Interaction and Photodissociation of Electronic Excited States of HS2

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A: Kinetics, Dynamics, Photochemistry, and Excited States

Interaction and Photodissociation of Electronic Excited States of HS in the Ultraviolet Region: A Theoretical Contribution 2

Shuang Feng, Shimin Shan, Huijie Guo, Haifeng Xu, and Bing Yan J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b00800 • Publication Date (Web): 05 Apr 2019 Downloaded from http://pubs.acs.org on April 7, 2019

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The Journal of Physical Chemistry

Interaction and Photodissociation of Electronic Excited States of HS2 in the Ultraviolet Region: a Theoretical Contribution Shuang Feng 1, Shimin Shan 2, Huijie Guo1, Haifeng Xu 1*, Bing Yan 1* 1 Institute

of Atomic and Molecular Physics, Jilin University, Changchun 130012,

China 2

School of Science, North University of China, Taiyuan 030051, China

* Corresponding authors: Tel: 86-431-85168817; Fax: 86-431-85168816; Email: [email protected] (Haifeng Xu) and [email protected] (Bing Yan)

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ABSTRACT: The HS2 molecules play an important role in photo-chemical processes in combustion, atmosphere as well as interstellar medium, yet our knowledge about the electronic excited states in the ultraviolet (UV) region is limited. In this study, we perform highlevel ab initio calculations on electronic states of HS2 using the internally contracted multireference configuration interaction method including Davidson correction (icMRCI+Q). The vertical transition energies, oscillator strengths, electron configurations, and transitions of thirteen electronic states of HS2 with energy up to 8 eV are calculated at the icMRCI+Q/aug-cc-pv(5+d)Z level. Base on the calculated potential energy curves, we investigate the interaction and photo-dissociation mechanism of electronic states, which should shed some light on the decomposition processes of gas-phase HS2 molecules in the ultraviolet region.

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INTRODUCTION Sulfur-containing molecules have attracted intense research interest due to their important roles in biochemistry1, combustion2-5, atmospheric chemistry6,7 and interstellar medium (ISM)8-12. Gas-phase sulfur chemistry is pivotal in the sulfurcycle of the Earth’s earliest atmosphere6, and Sulfur-containing molecules have been demonstrated to be exist in the atmosphere of planets, dwarfs and meteorites.13,14 Knowledge of the spectroscopic properties and dynamics of electronic states is thus of vital importance for understanding the mechanism of various photochemical processes involving sulfur-containing molecules. HS2 is the simplest sulfur-containing molecule that has a disulfide bond. Since Porter et. al.15 firstly observed the spectrum in photolysis-kinetic absorption spectroscopic study of hydrogen sulfide in 1950, numerous studies have been carried out to investigate the spectra and dynamics of electronic states of HS2 radicals, both experimentally and theoretically. An early study has assigned the absorption band to be the A2A' ← X2A'' transition of HS216. More accurate information about the ground state X2A'' has been determined experimentally by millimeter spectrum17, microwave spectrum18 and infrared spectrum19. The A2A' ← X2A'' transition has been recently reinvestigated by several advanced techniques including high-resolution Fouriertransform20,

photodetachment-photoelectron

spectroscopy21

and

low-energy

photoelectron imaging22, from which the geometries and spectroscopic constants of both states have been obtained. Theoretically, the X2A'' and A2A' states have been extensively studied using various methods, such as self-consistent field (SCF), configuration interaction (CI)23, coupled-cluster singles and doubles model (CCSD)24, coupled cluster singles and doubles with perturbative triples (CCSD(T))24-27 and B3LYP25 methods. Very recently, accurate double many-body expansion global 3



