Potential Energy Curves, Transition Dipole Moments, and Franck

Oct 10, 2017 - This work investigates the spectroscopic parameters, vibrational levels, and transition probabilities of 12 low-lying states, which are...
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Potential Energy Curves, Transition Dipole Moments, and Franck− Condon Factors of the 12 Low-Lying States of BrO− Anion Yuan Yin, Deheng Shi,* Jinfeng Sun, and Zunlue Zhu College of Physics and Material Science, Henan Normal University, Xinxiang 453007, China S Supporting Information *

ABSTRACT: This work investigates the spectroscopic parameters, vibrational levels, and transition probabilities of 12 low-lying states, which are generated from the first dissociation limit, Br(2Pu) + O−(2Pu), of the BrO− anion. The 12 states are X1Σ+, 21Σ+, 11Σ−, 11Π, 21Π, 11Δ, a3Π, 13Σ+, 23Σ+, 13Σ−, 23Π, and 13Δ. The potential energy curves are calculated with the complete active-space self-consistent field method, which is followed by the internally contracted multireference configuration interaction approach with Davidson modification. The dissociation energy D0 of X1Σ+ state is determined to be approximately 26876.44 cm−1, which agrees well with the experimental one of 26494.50 cm−1. Of these 12 states, the 21Σ+, 11Σ−, 21Π, 11Δ, 13Σ+, 23Σ+, 23Π, and 13Δ states are very weakly bound states, whose well depths are only several-hundred cm−1. The a3Π, 23Π, and 13Δ states are inverted and account for the spin−orbit coupling effect. No states are repulsive regardless of whether the spin−orbit coupling effect is included. The spectroscopic parameters and vibrational levels are determined. The transition dipole moments of 12-pair electronic states are calculated. Franck−Condon factors of a number of transitions of more than 20-pair electronic states are evaluated. The electronic transitions are discussed. The spin−orbit coupling effect on the spectroscopic parameters and vibrational properties is profound for all the states except for X1Σ+, a3Π, and 11Π. The spectroscopic parameters and transition probabilities obtained in this paper can provide some powerful guidelines for observing these states in a proper spectroscopy experiment, in particular the states that have very shallow potential wells.

1. INTRODUCTION The bromine oxide (BrO) radical as well as its cation (BrO+) and anion (BrO−) play important roles in stratospheric chemistry.1 They are formed in the stratosphere from the reaction of Br with O3, resulting in destruction of the ozone layer.2 An understanding of the consequences of Br−O reactions requires knowledge of spectroscopic parameters and vibrational properties of BrO radical and its ion. For this reason, a large number of experimental and theoretical studies3 have been performed to understand the properties of the BrO radical. However, very little spectroscopic work1,2,4−8 has been addressed for the BrO− anion until now. There was only one experimental spectroscopic study on the BrO− anion, which was performed by Gilles et al.1 in 1992 with photoelectron spectroscopy. Gilles et al.1 affirmed that the ground state was X1Σ+ and determined that its Re and ωe were approximately 0.1814 ± 0.00009 nm and 575 ± 25 cm−1, respectively. In addition, Gilles et al.1 also obtained the groundstate D0 of BrO radical as approximately 2.353 ± 0.0006 eV, which was used to evaluate the D0 (X1Σ+) of the BrO− anion. There were six theoretical studies2,4−7 that reported the spectroscopic properties of the BrO− anion. In 1993, Oberle and Eysel4 made the first ab initio calculations at the SCF level with an effective core potential basis set and determined a few ground-state spectroscopic properties. In 1997, Ma et al.5 reported the ground-state properties at the level of MP2(full)/ 6-31G(d) theory, which included the zero-point vibration © XXXX American Chemical Society

energy and some higher level corrections. In 1998, Francisco et al.6 employed the CCSD(T) approach together with several one-particle basis sets to determine the spectroscopic properties of BrO− anion. However, they also only evaluated the groundstate spectroscopic parameters. In 1998, Alcami ́ and Cooper7 carried out ab initio calculations on bromine oxide and dioxides and their corresponding anions. As for the work done by Francisco et al.,6 Alcami ́ and Cooper7 only determined Re and ωe of the ground state. In 2000, Xie et al.2 calculated the electron affinities of BrOn molecules using the density functional theory method. However, they still evaluated only the ground-state ωe of BrO− anion. In 2006, Peterson et al.8 studied the spectroscopic and thermochemical properties of several radicals and their anions by the CCSD(T), CCSDT, and CCSDTQ methods. In their calculations, core−valence correlation and scalar relativistic corrections were included. For the BrO− anion, they8 determined the ground-state De, Re, and ωe to be approximately 11653.84 cm−1, 0.18099 nm, and 599.2 cm−1, respectively. Summarizing the experimental1 and theoretical2,4−8 results noted here, we find that all these studies are focused on the X1Σ+ state and that few spectroscopic parameters and transition probabilities are accurately determined. Received: July 21, 2017 Revised: October 9, 2017 Published: October 10, 2017 A

DOI: 10.1021/acs.jpca.7b07207 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

second dissociation channels are approximately 15344.51 cm−1.9 The present calculations show that the PECs of 12 states (X1Σ+, 21Σ+, 11Σ−, 11Π, 21Π, 11Δ, a3Π, 13Σ+, 23Σ+, 13Σ−, 23Π, and 13Δ) converge at the same dissociation asymptote. In combination with these results, we confirm that the first dissociation limit must be Br(2Pu) + O−(2Pu). As discussed later in this paper, the experimental D0 of the X1Σ+ state is determined to be approximately 26494.50 cm−1 when the first dissociation channel is Br(2Pu) + O−(2Pu). To determine more reliable and accurate interactions (such as avoided crossings) between different PECs, we put altogether 20 states into the calculations. The additional eight states are 31Σ+, 33Σ+, 31Π, 33Π, 21Σ−, 23Σ−, 21Δ, and 23Δ, respectively. This paper deals with only the 12 states arising from the first dissociation asymptote. All the PECs are calculated with the complete active-space self-consistent field (CASSCF) method, which is followed by the internally contracted multireference configuration interaction (icMRCI) approach10,11 with Davidson modification (icMRCI + Q) for internuclear separations from approximately 0.14 to 1.0 nm. All the calculations are done with the MOLPRO 2010.1 program package12 in the C2v point group. Here, the CASSCF is employed as the reference wave function for the icMRCI calculations. The basis sets used here are aug-cc-pVQZ (AVQZ) and aug-cc-pV5Z (AV5Z).13−15 The point spacing interval employed here is 0.03 nm for each state. For the PECs to be accurately determined, the point spacing interval is 0.005 nm for internuclear separations from approximately 0.14 to 0.62 nm. The equilibrium positions of all the states involved here fall into this internuclear separation range. The molecular orbitals (MOs) used for the icMRCI calculations come from the CASSCF results. The state-averaged technique is used in the CASSCF calculations. Each state has the same weight factor of 0.05. The eight outermost MOs (4a1, 2b1, and 2b2) are put into the active space, corresponding to the 9-15σ, 4π, and 5π MOs in the BrO− anion. The 14 valence electrons are distributed into the eight valence MOs. Therefore, this active space is referred to as CAS (14, 8). The rest of the 30 inner electrons are put into the 15 lowest MOs (8a1, 3b1, 3b2, and 1a2) corresponding to the 1-8σ and 1-3π MOs in the BrO− anion. In summary, altogether 23 MOs (12a1, 5b1, 5b2, and 1a2) are used to calculate the present PECs. For the AV5Z basis set, the total number of external orbitals (86a1, 60b1, 60b2, and 38a2) is 244. The 18 electrons in the 3s23p63d10 orbitals of Br atom and the two electrons in the 1s2 orbitals of O atom are employed as core electrons for the core−valence correlation calculations, whereas they are frozen for the frozen-core calculations. Core−valence correlation correction is calculated with the cc-pCVQZ basis set.16,17 In detail, we first calculate the potential energies by the cc-pCVQZ basis set and by the frozen-core cc-pCVQZ basis set at the same internuclear separation, respectively, and then we determine the difference of the two energies. The difference is the contribution to the total energy by the core−valence correlation correction, which is denoted as CV in this paper for convenience of description. Scalar relativistic correction is computed using the cc-pVQZDK basis set18 by the third-order Douglas−Kroll−Hess (DKH3) Hamiltonian approximation. Its contribution to the total energy is denoted as DK. The SOC effect is determined by the state interaction approach with the Breit−Pauli operator19 at the level of icMRCI theory with the all-electron cc-pCVQZ basis set. The all-electron cc-pCVQZ basis set with and without

