Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 131 (2014) 42–54

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Accurate calculations of spectroscopic properties for the 13 K–S states and the 23 X states of BO radical including the spin–orbit coupling effect Zunlue Zhu, Wei Yu, Shuai Wang, Jinfeng Sun, Deheng Shi ⇑ College of Physics and Electronic Engineering, Henan Normal University, Xinxiang 453007, China

g r a p h i c a l a b s t r a c t

 PECs are extrapolated to the CBS

The spectroscopic properties of 23 X states generated from the 13 K–S states of BO radical are studied. Of the 13 K–S states, the F2P, 12U and 12D states possess the double well. The 14P, C2P, 12R and 22R states possesses one well with one barrier. The A2P, 14P and F2P are the inverted states with the SO coupling effect included. All the states possess the deep well except for the 12U. The PECs are calculated by the CASSCF method followed by the icMRCI approach with Davidson correction. Core–valence correlation and scalar relativistic corrections are taken into account. The PECs are extrapolated to the CBS limit. The SO coupling effect is accounted for. The spectroscopic parameters are evaluated. The Franck–Condon factors and radiative lifetimes of transitions from the B2R+, C2P, D2R+, 12R and 14P K–S states to the ground state are calculated for several low vibrational levels. The spectroscopic parameters reported here can be expected to be reliably predicted ones.

limit.  Effect of SO coupling on the spectroscopic parameters is evaluated.  Spectroscopic parameters of 13 K–S states and 23 X states are obtained.  Effect of core–valence correlation and scalar relativistic corrections is included.  Franck–Condon factors and radiative lifetimes of some transitions are calculated.

Potential energy /Hartree

h i g h l i g h t s

-99.6 7 -99.7

B(2Pu) + O(1Dg) 6

4

-99.8

5

B(2Pu) + O(3Pg)

3

2 -99.9 1 0.1

0.2

0.3

0.4

0.5

0.6

Internuclear separation /nm

PECs of seven states of the BO radical 1-A2Π; 2-14Σ-; 3-12Σ-; 4-C2Π; 5-22Σ-; 6-14Π; 7-F2Π

a r t i c l e

i n f o

Article history: Received 22 January 2014 Received in revised form 13 March 2014 Accepted 3 April 2014 Available online 18 April 2014 Keywords: Potential energy curve Spectroscopic parameter Franck–Condon factor Radiative lifetime Spin–orbit coupling effect

⇑ Corresponding author. Tel./fax: +86 373 3326375. E-mail address: [email protected] (D. Shi). http://dx.doi.org/10.1016/j.saa.2014.04.023 1386-1425/Ó 2014 Elsevier B.V. All rights reserved.

a b s t r a c t The spectroscopic properties of 23 X states generated from the 13 K–S states of BO radical are studied for the first time for internuclear separations from about 0.07 to 1.0 nm. Of the 13 K–S states, each of the F2P, 12U and 12D states is found to possess the double well. Each of the 14P, C2P, 12R and 22R states possesses one well with one barrier. The A2P, 14P and F2P are the inverted states with the spin–orbit coupling effect taken into account. All the states possess the deep well except for the 12U. The potential energy curves (PECs) are calculated by the complete active space self-consistent field method, which is followed by the internally contracted multireference configuration interaction approach with the Davidson correction. Core–valence correlation and scalar relativistic corrections are included into the calculations. The PECs are extrapolated to the complete basis set limit. The spin–orbit coupling effect is accounted for by the state interaction approach with the Breit–Pauli Hamiltonian. The spectroscopic parameters are evaluated, and compared with the available measurements and other theoretical results. The Franck–Condon factors and radiative lifetimes of the transitions from the B2R+, C2P, D2R+, 12R and

Z. Zhu et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 131 (2014) 42–54

43

14P K–S states to the ground state are calculated for several low vibrational levels, and some necessary discussion is made. Analyses show that the spectroscopic parameters reported in this paper can be expected to be reliably predicted ones. Ó 2014 Elsevier B.V. All rights reserved.

Introduction Boron monoxide is one of the fundamental oxides that appear as intermediates in the oxidation reactions. It plays an important role in the early development of molecular spectroscopy and quantum theory [1]. In addition, boron is present as an active component in several high temperature systems, in which the products of its oxidation are very easy to be formed. The accurate spectroscopic information of these products is of importance to understand the energy storage and disposal in highly exothermic combustion environments [2]. For this reason, the BO has attracted great attention of spectroscopists. Much experimental and theoretical work has been performed so as to obtain its various physical and chemical properties. The first measurements of BO emission spectrum are due to Jevons [3] in 1914, who identified the two systems, A2P–X2R+ and B2R+–X2R+. Later on, Mulliken [4] in 1925 made an extensive study of the two systems and identified over 300 band heads. In 1932, Jenkins and McKellar [5] measured the rotational structure of A2P–X2R+ transitions, and determined the rotational constants of A2P and X2R+ states besides the ground-state spin–orbit (SO) coupling constant. In 1958, Lagerqvist et al. [6] analyzed the B2R+– X2R+ transitions. In 1960, Mal0 tsev et al. [7] and Kuzyakov et al. [8] showed that the SO coupling constant of the C2P state was about 46.5 cm1. In 1965 and 1968, respectively, de Galan [9] and Coppens et al. [10] evaluated the ground-state dissociation energy of the radical. In 1970, Dunn and Hanson [11] reported an analysis of the 0–2 band of A2P–X2R+ transition. A number of spectroscopic parameters and molecular constants were evaluated from these measurements [3–11]. In 1979, Huber and Herzberg [12] summarized the accurate spectroscopic parameters and molecular constants of the involved states (X2R+, A2P, B2R+ and C2P) as of that time. Since 1979, there have still been a number of experiments [1,2,13–20], in which some relevant spectroscopic properties were extracted for several states. In detail, in 1980, Clyne and Heaven [13] made the first observation of quantum-resolved laser-induced fluorescence of BO radical, and evaluated the lifetimes of several vibrational states of A2P state. In 1984, Coxon et al. [14] photographed the 17 bands of A2P–X2R+ system at high resolution, and rotationally analyzed. In 1985, Mélen et al. [15] reported the A2P–X2R+ and B2R+–X2R+ transitions, and made the detailed analyses. And Chase et al. [16] thought that the accurate dissociation energy of the X2R+ state should be 8.34 ± 0.15 eV. In 1986, Tanimoto et al. [1] reported the microwave spectrum of BO (X2R+) radical. In 1997, Wenthold et al. [17] evaluated the xe of BO (X2R+) radical. In 2001, Mélen et al. [18] reported the emission spectrum of C2P–X2R+ transition under high resolution, and Gole et al. [2] studied the chemiluminescence between the A2P and X2R+ states resulting from the reaction of boron atoms with nitrogen dioxide and ozone. In 2003, Bredohl et al. [19] reported absorption spectrum of BO radical, and observed a new electronic transition. In 2004, Stancu et al. [20] measured the absorption spectra of the fundamental bands of the ground-state 10B16O and 11B16O radicals by diode laser spectroscopy. Summarizing the measurements [1– 11,13–20], we find the following. (1) These spectroscopic parameters mainly concentrate on the X2R+, A2P, B2R+, C2P, D2R+ and F2P states up to now, in particular for the X2R+, A2P, B2R+ and C2P.

Few spectroscopic knowledge is known for some states such as the D2R+ and F2P. And (2) the SO coupling information is available only for the A2P and C2P states to this day. Early spectroscopic calculations of the BO radical were made by Botschwina [21] in 1978 using the configuration interaction based on pseudonatural orbitals (PNO-CI) and the coupled electron pair approximation (CEPA) methods together with the Gaussian type orbitals’ (GTO’s) basis set. In 1981, Nemukhin et al. [22] computed the potential energy curves (PECs) of 6 states by the complete active space self-consistent field (CASSCF) method with a GTOs’ basis set, and Almlöf et al. [23] calculated the PECs of 4 states by the CASSCF approach with a GTOs’ basis set. In 1987, Karna and Grein [24] determined the PECs of 16 states by the multireference single and double excitation configuration interaction (MRD-CI) method with the Huzinaga–Dunning contracted Gaussian functions. With these PECs [20–24], the spectroscopic properties were evaluated for a number of electronic states. In addition, the ground-state Re, xe and De were also evaluated by Martin et al. [25] in 1992 at the MP2/6-31G level of theory, by Barone [26] in 1994 at the B3LYP/TZ2P + level of theory, by Papakondylis and Mavridis [27] in 2001 at the CCSD(T)/CBS level of theory, and by Stampfub and Wenzel [28] in 2003 at the level of CAS MR-ACPF/ aug-cc-pVTZ level of theory. And the ground-state Re and xe were obtained by Drummond et al. [29] in 2007 with the density functional theory. Recently, in 2009, Nguyen et al. [30] evaluated the Re, xe, xexe and De of X2R+ and A2P states, and Tai and Nguyen [31] obtained few ground-state spectroscopic parameters. Very recently, in 2010, our group [32] calculated the PECs of four states of the BO, and also evaluated several spectroscopic parameters. Summarizing these theoretical spectroscopic results [21–32], we find that, firstly, most spectroscopic calculations are focused on the few states (X2R+, A2P, B2R+ and C2P), and few results achieve high quality; secondly, no effect of SO coupling on the PECs has been included, though the SO coupling effect can bring about the important influence on the accurate prediction of spectroscopic properties; and thirdly, very few transition properties such as Franck–Condon factors and radiative lifetimes of the transitions are calculated, though the transition properties are very useful in observing the corresponding states. Therefore, to improve the quality of spectroscopic parameters of the radical, more accurate calculations should be done. The aim of this work is to extend the spectroscopic knowledge of BO radical. Firstly, extensive ab initio calculations of the PECs will be made, in which both the core–valence correlation and scalar relativistic corrections are included so that the spectroscopic properties will be evaluated as accurately as possible; secondly, the effect of SO coupling on the PECs will be introduced into the calculations since no PECs have been calculated for any X states up to now; and thirdly, the Franck–Condon factors and radiative lifetimes of the transitions from several excited K–S states to the X2R+ state are calculated for several low vibrational levels since these transition properties are very useful in observing the BO radical in experiment. In the next section, we will briefly describe the theory and method used in this paper. In Section ‘Results and discussion’, the PECs of 13 states [12R+ (X2R+), 14R+, 12R, 22R, 14R, 12P (A2P), 22P (C2P), 22R+ (B2R+), 32R+ (D2R+), 14P, 12D, 32P (F2P) and 12U] are calculated. The PECs of 23 X states generated from