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potential energy surface of X2A'' is reported based on multi-reference configuration interaction including Davidson correction (MRCI+Q) calculations28-30. On the other hand, our knowledge about the excited states beyond A2A′ of HS2 is not sufficient to understand the behavior of gas-phase HS2 molecules in the UV region, which should be important in various photo-chemical processes. For instance, dissociation dynamics of the electronic excited states has not been discussed yet, which would give a clue to shed some light on the decomposition of HS2 molecules in ISM where Photo-dominated Region (PDR) is dominated. Indeed, despite that the abundance of HS2 in ISM is expected to be only several times lower than that of the widespread H2S molecules, it has not been observed until 2017 in the Horsehead Nebula.31 While very recent theoretical study indicated a possible formation channel of HS2 in ISM by dissociation of HSSH+ ions31,32, the decomposition of HS2 in gasphase nebula remains unknown. For this purpose, we present here a high-level ab initio

study on excited states of HS2, using internally contracted multireference

configuration interaction (icMRCI) method. The potential energy curves (PECs), spectroscopic properties and interaction of electronic states of HS2 are investigated. Based on our calculation results, we discuss the photo-dissociation mechanism of HS2 in the UV region. METHODS All calculations were performed by MOLPRO201233 program package. The calculations on the excited electronic states were performed by using complete active space self-consistent field (CASSCF)34 and internally contracted multi-reference configuration interaction

35

with Davidson correction36 (icMRCI+Q) method. We

first employed the Hartree−Fock (HF) self-consistent field method to calculate the molecular orbitals (MOs) and energies of the ground state. Then, we used CASSCF 4


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for optimization of orbitals with the HF MOs as the starting orbitals and obtained a state average multi-reference configuration wave function that better described the electronic static or near degeneracy effect. Finally, using all configurations in the CI expansion of the CASSCF wave functions as the reference, we calculated the energies using the icMRCI+Q method, taking into account the kinetic correlation effect. The active space included 13 electrons and 11 orbitals (1s1 electron of H and 3s23p4 electrons of S). The basis sets were correlation-consistent aug-cc-pVXZ (X = T, Q, 5)37 for hydrogen and aug-cc-pV(X+d)Z

38

that included tight d functions for sulfur.

Extrapolation to the complete basis set (CBS) limit was determined using E(x) = Ecbs + Be–αx (x = 3, 4 or 5, B and α are constants) 39. The convergence thresholds for energy and gradient in optimization of geometries were 10−10 hartree and 10−4 a.u., respectively.

RESULT AND DISCUSSION A. Vertical Transition Energies, Equilibrium Geometries and Harmonic Vibrational Frequencies of Electronic States of HS2 In our study, we aim to understand the behavior of electronic excited states of HS2, in particular the photodissociation mechanism in the UV region which would shed some light on the decomposition processes of gas-phase sulfide molecules. Thirteen states with VTE < 8 eV are investigated using the icMRCI+Q method, including eight doublet states (X2A'', A2A', 22A', 22A'', 32A', 32A'', 42A', 42A'') and five quartet states (14A'', 24A'', 14A', 24A', 34A'). Table 1 summarizes the calculated results of VTE, oscillator strength (OS), configuration and transition of electronic states by icMRCI+Q with the aug-cc-pV(5+d)Z basis. For VTE we performed additional calculations with the aug-cc-pV(t+d)Z basis. It can be seen that the 5



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difference between different basis sets is not very significant. We also compare our calculated VTE with previous works, which are only available for the A2A' state as listed in the table. Considering that the values of T00 (instead of VTE) are reported in the literature, our results are in relatively agreement with those of previous studies. The ground state of HS2 is X2A'' with main electronic configuration of (12a’)2(13a’)2(3a’’)2(4a’’). The first excited state A2A', which corresponds to the 13a’→ 4a’’ transition, lies at a VTE of only 1.02 eV above the ground X2A'' state. Eight out of the 13 electronic states fall in the VTE range of 3.65-5.42 eV, indicating strong interactions between the states which will complicate the corresponding dynamics in the UV region and will be discussed in the following sections. As shown in Table 1, the OS of 22A'' with VTE of 3.65 eV is more than one order of magnitude larger than that of any of other optical bright doublet states. Thus the 22A'' state should play an essential role in the UV photodissociation of HS2. In our study we will particularly focus on the 22A'' state to elucidate the behavior of HS2 in the UV region. To date no information is available for the 22A'' state of HS2. Table 2 lists our calculated equilibrium geometries (H-S and S-S bond lengths, RH-S and RS-S, and bond angle ∠H-S-S) and harmonic vibrational frequencies (high-frequency stretching mode ω1, bending ω2 and low-frequency stretching ω3) of the 22A'' state. We also list in the table our results of the ground state X2A'' and the first excited state A2A' calculated by the icMRCI+Q method. The results of previous available experimental and theoretical studies on X2A'' and A2A' states are also presented in the table for comparison. The spectroscopic constants shown in Table 2 are calculated with different basis sets for all the three states. It can be seen that the deviation between the calculated results of aug-cc-pVQZ and aug-cc-pV5Z is generally smaller than that between aug6