Recently, we calculated the potential energy curves (PECs) of 20 Λ-S states as well as their corresponding Ω states of the BrO− anion. Employing these PECs, we evaluated their spectroscopic parameters and transition probabilities. Summarizing these spectroscopic parameters and transition probabilities, we find that our results have the following features: (1) Previous work8 thought that the X1Σ+ state arose from the Br− + O dissociation channel when they calculated its D0. Using this dissociation asymptote, they8 determined the D0 of X1Σ+ state to be approximately 11716.79 cm−1. However, we affirm that the X1Σ+ state contributes to the Br(2Pu) + O−(2Pu) dissociation limit. With this dissociation asymptote, we obtain the D0 of X1Σ+ state as approximately 26876.44 cm−1. This result is in excellent agreement with the experimental one of 26494.50 cm−1, which is derived from the Br(2Pu) + O−(2Pu) dissociation channel. (2) The Br(2Pu) + O−(2Pu) dissociation limit generates the 12 Λ-S states. However, eight states are very weakly bound states with well depths within several hundred cm−1, and only three states are very strongly bound. To our surprise, all these weakly bound states except for 13Σ+ have more than 20 vibrational states. (3) The spin−orbit coupling (SOC) effect on the spectroscopic parameters and vibrational levels are profound. For example, the SOC splitting energies of some Λ-S states are several-hundred cm−1, which are very large. These features make us believe that it deserves to report the spectroscopic parameters, vibrational levels, and transition probabilities of these states in this paper. Undoubtedly, the X1Σ+ state is the most important among the 12 states arising from the first dissociation channel. Because most states are very weakly bound, the transitions generated from them might be very weak. To give a glance at these states and determine a proper spectroscopic approach for observing the X1Σ+ state and the other two strongly bound states, we study the electronic transitions between the 12 states in this paper, in particular the transitions arising from the X1Σ+ state. In the next section, we will briefly introduce the methodology used. In section 3, the PECs of 12 states of BrO− anion are reported. These states are generated from the first dissociation asymptote of the BrO− anion. The spectroscopic parameters and vibrational levels are predicted. The transition dipole moments (TDMs) are computed. Franck−Condon (FC) factors of a number of electronic transitions are determined. The transition probabilities are discussed. The SOC effect on the spectroscopic parameters and vibrational levels is evaluated. In section 4, some conclusions are drawn. The spectroscopic properties and transition probabilities obtained here can be considered very reliable and can provide some useful guidelines for detecting these states in a proper spectroscopy experiment.

2. THEORY AND METHOD The ground states of O atom and O− anion are 3Pg and 2Pu, and the ground states of Br atom and Br− anion are 2Pu and 1Sg, respectively. According to the molecular group theory, (1) if the first dissociation asymptote of BrO− anion is Br(2Pu) + O−(2Pu), 12 states are generated. These states are 11Σ+ (X1Σ+), 21Σ+, 11Σ−, 11Π, 21Π, 11Δ, 13Π (a3Π), 13Σ+, 23Σ+, 13Σ−, 23Π, and 13Δ. (2) If the first dissociation channel of the BrO− anion is Br−(1Sg) + O(3Pg), only the 13Σ− and 13Π states are produced. At this time, the second dissociation limit is Br(2Pu) + O−(2Pu), which yields the 12 states. The 12 states are 11Σ+, 13Σ+, 11Π, 23Π, 21Π, 33Π, 23Σ+, 21Σ+, 11Σ−, 23Σ−, 11Δ, and 13Δ. The experimental energy separation between the first and B

DOI: 10.1021/acs.jpca.7b07207 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A the Breit−Pauli operator is used to calculate the contribution to the potential energy by the SOC effect. The difference between the two energies is the SOC splitting energy and is denoted as SOC. The extrapolation of the potential energies to the complete basis set (CBS) limit is made with the AVQZ and AV5Z basis sets. The energy obtained by the extrapolation is denoted as Q5. The extrapolation scheme20 is written as ref ΔEXref = E∞ + Aref X −α

(1)

corr ΔEXcorr = E∞ + Acorr X −β

(2)

ΔEref X

ΔEcorr X

where and are the reference and correlation energies obtained by the aug-cc- pVXZ set, respectively, ΔEref ∞ corr and ΔE∞ are the reference and correlation energies extrapolated to the CBS limit, and the extrapolation parameters α and β are taken as 3.4 and 2.4 for the reference and correlation energies,20 respectively. With the PECs, the spectroscopic parameters, Te, Re, ωe, ωexe, ωeye, αe, Be, and De are evaluated. The meanings of these spectroscopic notations are explained in our earlier paper.21 All the PECs are fitted to an analytical form by cubic splines. The rovibrational constants are first determined from the analytic potential by solving the rovibrational Schrödinger equation, and then the spectroscopic parameters are evaluated by fitting the first ten vibrational levels when the total number of vibrational levels is not less than ten. The spectroscopic parameters are evaluated by fitting all the vibrational levels when the total number of vibrational levels is less than ten.

Figure 2. Curves of TDM versus internuclear separation for the 12pair Λ-S states: 1, 23Σ+-13Σ+; 2, a3Π-13Σ−; 3, a3Π-13Σ+; 4, 23Π-13Σ−; 5, 21Π-11Δ; 6, 23Π-13Σ+; 7, 21Π-11Σ−; 8, 11Π-11Σ−; 9, a3Π-13Δ; 10, 23Π13Δ; 11, 11Π-X1Σ+;12, 21Σ+-X1Σ+.