44

Z. Zhu et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 131 (2014) 42–54

Table 1 Dissociation relationships of a few electronic states of the BO radical determined by the icMRCI + Q/56 + CV + DK calculations. Dissociation channel

K–S state

Relative energy (cm1) This work

Exp. [37]

B(2Pu) + O(3Pg) B(2Pu) + O(1Dg)

12R+, 14R+, 12R, 22R, 14R, 24R, 12P, 22P, 14P, 24P, 12D, 14D 22R+, 32R+, 32R, 32P, 42P, 52P, 22D, 32D, 12U

0.0 15551.80

0.0 15485.84

the 13 K–S states are investigated over the same internuclear separation. The PECs are calculated using the CASSCF method, which is followed by the internally contracted multireference CI (icMRCI) approach [33,34] with Davidson correction (icMRCI + Q) [35,36]. The SO coupling effect is accounted for by the state interaction method with the Breit–Pauli Hamiltonian. The Franck–Condon factors and radiative lifetimes of several transitions are calculated. The spectroscopic parameters are evaluated, compared with those available in the literature. Concluding remarks are given in Section ‘Conclusions’. Theory and method To determine the relationships of different K–S states involved in this paper, we collect all the states resulting from the first two dissociation channels of the BO radical in Table 1. As seen in Table 1, altogether, the 21 states are attributed to the first two dissociation channels. For the sake of length limitation, here we only study the first three 2R+, the first two 2R, the first three 2P, the first 2D, the first 2U, the first 4R+, the first 4R and the first 4P states. For convenience of discussion, we also collect the experimental energy separation between the two dissociation channels [37] in Table 1. All the PECs are calculated by the CASSCF method, which is followed by the icMRCI approach. Here, the CASSCF is used as the reference wave function for the icMRCI calculations. The basis set used here is the aug-cc-pV6Z (AV6Z) [38]. All the PECs are calculated with the MOLPRO 2010.1 program package [39] for internuclear separations from 0.07 to 1.0 nm. To determine accurately the PECs, the point spacing interval used here is 0.02 nm for each state, except around the equilibrium separation where the point spacing is 0.002 nm. Here, the smaller step is adopted near the equilibrium position of each state so that the properties of each PEC can be displayed more clearly. We substitute the C1v symmetry with the C2v point group to perform the present calculations by orienting the BO radical along the Z axis. The orbitals are optimized by the CASSCF method. The state-averaged technique is employed in the CASSCF calculations. Eight outermost molecular orbitals (MOs), 4a1, 2b1 and 2b2, are put into the active space for the present CASSCF and the subsequent icMRCI calculations. The 3 valence electrons in the 2s2p orbitals of B atom and the 6 valence electrons in the 2s2p orbitals of O atom are placed into the active space, which consists of full valence space. That is, the 9 valence electrons in the radical are distributed into the eight valence MOs. The energy ordering of these valence MOs is 3r1p4r5r2p6r. As a result, this active space is referred to as CAS (9, 8). The inner 4 electrons in the BO radical are put into the 2 closed-shell MOs (2a1), which correspond to the 1r and 2r MOs in the radical. In the calculations, the total number of external orbitals is 368, including 126a1, 90b1, 90b2 and 62a2 symmetry MOs. The 2 electrons in the 1s closed shell of B atom and the 2 electrons in the 1s closed shell of O atom are used as ‘core electrons’ for the core–valence correlation calculations. That is, when we make the core–valence correlation calculations [40], all the electrons in the B and O atoms are correlated. And when we make the frozen-core calculations, the 4 electrons in the 1s orbital of B and O atoms are frozen. In summary, the 10

MOs (6a1, 2b1 and 2b2) are used for the PEC calculations of all the states, including the calculations of core–valence correlation and scalar relativistic corrections. At this time, we find that all the PECs are convergent. The convergence of each PEC clarifies that the dissociation energy can be obtained by the difference between the total energy of the radical at the equilibrium position (which is determined by fitting) and the energy sum of the two atomic fragments at 1.0 nm. It should be pointed out that the core–valence correlation correction is calculated at the icMRCI level of theory with a cc-pCV5Z basis set [40] across the entire PEC of each state. Here, the contribution of core–valence correlation correction is denoted as CV. Scalar relativistic correction is included by the third-order Douglas–Kroll Hamiltonian (DKH3) approximation at the level of a cc-pV5Z basis set [41] by both taking and not taking into account the scalar relativistic effect. In detail, the cc-pV5Z-DK basis set with the DKH3 approximation and the cc-pV5Z basis set with no DKH3 approximation are used to calculate the scalar relativistic correction contributions. The difference between the two energies produces the scalar relativistic correction result, and is denoted as DK. Similar to the core–valence correlation correction, the present scalar relativistic correction is also calculated at the level of icMRCI theory across the entire PEC of each state. The SO coupling effect is included into the PEC calculations by the state interaction method with the Breit–Pauli Hamiltonian [42,43]. Berning et al. [43] thought that the Breit–Pauli operator could be very well approximated by an effective one-electron Fock operator. Using the effective one-electron Fock operator, Berning et al. have incorporated the most important two-electron contributions of SO operator and presented an efficient approach to calculate the Breit–Pauli SO matrix elements for the icMRCI wavefunctions, which has been implemented in MOLPRO 2010.1 program package [39]. Two successive correlation-consistent basis sets, aug-cc-pV5Z (AV5Z) and AV6Z, are used for the extrapolation scheme (denoted as 56). The extrapolation formula is written as [44]

DEtotal;1 ¼

DEtotal;nþ1 ðn þ 1Þ3  DEtotal;n n3 ðn þ 1Þ3  n3

:

ð1Þ

Here, DEtotal,1 is the total energy extrapolated to the CBS limit, and DEtotal,n and DEtotal,n+1 are the total energies obtained by the basis sets, aug-cc-pVnZ (AVnZ) and aug-cc-pV(n + 1)Z [AV(n + 1)Z]. By the way, we have used Eq. (1) to make the total-energy extrapolation for a number of states of many diatomic molecules such as GeS, SiN, C+2 and CS [45–48]. Fair agreement with the measurements is found. Thus, we also use Eq. (1) for the total-energy extrapolation of BO radical in this paper. From the PECs obtained here, the spectroscopic parameters, including the excitation energy term Te referred to the ground state, harmonic frequency xe, equilibrium separation Re, vibration coupling constant ae, first anharmonic constant xexe, rotational constant Be and dissociation energy D0 and De, are evaluated. In order to determine accurately the spectroscopic parameters, all the PECs are fitted to an analytical form by cubic splines so that the corresponding rovibrational Schrödinger equation is conveniently solved. In this paper, we solve the rovibrational Schrödinger equation with Numerov’s method [49]. That is, the rovibrational

45

Z. Zhu et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 131 (2014) 42–54 Table 2 Convergence observations of spectroscopic parameters with respect to the basis set and level of theory for the 14R+ and 14P states of the BO radical. icMRCI

icMRCI + Q )

Re (nm)

xe (cm )

De (eV)

Te (cm1)

Re (nm)

xe (cm1)

De (eV)

1 R AVTZ AVQZ AV5Z AV6Z 56

44897.71 45696.59 45861.90 45999.47 46119.96

0.14062 0.14000 0.13986 0.13981 0.13975

1223.43 1230.61 1232.88 1234.24 1235.43

2.6162 2.6895 2.7073 2.7142 2.7236

44673.18 45509.82 45684.34 45825.64 45950.53

0.14093 0.14029 0.14014 0.14010 0.14003

1212.32 1219.32 1221.91 1223.80 1224.02

2.6138 2.6919 2.7108 2.7182 2.7284

14P AVTZ AVQZ AV5Z AV6Z 56

69103.34 69742.01 69915.18 69996.95 70085.93

0.13713 0.13642 0.13627 0.13623 0.13617

1196.86 1206.09 1208.03 1209.47 1210.61

1.8173 1.8798 1.8952 1.9001 1.9068

68978.58 69654.66 69836.83 69922.33 70015.48

0.13744 0.13671 0.13655 0.13651 0.13645

1185.13 1194.95 1197.20 1198.70 1199.89

1.7587 1.8237 1.8398 1.8450 1.8522

Te (cm 4

1

1

+

constants are first determined in a direct forward manner from the analytic potential by solving the rovibrational Schrödinger equation, and then the spectroscopic parameters are evaluated by fitting the first ten vibrational levels whenever available.