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cc-pVTZ and aug-cc-pVQZ. By comparing the results of aug-cc-pV5Z and those of CBS (Q5 extrapolation), we found the values of bond lengths and ∠H-S-S of HS2 converge in the magnitude order of 10-2 Å and 0.01° respectively. It is indicated that as the basis set increases from aug-cc-pVQZ to CBS, the accuracy of the calculated spectroscopic constants is systematically improved40. Our results for the X2A'' and A2A' states calculated at the icMRCI+Q/CBS level are in relatively good agreement with previous experimental and theoretical results. B. Potential Energy Curves of Electronic States of HS2 Figures 1−3 show the rigid one-dimensional PECs along ∠H-S-S (Figure 1), S−S bond (Figure 2), and H−S bond (Figure 3), respectively, which are calculated by the icMRCI/aug-cc-pV(T+d)Z mehtod. As shown in Figure 1, the ground state X2A'' and seven excited states (A2A', 22A'', 22A', 42A'', 42A', 14A' and 24A'') are all bent states. The lowest energy of the 32A'' state appears at ∠H-S-S = 176°. The other four excited states (32A', 24A', 34A' and 14A'') are linear states. In bending PECs, avoided crossing between states with the same symmetry can be found. For example, avoided crossings of 22A'−32A', 32A''−42A'' and 32A'−42A' can be observed at ∠H-S-S of 104°, 85° and 150° respectively, and two avoided crossings occur between 24A'−34A' at 65° and 115° respectively. The results indicate the presence of strong coupling along the bending coordinate in these avoided intersection regions, which would affect the structure and spectroscopy of the excited states of HS2. Before we turn to discuss the PECs along the bond lengths shown in Figures 2 and 3, we present in Figure 4 the dissociation limits and the corresponding energies which are associated adiabatically to the 13 electronic states of HS2. For cleavage of the H-S bond, there are seven H+S2 channels related to the electronic states with the energy range from 2.73 eV to 7.14 eV. On the other hand, there are only two HS+S 7



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channels. And except for 42A' and 42A'' states which are related to S(1D)+HS(2П) channel at 4.35 eV, all other electronic states are related to S(3P)+HS(2П) channel at 3.25 eV. The energy difference of S(3P)-S(1D) is 1.1 eV which is consistent with experimental result of 1.14 eV 41. Besides, the energy differences of electronic states of S2 molecules derived from our calculated dissociation limits agree well with the results of previous experimental42-45 and theoretical46 studies. For example, the energy difference of S2(1 Δ g)-S2(3 Σ g-) in the present study is 0.54 eV, which repeats the experimental measurement of 0.51 eV. As shown in Figure 2, the states X2A'' and A2A' are typical bound states with deep potential wells of 3.08 eV and 2.16 eV respectively. Other excited doublet states are either a repulsive state (22A') or bound states with shallow potential wells (22A'', 32A', 32A'', 42A', 42A''). For quartet states, the 14A'', 24A'' and 34A' states exhibit a small potential well of 0.36 eV, 0.4 eV and 0.12 eV respectively, while the other quartet states are all repulsive. As we have mentioned above, these repulsive states are all related to the lowest dissociation limit HS(2П) + S(3P) along the S-S bond, implying the important role in ultraviolet photolysis of HS2. On the other hand, all the 13 electronic states of HS2, which are adiabatically related to seven different H+S2 channels, are typical bound states or have local minima along the H-S bond due to the avoided crossings between states with same symmetry (see Figure 3). This indicates that dissociation to H+S2 channels may be less significant comparing to the HS(2П) + S(3P) channel. However, complicated interaction is expected in PECs along both bonds since a large state-density in the energy range of 3 eV to 5 eV, making it possible for dissociation to both H+S2 and HS+S channels, as we will discuss in detail in the following section. C. State-Interaction and Photodissociation Mechanism of HS2 in the UV region 8