calculated with the MOLPRO 2010.1 program package12 in the C2v point group. To display more details of each TDM curve, we depict them only over a small internuclear separation range from approximately 0.12 to 0.50 nm. The point spacing intervals employed to calculate the TDMs are the same as those of the PEC determinations used. From the PECs shown in Figure 1, we can summarize the following features: (1) The 12 PECs converge to the same dissociation limit, which clearly proves that the first dissociation asymptote of the BrO− anion must be Br(2Pu) + O−(2Pu). (2) The 21Σ+, 11Σ−, 21Π, 11Δ, 13Σ+, 23Σ+, 23Π, and 13Δ states are very weakly bound states, whose potential wells cannot be clearly seen in this figure. (3) The 13Σ− state has one barrier, which is generated by the avoided crossing of this state with the 23Σ− state. (4) The PECs of 23Π, 21Π, 11Δ, 21Σ+, 11Σ−, 13Δ, and 23Σ+ states are very crowded in the figure because Te and Re of these states are very near. (5) Only three states, X1Σ +, a3Π, and 11Π, are very strongly bound states. To conveniently discuss the transition properties, we have collected the dominant valence electronic configurations of all the states around their respective internuclear equilibrium positions in Table S3. It should be noted that the valence configurations are obtained by the icMRCI/AV5Z calculations. Here, we only collect the valence configurations in Table S3 whose coefficients squared of configuration-state function (CSF) are larger than 0.04. From Table S3, we can confirm that almost all the states except for X1Σ+, 23Σ+, 13Σ−, and 13Δ have obvious multireference characters around their respective internuclear equilibrium positions. This is the reason why we employ the MRCI approach to calculate the PECs in this work. From Table S3, we can instantly see how the electronic transitions occur between two different states. 3.1. Spectroscopic Parameters and Transition Probabilities of the 12 Λ-S States. Employing the PECs determined by the icMRCI + Q/Q5 + CV + DK calculations, we evaluate the spectroscopic parameters of these states. The results are collected in Table 1. For reasons of comparison, we also collect available experimental1 and other theoretical2,4−8 spectroscopic parameters in Table 1. To conveniently discuss the spectroscopic parameters and transition probabilities, we divide the 12 Λ-S states into two categories. One is the six singlet states X1Σ+, 21Σ+, 11Σ−, 11Π, 21Π, and 11Δ. The other is the six triplet states a3Π, 13Σ+, 23Σ+, 13Σ−, 23Π, and 13Δ.

3. RESULTS AND DISCUSSION Using the approaches outlined above, we determine the PECs of 20 states by the icMRCI + Q/Q5 + CV + DK calculations. As noted above, we deal with only the 12 states originating from the first dissociation limit. The PECs of the 12 states are depicted in Figure 1. To display more details of each PEC, we

Figure 1. PECs of the 12 Λ-S states generated from the first dissociation limit: 1, X1Σ+; 2, a3Π; 3, 11Π; 4, 13Σ+; 5, 13Σ−; 6, 23Π; 7, 21Π; 8, 11Σ−; 9, 11Δ; 10, 21Σ+; 11, 13Δ; 12, 23Σ+.

demonstrate them only over a small internuclear separation range from approximately 0.12 to 0.68 nm. For more details, we collect some data of each PEC, which are presented in Tables S1 and S2. To better investigate the transition probabilities, we calculate the TDMs between two electronic states using the icMRCI/ AV5Z approach so that we can evaluate the electric dipole transitions. The curves of TDM versus internuclear separation are shown in Figure 2. Similar to the PECs, the TDMs are also C

DOI: 10.1021/acs.jpca.7b07207 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A Table 1. Spectroscopic Parameters of 12 States Obtained by the icMRCI + Q/Q5 + CV + DK Calculations XΣ exptl1 calcd2 calcd4 calcd5 calcd6 calcd7 calcd8 a3Π 11Π 13Σ+ 13Σ− 23Π 21Π 11Σ− 11Δ 13Δ 21Σ+ 23Σ+ 1 +

Te /cm−1

De /cm−1

Re /nm

ωe /cm−1

ωexe /cm−1

ωeye /cm−1

Be /cm−1

102αe /cm−1

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 10970.00 17042.64 24625.01 26129.26 26131.11 26155.59 26403.02 26406.21 26467.76 26474.10 26509.92

27172.81 11716.79a

0.18349 0.1814 ± 0.00004

2.932

0.123

0.37643

0.264

11653.84 16500.48 10410.19 756.55 1469.77 746.06 696.87 525.87 504.10 492.10 381.50 425.86

0.18821 0.1836b 0.1857c 0.1817d 0.18099 0.22271 0.22300 0.25298 0.25298 0.31030 0.31111 0.35468 0.34542 0.35429 0.35457 0.36412

594.24 575 ± 25 593 487

1.181 1.937 76.62 5.500 17.41 15.44 8.636 3.447 2.202 1.663 2.739

0.036 0.151 4.219 1.123 2.679 2.165 0.137 0.227 0.091 0.182 0.006

0.25555 0.25489 0.15057 0.19794 0.13081 0.13037 0.10469 0.10604 0.10049 0.10048 0.09639

0.113 0.169 12.40 0.227 0.803 0.795 0.250 0.494 0.506 0.574 0.584

591c 596d 599.2 376.82 339.03 275.42 306.21 111.01 106.28 79.74 53.69 49.92 45.20 45.27

De was taken from ref 8, which was calculated by the Br−(1Sg) + O(3Pg) dissociation limit. br0 was obtained by MP2/6-31G(d) calculations. cValue obtained by RCCSD(T)/ANO4 calculations. dValue obtained by CASPT2/TZ+(2df) calculations. a

literature4−8 and the theoretical ωe given in the earlier papers2,6−8 also compare well with the measurements1 within the experimental uncertainties. Only one group of De is available in previous work,8 but this result is significantly closer to the experimental one deduced here. As seen in Table S3, the X1Σ+ state has single reference character. This state has the deepest potential well among all of the states involved here and possesses the 92 vibrational states. As discussed later in this paper, the X1Σ+ state can be detected in a proper spectroscopy experiment by observing many electronic transitions such as 11Π-X1Σ+. The dominant valence electronic configurations of the 11Π state are 9σ210σ211σ24π4 5π312σ1 and 9σ210σ211σ24π35π412σ1 near the internuclear equilibrium position. Therefore, the leading electronic transitions between the 11Π and X1Σ+ states can be regarded as the 4π-5π and 5π-12σ promotions. The 11Π state has a well depth of approximately 10410.19 cm−1, which possesses the 62 vibrational states. As seen in Table 1, Re of the 11Π and X1Σ+ states are near each other, and both electronic states have many vibrational states, as given above. According to these results, we believe that the electric dipole transitions between the two states should be numerous. The following calculations have approved this suggestion. With the PECs and TDMs obtained in this paper, we calculate the FC factors of several singlet-singlet electric dipole transitions (such as 11Π-X1Σ+, 11Σ−-11Π, 11Σ−-21Π, 11Δ-21Π, and 21Π-21Σ+) by using the LEVEL program.22 For reasons of discussion, Table S4 collects some relatively large FC factors of these transitions. According to Table S4, we affirm that many electric dipole transitions exist between the 11Π and X1Σ+ states, and some of these transitions are very powerful. This suggests that we could observe the two states in a spectroscopy experiment by recording the 11Π-X1Σ+ electronic transitions. The dominant valence electronic configurations of 11Σ− state are 9σ210σ211σ2 4π45π212σ2 and 9σ210σ211σ24π25π412σ2 near the equilibrium position. Consequently, the leading electronic transitions between the 11Σ− and 11Π states can be regarded as the 4π-12σ and 5π-12σ promotions. The well depth of the 11Σ−

3.1.1. Spectroscopic Parameters and Transition Probabilities of the Six Singlet States. Now we calculate the groundstate dissociation energy D0 of the BrO− anion according to the dissociation limit Br(2Pu) + O−(2Pu). The equation used to determine the ground-state D0 is as follows1,8 D0(BrO−) = D0(BrO) − EA(O) + EA(BrO)

(3)