Results and discussion Any high-quality ab initio calculations must be convergent with respect to the basis set and level of theory. Otherwise, the spectroscopic results determined by the calculations must be little significant because of their poor reliability and low accuracy. For this reason, here we first discuss the convergence behavior of the present calculations with respect to the basis set and level of theory. We collect the spectroscopic parameters (Te, Re, xe and De) of 14R+ and 14P states in Table 2, which are obtained by the icMRCI and icMRCI + Q calculations. It should be pointed out that the two states, 14R+ and 14P, used for the present discussion are selected optionally. From Table 2, we can see that Te of 14R+ and 14P states converge toward the CBS limit when we systematically increase the quality of correlation-consistent basis sets. For the 14R+ state, the basis sets from the AVTZ to the AVQZ, from the AVQZ to the AV5Z and from the AV5Z to the AV6Z raise Te by 798.88, 165.31 and 137.57 cm1 at the icMRCI, and raise Te by 836.64, 174.52 and 141.30 cm1 at the icMRCI + Q level of theory, respectively. For the 14P state, the basis sets from the AVTZ to the AVQZ, from the AVQZ to the AV5Z and from the AV5Z to the AV6Z raise Te by 638.67, 173.17 and 81.77 cm1 for the icMRCI, and raise Te by 676.08, 182.17 and 85.50 cm1 for the icMRCI + Q calculations, respectively. It suggests that Te of the 14R+ and 14P states may converge at about 140 and 86 cm1 with respect to the basis set. It has been proved by the extrapolation to the CBS limit. From Table 2, we can clearly see that Te of the 14R+ and 14P states are raised within 125 and 94 cm1, respectively, whether for the icMRCI or the icMRCI + Q calculations, when we extrapolate the AVnZ to the aug-cc-pV1Z (AV1Z) basis set. As a conclusion, we think that Te of the two states is convergent with respect to the basis set at the present level of theory. Similar to the Te, convergent behavior is still observed for Re and xe of the two states. As seen in Table 3, with the quality of basis sets increased from the AVTZ to the AVQZ, from the AVQZ to the AV5Z and from the AV5Z to the AV6Z, Re of the 14R+ state are shortened by 0.00062, 0.00014 and 0.00005 nm at the icMRCI, and by 0.00064, 0.00015 and 0.00004 nm at the icMRCI + Q level of theory; and Re of the 14P state are shortened by 0.00071, 0.00015 and 0.00004 nm for the icMRCI, and by 0.00073, 0.00016 and 0.00004 nm for the icMRCI + Q calculations, respectively. As per the discussion made here, we think that the present Re should be

converged quickly with respect to the basis set for the two states. As shown in Table 2, when we extrapolate the AVnZ to the AV1Z basis set, Re of the two states are shortened within 0.00007 nm. That is, the present Re is convergent with respect to the basis set at the present level of theory. Having studied the xe of the two states, we have found that their convergence also exists with respect to the basis set. For the 14R+ state, as seen in Table 2, the differences of Te between the icMRCI and the icMRCI + Q methods are 224.53, 186.77, 177.56, 173.83 and 169.43 cm1 at the AVTZ, AVQZ, AV5Z and AV6Z basis sets and the CBS limit, respectively. The results tell us that the triplet and quadruple excitations in the present calculations lower Te of the 14R+ state by less than 224.4 cm1. It reminds us that the contribution to the Te of 14R+ state by the corrections higher than quadruple excitations can be estimated by less than 112.2 cm1. Similar analysis tells us that the contribution to the Te of 14P state by the corrections higher than quadruple excitations is estimated by less than 62.4 cm1. Summarizing the discussion made here, we think that the present approach has excellent convergent behavior for the two states, 14R+ and 14P. In addition to the above two states, we have studied the convergent behavior with respect to the basis set and level of theory for other 11 K–S states of BO radical. Similar conclusion can be gained. In conclusion, we think that the present calculations are convergent with respect to the basis set and present level of theory. Consequently, we use the PECs obtained by the icMRCI + Q method and the extrapolation to the CBS limit for the present spectroscopic calculations. Using the approach described in Section ‘Theory and method’, we have calculated the PECs of 13 K–S states of BO radical for internuclear separations from about 0.07 to 1.0 nm. At the same time, we have included the core–valence correlation and scalar relativistic corrections and extrapolation scheme into the present PEC calculations. To show clearly the relationships of all these PECs, we depict them in Figs. 1 and 2, respectively. To make Figs. 1 and 2 more informative, we demonstrate these PECs only over a small internuclear separation range from about 0.07 to 0.63 nm. The valence configurations of 13 states as obtained from the icMRCI wavefunctions near the equilibrium positions are collected in Table 3. Here we briefly summarize some features demonstrated in Figs. 1 and 2. According to Figs. 1 and 2, we can clearly find out the following. Firstly, almost all the states possess the deep well except for the 12U. Secondly, the three states (F2P, 12U and 12D) possess the double well, and the four states (14P, C2P, 12R and 22R) have one well with one barrier. And finally, the avoided crossing is obviously observed between the C2P and the F2P state. We briefly study the multiconfiguration characterizations of these states. According to Table 3, we clearly see that the A2P,

46

Z. Zhu et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 131 (2014) 42–54 Table 3 Valence configurations of 13 states of the BO radical around the equilibrium positions. State

Valence configuration around the equilibrium position 3rab1pabab4rab5ra2p06r0 (0.6694)a 3rab1pab4rab5ra2pab6r0 (0.0116) 3rab1pbab4ra5rab2pa6r0 (0.0066) 3rab1pbab4rab5ra2pa6r0 (0.0047)

3rab1pabab4ra5rab2p06r0 (0.2003) 3rab1pabb4ra5rab2pa6r0 (0.0066) 3rab1pabb4rab5ra2pa6r0 (0.0047)

A2P

3rab1paab4rab5rab2p06r0 (0.8719) 3rab1pabab4rab5r02pa6r0 (0.0053) 3rab1pabab4ra5rb2pa6r0 (0.0042)

3rab1pabab4ra5ra2pb6r0 (0.0093) 3rab1pabab4r05rab2pa6r0 (0.0049)

B2R+

3rab1pabab4ra5rab2p06r0 (0.6714) 3rab1pbab4rab5ra2pa6r0 (0.0622) 3rab1paab4rab5ra2pb6r0 (0.0043) 3rab1paba4ra5rab2pb6r0 (0.0037)

3rab1pabab4rab5ra2p06r0 (0.1387) 3rab1paba4rab5ra2pb6r0 (0.0043) 3rab1paab4ra5rab2pb6r0 (0.0037)

C2P

3rab1pabab4rab5r02pa6r0 (0.7881) 3rab1pabab4r05rab2pa6r0 (0.0321) 3rab1paab4rab5rab2p06r0 (0.0089)

3rab1pabab4ra5ra2pb6r0 (0.0464) 3rab1pabab4r05rab2pb6r0 (0.0100) 3rab1pabab4ra5rb2pa6r0 (0.0076)

D2R+

3rab1pabb4rab5ra2pa6r0 (0.3198) 3rab1pabab4ra5rab2p06r0 (0.0850) 3rab1paba4rab5ra2pb6r0 (0.0618)

3rab1pbab4rab5ra2pa6r0 (0.3198) 3rab1paab4rab5ra2pb6r0 (0.0618) 3rab1pabab4rab5ra2p06r0 (0.0259)

3rab1pabb4rab5ra2pa6r0 (0.3707) 3rab1paab4rab5ra2pb6r0 (0.0830) 3rab1pab4rab5ra2pab6r0 (0.0080) 3rab1pabb4rab5ra2pa6r0 (0.3439) 3rb1paab4rab5ra2pb6r0 (0.0932) 3rab1pab4rab5ra2pab6r0 (0.0258)

3rab1pbab4rab5ra2pa6r0 (0.3707) 3rab1paba4rab5ra2pb6r0 (0.0830)

2

X R

+

12D 1st well

2nd well

F2P 1st well

2nd well

12U 1st well

2nd well 14R+ 14R 12R 14P 22R a

3rab1pbab4rab5ra2pa6r0 (0.3439) 3rab1paba4rab5ra2pb6r0 (0.0932)

3rab1pabab4ra5rb2pa6r0 (0.4416) 3rab1pabab4rab5r02pa6r0 (0.1641) 3rab1paba4rab5r02pab6r0 (0.0235) 3rab1pabab4rab5r02pa6r0 (0.7466) 3rab1pabab4ra5rb2pa6r0 (0.0391) 3rab1pabab4r05rab2pa6r0 (0.0122)

3rab1pabab4ra5ra2pb6r0 (0.2020) 3rab1pabab4ra5ra2pa6r0 (0.0403) 3rab1paab4rab5rab2p06r0 (0.0069) 3rab1paab4rab5ra2p06rb (0.0399) 3rab1pabab4ra5ra2pb6r0 (0.0126) 3rab1pabab4r05r02paab6r0 (0.0121)

3rab1pabab4ra5ra2pb6r0 (0.5873) 3rab1pabab4rab5r02pa6r0 (0.0080) 3rab1pabab4ra5r02pab6r0 (0.0035) 3rab1paab4rab5ra2p06rb (0.7134) 3rab1paab4rab5rab2p06r0 (0.0419)

3rab1pabab4ra5rb2pa6r0 (0.2619) 3rab1pabab4ra5ra2pa6r0 (0.0042)

3rab1paab4rab5ra2pa6r0 (0.4590) 3rab1pa4rab5ra2paab6r0 (0.0027) 3rab1paba4rab5ra2pa6r0 (0.4656) 3rab1pabb4rab5ra2pa6r0 (0.9315) 3rab1paba4rab5rab2p06ra (0.8970) 3rab1paab4rab5ra2pb6r0 (0.4611) 3rab1pbab4rab5ra2pa6r0 (0.1434)

3rab1paba4rab5ra2pa6r0 (0.4589) 3rab1pa4rab5ra2paba6r0 (0.0027) 3rab1paab4rab5ra2pa6r0 (0.4656) 3rab1pabb4r0 5ra2pa6rab (0.0045) 3rab1p04rab5ra2paab6ra (0.0235) 3rab1paba4rab5ra2pb6r0 (0.2615) 3rab1paab4ra5rab2pb6r0 (0.0124)

3rab1pbab4rab5ra2p06ra (0.0433) 3rab1paab4ra5rab2p06rb (0.0085)

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

-99.6

6

B(2Pu) + O(1Dg)

-99.7

2

5 4

-99.8 -99.9

3

B( Pu) + O( Pg)

3

2

-100.0

Potential energy /Hartree

Potential energy /Hartree

-99.5 -99.6

7 B(2Pu) + O(1Dg) -99.7

6

B(2Pu) + O(3Pg)

4

-99.8

2 -99.9

1 -100.1

5 3

0.1

1 0.2

0.3

0.4

0.5

0.6

Internuclear separation /nm Fig. 1. PECs of six states of the BO radical 1 – X2R+; 2 – B2R+; 3 – 14R+; 4 – 12D; 5 – D2R+; 6 – 12U.

