4 4842.7 25.2 4775.2 24.8 2664.0 13.8 1017.9 5.3 268.2 1.4 51.95

119.5 0.8 1167.6 7.7 602.1 4.0 4122.6 27.2 953.6 6.3 242.8 1.6 2234.7 14.8 2900.1 19.2 1890.0 12.5 66.03

167.9 1.3 136.2 0.2 1857.9 15.0 1321.5 0.0 764.3 27.2 2756.3 8.3 1231.7 2.9 6.8 17.5 996.9 8.6 81.88

130.1 0.9 16.2 1.7 1536.9 7.2 0.2 7.3 2785.0 22.5 849.7 1.5 299.3 20.7 1796.1 7.4 883.9 2.3 97.51

74.9 0.5 151.9 3.0 630.4 1.4 641.0 15.4 1964.6 5.9 133.5 19.0 1810.0 13.8 643.7 1.4 201.3 16.2 114.36

35.4 0.2 220.3 3.2 102.5 0.0 1136.5 15.4 438.4 0.0 1398.7 29.1 1019.8 0.9 99.7 14.9 1196.2 9.6 135.55

1 2 3 4 5 6 7 8 Fig. 4. The TDMs for selected low-lying U states to the ground state.

S. Li et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 227 (2020) 117667

9

Table 10 Einstein emission coefficients Av’v’’ (in s1), vibrational branching ratios Rv’v’’ (in italics and are given in %) and radiative lifetimes tv’ (in ms) for the 13 P0  X1 Sþ 0þ band. v’’

v’ ¼ 0

v’ ¼ 1

v’ ¼ 2

v’ ¼ 3

v’ ¼ 4

v’ ¼ 5

v’ ¼ 6

v’ ¼ 7

0

38886.7 76.2 9257.9 18.1 2390.7 4.7 444.5 0.9 72.5 0.1 8.9 0.0 0.9 0.0 0.0 0.0 0.0 0.0 19.58

17092.6 74.3 413.2 1.8 2181.8 9.5 2013.1 8.7 925.0 4.0 302.3 1.3 70.1 0.3 11.3 0.0 1.0 0.0 43.46

3218.4 63.9 644.7 12.8 761.8 15.1 343.7 6.8 52.6 1.0 0.3 0.0 4.6 0.1 5.1 0.1 1.9 0.0 198.68

2668.9 59.9 813.1 18.2 699.3 15.7 236.4 5.3 15.1 0.3 3.8 0.1 12.4 0.3 7.7 0.2 2.1 0.0 244.28

1514.2 56.4 619.5 23.1 417.4 15.5 106.6 4.0 1.2 0.0 8.7 0.3 12.1 0.5 5.6 0.2 1.2 0.0 372.23

606.8 54.4 287.3 25.8 169.9 15.2 36.4 3.3 0.0 0.0 5.6 0.5 6.0 0.5 2.4 0.2 0.4 0.0 897.02

118.4 53.8 58.6 26.6 33.3 15.1 6.7 3.0 0.0 0.0 1.2 0.6 1.2 0.6 0.5 0.2 0.1 0.0 4545.45

10.2 53.7 5.1 26.8 2.9 15.1 0.6 3.0 0.0 0.0 0.1 0.6 0.1 0.6 0.0 0.2 0.0 0.0 52631.58

1 2 3 4 5 6 7 8

Table 11 Einstein emission coefficients Av’v’’ (in s1), vibrational branching ratios Rv’v’’ (in italics and are given in %) and radiative lifetimes tv’ (in ms) for the 13 P0  X1 Sþ 0þ band. v’’

v’ ¼ 0

v’ ¼ 1

v’ ¼ 2

v’ ¼ 3

v’ ¼ 4

0

8746.9 14.4 15548.9 25.5 15785.0 25.9 11289.2 18.5 6066.2 10.0 2485.1 4.1 761.7 1.3 163.2 0.3 20.3 0.0 16.43

28971.8 25.8 38649.7 34.4 27865.7 24.8 12704.1 11.3 3533.5 3.1 443.3 0.4 0.2 0.0 39.4 0.0 30.9 0.0 8.91

49555.6 37.5 50203.6 38.0 25160.4 19.0 6350.1 4.8 404.9 0.3 105.9 0.1 298.7 0.2 151.7 0.1 26.0 0.0 7.56

55966.0 47.2 44446.7 37.5 15448.1 13.0 1672.2 1.4 81.6 0.1 603.9 0.5 377.7 0.3 73.8 0.1 0.9 0.0 8.43