In eq 3, D0(BrO) is the dissociation energy of the BrO radical; EA(O) and EA(BrO) are the electron affinities of the BrO radical and O atom, respectively. The experimental D0(BrO), EA(O), and EA(BrO) are determined to be approximately 2.393, 2.353, and 1.4611 eV in the literature,1,9 respectively. Using these experimental data, we determine the ground-state D0 of the BrO− anion to be approximately 26494.50 cm−1. As collected in Table 1, the present De, ωe, ωexe, and ωeye of the ground state are approximately 27172.81, 594.24, 2.932, and 0.123 cm−1, respectively. Employing the equation De = D0 + ωe/2 − ωexe/4 + ωeye/8, we determine the theoretical D0 to be approximately 26876.44 cm−1. Obviously, this result compares well with the experimental one deduced here. We firmly confirm that the first dissociation asymptote of BrO− anion is Br(2Pu) + O−(2Pu). The reasons are as follows: (1) Br(2Pu) + O−(2Pu) can generate the 12 states, whose PECs converge together when the internuclear separation is large enough. As demonstrated in Figure 1, the convergence of the PECs of the 12 Λ-S states is completely consistent with this prediction. (2) If the first dissociation channel is Br−(1Sg) + O(3Pg), only the PECs of two states converge to this limit, and the PECs of 10 states converge to the Br−(1Sg) + O(3Pg) dissociation asymptote. Experimental results show that the energy separation between the two dissociation limits is approximately 15344.51 cm−1, as given above. The energy separation is so large that it can be clearly seen in Figure 1. However, Figure 1 does not approve this kind of expectation. Only one group of experimental spectroscopic parameters1 is currently available for the X1Σ+ state. The present Re and ωe agree well with these measurements1 within the experimental uncertainties. In addition, the theoretical Re reported in the D

DOI: 10.1021/acs.jpca.7b07207 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A state is approximately 525.87 cm−1. It has 23 vibrational states with vibrational levels of 37.69, 99.72, 143.25, 184.69, 219.42, 248.19, 272.17, 291.73, 307.33, 319.57, 331.69, 344.78, 356.62, 368.33, 379.81, 392.25, 405.74, 420.74, 436.75, 454.02, 472.25, 491.47, and 511.33 cm−1. Calculations confirm that a large number of electric dipole transitions exist between the 11Σ− and 11Π states, and some of them are very powerful. Table S4 collects some relatively large FC factors of these transitions. As a result, we can observe the 11Σ− state in a spectroscopy experiment by recording the 11Σ−-11Π transitions. Nevertheless, the 11Σ− state is a very weakly bound state, and the strong transitions correspond to the highly vibrational states of the 11Π state. Therefore, great efforts would be made when we detect this state. As discussed below, we can also observe the 11Σ− state by exploring the 11Σ−-21Π electric dipole transitions. In addition, calculations approve that the transitions between the 11Σ− and X1Σ+ states are very weak. The well depth of the 11Δ state is only 504.10 cm−1. It has 24 vibrational states with vibrational levels of 26.01, 73.55, 116.23, 154.51, 187.83, 216.53, 240.80, 261.03, 277.44, 290.46, 302.37, 315.36, 327.74, 339.57, 351.22, 363.27, 376.30, 390.67, 406.16, 422.81, 440.45, 458.95, 478.29, and 498.06 cm−1. According to the transition selection rule, the electric dipole transitions between the 11Δ and 11Π states as well as between 11Δ and 21Π states are allowed. However, the three states (11Δ, 11Π, and 21Π) are all weakly bound states. Detailed calculations affirm that only a few of the 11Δ-11Π and 11Δ-21Π transitions are very strong, although there are many of these electric dipole transitions. According to the calculated results, we believe that it is very difficult to observe the three states by detecting the spectroscopic transitions between them. Here, we only collect some relatively large FC factors of 11Δ-21Π transitions in Table S4. Only with the PECs obtained in this paper, we calculate the FC factors of several singlet-singlet symmetry-forbidden transitions (such as 11Δ-11Σ−, 11Δ-21Σ+, and 21Σ+-11Σ−). For convenience of discussion, Table S5 tabulates some relatively large FC factors of these transitions. Detailed calculations confirm that few of these transitions are strong, though there are many transitions between the 11Δ and 11Σ− states as well as between the 11Δ and 21Σ+ states, which means that it is very hard to detect the 11Δ state in a spectroscopy experiment by observing the 11Δ-11Σ− and 11Δ-21Σ+ transitions. The leading valence electronic configurations of the 21Σ+ state are the 9σ210σ211σ24π4 5π212σ2 and 9σ210σ211σ24π25π412σ2 near the internuclear equilibrium position. Therefore, the 21Σ+ state has multireference characters, which has a well depth of approximately 381.50 cm−1. The 21Σ+ state has the 20 vibrational states with vibrational levels of 2.16, 63.45, 99.77, 131.61, 158.79, 181.37, 199.57, 214.31, 226.02, 236.95, 248.17, 258.40, 268.75, 279.57, 291.61, 304.78, 319.28, 334.79, 351.27, and 368.45 cm−1. According to the transition selection rule, electric dipole transitions between the 21Σ+ and X1Σ+ states, the 21Σ+ and 11Π states, as well as the 21Σ+ and 21Π states are allowed. Similar to the 11Δ-21Π transitions, only a few transitions between these states are very strong. Here, we only collect some relatively large FC factors of 21Π-21Σ+ transitions in Table S4. In addition, we also determine the FC factors of 21Σ+-11Σ− and 11Δ-21Σ+ symmetry-forbidden transitions. As tabulated in Table S5, few transitions are powerful. Summarizing these results, we conclude that we would make great efforts when we

detect the 21Σ+ state by observing the transitions noted here in a spectroscopy experiment. As with the 21Σ+, 11Σ−, and 11Δ states, the 21Π state is also a very weakly bound state and has a number of vibrational levels. The 21Π state has 24 vibrational states with vibrational levels of 49.55, 132.00, 203.05, 264.12, 317.67, 363.96, 404.43, 438.39, 467.03, 490.69, 510.01, 528.00, 543.28, 554.55, 567.46, 578.72, 589.63, 600.68, 613.02, 626.15, 641.15, 656.70, 673.44, and 690.65 cm−1, though the well depth of this state is only 696.86 cm−1. According to the transition selection rule, the transitions from the 21Π state to the 11Π, 11Δ, 11Σ −, X1Σ+, and 21Σ + states are all allowed. Employing the LEVEL program,22 we calculate the FC factors of all the transitions from the 21Π state to these five states. Here, we only collect the relatively large FC factors of the 11Δ-21Π, 21Π-11Σ−, and 21Π-21Σ+ transitions in Table S4. From Table S4, we see that few transitions are strong. The reasons might be that the 21Π state is very weakly bound, as noted above. According to these FC factors, we affirm that the 21Π state is very hard to observe in a spectroscopy experiment by detecting the electric dipole transitions arising from the 21Π state. In conclusion, of these singlet states, (1) only the X1Σ+ and 1 1 Π states are strongly bound, which can be detected in a spectroscopy experiment by observing the 11Π-X1Σ+ and 11Σ−11Π electric dipole transitions; (2) the 11Σ− state is very weakly bound, but it may be explored by observing the 11Σ−-11Π transitions; (3) the 21Π, 11Δ, and 21Σ+ states are very weakly bound. Few transitions arising from them are strong. The three states are very difficult to be observed by spectroscopy approaches, though each state has more than 20 vibrational states. 3.1.2. Spectroscopic Parameters and Transition Probabilities of the Six Triplet States. The dominant valence electronic configurations of the a3Π state are 9σ210σ211σ24π4 5π312σ1 and 9σ210σ211σ24π35π412σ1 near the internuclear equilibrium position. Therefore, the leading electronic transitions between the a3Π and X1Σ+ states can be regarded as the 4π-12σ and 5π-12σ promotions. The a3Π state has a well depth of approximately 16500.48 cm−1, whose well is the deepest among all the triplet states involved in this paper. It has 64 vibrational states. A large number of electronic transitions exist between the a3Π and X1Σ+ states, though the a3Π-X1Σ+ transitions are spin-forbidden according to the transition section rule. Table S6 collects some relatively large FC factors of these transitions. From Table S6, we can see that some transitions (such as 0-9, 0-10, 0-11, 0-12, 1-7, 1-8, 1-13, and 114) are very powerful. Accordingly, we can detect the a3Π state by observing these strong transitions in a spectroscopy experiment. 13Σ+ is a weakly bound state whose well depth is only approximately 756.55 cm−1. It has 10 vibrational states with vibrational levels of 151.59, 443.12, 508.17, 530.39, 549.79, 566.13, 579.46, 591.71, 605.28, 618.37, 630.78, 642.86, 655.02, 668.27, 682.87, 698.60, 713.49, and 733.53 cm−1. Using the PECs, we calculate the FC factors of 13Σ+-X1Σ+ spin-forbidden transitions. To our surprise, almost all the FC factors of the transitions are near zero. That is, almost all of the 13Σ+-X1Σ+ transitions are very weak. In addition, using the PECs and TDMs, we also compute the FC factors of a3Π-13Σ+, 23Π-13Σ+, and 23Σ+-13Σ+ transitions. Some relatively large FC factors of these transitions are collected in Table S7. From Table S7, we confirm that only a few transitions are powerful (such as 0-0, 10, 2-0, and 3-0 for the 23Π-13Σ+ transitions as well as 5-0, 6-0, E