0.1

0.2

0.3

0.4

0.5

0.6

Internuclear separation /nm Fig. 2. PECs of seven states of the BO radical 1 – A2P; 2 – 14R; 3 – 12R; 4 – C2P; 5 – 22R; 6 – 14P; 7 – F2P.

47

Z. Zhu et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 131 (2014) 42–54

C2P, 12R and 14P states and the second wells of F2P and 12U states have poor multireference characterizations around the equilibrium positions. The 12D, D2R+, 14R+, 14R and 22R states and the first well of 12U state possess the obvious multireference characterizations around the equilibrium positions when the spin orientation of electrons is included, but their multireference characterizations become poor when the spin orientation of electrons is dismissed. As clearly shown in Table 3, only the spin orientation of electrons in the 1p orbital is different for each main valence configuration of the 12D, D2R+, 14R+ and 14R states. Only the spin orientation of electrons in the 5r and 2p orbitals is different for each main valence configuration for the first well of the 12U state. And only the spin orientation of electrons in the 1p and 2p orbitals is different for each main valence configuration of the 22R state. Of these 13 K–S states, only the X2R+ and B2R+ states and the first well of the F2P state possess the multireference characterizations around the equilibrium positions whether the spin orientation of electrons is neglected or not. From these configurations, we can instantly find out how the electronic transition occurs from one state to another. Spectroscopic parameters of the 13 electronic states The present calculations are involved with the first two dissociation channels of BO radical. For comparison with the measurements [37], we have determined the energy separation between the two dissociation channels by the icMRCI + Q/56 + CV + DK calculations, and collected the result in Table 1. As seen in Table 1, the present energy separation of 15551.80 cm1 agrees well with the measurements of 15485.84 cm1 [37]. The comparison shows that the present 13 K–S states can properly dissociate into the atomic fragments.

Employing the PECs determined by the icMRCI + Q/56 + CV + DK calculations, we have evaluated the spectroscopic parameters of present 13 states by the theoretical method outlined in Section ‘Theory and method’. For convenience of discussion, we divide the present 13 states into two categories. One is the X2R+, A2P, B2R+, C2P, D2R+ and F2P, which are the states possessing the experimental spectroscopic parameters [12,14–20]. The other is the 14R+, 14R, 12R, 14P, 22R, 12D and 12U, which are the states without any spectroscopic measurements so far. We collect the spectroscopic results of the X2R+, A2P, B2R+, C2P, D2R+ and F2P states in Table 4, and tabulate the spectroscopic parameters of the 14R+, 14R, 12R, 14P, 22R and 12D and 12U states in Table 5. X2R+, A2P, B2R+, C2P, D2R+ and F2P states For the sake of length limitation, we only tabulate some selected measurements [12,15,18–20] in Table 4 for discussion. Only the theoretical spectroscopic parameters [24,26,27,30–32] are collected in Table 4, which can be comparable with the present results in quality. As seen in Table 3, each of the X2R+ and A2P states possesses at least five valence configurations around the equilibrium positions. From this point, we can say that the two states have multireference characterizations. Furthermore, the 3rab1pabab4rab5ra2p06r0 and 3rab1pabab4ra5rab2p06r0 are the main valence configurations for the X2R+, whereas only the 3rab1paab4rab5rab2p06r0 is the main one for the A2P state. From this point, the multireference characterizations of the X2R+ state are obvious, whereas those of A2P state are very poor. From the valence configurations, we easily see that the transitions between the X2R+ and the A2P state can be regarded as arising from the 1p ? 4r and 1p ? 5r electron promotion. Several groups of experiments [14,15,19] have reported the energy separation between the two states. As seen in Table 4,

Table 4 Comparison of spectroscopic parameters of the BO radical obtained by the icMRCI + Q/56 + CV + DK calculations with available measurements and other theoretical results.

2

+

X R Exp. [12] Exp. [20] Cal. [26] Cal. [27]b Cal. [30] Cal. [31] Cal. [32] A2P Exp. [12] Exp. [15] Cal. [30] Cal. [32] 2 + B R Exp. [12] Exp. [15] Cal. [24] Cal. [32] C2P Exp. [12] Exp. [18] Cal. [32] D2R+ Exp. [19] Cal. [24] F2P 1st well Exp. [19] Cal. [24] 2nd well a b c d

Te (cm1)

Re (nm)

xe (cm1)

xexe (cm1)

Be (cm1)

102 ae (cm1)

D0 (eV)

De (eV)

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 24009.65 – 23897.15 – 23749.79 42940.26 43174.05 43173.19 43150.64 44485.49 55491.53 55346.1 55345.42 55625.62 64295.09 64826.94 63879.08

0.12020 0.12045 0.12046 0.1204 0.12079 0.12094c 0.1203 0.1207 0.13530 0.13533 – 0.13600c 0.1357 0.13046 0.13054 – 0.1308 0.1310 0.13194 0.1320 – 0.1328 0.13693 – 0.1356

1885.72 1885.69 1885.55 1915 1862.0 1873.8c 1916 1888.55 1264.08 1260.70 1260.78 1250.7c 1262.09 1281.81 1281.69 1283.32 1289.6 1281.16 1315.51 1315.3 1315.75 1304.30 1528.59 1517 1540.9

11.824 11.81 – – – 11.7c

1.7863 1.7820 1.7817 – – –

1.88 1.66 1.6576 – – –

8.3608 8.28 8.34 ± 0.15a – 8.2739 8.3437d

8.4773 8.3965

11.553 11.139 11.157 11.191 11.0c 11.158 10.898 10.66 11.562 3.3 11.322 11.274 11.1 11.125 10.895 35.923 19.4 20.0

1.7745 1.4123 [1.4018] 1.4112 – 1.4047 1.5223 1.5171 1.5168 1.511 1.5060 1.4851 1.483 1.4842 1.4669 1.4618

1.617 1.85 1.96 1.8523 – 1.810 2.614 2.10 2.2021 2.67 2.081 1.84 1.8 1.8042 1.825 6.09

8.3397 5.4260

8.4564 5.5040

– 5.4049d 5.4230 – – – – 4.9218 1.4724

5.49 ± 0.15 5.4821 5.5009 5.0110 5.05 ± 0.15 5.05 ± 0.15 4.69 5.0008 1.5275

1.5406 2.3800

1.6211 2.4694

1.406

1.09



2.12

84179.49 81623.27 83075.07 74298.31

0.12744

1580.61

12.985

1.5916

1.727

1.7034

1.8010

0.1303 0.18728

1428.2 3340.96

36.5 565.78

1.525 0.7568

0.12 6.112

1.1473

1.3368

Taken from Ref. [16]. CBS limit. CCSD(T)/aVQZ. CCSD(T)/DTQ.

8.38 8.4595

48

Z. Zhu et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 131 (2014) 42–54

Table 5 Comparison of spectroscopic parameters of the BO radical obtained by the icMRCI + Q/56 + CV + DK calculations with other theoretical results.

4

+

1 R Cal. [22] Cal. [24] 4  1 R Cal. [24] 12R Cal. [24] 14P Cal. [22] Cal. [24] 2  2 R 2 1 D 1st well 2nd well Cal. [22] Cal. [24] 2 1 U 1st well 2nd well Cal. [24]

Te (cm1)

Re (nm)

xe (cm1)

xexe (cm1)

Be (cm1)

102ae (cm1)

D0 (eV)

De (eV)

46340.60 46738 44279.82 50730.24 52990.60 54651.60 52829.29 70241.54 56668 68799.06 71073.57