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As we have mentioned in Section A, the 22A'' state at 3.65 eV has the largest oscillator strength among electronic excited states of HS2. Thus we will focus our discussion on the interaction involving the 22A'' state based on our calculations, which will aid us to reveal the photodissociation mechanism of HS2 in the UV region. As we can see from Figure 2 and Figure 3, there are several states that may interact with 22A''. We will mainly consider two kinds of interactions, i.e., the spin-orbit coupling (SOC) between multiplet states and the non-adiabatic coupling between the states with same symmetry. For clarification we show in Figure 5 the PECs of 22A'' and the states that may interact with it along the S-S bond (Fig. 5A) and the H-S bond (Fig. 5B). The adiabatic dissociation limit of the 22A'' state is HS(2П) + S (3P ) at 3.03 eV (breaking the S-S bond) or H(2S)+S2(1Δg) at 3.28 eV (breaking the H-S bond). The calculated PEC of 22A'' shows a small dissociation barrier of 0.25 eV along the S-S bond at Rs-s =2.59 Å, and a slightly higher one of 0.73 eV along the H-S bond at RH-S = 1.75 Å. These barriers are attributed to the avoided crossings induced by nonadiabatic coupling between the 22A'' and 32A'' state. Using the CASSCF/AVTZ method, we calculate the non-adiabatic coupling matrix element of 22A''-32A'' as a function of Rs-s or RH-S. The results show strong coupling near RH-S = 1.74 Å and RSS

= 2.53 Å (see Figure 6), and the coupling along the S-S bond length is about twice

as large as that along the H-S bond length (114.45 vs 44.62 cm-1). Such non-adiabatic coupling affects the evolution of the 22A'' state when initially excited in the FranckCondon region, which would be an interesting subject for ultrafast time-resolved measurements. We would like to mention that the zero point energy of the 22A'' state (1813.42 cm-1) is only 0.02 eV lower than the barrier along the S-S bond length and 0.50 eV lower than that along the H-S bond length. This indicates that even the 9



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ground vibrational state of 22A'' could occur predissociation via the barrier formed by non-adiabatic coupling with 32A''. Moreover, the 22A'' state crosses with both the doublet state 22A' and the quartet state 14A''. The crossing points of 22A''-22A' and 22A''-14A'' are in the shallow well of the PEC of 22A''. Along the S-S bond length, the crossing point of 22A''-22A' is at Rss= 2.44 Å and that of 22A''-14A'' at Rs-s= 2.22 Å; along the H-S bond length, the crossing points of 22A''-22A' and 22A''-14A'' both are at RH-s= 1.65 Å (see Figure 5). The non-adiabatic coupling between 22A''-22A' is expected to be weak due to their different symmetries, however the multiple states 22A''-22A' (as well as 22A''-14A'') could interact via the SOC effect. The non-zero components of SOC matrix elements of 22A''-22A' and 22A''-14A'' along the H-S and S-S bond length are presented in Table 3. It can be seen from the table that the SOC along the H-S bond is much weaker than that along the S-S bond, for either 22A''-22A' or 22A''-14A'', indicating the interaction may induce efficient predissociation along the S-S bond. Moreover, both the crossing points of 22A''-22A' and 22A''-14A'' are near the equilibrium along the S-S bond, while the crossing points along the H-S bond are about 0.3 eV higher than equilibrium position of 22A'' state. It is expected that comparing to the H+S2 channels, the 22A'' state would be more likely to dissociate to produce the HS(2П)+S(3P) channel via the SOC with the 22A' or 14A'' state. The above analysis indicates that both SOC and non-adiabatic coupling could lead to predissociation of HS2 in the UV region. According to our discussion, we can summarize the dissociation mechanism of the 22A'' state of HS2: After excitation to the 22A'' state, the molecule could undergo pre-dissociation through a small barrier formed by the non-adiabatic coupling between 22A''-32A'', producing either HS(2П)+S(3P) or H(2S)+S2(1Δg) product; It can also dissociate to the HS(2П)+S(3P) 10