DOI: 10.1021/acs.jpca.7b07207 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A Table 2. Dissociation Relationships of 23 Ω States Yielded from the First Dissociation Limit of the BrO− Anion relative energy /cm−1 possible Ω state

dissociation asymptote Br(2P3/2) Br(2P3/2) Br(2P1/2) Br(2P1/2) a

+ + + +

O−(2P3/2) O−(2P1/2) O−(2P3/2) O−(2P1/2)

3, 2, 2, 1,

this work

2 (2), 1 (3), 0+ (2), 0− (2) 1 (2), 0+, 0− 1 (2), 0+ (2) 0+, 0−

0.0 218.47 3648.55 3795.16

a

exp.9,23 0.0 177.10 3685.00 3862.34

Obtained by the icMRCI + Q/Q5 + CV + DK + SOC calculations.

7-0, and 8-0 for the 23Σ+-13Σ+ transitions). In other words, great efforts would be made when we detect the 13Σ+ state by observing these spectroscopic transitions. The PEC of the 13Σ− state has one barrier. The barrier is at approximately 0.310 nm, which is generated by the avoided crossing of this state with the 23Σ− state. As shown in Figure 1, the potential energy at the top of the barrier is obviously higher than that at the dissociation asymptote. Accordingly, the well depth and dissociation energy of the 23Σ− state should be relative to the barrier and must be equal to each other. Similar to the X1Σ+, 13Δ, and 23Σ+ states, the 13Σ− state also has the single reference character. The dominant electronic transitions between the 13Σ− and a3Π states can be regarded as 11σ-4π and 11σ-5π promotions. The 13Σ− state has a well depth of approximately 1469.77 cm−1, which has the 14 vibrational states with vibrational levels of 77.45, 222.90, 351.50, 473.65, 588.54, 698.03, 802.07, 901.02, 995.16, 1084.49, 1169.33, 1250.26, 1327.21, and 1399.95 cm−1. The electric dipole transitions between the a3Π and 13Σ− states are many, though few are strong, as seen in Table S7. Further calculations show that the electronic transitions from the 13Σ− state to other triplet states (such as 23Π) are also very weak. Combining these results, we believe that it is very difficult to detect the 13Σ− state by observing these spectroscopic transitions. The dominant valence electronic configurations of the 23Π state are 9σ210σ211σ2 4π45π312σ1, 9σ210σ211σ24π35π412σ1, and 9σ210σ211σ14π45π312σ2 near the equilibrium position. Accordingly, the leading electronic transitions between the 23Π and X1Σ+ states can be regarded as the 4π-12σ, 5π-12σ, and 11σ11σ promotions, which are somewhat complicated. However, the FC factors of 23Π-X1Σ+ transitions are almost zero. That is, the electronic transitions between the two states are very weak. The 23Π state has a well depth of approximately 746.06 cm−1, which has 25 vibrational states with vibrational levels of 51.49, 136.39, 210.59, 275.00, 331.80, 381.34, 424.57, 461.48, 492.51, 517.76, 538.21, 556.31, 572.88, 584.16, 597.42, 609.23, 620.71, 632.08, 643.77, 656.90, 671.37, 686.73, 703.48, 720.85, and 738.91 cm−1. Using the PECs and TDMs, we calculate the FC factors of 23Π-13Δ, 23Π-13Σ−, and 23Π-13Σ+ electic dipole transitions. Some relatively large FC factors are collected in Table S7. As clearly seen in Table S7, only very few transitions are powerful (such as 0-1, 0-2, 0-3 for the 23Π-13Δ transitions, 5-0 for the 23Π-13Σ+ transitions, as well as 0-0, 1-0, 2-0, and 3-0 for the 23Π-13Σ+ transitions). According to the discussion made here, we think that great efforts would be made when we observe these spectroscopic transitions. As with the X1Σ+, 23Σ+, and 13Σ− states, the 13Δ state has single reference character. The well depth of 13Δ state is only approximately 492.10 cm−1, which is very shallow. However, it has 24 vibrational states with vibrational levels of 24.40, 69.61, 109.60, 144.63, 174.08, 199.69, 220.43, 237.35, 250.69, 262.30, 274.94, 287.79, 300.04, 312.11, 324.11, 337.12, 351.16, 366.60, 383.20, 400.91, 419.58, 439.39, 459.90, and 481.02 cm−1. The

dominant electronic transitions between the 13Δ and a3Π states should be regarded as the 4π-12σ and 5π-12σ promotions. A number of electronic transitions exist between the 13Δ and a3Π states. However, all these transitions are not strong, as collected in Table S7. As a result, great efforts would be made when we observe the 13Δ-a3Π transitions. In Table S7, several strong transitions can be found between the 23Π and 13Δ states, though the two states are very weakly bound. As collected in Table S6, few FC factors of 13Δ-11Δ and 13Δ-X1Σ+ spinforbidden transitions are large. Accordingly, we can also observe the 13Δ state by exploring these electronic transitions. Nevertheless, more or less difficulties would be encountered when we detect the 13Δ state because the strong transitions are very few. The well depth of 23Σ+ state is approximately 425.86 cm−1, which is the shallowest among the six triplet states. 23Σ+ has 23 vibrational states with vibrational levels of 21.95, 61.76, 96.15, 125.47, 150.22, 170.30, 185.88, 197.81, 209.05, 221.13, 233.60, 245.22, 256.76, 268.47, 280.99, 294.77, 309.73, 325.86, 343.07, 361.19, 380.41, 400.23, and 420.61 cm−1. Using the PECs, we calculate the FC factors of 23Σ+-11Σ− and 23Σ+-X1Σ+ spinforbidden electronic transitions. With the PECs and TDMs, we also determined the FC factors of 23Σ+-13Σ+ electric dipole transitions. Some relatively large FC factors are collected in Tables S6 and S7. As seen in Tables S6 and S7, only several FC factors are very large, though the electronic transitions between them are many. On the whole, we can detect the 23Σ+ state by observing the 23Σ+-11Σ− and 23Σ+-X1Σ+ spin-forbidden transitions or by exploring the 23Σ+-13Σ+ electric dipole transitions, though great efforts would be made. As a conclusion, (1) only the a3Π state is a very strongly bound triplet state. This state has a number of vibrational states and can be detected by observing the a3Π-X1Σ+ spin-forbidden transitions; (2) all the weakly bound triplet states (13Σ+, 23Σ+, 13Σ−, 23Π, and 13Δ) have at least 10 vibrational states. On the whole, the electronic transitions arising from the five states are weak, which means that great efforts would be made when we observe these triplet states; (3) the 13Σ− state has one barrier. The potential energy at the top of the barrier is higher than that at the dissociation asymptote; (4) the PECs of 23Π, 21Π, 11Δ, 21Σ+, 11Σ−, 13Δ, and 23Σ+ states are very crowded because their Te and Re are very near each other. 3.2. Spectroscopic Parameters and Vibrational Levels of the 23 Ω States. With the SOC effect included, the ground state Br(2Pu) splits into two components, Br(2P3/2) and Br(2P1/2), and the ground state O−(2Pu) also splits into two Ω states, O−(2P3/2) and O−(2P1/2). Therefore, the first dissociation asymptote of BrO− anion splits into the four dissociation channels, Br(2P3/2) + O−(2P3/2), Br(2P3/2) + O−(2P1/2), Br(2P1/2) + O−(2P3/2), and Br(2P1/2) + O−(2P1/2). These dissociation limits are collected in Table 2. For convenience of comparison, the experimental energy separaF