0.13961 0.136 0.1397 0.14121 0.1428 0.14268 0.1434 0.13603 0.130 0.1360 0.14461

1233.14 1279 1237.6 1165.35 1184.7 1138.11 1179.5 1210.26 1558 1266.0 980.85

10.293 – 3.6 10.465 20.2 10.811 6.8 11.450

1.3263 – 1.324 1.2963 1.268 1.2700 1.257 1.3971

1.570 – 1.32 1.680 2.19 1.573 1.30 1.800

2.3735 – – 1.8086 – 1.8513 – 1.8308

2.4496 2.04 2.64 1.8805 1.57 1.9215 1.59 1.9055

14.8 35.278

1.397 1.2366

1.85 2.9801.8260

1.8857

83341.84 54307.90 55471 52829.29

0.10422 0.14273 0.155 0.1431

1363.09 1145.18 1231 1185.3

11.440 18.897 – 14.5

3.2363 1.2675 – 1.262

0.52 1.41 – 1.48

1.1099 3.6371 – –

1.1940 3.7076 0.83 1.20

93871.49 83981.09 85172.11

0.13358 0.32679 0.1275

1309.80 66.71 1430.7

12.734 5.5892 41.7

1.4515 0.2390 1.588

1.71 0.56 4.65

0.5170 0.0237

0.5978 0.0274

the present prediction of energy separation is 24009.6 cm1, which agrees favorably with the measurements of 23897.15 cm1 [15]. The difference between the present result and the measurements [15] is only 112.45 cm1. As collected in Table 4, no previous theoretical energy separations [21–24,30,32] between the two states are closer to the measurements [15] than the present one. The main valence electronic configurations of the B2R+ state are the 3rab1pabab4ra5rab2p06r0 and 3rab1pabab4rab5ra2p06r0. Similar to the ground state, the B2R+ state also possesses the multireference characterizations. Obviously, the electronic transition between the X2R+ and the B2R+ state is 4r ? 5r. For the X2R+– B2R+ electronic transition, the present energy separation of 42940.26 cm1 agrees well with the measurements [15] of 43173.19 cm1. The difference between them is only 232.93 cm1. Only the energy separation between the X2R+ and the B2R+ state calculated by Karna and Grein [24] is closer the measurements [15] the present one. Of the six states collected in Table 4, only the C2P has one well with one barrier. The well of this state is at 0.13194 nm, and the well depth is about 25889.67 cm1. The barrier of this state is at about 0.21341 nm, and its barrier height relative to the dissociation limit is about 13382.69 cm1. Careful calculations tell us that the barrier comes from the avoided crossing between the C2P and the F2P state. Such avoided crossing was also reported by Almlöf et al. [23] in 1981. As collected in Table 3, the main valence configuration of the C2P state is only the 3rab1pabab4rab5r02pa6r0. Therefore, the electronic transition between the X2R+ and the C2P state can be regarded as arising from the 5r ? 2p. The present prediction of energy separation between the two states is 55491.53 cm1, which is in fair agreement with the measurements of 55346.1 [12] and 55345.42 cm1 [18]. As shown in Table 4, the F2P state possesses the double well. The double well is generated from the avoided crossing between the C2P and the F2P state. As demonstrated in Fig. 2, the energy of the first well at the equilibrium position is higher than that at the dissociation limit. However, the depth of the first well amounts to 33846.06 cm1, which is very deep. Therefore, the first well should be stable and can be easily observed. In fact, Bredohl et al. [19] have observed the first well, and determined its Te to be 81623.27 cm1, which is smaller than the present one by 2556.22 cm1. The second well is at about 0.18728 nm, and its depth is 10782.02 cm1, which is also very deep. Present calculations have determined that the second well possesses the 20 vibrational states, which vibrational levels are 1075.78, 2981.87,

4582.95, 5905.77, 6977.05, 7823.53, 8471.94, 8949.02, 9281.50, 9496.13, 9619.62, 9678.73, 9700.17, 9710.69, 9737.02, 9805.90, 9944.06, 10178.24, 10535.16 and 11041.57 for t = 0–19, respectively. To some extent, we think that the second well is very stable and is easy to be observed, though the energy of the second well at the equilibrium position is lower than that at the dissociation limit. To our surprise, no spectroscopic measurements have been reported about the second well of F2P state to this day. We hope that some spectroscopic experiments will be made in the near future for the second well of the F2P state so that some predictions in this paper can be validated. A number of calculations [20–32] have reported the spectroscopic parameters of the BO radical. By comparison, we have found that few spectroscopic parameters are closer to the measurements [12,15,18–20] than the present ones. For example, for the X2R+ state, only the Re calculated by Barone [26] and Tai and Nguyen [31] are closer to the measurements [12,20] than the present result; and no other theoretical xe results [20–32] are closer to the measurements [12,20] than the present one. Chase et al. [16] reported the ground-state D0 as 8.34 ± 0.15 eV, which is the most recent experimental one. With the D0, we can determine the ground-state De as about 8.45 ± 0.15 eV. As seen in Table 4, only the De obtained by our previous calculations [32] is slightly superior to the present one when compared with the deduced result. We should notice that the present calculations have eliminated the residual errors behind the basis sets. Therefore, the present results should be more reliable than those obtained in Ref. [32]. For the A2P state, no other theoretical Te and Re are closer to the measurements [12,15] than the present ones, and only the xe evaluated in Ref. [32] is closer to the measurements [12,15] than the present result. From Fig. 2, we clearly see that no barrier occurs on the PEC of A2P state. Therefore, we can use the approach given in Ref. [50] to extrapolate the De of A2P state with the help of ground-state experimental De [16]. As seen in Table 4, such value is about 5.49 ± 0.15 eV. Only the theoretical De reported in Refs. [30,32] are comparative with the present one in quality when compared with the present deduced De result. For the B2R+ state, no other theoretical Re and xe [23,24,32] are closer to the measurements [12,15] than the present ones; and only the Te calculated by Karna and Grein [24] is closer to the measurements [12,15] than the present result. Similar to the A2P, we can also deduce the experimental De of the B2R+ state to be about 5.05 ± 0.15 eV [12,15]. No other theoretical De results available in the literature are closer to the deduced De than the present one. For the C2P and D2R+ states, no other theoretical spectroscopic

Z. Zhu et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 131 (2014) 42–54

parameters [23,24,32] are closer to the measurements [12,18,19] than the present ones. We cannot deduce the experimental De of the C2P state with the help of ground-state experimental De [16], since obvious barrier happens on the PEC of this state. As for the F2P state, only the theoretical Te evaluated by Karna and Grein [24] is superior to the present one when compared with the measurements [19]. On the whole, the present spectroscopic parameters are in excellent agreement with the available measurements. For example, for the ground state, the present Re of 0.12020 nm compares well with the recent measurements of 0.12046 nm [20], and the difference between them is only 0.00026 nm (0.22%). The present xe of 1885.72 cm1 agrees favorably with the recent measurements of 1885.55 cm1 [20], and the difference between them is only 0.17 cm1 (0.01%). The present D0 of 8.3608 eV is in line with the recent measurements of 8.34 ± 0.15 eV [20], and the difference between them is only about 0.02 eV (0.24%). For the A2P state, the present Te, xe and De deviate from their respective measurements [15] only by 112.5 cm1 (0.47%), 3.30 cm1 (0.26%) and 0.01 eV (0.18%). And the present Re and xe deviate from their respective measurements [12] only by 0.00003 nm (0.02%) and 3.38 cm1 (0.27%). For the B2R+ state, the Te, xe and De obtained here deviate from their respective experimental ones [15] only by 232.93 cm1 (0.54%), 1.51 cm1 (0.12%) and 0.04 eV (0.79%), and the Re obtained here deviate from the measurements [12] only by 0.00008 nm (0.06%). For the C2P state, the differences of Te, Re and xe between the present results and the measurements [15] are only 145.43 cm1 (0.26%), 0.00006 nm (0.0.05%) and 0.21 cm1 (0.0.02%), respectively. As for the Te and xe of D2R+ state as well as the Te of F2P state, the differences between present results and the corresponding measurements [19] are somewhat large. On the whole, such comparison indicates that the present spectroscopic parameters obtained by the icMRCI + Q/56 + CV + DK calculations should be high quality. We think that the reasons for achieving such high-quality spectroscopic parameters may be several aspects. Two main reasons are as follows. One is that the core–valence correlation and scalar relativistic corrections are included into the present calculations. The other is that the residual errors behind the basis sets are eliminated by the total-energy extrapolation to the CBS limit. 14R+, 14R, 12R, 14P, 22R and 12D and 12U states For the 14R+, 14R, 12R, 14P, 22R and 12D and 12U states, no measurements can be found in the literature, and only two groups of theoretical results have been reported to this day. We collect the present spectroscopic parameters together with the available theoretical ones in Table 5. Of the seven states, the 12R, 22R and 14P states possess one well with one barrier. For the 12R state, the well is at 0.14268 nm, and the well depth reaches about 15497.98 cm1, which is very deep. Its barrier is at about 0.22024 nm, and the barrier height relative to the dissociation limit is about 1643.43 cm1. As seen in Fig. 2, the energy of 12R state at the equilibrium position is obviously lower than that at the dissociation limit. According to these, we think that the 12R state is stable and is not difficult to be observed in experiment. For the 22R state, the well is at 0.14461 nm, and the well depth amounts to about 15208.93 cm1. Calculations tell us that the barrier of 22R state is at about 0.22001 nm, and its height relative to the dissociation limit reaches about 16885.72 cm1. As for the 14P state, the well is at 0.13603 nm, and the well depth is about 15368.71 cm1. Calculations tell us that the barrier of 14P state is at about 0.18850 nm, and its height relative to the dissociation limit is about 18427.97 cm1. Similar to the 12R state, the wells of 22R and 14P states are also very deep. On the whole, the 22R and 14P states should be stable and are not difficult to be observed