20620.6 52.6 14102.7 35.9 3799.3 9.7 158.7 0.4 155.5 0.4 275.2 0.7 106.6 0.3 9.4 0.0 0.6 0.0 25.49

1 2 3 4 5 6 7 8

constants and vibrational energy levels of these electronic states are derived and compared with available experimental values. The excellent consistency between our theoretical results and experimental ones indicate our computation performed on this species is of high quality, and our derived data are trustworthy determinations. Through our analyses on the spin-orbit matrix elements, it is found that the wavefunctions of related electronic states have experienced dramatic variations, which reveals the spin-orbit coupling effect has a significant impact on these electronic states. Comparisons of characters of several U states of SnHþ with those of analogue cations indicate the spin-orbit coupling effect becomes more and more significant from CHþ, SiHþ, GeHþ to SnHþ. Moreover, the transition properties of bands from several low-lying excited states to the ground one of SnHþ are also derived, including the transition dipole moments, Franck-Condon factors and radiative lifetimes. It is anticipated that the knowledge derived from the present study will extend our understanding of the structures and spectroscopic properties of this cation and shed some light on future laboratory detections.

Table 12 Franck-Condon factors qv’v’’ for the three bands. v’’

v’ ¼ 0

v’ ¼ 1

v’ ¼ 2

v’ ¼ 3

v’ ¼ 4

v’ ¼ 5

v’ ¼ 6

v’ ¼ 7

13 P0þ  X1 Sþ 0þ 0 1 2 3 4 5 6 7 8

0.7201 0.1949 0.0643 0.0160 0.0038 0.0008 0.0001 0.0000 0.0000

0.2175 0.1776 0.2498 0.1982 0.0991 0.0404 0.0131 0.0035 0.0007

0.0501 0.2881 0.0088 0.0473 0.1678 0.1892 0.1379 0.0722 0.0286

0.0103 0.1911 0.0615 0.1098 0.0322 0.0100 0.1008 0.1761 0.1628

0.0016 0.0945 0.1622 0.0226 0.0212 0.0988 0.0494 0.0003 0.0733

0.0001 0.0377 0.1771 0.0076 0.0736 0.0299 0.0126 0.0838 0.0554

0.0000 0.0120 0.1308 0.0678 0.0421 0.0032 0.0679 0.0266 0.0108

0.0001 0.0030 0.0756 0.1134 0.0031 0.0372 0.0371 0.0046 0.0585

13 P1  X1 Sþ 0þ 0 0.5644 0.2029 1 0.2466 0.0078 2 0.1154 0.0876 3 0.0460 0.1540 4 0.0179 0.1592 5 0.0065 0.1338 6 0.0023 0.0983 7 0.0008 0.0662 8 0.0002 0.0414

0.0352 0.0118 0.0275 0.0230 0.0078 0.0001 0.0046 0.0195 0.0409

0.0284 0.0146 0.0244 0.0150 0.0021 0.0013 0.0121 0.0278 0.0413

0.0157 0.0109 0.0142 0.0065 0.0002 0.0029 0.0113 0.0191 0.0218

0.0062 0.0050 0.0057 0.0022 0.0000 0.0018 0.0054 0.0079 0.0077

0.0012 0.0010 0.0011 0.0004 0.0000 0.0004 0.0011 0.0016 0.0014

0.0001 0.0001 0.0001 0.0000 0.0000 0.0000 0.0001 0.0001 0.0001

11 P1  X1 Sþ 0þ 0 0.0061 0.0177 1 0.0242 0.0522 2 0.0558 0.0850 3 0.0956 0.0924 4 0.1325 0.0668 5 0.1549 0.0259 6 0.1563 0.0008 7 0.1373 0.0140 8 0.1050 0.0629

0.0270 0.0605 0.0684 0.0418 0.0080 0.0025 0.0301 0.0591 0.0547

0.0279 0.0492 0.0388 0.0108 0.0005 0.0180 0.0362 0.0279 0.0047

0.0098 0.0149 0.0092 0.0011 0.0015 0.0080 0.0099 0.0039 0.0001

e e e e e e e e e

e e e e e e e e e

e e e e e e e e e

Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the ork reported in this paper. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant Nos. 11847058, 11804031 and 11747139), the Yangtze Youth Talents Fund of Yangtze University (Grant No. 2015cqr21, S. Li), and the Youth Fund of Yangtze University (Grant No. 2016cqn54, Y.Y. Jin).

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