DOI: 10.1021/acs.jpca.7b07207 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A tions9,23 between each higher asymptote and the lowest one, Br(2P3/2) + O−(2P3/2), are also presented in Table 2. Using the icMRCI + Q/Q5 + CV + DK + SOC calculations, we determine the energy separations between each higher dissociation asymptote of Ω state and the lowest one, Br(2P3/2) + O−(2P3/2). The results calculated here are tabulated in Table 2. As seen in Table 2, the energy separations between the Br(2P3/2) + O−(2P1/2) and Br(2P3/2) + O−(2P3/2) limits, the Br(2P1/2) + O−(2P3/2) and Br(2P3/2) + O−(2P3/2) channels, as well as the Br(2P1/2) + O−(2P1/2) and Br(2P3/2) + O−(2P3/2) asymptotes are 218.47, 3648.55, and 3795.16 cm−1, respectively, which are in fair agreement with the corresponding measurements of 177.10, 3685.00, and 3862.34 cm−1,9,23 respectively. With the SOC effect accounted for, the 12 Λ-S states generate the 23 Ω states, and all of the Ω states are bound. In detail, the 10 Ω states (13Δ3, a3Π2, 13Δ2, a3Π1, 11Π1, 13Σ+1, a3Π0+, X1Σ+0+, a3Π0−, and 13Σ−0−) arise from the Br(2P3/2) + O−(2P3/2) dissociation asymptote. The five Ω states (11Δ2, 13Σ−1, 13Δ1, 13Σ+0+, and 11Σ−0−) are generated from the Br(2P3/2) + O−(2P1/2) dissociation limit. The five Ω states (23Π2, 23Σ+1, 21Π1, 23Σ+0+, and 21Σ+0+) are yielded from the Br(2P1/2) + O−(2P3/2) dissociation channel, and the three Ω states (23Π1, 23Π0+, and 23Π0−) contribute to the Br(2P1/2) + O−(2P1/2) dissociation asymptote. For convenience of comparison, these Ω states are also collected in Table 2. Of these 23 Ω states, there are four states with Ω = 0−, six states with Ω = 0+, eight states with Ω = 1, four states with Ω = 2, and one state with Ω = 3. The a3Π, 23Π, and 13Δ states are inverted with the SOC effect taken into account. For reasons of comparison, we depict the PECs of 22 Ω states in combination with their dissociation asymptotes in Figures 3−6. The PEC of the 13Δ3 state is

Figure 4. PECs of the six states with Ω = 0+: 1, X1Σ+0+; 2, a3Π0+; 3, 13Σ+0+; 4, 21Σ+0+; 5, 23Σ+0+; 6, 23Π0+.

Figure 5. PECs of the eight states with Ω = 1: 1, a3Π1; 2, 11Π1; 3, 13Σ−1; 4, 13Σ+1; 5, 13Δ1; 6, 23Σ+1; 7, 23Π1; 8, 21Π1.

3,

Figure 6. PECs of the four states with Ω = 2: 1, a3Π2; 2, 13Δ2; 3, 11Δ2; 4, 23Π2.

dismissed here because it is unworthy of being shown in a separate figure. Similar to Figure 1, to clearly show the details of these PECs, we demonstrate them only over a small internuclear separation range from approximately 0.13 to 0.68 nm. As shown in Table 2, the energy separation between the Br(2P3/2) + O−(2P1/2) and Br(2P3/2) + O−(2P3/2) dissociation asymptotes is obviously smaller than that between the Br(2P1/2) + O−(2P3/2) and Br(2P3/2) + O−(2P3/2) asymptotes. Thus, the two channels, Br(2P1/2) + O−(2P3/2) and Br(2P3/2) + O−(2P3/2), seem to converge together when the Br(2P1/2) + O−(2P3/2) or Br(2P1/2) + O−(2P1/2) asymptote appears, as seen in Figures

3−6. Similarly, the two channels, Br(2P1/2) + O−(2P3/2) and Br(2P1/2) + O−(2P1/2), also converge together when the Br(2P1/2) + O−(2P3/2) or Br(2P3/2) + O−(2P3/2) comes out. Using the PECs obtained by the icMRCI + Q/Q5 + CV + DK + SOC calculations, we evaluate Te, De, Re, and ωe of the 23 Ω states. The spectroscopic parameters are given in Table 3. For reasons of discussion, the dominant Λ-S state compositions of each Ω state around their respective equilibrium positions are also tabulated in Table 3. In Table 3, we omit these Λ-S state compositions, whose contribution to the total composition is smaller than 1.0%. For reasons of discussion, we divide the 23 Ω states into three categories according to their symmetries. The first group

−

Figure 3. PECs of the four states with Ω = 0 : 1, a Π0−; 2, 11Σ−0−; 4, 23Π0−. 3

13Σ−0−;

G

DOI: 10.1021/acs.jpca.7b07207 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

Table 3. Spectroscopic Parameters of the 23 Ω States Obtained by the icMRCI + Q/Q5 + CV + DK + SOC Calculations X Σ 0+ a3Π2 a3Π1 a3Π0+ a3Π0− 11Π1 13Σ−0− 13Σ−1 13Σ+0+ 13Σ+1 13Δ3 13Δ2 13Δ1 11Δ2 11Σ‑0− 21Σ+0+ 23Σ+0+ 23Σ+1 23Π2 23Π1 23Π0+ 23Π0− 21Π1 1 +

Te /cm−1

Re /nm

ωe /cm−1

De /cm−1

leading Λ-S state compositions near Re /%

0.0 10737.57 10844.01 10998.86 11028.71 16938.43 23960.35 24304.72 24993.10 25006.27 26385.34 26387.76 26407.53 26422.24 26448.01 26456.98 26497.00 26507.18 26506.10 26659.77 26737.58 26801.92 26651.12

0.18352 0.22258 0.22283 0.22214 0.22294 0.23323 0.26435 0.26471 0.26767 0.26788 0.33030 0.33010 0.32846 0.35079 0.35170 0.34903 0.31851 0.31498 0.31201 0.30938 0.31090 0.31287 0.30787

594.53 374.43 374.08 376.37 374.84 336.02 290.19 288.70 152.22 142.52 92.79 90.81 74.23 71.12 97.16 103.48 135.14 151.65 132.39 135.36 99.01 88.08 76.06

27187.38 16897.42 16743.37 16588.51 16558.67 10448.95 1455.02 4141.66 1226.77 751.71 1776.03 1773.61 1655.86 804.13 801.29 1583.39 551.89 1455.02 1437.28 3461.60 959.80 1065.45 1508.26