49

in experiment due to their deep wells, though the energies of the two states at their respective equilibrium positions is slightly higher than that at the corresponding dissociation limits. We expect that the results proposed here can provide some guidelines for future experiments. The 12U state possesses the double well with one barrier. Its first well is at about 0.13358 nm, and the well depth is about 4821.58 cm1. As demonstrated in Fig. 1, the energy of the first well at the equilibrium position is obviously higher than that at the dissociation limit. From this point, this well seems to be somewhat unstable. Present calculations have determined that the first well possesses the 5 vibrational states, which vibrational levels are 937.20, 1163.95, 1167.58, 4195.08 and 8610.79 cm1 for t = 0–4, respectively. According to these results, we think that the first well should be observed in experiment. As for the second well of 12U state, its well depth is only 221.00 cm1, and the energy at its equilibrium position is lower than that at the dissociation limit. To our surprise, the second well has the 6 vibrational states, which vibrational levels are 33.47, 87.98, 127.92, 155.68, 173.68 and 184.30 cm1 for t = 0–5, respectively. Therefore, the second well of 12U state can be observed, though it is very shallow and has not been found in experiment till now. The detailed calculations tell us that the barrier between the two wells is at about 0.16700 nm, and that the barrier height relative to the dissociation limit is about 4821.58 cm1. Similar to the 12U, the 12D state also possesses the double well with one barrier. The barrier is at about 0.11500 nm, and the barrier height relative to the dissociation limit is about 24489.42 cm1. The first well is at about 0.10422 nm, and the well depth is about 9630.25 cm1. As demonstrated in Fig. 1, the energy of the first well at its equilibrium position is greatly higher than that at the dissociation limit. Calculations have determined that the first well possesses the 20 vibrational states, which vibrational levels are 648.2, 1972.13, 3332.39, 4728.56, 6160.21, 7626.89, 9128.18, 10663.63, 12232.83, 13835.33, 15470.70, 17138.50, 18838.30, 20569.68, 22332.19, 24125.40, 25948.87, 27802.18, 29684.89 and 31596.56 for t = 0–19, respectively. As seen in Fig. 1, the second well of the 12D state is very deep. According to these, we think that the double well of 12D state should be easy to be observed, though no experimental observations have been reported to this day. The spectroscopic parameters tabulated in Table 5 should be reliable. The reasons may be several aspects. Three main reasons are as follows. The first one is that the present calculations are convergent with respect to the basis set and the present level of theory, as discussed above. The second one is that the two main corrections, core–valence correlation and scalar relativistic corrections, are included into the present calculations. And the last one is that the residual errors behind the basis sets are eliminated by the extrapolation to the CBS limit. On the one hand, as pointed out above, the PECs of all the states involved here are calculated by the same approach; on the other hand, the spectroscopic parameters of all these states are evaluated by the same method. As pointed out above, the spectroscopic parameters of six states collected in Table 4 agree well with available measurements [12,15,18–20]. In addition, as discussed in the following section, we can still see that the spectroscopic parameters of the A2P3/2 and A2P3/2 states also compare favorably with the available experimental results [12]. According to these, we think that the spectroscopic parameters collected in Table 5 can be expected to be reliably predicted ones, and can be good references for the future laboratory research and theoretical work. Spectroscopic parameters of the 23 X states The ground state of B atom splits into the two components, 2P1/2 and 2P3/2. And the ground state of O atom splits into three

50

Z. Zhu et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 131 (2014) 42–54

Table 6 Dissociation relationships of possible X states of BO radical determined by the icMRCI + Q/56 + CV + DK + SO calculations. Atomic state

Possible X states

Relative energy (cm1) This work

Exp. [37]

B(2P1/2) + O(3P2) B(2P3/2) + O(3P2) B(2P1/2) + O(3P1) B(2P3/2) + O(3P1) B(2P1/2) + O(3P0) B(2P3/2) + O(3P0) B(2P1/2) + O(1D2) B(2P3/2) + O(1D2)

1/2, 1/2, 1/2, 1/2, 1/2 1/2, 1/2, 1/2,

0 15.26 152.68 175.75 219.74 236.85 15551.80 15566.02

0 15.29 158.27 173.55 226.98 242.26 15485.84 15501.13

1/2, 1/2, 1/2, 1/2,

3/2, 3/2, 5/2 1/2, 1/2, 3/2, 3/2, 3/2, 5/2, 5/2, 7/2 3/2 1/2, 3/2, 3/2, 5/2

3/2 1/2, 3/2, 3/2, 5/2 1/2, 1/2, 1/2, 3/2, 3/2, 3/2, 5/2, 5/2, 7/2

Potential energy /Hartree

-99.54

-99.61

-99.68

5

B(2P1/2) + O(1D2)

4 3

B(2P3/2) + O(3P0) B(2P3/2) + O(3P1)

-99.75

2

B(2P3/2) + O(3P2)

-99.82

1 -99.89 0.1

0.2

0.3

0.4

0.5

Internuckear separation /nm Fig. 4. PECs of X = 1/2 states of the BO radical 1 – C2P1/2; 2 – D2R+1/2; 3 – 14P1/2; 2 4 – 22R 1/2; 5 – F P1/2.

Potential energy /Hartree

components, 3P2, 3P1 and 3P0. Therefore, the first dissociation channel splits into the six dissociation asymptotes when the SO coupling effect is included, as collected in Table 6. Because the first excited state 1D of O atom does not split, the second dissociation channel only splits into two asymptotes. Table 6 collects the dissociation relationships of all the possible X states generated from the eight dissociation asymptotes. In the present work, the SO coupling effect is accounted for by the state interaction method with the Breit–Pauli Hamiltonian. The calculations are performed at the icMRCI level of theory with the all-electron aug-cc-pCVTZ (ACVTZ) basis set. From that, the PECs of 23 X states involved here are obtained. It should be pointed out that all the SO coupling calculations are performed across the entire PEC of each X state. The all-electron ACVTZ basis set with the Breit–Pauli Hamiltonian and the all-electron ACVTZ basis set with no Breit–Pauli Hamiltonian are employed to calculate the SO coupling contribution. The difference between the two energies generates the SO coupling splitting result. By adding the SO coupling splitting energies to the icMRCI + Q/56 + CV + DK results, we can obtain the final PEC of each X state. We have calculated the energy separation relative to the lowest dissociation channel for each higher dissociation asymptote, and collected the corresponding results in Table 6. In addition, Table 6 also tabulates the experimental energy separation [37] between each of the higher dissociation asymptotes and the lowest one. In this work, three X states (X2R+1/2, A2P3/2 and A2P1/2) are attributed to the lowest dissociation asymptote, B(2P1/2) + O(3P2). 2 4 + 2 2 Eight X states (C2P1/2, 14R+1/2, 12R 1/2, C P3/2, 1 R3/2, 1 D3/2, 1 D5/ 4 2 3 2 and 1 P5/2) correlate to the B( P3/2) + O( P2) asymptote. Two X 4  2 3 states (14R 1/2 and 1 R3/2) belong to the B( P1/2) + O( P1) asymptote. 4 4 4 Three X states (1 P3/2, 1 P1/2 and 1 P-1/2) correlate to the B(2P3/ 3 2  2) + O( P1) asymptote. Only the 2 R1/2 state is attributed to the 2 3 B( P3/2) + O( P0) asymptote. Two X states (F2P1/2 and F2P3/2) correlate to the B(2P1/2) + O(1D2) asymptote. And four X states (12U5/2,

-99.6 7

B(2P1/2) + O(1D2)

-99.7

B(2P 3/2) + O(3P1) B(2P1/2) + O(3P1)

6 45

-99.8

B(2P3/2) + O(3P2) B(2P1/2) + O(3P2)

3 2

-99.9

1 0.1

0.2

0.3

0.4

0.5

0.6

Internuclear separation /nm B(2P3/2) + O(1D2)

Potential energy /Hartree

-99.7

3

5

B(2P1/2) + O(3P1) B(2P3/2) + O(3P2)

6

B(2P1/2) + O(3P2)

4

-99.8

-99.9 2 -100.0 1 0.1

0.2

0.3

0.4

0.5

Internuclear separation /nm Fig. 3. PECs of X = 1/2 states of the BO radical 1 – X2R+1/2; 2 – A2P1/2; 3 – B2R+1/2; 2  4 – 14R+1/2; 5 – 14R 1/2; 6 – 1 R1/2.

Fig. 5. PECs of X = 3/2 states of the BO radical 1 – A2P3/2; 2 – C2P3/2; 3 – 14R+3/2; 4 – 4 2 12D3/2; 5 – 14R 3/2; 6 – 1 P3/2; 7 – F P3/2.

12U7/2, B2R+1/2 and D2R+1/2) are attributed to the B(2P3/2) + O(1D2) asymptote. Here, the PECs of 21 X states are depicted in Figs. 3–6, and their respective dissociation asymptotes are labeled in the same figure. Similar to Figs. 1 and 2, we depict the PECs of all the X states only over a small internuclear separation from 0.07 to 0.63 nm so that more details of the involved PECs can be demonstrated. In addition, only one X = 1/2 state (14P1/2) and only one X = 7/2 state (12U7/2) exist in this work. For the sake of length limitation, we do not depict the PECs of the two X states in the separation figures. To avoid overlapping with other PECs, we either do not include them in Figs. 3–6. The present 23 X states can be divided into three categories according to their symmetries for convenience of discussion. The

Z. Zhu et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 131 (2014) 42–54

is the 12 X states, which are yielded by the A2P, C2P, 14P and F2P states. And the last group is the 4 X states, which are produced from the 12D and 12U states. Using the PECs determined by the icMRCI + Q/56 + CV + DK + SO calculations, we have evaluated the spectroscopic parameters (Te, Re, xe and Be) of these X states by the approach outlined in Section ‘Theory and method’. The spectroscopic results are collected in Tables 7–9. Meanwhile, the K–S state compositions of each X state around the equilibrium positions are also tabulated in Tables 7–9.

Potential energy /Hartree

-99.60

-99.65

3 B(2P3/2) + O(1D2)

-99.70

2 B(2P3/2) + O(3P2)

-99.75

-99.80

1 0.1

0.2

0.3

0.4

0.5

51

0.6

Internuclear separation /nm Fig. 6. PECs of X = 5/2 states of the BO radical 1 – 12D5/2; 2 – 14P5/2; 3 – 12U5/2.

first group is the 9 X states, which are generated from the X2R+, B2R+, 14R+, 14R, 12R, D2R+ and 22R states. The second group

Nine X states yielded from the X2R+, B2R+, 14R+, 14R, 12R, D2R+ and 22R states Table 7 tabulates the spectroscopic parameters of nine X states, which are generated from the X2R+, B2R+, 14R+, 14R, 12R, D2R+ and 22R states. Table 7 also collects the K–S state compositions of each X state around the equilibrium position. For the X2R+, B2R+, 12R, D2R+ and 22R states, K equals 0 and R is 1/2. Therefore, these five K–S states do not split. As clearly seen from Table 7, around the equilibrium positions, the K–S state compositions of each X state generated from the five electronic states is almost

Table 7 Spectroscopic parameters obtained by the icMRCI + Q/56 + CV + DK + SO calculations for the 9 X states generated from the X2R+, B2R+, 14R+, 14R, 12R, D2R+ and 22R states.

