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1 Chemical Physics 1 (013) Contents lists available at SciVerse ScienceDirect Chemical Physics journal homepage: Electronic structure with spin orbit calculations of the low-lying electronic states of the molecule YS A. Farhat a,b, M. Korek c,, S.N. Abdul-Al d, M.A.L. Marques a,b a Université de Lyon, F Lyon, France b LPMCN, CNRS, UMR 5586, Université Lyon 1, F-696 Villeurbanne, France c Faculty of Science, Beirut Arab University, P.O. Box Riad El Solh, Beirut , Lebanon d Lebanese International University, Museitbeh, P.O. Box 160, Beirut, Lebanon article info abstract Article history: Received 7 April 01 In final form 10 December 01 Available online 8 December 01 Keywords: YS molecule Theoretical spin orbit calculation Spectroscopic constants Potential energy curves Dipole moment Rovibrational calculation An ab initio calculation (single and double excitation plus Davidson correction) have been performed for the molecule Yttrium monosulfide YS. The potential energy curves of 55 electronic states in the representation X (±), including the spin orbit (SO) effects, have been calculated along with the corresponding spectroscopic constants. The SO effects are taken into account via a semi-empirical pseudo-potential for yttrium atom, while they have been neglected for sulfur. A very good agreement is displayed by comparing the present results with those obtained experimentally for the two states P 1/ and P 1/. For the investigated electronic states without spin orbit, the permanent dipole moments as a function of the internuclear distance, the eigenvalues E v, the rotational constants B v, the centrifugal distortion constant D v and the abscissa of the turning points r min and r max have been investigated. New results have been obtained for 1 electronic states including their SO components. Ó 013 Elsevier B.V. All rights reserved. 1. Introduction Interests in transition metal diatomic molecules arise because they can be considered as prototypes to understand the role played by the d orbitals in bonding, catalysis, organic synthesis, and cosmochemistry [1]. In astrophysics, the presence of Yttrium monosulfide in stellar atmospheres is possible similarly to Zirconium sulfide which has been identified as the carrier of the Keenan bands in the spectrum of cool S-type stars []. These molecules are useful for examining bonding schemes in simple metal systems, which then can be generalized to bulk properties [3]. Transition metal sulfides are another class of interesting d molecules. Unlike the oxides, these species are not well studied experimentally. The spectra and structure of Yttrium mono-sulfide YS has been the subject of limited number of theoretical and experimental studies. The experimental observations of the spectra of this molecule revealed the existence of strong perturbations leading to unobvious assignment of the perturbing states [,5]. In literature the five states X R +,A 0 D,A P, U, and P have been studied theoretically without spin orbit [6,7] while the states X R +,B R,A P 1/, A P 3/ and P ±1/ have been studied experimentally [,7 10]. Kowalczyk et al. [11] performed a high resolution excitation spectrum of gaseous YS and reported the (0, 0) band of the Corresponding author. Fax: addresses: fkorek@yahoo.com, mahmoud.korek@bau.edu.lb (M. Korek). A Q 1/ X P+ transition, which was rotationally analyzed, and a set of spectroscopic constants were given. More recently, Steimle and Virgo [5] studied the optical Stark effect in the (0, 0) A Q 1/ X P+ band systems of YS molecule, and measured the magnitude of the permanent dipole moment for the A Q 1/ and A Q 3/ states. Stringat et al. [9] obtained electronic spectra of the YS molecule in the red and near-infrared spectral regions where several bands belonging to the A P X R + and B R + X R + systems have been reported. Further, James et al. [] reported the X R + and B R + states with the two low-lying stable quartet states U and P of the molecule YS through a molecular beam fluorescence spectroscopy technique. By using the optical Stark effect, the permanent dipole moments of the X R + and B R + states and those of A P 1/ and A P 3/ states were determined by James and Simard [7] and Steimle and Virgo [5], respectively. Recently we studied the lowest lying electronic states in the representation s+1 K (±), without spin orbit effect SO, of the YS molecule [1] while the molecules YCl [13] and YI [1] have been studied by taking into consideration the SO effects. The present investigation is devoted to the prediction of the electronic structure of the YS molecule including the relativistic SO effects.. Computational approach The potential energy curves (PECs) of the lowest-lying electronic states of the molecule YS, taking into consideration the spin /$ - see front matter Ó 013 Elsevier B.V. All rights reserved.