X1Σ+ (99.88) a3Π (99.16) a3Π (99.78) a3Π (99.69) a3Π (99.69) 11Π (99.30) 13Σ− (51.89), 21Σ+ (47.99) 13Σ− (62.69), 23Σ+ (36.31) 13Σ+ (83.57), 23Π (7.51), 21Π (6.16), 13Σ− (1.88) 13Σ+ (86.25), 23Π (13.68) 13Δ (52.90), 11Δ (47.91) 13Δ (53.86),11Δ (42.24), 23Π (2.27) 13Δ (54.23), 11Δ (41.87), 23Π (2.26) 11Δ (45.27), 13Δ (33.30), 23Π (21.42) 11Σ− (54.38), 23Σ+ (45.31) 21Σ+ (53.66), 23Σ+ (46.11) 23Σ+ (84.13), 13Σ− (10.86), 11Π (1.83) 23Σ+ (60.21), 11Σ− (38.37) 23Π (80.98), 21Σ+(12.17), X1Σ+ (2.97), 12Σ− (3.49) 23Π (73.00), 11Σ− (7.17), 13Σ+ (14.51), 23Σ+ (5.30) 23Π (50.68), 21Π (46.24), 23Σ+ (2.26) 23Π (84.20), 11Δ (14.10), 13Δ (1.71) 21Π (54.76), 23Π (37.05), 13Σ+ (7.37)

obvious can be explained as follows. Both the 21Σ+ and 11Σ− states are very weakly bound. A slight SOC effect can generate a significant change in PEC shape. Accordingly, the spectroscopic parameters and vibrational levels can be easily influenced. The same analyses are also suitable for the other weakly bound states involved in this paper. The 13Σ− state splits into the 13Σ−0− and 13Σ−1 states when the SOC effect is taken into account. As clearly seen in Table 3, the Λ-S state compositions of the 13Σ−0− state strongly mix with the 21Σ+ state, and those of the 13Σ−1 state strongly mix with the 23Σ+ state near their respective internuclear equilibrium positions. The SOC splitting energy of the 13Σ− state is approximately 344.37 cm−1, which is somewhat large. When we examine the ground state of the BrO radical, we instantly find that its experimental splitting energy is approximately 975.43 cm−1.24 The reasons why the splitting energies of BrO radical and BrO− anion are so large are that a strong SOC effect exists near their equilibrium positions. The SOC effect on the spectroscopic parameters and vibrational levels is profound for the 13Σ−0− and 13Σ−1 states, in particular, Te and De. Te of the two Ω states is significantly smaller than, and their wells are greatly deeper than, those of the 13Σ− state. These results can be clearly seen by comparison of Te and De collected in Tables 1 and 3. The 13Σ−0− and 13Σ−1 states have 45 and 31 vibrational states, respectively, which are obviously more than those of the 13Σ− state. It might be explained as follows. The SOC effect greatly deepens the potential wells of 13Σ−0− and 13Σ−1 states. Accordingly, the deepened potential wells increase the number of their vibrational states. The Λ-S state compositions of 13Σ+0+ and 13Σ+1 states mix with several other states around their respective equilibrium positions. Different from that of the 13Σ− state, the SOC splitting energy of 13Σ+ state is only approximately 13.17 cm−1, which is very small. However, the SOC effect on their spectroscopic parameters and vibrational states are obvious. The reasons might be 2-fold. One is that the 13Σ+ state is a

is the nine Ω states, which are generated from the six Σ states (X1Σ+, 21Σ+, 11Σ−, 13Σ−, 13Σ+, and 23Σ+); the second group is the 10 Ω states, which arise from the four Π states (a3Π, 23Π, 11Π, and 21Π), and the third group is the four Ω states, which are contributed to the two Δ states (11Δ and 13Δ). 3.2.1. Nine Ω States Generated from the X1Σ+, 13Σ−, 13Σ+, 23Σ+, 21Σ+, and 11Σ− States. The X1Σ+ state does not split with the SOC effect included. As collected in Table 3, the Λ-S state compositions of the X1Σ+0+ state are almost pure near the equilibrium position. Accordingly, the SOC effect on the spectroscopic parameters of the X1Σ+0+ state is small, which can be clearly seen by comparison of Te, Re, ωe, and De collected in Tables 1 and 3. In addition, the SOC effect on the vibrational states of the X1Σ+0+ state is also tiny. As with the X1Σ+ state, neither the 21Σ+ or 11Σ− state split accounting for the SOC effect. Different from the X1Σ+0+ state, the Λ-S state compositions of the 21Σ+0+ and 11Σ−0− states strongly mix with the 23Σ+ state near their respective internuclear equilibrium positions. Therefore, the SOC effect on their spectroscopic parameters is profound. In detail, the deviations of Te, Re, ωe, and De of the 21Σ+0+ state from those of the 21Σ+ state are 17.12 cm−1, 0.00554 nm, 78.02 cm−1, and 1201.89 cm−1, respectively, and the deviations of Te, Re, ωe, and De of the 11Σ−0− state from those of the 11Σ− state are 44.99 cm−1, 0.00298 nm, 17.42 cm−1, and 275.42 cm−1, respectively. The SOC effect greatly deepens the well of the 21Σ+ state. In addition, the SOC effect on the vibrational states of 21Σ+0+ and 11Σ−0− states is also very obvious. For example, the 11Σ−0− state has 14 vibrational states with vibrational levels of 48.19, 141.66, 230.03, 311.40, 385.29, 452.31, 513.03, 568.03, 617.72, 662.52, 702.69, 738.55, 770.30, and 797.09 cm−1; the 21Σ+0+ state possesses 18 vibrational states with vibrational levels of 51.34, 189.53, 310.04, 425.75, 536.64, 642.71, 743.94, 840.27, 931.72, 1018.23, 1099.80, 1176.44, 1248.13, 1314.93, 1376.88, 1434.10, 1486.85, and 1535.44 cm−1. The reasons why the SOC effect on the spectroscopic parameters and vibrational levels is so H

DOI: 10.1021/acs.jpca.7b07207 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

position. For this reason, the SOC effect on the spectroscopic parameters of the 21Π1 state should be obvious, though the 21Π state does not split when the SOC effect is included. The deviations of Te, Re, ωe, and De of the 21Π state from those of the 21Π state are 495.53 cm−1, 0.00324 nm, 30.22 cm−1, and 811.39 cm−1, respectively, which are very large. The 21Π1 state possesses 31 vibrational states with vibrational levels of 37.22, 109.02, 185.71, 262.59, 339.13, 415.30, 491.13, 566.03, 639.26, 710.32, 778.85, 844.86, 908.40, 969.63, 1028.51, 1084.75, 1138.05, 1188.01, 1234.18, 1276.19, 1313.68, 1346.69, 1375.80, 1400.38, 1419.80, 1435.98, 1449.34, 1460.92, 1473.14, 1487.24, and 1502.98 cm−1. These vibrational levels are greatly different from those of the 21Π state noted in section 3.1.1. In summary, (1) the a3Π and 23Π states are inverted with the SOC effect accounted for, and (2) the SOC effect on the spectroscopic parameters and vibrational properties is small for the a3Π and 11Π states but is very profound for the 21Π and 23Π states. 3.2.3. Four Ω States Generated from the 13Δ and 11Δ States. The Te of the 13Δ3 state is smaller than that of the 13Δ1 state. Therefore, the 13Δ state is inverted with the SOC effect taken into account. The Λ-S state compositions of each Ω state generated from the 13Δ state strongly mix with the 11Δ state near their internuclear equilibrium positions. Comparing Te, Re, ωe, and De of the 13Δ state collected in Table 1 with those of the corresponding Ω states collected in Table 3, we confirm that the SOC effect on the spectroscopic parameters of these Ω states is profound. The SOC splitting energies between 13Δ3 and 13Δ2 states as well as between the 13Δ2 and 13Δ1 states are only 2.42 and 19.77 cm−1, respectively. Because the SOC effects on Re and De of the 13Δ3, 13Δ2, and 13Δ1 states are very obvious, the vibrational levels of each Ω state should be significantly different from those of the 13Δ state. In detail, the number of vibrational states of each Ω state is 32, but it is only 24 for the 13Δ state. The 11Δ state does not split with the SOC effect included. The Λ-S state compositions of the 11Δ2 state strongly mix with the 13Δ and 23Π states near the equilibrium positions. For this reason, the SOC effect on Re, ωe, and De of the 11Δ2 state is profound. The deviations of Re, ωe, and De of the 11Δ2 state from those of the 11Δ state are 0.00537 nm, 17.43 cm−1, and 300.03 cm−1, respectively. These deviations are very large. The 11Δ state has a well depth of approximately 804.13 cm−1, which has 16 vibrational states with vibrational levels of 35.08, 102.79, 167.48, 228.70, 286.59, 341.78, 395.17, 446.96, 496.82, 544.20, 588.75, 630.27, 668.37, 702.56, 732.04, and 755.45 cm−1. These vibrational levels are significantly different from those of the 11Δ state given in section 3.1.1. In conclusion, (1) the 13Δ state is inverted with the SOC effect accounted for, and (2) the SOC effect on the spectroscopic parameters and vibrational properties is profound for the 13Δ and 11Δ states.