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channel via strong SOC effect between 22A'' and 22A' (or 14A''). It requires further experimental investigations to determine which channel is dominant in the dissociation of the 22A'' state. Our study indicates that the final electronic state of dissociation process could be an A' or A'' symmetry. While the 22A' state is a bent state, 32A'' and 14A'' are both linear states. Thus, different ro-vibrational population of the diatomic molecular fragment is expected for different channels, which could be experimentally feasible with spectroscopic or imaging measurements on the products. CONCLUSION In this work, we perform a high-level ab initio study on the electronic excited states of HS2 with VTE up to 8 eV using the icMRCI+Q method. It is shown that the 22A'' state has the largest oscillator strength among the excited states, indicating its essential role in the photo-chemical processes of HS2 in the UV region. The structure and vibrational frequencies of 22A'' are obtained for the first time. Based on the calculated PECs, we discuss the interaction of 22A'' with other electronic excited states. The results indicate that the molecule can undergo pre-dissociation through a small barrier formed by the non-adiabatic coupling between 22A''-32A'', producing either HS(2П)+S(3P) or H(2S)+S2(1Δg) product; or dissociate to the HS(2П)+S(3P) channel via strong SOC effect between 22A'' and 22A' (or 14A''). Our study adds our knowledge on the behavior of the electronic excited states to reveal complicate stateinteraction and photo-dissociation mechanism in the UV region, which could be of value for understanding various photo-chemical processes of HS2. AUTHOR INFORMATION Corresponding Authors *Tel: 86-431-85168817. Fax: 86-431-85168816. E-mail: [email protected]. 11



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*Tel: 86-431-85168817. Fax: 86-431-85168816. E-mail: [email protected]. Notes The authors declare no competing financial interest. ACKNOWLEDGEMENTS This work was supported by the National Key Research and Development Program of China (Grant No. 2017YFA0403300) the National Natural Science Foundation of China (Grant Nos.11874179, 11574114, and 11874177) the Natural Science Foundation of Jilin Province, China (Grant Nos. 20180101289JC) and the High Performance Computing Center of Jilin University. REFERENCE (1) Huxtable, R. J., The Chemistry of Sulfur. Biochemistry of the Elements, vol 6. Springer, Boston 1986. (2) Sendt, K.; Jazbec, M and Haynes, B. S., Chemical kinetic modeling of the H2S system. P. Combust. Inst. 2002. 29, 2439-2446. (3) Gargurevich, I. A., Hydrogen Sulfide Combustion Relevant Issues under Claus Furnace Conditions. Ind. Eng. Chem. Res. 2005. 44, 7706-7729. (4) Denis, P. A., The enthalpy of formation of the HSO radical revisited. Chem. Phys. Lett. 2005. 402, 289-293. (5) Denis, P. A. and Ventura O. N., Density functional investigation of atmospheric sulfur chemistry II. The heat of formation of the XSO2 radicals X=H, CH3. Chem. Phys. Lett. 2001. 344, 221-228. (6) Farquhar, J.; Huiming B. and Thiemens M., Atmospheric Influence of Earth's Earliest Sulfur Cycle. Science. 2000. 289, 756-758. 12