2 110 A. Farhat et al. / Chemical Physics 1 (013) Fig. 1. Potential energy curves for 10 states X = 1/ of the molecule YS. orbit effect, has been investigated via CASSCF method. Multireference CI calculations (single and double excitations with Davidson corrections) were performed to determine the correlation effects. The entire CASSCF configuration space was used as the reference in the MRCI calculations. Yttrium is treated in an all-electron scheme, the 39 electrons of the yttrium atom are considered using a contracted Gaussian basis set from literature [15,16] for s, p, d functions and to which we added one f function (7s 0p 17d 1f/ 1s 7p 7d 1f). The exponent of this f-function was taken to be 0.6. The SO effects for Yttrium have been introduced via a semiempirical pseudo-potential which has been used previously for the SO calculations of YCl and YI molecules [13,1]. The sulfur species is treated as a system of 16 electrons by using the Rydberg basis set [17] for s, p, and d functions. The SO effects for sulfur atom have been neglected. The calculations were performed in two ways: (i) in the first the active space contains 3r(Y: 5s, 5p z,d 0 ), 1p(Y: 5p x,y,d ± ), and 1d(Y: d ± ) orbitals in the C v symmetry, this corresponds to 3 valence electrons distributed over 9 active molecular orbitals classified into the irreducible representations a 1,b 1,b and a in the following way: a 1,b 1,b,1a, noted [,,,1], while the doubly occupied orbital 1r(Y:s) of Yttrium was considered inactive in CAS-SCF calculations. (ii) In the second type of calculations the active space contains r(y: 5s, 5p z,d 0,S:3p z ), 3p(Y: 5p x,y,d ±1,S:3p x,y ), and 1d(Y: d ± ) orbitals, this corresponds to Fig.. Potential energy curves for nine states X = 1/ of the molecule YS.

3 A. Farhat et al. / Chemical Physics 1 (013) Fig. 3. Potential energy curves for 15 states X = 3/ of the molecule YS. seven valence electrons distributed over 1 active molecular orbitals classified into the irreducible representation [5,3,1] while the doubly occupied orbital 1r(Y:s) of Yttrium was considered inactive in CAS-SCF calculations. The energies for X (±) states have been obtained from the diagonalization of the matrix energy corresponding to a total hamiltonian, which is the sum of the electrostatic hamiltonian previously treated at the CASSCF/MRCI level and the SO pseudo-potential W PS SO. This matrix was built up on Fig.. Potential energy curves for the states X = 5/ (1-full lines), X = 7/ (8-dotted lines), X = 9/ (1 ) of the molecule YS.