2

+ 1/2 + 1/2 + 1/2 + 3/2  1/2  3/2  1/2 + 1/2  1/2

X R B2R 14R 14R 14R 14R 12R D2R 22R

Te (cm1)

Re (nm)

xe (cm1)

Be (cm1)

K–S state compositions near the Re (%)

0.0 42940.06 46340.53 46340.62 50730.07 50730.25 54651.60 64295.09 71073.60

0.12053 0.13017 0.13961 0.13961 0.14122 0.14122 0.14268 0.13693 0.14461

1885.05 1281.56 1233.38 1233.05 1165.56 1165.15 1138.11 1528.59 980.85

1.7796 1.5231 1.2496 1.3411 1.2963 1.2963 1.2700 1.4618 1.2366

X2R+(100.00) B2R+(100.00) 14R+(92.08), C2P(7.92) 14R+(98.11), C2P(1.88) 14R(98.79), A2P(0.65), C2P(0.57) 14R(98.11), A2P(1.23), C2P(0.65) 12R(99.99) D2R+(100.00) 22R(100.00)

Table 8 Spectroscopic parameters obtained by the icMRCI + Q/56 + CV + DK + SO calculations for the 10 X states generated from the A2P, C2P, 14P and F2P states.

A2P3/2 A2P1/2 C2P1/2 C2P3/2 14P5/2 14P3/2 14P1/2 14P1/2 F2P3/2 1st well 2nd well 2 F P1/2 1st well 2nd well

Te (cm1)

Re (nm)

xe (cm1)

Be (cm1)

K–S state compositions near the Re (%)

23948.91 24066.50 55466.33 55516.81 70220.50 70231.49 70244.87 70255.82

0.13531 0.13531 0.13194 0.13194 0.13602 0.13602 0.13603 0.13603

1265.17 1265.28 1315.45 1315.58 1210.14 1209.85 1210.06 1209.78

1.4120 1.4120 1.4852 1.4853 1.3972 1.3972 1.3971 1.3971

A2P(100.00) A2P(49.62), C2P(49.62) C2P(49.95), 12U(49.95), A2P(0.05), F2P(0.05) C2P(49.95), 12U(49.95), A2P(0.05), F2P(0.05) 14P(98.53), 12U(0.75), C2P(0.72) 14P(50.05), F2P(49.95) 14P(50.05), 12U(49.95) 14P(49.27), C2P(49.26), F2P(0.75), A2P(0.72)

84157.99 74295.02

0.12746 0.18729

1580.18 3337.06

1.5916 0.7570

F2P(100.00) F2P(100.00)

84201.00 74301.60

0.12745 0.18728

1581.73 3344.97

1.5919 0.7566

F2P(100.00) F2P(100.00)

Table 9 Spectroscopic parameters obtained by the icMRCI + Q/56 + CV + DK + SO calculations for the 12D3/2, 12D5/2, 12U5/2 and 12U7/2 states of the BO radical. Te (cm1)

Re (nm)

xe (cm1)

Be (cm1)

K–S state compositions near the Re (%)

83307.14 54295.90

0.10421 0.14273

1362.11 1145.32

1.2364 1.2675

12D(96.32), 14R+(3.67) 12D(97.66), 14R+(2.33)

83346.58 54312.93

0.10422 0.14269

1363.89 1144.57

1.2364 1.2674

12D(95.14), 14R+(4.86) 12D(96.61), 14R+(3.38)

93861.18 83976.48

0.13361 0.32679

1313.02 66.70

1.4509 0.2390

12U(99.86), 14P(0.14) 12U(99.86), 14P(0.14)

93882.03 83985.92

0.13354 0.32679

1306.36 66.71

1.4521 0.2390

12U(99.86), 14P(0.14) 12U(99.86), 14P(0.14)

2

1 D3/2 1st well 2nd well 12D5/2 1st well 2nd well 12U5/2 1st well 2nd well 2 1 U7/2 1st well 2nd well

Z. Zhu et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 131 (2014) 42–54

pure. As a result, the effect of SO coupling on their spectroscopic parameters is very small. As tabulated in Table 7, the K–S state compositions of 14R+1/2 and 14R+3/2 X components slightly mix with the C2P state near the equilibrium positions. Therefore, the effect of SO coupling on the spectroscopic parameters should be small. In fact, from Tables 5 and 7, we can see that Re of the two X states is the same as that of the 14R+ state, and that the largest deviation of xe from that of the 14R+ state is only 0.24 cm1. In addition, the SO coupling constant of the 14R+ state is determined to be only 0.47 cm1 in the present work, which is very small. 4  The K–S state compositions of 14R 1/2 and 1 R3/2 X components slightly mix with the A2P and C2P states near the equilibrium positions. That is, the effect of SO coupling on the spectroscopic parameters should be small, which can be clearly seen by comparison of the spectroscopic parameters collected in Tables 5 and 7. In conclusion, the effect of SO coupling on the spectroscopic parameters of the X2R+, B2R+, 14R+, 14R, 12R, D2R+ and 22R states is very small. Ten X states generated from the A2P, C2P, 14P and F2P states Table 8 collects the spectroscopic parameters of the 12 X states generated from the A2P, C2P, 14P and F2P states, and also tabulates the K–S state compositions of each X state around the internuclear equilibrium positions. Te of the A2P3/2 state is smaller than, and Te of the A2P1/2 state is larger than that of the A2P state. As a result, the A2P is an inverted state. According to Table 8, the SO coupling constant of A2P state is determined as 117.59 cm1. At least two groups of measurements [11,15] reported its SO coupling constant. One is 122.26 cm1, which was measured by Dunn and Hanson [11] in 1970. The other is 122.46 cm1, which was evaluated by Mélen et al. [15] in 1985. Obviously, the present SO coupling constant compares favorably with these experimental ones [11,15]. As collected in Table 8, the K–S state composition of A2P3/2 component is pure, and those of A2P1/2 component strongly mix with the C2P state. As a result, slight effect of SO coupling on the spectroscopic parameters is demonstrated. For example, the xe of A2P1/2 and A2P3/2 components deviate from that of A2P state by about 1.09 and 1.20 cm1, respectively, though the effect of SO coupling on the Re is very small. For the C2P state, the effect of SO coupling on the Re, xe and Be is very small, though the K–S state compositions of C2P1/2 and C2P3/2 components strongly mix with the 12U state. The present SO coupling constant of C2P state is 50.48 cm1, which agrees well with the measurements of 47.70 cm1 reported by Mélen et al. [18] in 2001. Te of the 14P5/2 state is the smallest, and the Te of the 14P-1/2 state is the largest among the Te of four X states generated from the 14P state. As a result, the 14P is an inverted state. Similar to the C2P, the effect of SO coupling on the Re, xe and Be is very small, though the K–S state compositions of 14P3/2 component strongly mix with F2P; those of the 14P1/2 strongly mix with the 12U, and those of the 14P1/2 component strongly mix with the C2P state. The present energy separations between the two neighboring X states from the 14P5/2 to the 14P-1/2 are 10.99, 13.38 and 10.95 cm1, respectively, which are all very small. Te of the F2P3/2 is smaller than, whereas Te of the F2P1/2 is larger than that of the F2P K–S state, whether for the first or the second well. Similar to the A2P and 14P, the F2P is also an inverted state. As tabulated in Table 8, the K–S state composition of F2P3/2 and F2P1/2 X components is pure near the equilibrium positions. For this reason, the effect of SO coupling on its spectroscopic parameters are not obvious. For example, the energy separations between the two X states are 43.01 and 6.58 cm1 for the first and the second well, respectively. The largest deviations of Re and xe from

those of F2P state are 0.00002 nm and 1.12 cm1 for the first well, and are 0.00001 nm and 3.90 cm1 for the second well, respectively. In conclusion, (1) the A2P, 14P and F2P are the inverted states when the SO coupling effect is included; and (2) on the whole, the effect of SO coupling on the spectroscopic parameters of these four P states is not obvious. Four X states generated from the 12D and 12U states Table 9 collects the spectroscopic parameters of four X states generated from the 12D and 12U states. Similar to Tables 7 and 8, in Table 9, we also collect the K–S state compositions of each X state around the equilibrium position. For the 12D state, K is 2 and R equals 1/2. Two X components are generated with the SO coupling effect taken into account, as tabulated in Table 9. The K–S state compositions of each X component only slightly mix with the 14R+ near the equilibrium position. As a result, the effect of SO coupling on the spectroscopic parameters is small. It can be clearly seen by comparison of the Re and xe collected in Tables 5 and 9. Calculations have determined that the energy separations between the two X states are only 39.44 and 17.03 cm1 for the first and the second well, respectively, which are very small when compared with those of the A2P state. The largest deviations of Re and xe of the two X states from those of the 12D state are only 0.00004 nm and 0.98 cm1, respectively. Similar to the 12D, the effect of SO coupling on its spectroscopic parameters is either not obvious. Transition properties For the sake of length limitation, here we only briefly investigate five electronic transitions, 14P–X2R+, D2R+–X2R+, C2P–X2R+, B2R+–X2R+ and 12R–X2R+. For this reason, here we have calculated the transition dipole moments (TDMs) vs. internuclear separation for the five transitions, and depicted the results in Fig. 7. It should be pointed out that the TDMs demonstrated in Fig. 7 are calculated by the Breit–Pauli Hamiltonian in combination with the all-electron ACVTZ basis set at the icMRCI level of theory. Fig. 7 clearly demonstrates that the TDMs of the transitions from the D2R+, C2P, B2R+ and 12R K–S states to the X2R+ state are large over a small internuclear separation range near the equilibrium position, which is consistent with the fact that the doublet– doublet transitions are allowed. In addition, Fig. 7 also shows that the TDMs of the 14P–X2R+ transitions are very small over the same internuclear separation, which is consistent with the fact that the

Transition dipole moment /debye

52

2.8

5

2.4 2.0 1.6 1.2

4 0.8

3 2

0.4

1

0.0 0.12

0.14

0.16

0.18

0.20

Internuclear separation /nm Fig. 7. TDM vs. internuclear separation of transitions from the B2R+, C2P, D2R+, 12R and 14P states to the X2R+ state. 1 – 14P–X2R+; 2 – D2R+–X2R+; 3 – C2P– X2R+; 4 – B2R+–X2R+; 5 – 12R–X2R+.