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(35) Werner, H. and Knowles P. J., An efficient internally contracted multiconfiguration–reference configuration interaction method. J. Chem. Phys. 1988. 89, 5803-5814. (36) Langhoff, S. R. and Davidson E. R., Configuration interaction calculations on the nitrogen molecule. Int. J. Quantum. Chem. 1974. 8, 1-72. (37) Dunning, T. H., Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys. 1989. 90, 1007-1023. (38) Dunning, T. H., et al., Gaussian basis sets for use in correlated molecular calculations. X. The atoms aluminum through argon revisited. J. Chem. Phys. 2001. 114(21): p. 9244-9253. (39) Halkier, A.; Helgaker, T.; Jørgensen, P.; Klopper, W. and Olsen, J., Basis-set convergence of the energy in molecular Hartree–Fock calculations. Chem. Phys. Lett. 1999. 302, 437-446. (40) Shan, S. M.; Yin, S.; Lian, Y.; Xu, H. F. and Yan, B., Accurate spectroscopic constants of the lowest three electronic states in halonitrenes with multireference configuration interaction. Int. J. Quantum. Chem. 2018. 118, 16. (41) Martin, W. C.; Zalubas, R and Musgrove A, Energy Levels of Sulfur, S I Through S XVI. J Phys Chem Ref Data. 1990. 19, 821. (42) Huber, K. P. and Herzberg G., Molecular spectra and molecular structure IV. Constants of diatomic molecules. 1979. 299. (43) Fink, E. H.; Kruse, H. and Ramsay, D. A., The high-resolution emission spectrum of S2 in the near infrared: The b1Σg+-X3Σg− system. J. Mol. Spectrosc. 1986. 119, 377-387. (44) Narasimham, N. A.; Sethuraman V. and Apparao K. V. S. R., Near-infrared bands of S2: 3Πg-3Δu system. J. Mol. Spectrosc. 1976. 59, 142-152. 16


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(45) Narasimham, N. A., Apparao K. V. S. R. and Balasubramanian T. K., Nearinfrared bands of S2: 3Πgi-3Σu+ system. J. Mol. Spectrosc. 1976. 59, 244-254. (46) Xing, W.; Shi, D. H.; Sun, J. F.; Liu, H. and Zhu, Z. L., Extensive ab initio study of the electronic states of S2 molecule including spin-orbit coupling. Mol. Phys. 2013. 111, 673-685.

17



Page 18 of 28

TABLE: Table 1. VTE, Oscillator strength (OS), main electronic configuration and transition of the 13 electronic states of HS2 State X2A’’

VTE (eV)

Oscillator strength

0

A2A’

1.02a/1.02b/ 0.89c/0.90d/ 0.92e

22A’’

3.65a/3.65b

22A’

4.12a/4.14b

14A’’

4.16a/4.20b

32A’

4.38a/4.38b

32A’’

Main configuration

Transitionf

(12a’)2(13a’)2(3a’’)2(4a’’)

3.551×10-5

(12a’)2(13a’)(3a’’)2(4a’’)2

13a’→4a’’(0.856)

0.0338

(12a’)2(13a’)2(3a’’)(4a’’)2

3a’’→4a’’(0.734)

3.307×10-4

(12a’)2(13a’)2(14a’)(3a’’)2

4a’’→14a’(0.765)

(12a’)2(13a’)(14a’)(3a’’)2(4a’’)

13a’→14a’(0.836)

7.559×10-4

(11a’)2(12a’)(13a’’)2(3a’’)2(4a’’)2

12a’→4a’’(0.822)

5.03a/5.05b

0.0011

(12a’)2(13a’)(14a’)(3a’’)2(4a’’)

13a’→14a’(0.601)

42A’’

5.05a/5.07b

0.0053

(12a’)2(13a’)(14a’)(3a’’)2(4a’’)

13a’→14a’(0.591)

42A’

5.18a/5.22b

7.185×10-5

(12a’)2(13a’)2(15a’)(3a’’)2

4a’’→15a’(0.754)

24A’’

5.36a/5.42b

(12a’)2(13a’)(15a’)(3a’’)2(4a’’)

13a’→15a’(0.776)

14A’

6.05a/6.09b

(13a’)2(14a’)(3a’’)(4a’’)

3a’’→14a’(0.854)

24A’

7.16a/7.21b

(13a’)2(15a’)(3a’’)(4a’’)

3a’’→15a’(0.844)

34A’

7.85a/7.90b

(11a’)2(12a’)(13a’)(14a’)(3a’’)2(4a’’)2

12a’,13a’→14a’,4a’’(0.839)

a

The value calculated by aug-cc-pV(T+d)Z; b The value calculated by aug-cc-pV(5+d)Z

c

The experimental value of T00 from reference[21]; d The experimental value of T00 from reference[20]; e The theoretical value of

T00 from reference[25]; f The

value in parentheses refers to the coefficient of the corresponding configuration.