weakly bound state; the other is that the SOC effect in this state is strong. The 13Σ+0+ state has a well depth of 1226.77 cm−1, which has 10 vibrational states with vibrational levels of 70.68, 208.66, 342.36, 471.70, 596.73, 717.45, 833.85, 945.96, 1053.83, and 1157.46 cm−1; the 13Σ+1 state has a well depth of only 751.71 cm−1, which possesses six vibrational states with vibrational levels of 65.92, 210.04, 333.60, 468.88, 588.50, and 712.96 cm−1. These vibrational levels are very different from those of the 13Σ+ state given in section 3.1.2. The Λ-S state compositions of the 23Σ+0+ state strongly mix with the 13Σ− state, and those of the 23Σ+1 state strongly mix with the 11Σ− state near their equilibrium positions. That is, the SOC effect in the 23Σ+ state is powerful. At the same time, the 23Σ+ state is a very weakly bound state. Accordingly, the SOC effect on the spectroscopic parameters and vibrational states should be profound. This expectation is firmly approved by comparison of Te, Re, ωe, and De collected in Tables 1 and 3. The SOC splitting energy of the 23Σ+ state is only 10.18 cm−1, which is very small when compared with that of the 13Σ− state. The 23Σ+0+ state has only five vibrational states with vibrational levels of 69.79, 185.87, 298.96, 401.84, and 496.50 cm−1, and the 23Σ+1 state has 15 vibrational states with vibrational levels of 66.80, 195.56, 317.42, 432.88, 542.72, 647.63, 748.26, 845.11, 938.55, 1028.76, 1115.85, 1199.81, 1280.69, 1358.44, and 1433.02 cm−1. These vibrational levels greatly differ from those of the 23Σ+ state. In conclusion, (1) the SOC effect on the spectroscopic parameters and vibrational levels of the X1Σ+ state is small but is profound on those of the 13Σ−, 13Σ+, 23Σ+, 21Σ+, and 11Σ− states, and (2) the splitting energy of the 13Σ− state is approximately 344.37 cm−1, which is very large. 3.2.2. Ten Ω States Generated from the 11Π, 21Π, a3Π, and 23Π States. Te of the a3Π2 state is smaller than that of the a3Π0− state. Therefore, the a3Π state is inverted with the SOC effect taken into account. The Λ-S state compositions of each Ω state generated from the a3Π state are almost pure around their respective equilibrium positions. Accordingly, the SOC effect on the spectroscopic parameters and vibrational levels is small. The SOC splitting energies between the two neighboring Ω states from the a3Π2 to the a3Π0− state are 106.44, 154.85, and 29.85 cm−1, respectively, which are not large indeed. In addition, the Λ-S state compositions of the 11Π1 state is also pure around the equilibrium position. On the whole, the SOC effect on the spectroscopic parameters and vibrational levels is tiny for the 11Π1 state, which can be clearly seen by comparison of Te, Re, ωe, and De collected in Tables 1 and 3. In detail, the deviations of Te, Re, ωe, and De of the 11Π1 state from those of the 11Π state are only 103.75 cm−1, 0.00023 nm, 3.01 cm−1, and 38.76 cm−1, respectively. With the SOC effect accounted for, the 23Π state splits into the four Ω components: 23Π2, 23Π1, 23Π0+, and 23Π0−. Similar to the a3Π state, the Te of the 23Π2 state is smaller than that of the 23Π0− state. That is, the a3Π state is inverted with the SOC effect taken into account. The SOC splitting energies between the two neighboring Ω states from the 23Π2 to the 23Π0− state are 153.67, 77.81, and 64.34 cm−1, respectively. As can be clearly seen in Table 3, the Λ-S state compositions of each Ω state yielded from the 23Π state strongly mix with several other Λ-S states near their equilibrium positions. Accordingly, the SOC effect on their spectroscopic parameters and vibrational states are profound, in particular for Te, ωe, and De. The Λ-S state compositions of 21Π1 state strongly mix with the 23Π and 13Σ+ states around the internuclear equilibrium

4. CONCLUSIONS The PECs of 12 Λ-S states of the BrO− anion are computed with the CASSCF method, which is followed by the icMRCI + Q approach. Using the PECs obtained in this paper, we evaluate the spectroscopic parameters and vibrational states of all 12 states and the corresponding Ω states. D0 of the X1Σ+ state is obtained as approximately 26876.44 cm−1, which compares well with the measurements of 26494.50 cm−1. The TDMs of 12-pair Λ-S states are determined by the icMRCI/ AV5Z calculations. Using the PECs and TDMs, we calculate I

DOI: 10.1021/acs.jpca.7b07207 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A the FC factors of more than 20-pair Λ-S states. According to the results calculated here, we confirm that only the X1Σ+, a3Π, and 11Π states are strongly bound states, which are not difficult to observe in a spectroscopy experiment. Only the a3Π, 23Π, and 13Δ states are inverted with the SOC effect included. The 13Σ− state has one barrier, whereas this barrier disappears accounting for the SOC effect. The 21Σ+, 11Σ−, 21Π, 11Δ, 13Σ+, 23Σ +, 23Π, and 13Δ states are very weakly bound states, whose well depths are only several-hundred cm−1. Great efforts would be made when we detect these weakly bound states by observing the electronic transitions arising from these states because almost all of these transitions are very weak. The SOC effect on the spectroscopic parameters and vibrational levels is very profound for all of the states except X1Σ+, a3Π, and 11Π. The spectroscopic parameters, vibrational levels, and transition probabilities obtained in this paper could be considered very reliable and could provide some powerful guidelines for observing these states.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b07207. Selected ab initio potential energies, leading valence configurations, and some relatively large FC factors (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Tel/fax: 86-373-3328876. E-mail: [email protected]; [email protected]. ORCID

Deheng Shi: 0000-0002-8577-3867 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is sponsored by the National Natural Science Foundation of China under Grant No. 11274097 and the Program for Science and Technology of Henan Province in China under Grant No. 142300410201.

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REFERENCES

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DOI: 10.1021/acs.jpca.7b07207 J. Phys. Chem. A XXXX, XXX, XXX−XXX