53

Z. Zhu et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 131 (2014) 42–54 Table 10 Frank–Condon factors of transitions from the B2R+, C2P, D2R+, 12R and 14P K–S states to the X2R+K–S state.

t0 /t00

0

1

2

3

4

5

0 1 2 3 4 5

0.2386 0.3158 0.2327 0.1258 0.0555 0.0212

0.3437 0.0485 0.0319 0.1509 0.1776 0.1277

0.2465 0.0485 0.1647 0.0293 0.0182 0.1059

0.1165 0.2019 0.0195 0.0787 0.1101 0.0136

0.0406 0.2055 0.0499 0.1078 0.0016 0.0914

0.0218 0.1170 0.1745 0.0013 0.1089 0.0305

C2P–X2R+

0 1 2 3 4 5

0.1329 0.2436 0.2442 0.1777 0.1053 0.0540

0.2812 0.1366 0.0021 0.0476 0.1252 0.1434

0.2844 0.0000 0.1192 0.1038 0.0110 0.0153

0.1820 0.1067 0.0952 0.0042 0.0908 0.0798

0.0824 0.2083 0.0000 0.1145 0.0355 0.0130

0.0279 0.1733 0.0946 0.0537 0.0339 0.0877

D2R+–X2R+

0 1 2 3 4 5

0.0011 0.0057 0.0158 0.0309 0.0502 0.0714

0.0088 0.0347 0.0696 0.0944 0.1014 0.0895

0.0342 0.0919 0.1161 0.0858 0.0365 0.0040

0.0834 0.1342 0.0797 0.0115 0.0050 0.0395

0.1437 0.1081 0.0084 0.0190 0.0607 0.0485

0.1864 0.0353 0.0198 0.0754 0.0375 0.0000

12R–X2R+

0 1 2 3 4 5

0.0011 0.0057 0.0164 0.0332 0.0537 0.0735

0.0087 0.0345 0.0705 0.0981 0.1028 0.0841

0.0339 0.0909 0.1164 0.0878 0.0362 0.0034

0.0828 0.1328 0.0792 0.0112 0.0057 0.0396

0.1432 0.1081 0.0084 0.0200 0.0633 0.0494

0.1857 0.0364 0.0188 0.0747 0.0359 0.0000

14P–X2R+

0 1 2 3 4 5

0.0315 0.0938 0.1510 0.1753 0.1645 0.1329

0.1184 0.1822 0.1190 0.0301 0.0001 0.0264

0.2118 0.1110 0.0011 0.0442 0.0926 0.0683

0.2403 0.0069 0.0695 0.0914 0.0154 0.0088

0.1937 0.0354 0.1092 0.0043 0.0420 0.0736

0.1179 0.1357 0.0254 0.0501 0.0711 0.0020

State–state 2

+

2

B R –X R

+

quartet-doublet transitions are forbidden. By the way, the TDM curve of the D2R+–X2R+ transitions is almost overlapped with that of the C2P–X2R+. For the sake of length limitation, we do not demonstrate each of them in a separate figure. We use the following formula [51] to calculate the radiative lifetime for a given vibrational t0

st0 ¼ ðAt0 Þ1 ¼ ¼

64p

4 ja 0

3h g0  2P 3 g 00  e  TDMj t0 qt0 ;t00 ðDEt0 ;t00 Þ

4:936  105 g0  ; 2P 3 g 00 jTDMj t0 qt0 ;t00 ðDEt0 ;t00 Þ

ð2Þ

where qt0 ,t00 denotes the Franck–Condon factor. TDM is the averaged TDM in atomic unit. g0 and g00 are the degeneracy of upper and lower states, respectively. The energy separation DEt0 ,t00 is in cm1 and the radiative lifetime st0 is in s. Employing the PECs obtained by the icMRCI + Q/ 56 + CV + DK + SO calculations, with the help of LEVEL Program [52], we have evaluated the Frank–Condon factors at different vibrational levels for the five groups of electronic transitions 14P–X2R+, D2R+–X2R+, C2P–X2R+, B2R+–X2R+ and 12R–X2R+. For the lowest five vibrational levels of transitions selected here,

we have also evaluated their radiative lifetimes. We collect these results in Tables 10 and 11, respectively. From Tables 10 and 11, for the B2R+–X2R+, we can clearly see that a number of transitions, such as 0–0, 0–1, 0–2, 0–3, 1–0, 1– 3, 1–4, 1–5, 2–0, 2–2, 2–5, 3–0, 3–1, 3–4, 4–1, 4–3, 5–1 and 5–2 are remarkably strong with the short lifetimes. And there are still some transitions, such as 0–4, 0–5, 1–1, 1–2, 2–1, 2–3, 2–4, 3–2, 3–5 and 4–4, which are very weak since their Frank–Condon factors are small. For the C2P–X2R+, there are also a number of transitions, such as 0–0, 0–1, 0–2, 0–3, 1–0, 1–1, 1–3, 1–4, 1–5, 2–0, 2–2, 3–0, 3–2, 3–3, 4–0, 4–1 and 5–1, are also strong with the short lifetimes. Only few transitions (0–4, 0–5, 1–3, 1–4, 2–2 and 4–1) are strong for the D2R+–X2R+ and 12R–X2R+ transitions, since only the Frank–Condon factors of these transitions are large, though the D2R+–X2R+ and 12R–X2R+ are both the allowed transitions. As for the 14P–X2R+, there are still few transitions, such as 0–1, 0–2, 0–3, 0–5, 1–1, 1–2, 1–5, 2–0, 2–1, 2–4, 3–0, 4–0 and 5–0, which are strong with the long lifetimes. Conclusions In this paper, the PECs of 13 K–S states and 23 X states have been studied for internuclear separations from about 0.07 to

Table 11 Radiative lifetimes of transitions from the B2R+, C2P, D2R+, 12R and 14P K–S states to the X2R+ K–S state for several low vibrational states. Transition (t0 –t00 )

B2R+–X2R+ C2P–X2R+ D2R+–X2R+ 12R–X2R+ 14P–X2R+ a

Radiative lifetimes (s) 0–0

1–1

2–2

3–3

4–4

1.7678(8) 1.2618(8) 2.4370(8) 1.8469(9)a 9.7201(5)

1.6174(8) 1.4084(8) 2.3079(8) 1.7760(9) 1.3980(4)

1.3473(8) 1.9137(8) 2.2667(8) 1.6826(9) 1.7205(4)

1.3226(8) 2.0160(8) 2.2025(8) 1.6764(9) 1.7248(4)

1.0587(8) 2.3255(8) 2.0970(8) 1.6425(9) 1.8754(4)

Values in parenthesis are power to base 10.

54

Z. Zhu et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 131 (2014) 42–54

1.0 nm using the CASSCF method, which is followed by the icMRCI approach. Of the 13 states, each of the F2P, 12U and 12D states are found to possess the double well. Each of the 14P, C2P, 12R and 22R states possesses one well with one barrier. The A2P, 14P and F2P are the inverted states with the SO coupling effect included. All the states possess the deep wells except for the 12U. The SO coupling effect is accounted for by the Breit–Pauli Hamiltonian with the all-electron ACVTZ basis set. To obtain more reliable results, the Davidson correction is included, and the effect of core–valence correlation and scalar relativistic corrections on the PECs is taken into account. The spectroscopic parameters of 13 K–S states and 23 X states have been calculated, and compared in detail with those available in the literature. Excellent agreement has been found between the present results and the available measurements. The Franck–Condon factors and radiative lifetimes of the transitions from the B2R+, C2P, D2R+, 12R and 14P K–S states to the ground state are calculated for several low vibrational levels, and some necessary discussion is done. On the whole, the effect of SO coupling on the spectroscopic parameters is not obvious. The analyses show that the spectroscopic parameters reported in the present paper can be expected to be reliably predicted ones, and can be good references for the future laboratory research and theoretical work. Acknowledgments This work was sponsored by the National Natural Science Foundation of China under Grant Nos. 11274097 and 61177092, the Natural Science Foundation of Education Bureau of Henan Province in China under Grant No. 2010B140013 and the Program for Science & Technology of Henan Province in China under Grant No. 122300410303. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]

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Accurate calculations of spectroscopic properties for the 13 Λ-S states and the 23 Ω states of BO radical including the spin-orbit coupling effect.

The spectroscopic properties of 23 Ω states generated from the 13 Λ-S states of BO radical are studied for the first time for internuclear separations...
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