18


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Table 2. Equilibrium geometries(H-SS bond length RH-S, HS-S bond length RS-S,, H-S-S bond angle∠H-S-S) and harmonic vibrational frequencies(high-frequency stretching mode ω1, bending ω2 and low-frequency stretching ω3) of the X2A'', A2A' and 22A' R

H-S

(Å)

R (Å) S-S

∠H-S-S(deg)

ω1(cm-1)

ω2(cm-1)

ω3(cm-1)

X2A''

This work

aug-cc-pv(t+d)z

1.350

1.985

101.52

2593.46

908.66

580.41

aug-cc-pv(q+d)z

1.348

1.974

101.86

2596.92

913.86

592.26

aug-cc-pv(5+d)z

1.348

1.970

101.93

2595.78

915.92

595.62

1.348

1.969

101.95

2596.06

917.27

596.95

calc

CBS

1.346a/1.348b

1.961a/1.980b

102.37a/101.40b

2488a/2607b

909a/913b

552a/592b

expt

1.352c

1.960c

101.74c

2688±10d

892±10d

596.28d

A2A'

This work

aug-cc-pv(t+d)z

1.342

2.103

93.11

2664.06

765.50

492.16

aug-cc-pv(q+d)z

1.342

2.090

93.39

2666.43

767.87

502.04

aug-cc-pv(5+d)z

1.342

2.087

93.42

2666.79

768.23

505.58

CBS

1.341

2.085

93.43

2666.89

768.29

507.56

calc

1.342e/1.342f

2.095e/2.075f

93.43e/93.25f

2640.73e/2674.1f

862.64e/770.5f

425.84e/513.0f

expt

--

--

--

2585±81g

741±41g

490±41g

22A''

This work

aug-cc-pv(t+d)z

1.349

2.277

100.80

2599.11

673.70

354.03

aug-cc-pv(q+d)z

1.349

1.973

101.76

2603.97

683.87

360.34

aug-cc-pv(5+d)z

1.349

1.970

101.84

2602.78

688.51

364.56

CBS

1.349

1.968

101.90

2603.01

692.40

373.08

aReference[30]. bReference[25]. cReference[17]. dReference[20]. eReference[29]. fReference[28]. gReference[22].

19



Page 20 of 28

Table 3. SOC matrix elements between 22A'' and 22A' or 14A'' state with the aid of the BP operator.

H-S

S-S

Matrix elements

Crossing point(Å)

Value (cm-1)

||z

1.65

23.28

||x

1.65

2.74

||y

1.65

11.02

||z

2.44

5.48

||x

2.44

67.90

||y

2.22

59.69

20


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Figure Captions: Figure 1.Potential energy curves of HS2 along the H-S-S bond angle at the icMRCI+Q/aug-ccpV(T+d)Z level, with the other two parameters fixed at their respective equilibrium values of the ground state. Figure 2.Potential energy curves of HS2 along the HS-S bond length at the icMRCI+Q/aug-ccpV(T+d)Z level, with the other two parameters fixed at their respective equilibrium values of the ground state. Figure 3.Potential energy curves of HS2 along the H-SS bond length at the icMRCI+Q/aug-ccpV(T+d)Z level, with the other two parameters fixed at their respective equilibrium values of the ground state. Figure 4. Dissociation limits and energies corresponding to 13 electronic states of HS2 at the icMRCI/aug-cc-pV(5+d)Z level. Figure 5. Potential energy curves of the 22A'' state of HS2 and the electronic states interacting with this state along the H-S and S-S bonds, respectively. Figure 6. Non-adiabatic coupling matrix element of 22A''−32A'' along the H-S (black solid line) and S-S bonds (red solid line), respectively.

21



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Figure 1

22


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Figure 2

23



Page 24 of 28

Figure 3

24


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Figure 4

25



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Figure 5

26


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Figure 6

27



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TOC Graphic

28


Interaction and Photodissociation of Electronic Excited States of HS2

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