4 11 A. Farhat et al. / Chemical Physics 1 (013) the basis of CASSCF wave functions, while diagonal matrix elements came from CI plus Davidson correction calculations. All the calculations have been performed via the computational chemistry program MOLPRO [18] taking advantage of the graphical user interface GABEDIT [19]. 3. Results and discussion The calculations have been performed for the 55 electronic states in the representation X ðþ. From these calculations we noticed the undulation of the potential energy curves for some higher excited electronic states for r > 3.0 Å. Boutalib and Gadea [0] proved that this undulation may be explained by the breaks down of the Born Oppenheimer approximation and it may be related to the personal character of the considered states. By calculating the diabatic curves they found that these undulations are amplified. The PECs for the symmetries X = 1/, 3/, 5/, 7/, 9/, in the range.1 Å 6 r Å, are drawn respectively in the Figs. 1. Within the considered internuclear distance range several crossings and avoided crossings have been recorded between the potential energy curves of different electronic states; their positions r AC, the corresponding parent states and the energy difference DE AC between the states (n + 1)X/(n)X at these points are displayed in Table 1. The composition in percentage of the X state-wave functions in terms of the K states, calculated at r =.3 Å, is presented in Table. For each state X there is a predominant component K with a contribution larger than 80% so that a main parent SK may be identified. Nevertheless, there are states for which a small but significant contribution of other K, than the dominant one is obtained. At the Internuclear distance point r =.3 Å an avoided crossing occurs between the () ½ state and the () ½ state (Fig. 1). In this region, the percentage composition of spin for the state () ½ change from 96.6% (1) P to 93% () P while the percentage composition of the () ½ state change from 100% () P to 96% (1) P. By fitting the calculated energy values of the different investigated electronic states to a polynomial in r around the minimum, the harmonic frequencies x e, the equilibrium internuclear distance r e, the rotational constants B e, and the transition energies with respect to the minimum energy of the ground states T e have been calculated. These values for the states X (±) are displayed in Table 3 along with the available experimental data in literature. The calculations of these constants were performed by using the two sets of valence electrons 3 and 7. If we compare the values of the spectroscopic constants obtained by these two different ways we find a small difference with: dt e < 100 cm 1, dr e < 0.1 Å, dx e <0cm 1, db e < 0.01 cm 1 (Table 3 in supplementary materials). Because of this small relative difference in the values calculated either by three valence electrons or seven valence electrons, we give in the present paper the tables calculated by Table 1 Positions of the avoided crossings r AC and the energy difference DE AC at these points with the corresponding avoided crossings and crossings of K states for X states of YS molecule. X (n +1)X/ nx r AC (Å) DE AC (cm 1 ) Avoided crossing of K states Crossings of K states 3/ / (1) P and () P / () P/(1) U 3/ () P and () P 1/ (1) D/1) P 1/ / (1) P and () P / () P/(1) U / () P and(3) P 3/ () R + /(1) P Table Composition of X-state wave functions of the molecule YS, in terms of K-states (in percentage) at r =.3 Å. X %(K-parent) X %(K-parent) (1)1/ 99.9% X R + (11)3/ ()1/ 96.6% (1) P; 3.36% () R + (1) 3/ 6.9% () P; 31.3% () P;6% (1) R ;0.39% (1) D 7.3% () P;.5% (1) R ;.5% (1) D;3.% () P 99% (5) P; 0.61% () D; 0.39% (3) D 99.8% (6) P; 0.16% (1) R + 100% () D (3)1/ 96.69% () R + ; 3.31% (1) P (13)3/ ()1/ 100% () P (1)3/ (5)1/ 100% (1) P (15)3/ (6)1/ 99.08% (3) P; 0.56% (1)5/ 99.99% (1) D (1) R + ; 0.1(3) R + ; 0.(1) P (7)1/ 98.87% (1) R + ; 0.38% ()5/ 99.8% (1) P; 0.16% (1) (1) P; 0.75% (3) P D (8)1/ 91.91% (1) D; 6.3% (1) D; (3)5/ 100% (1) U 1.75% () P; 0.0% (6) P (9)1/ 96.% (3) R + ; 1.1% () P; ()5/ 98.57% (1) U; 1.3() D 0.53% (5) P;.95% (1) R (10) 1/ 75.1% (1) R ; 3.% (6)5/ 97.7% () D; % () U; (7)5/ 96.33% () U; 0.9% (5)5/ 97.56% (1) D; 0.6% () P; () P; 1.5% (1) D 0.06% (1) U;.78% (1) D (11)1/ 18% (3) R + ; 1.16% () P; 9.95% () P; 30% (1) R 0.3% (1) D (1) 1/ 86% () P; 1% (1) R ;% (1) R () P; 1.7% () D (13) 1/ 97.69% (1) R ; 1.59% (3) R + ; 0.7% (5) P (8) 5/ 100% () P (9)5/ 99.97% (3) D; 0.03% (3) U (10)5/ (1)1/ 98.68% (5) P; 0.9% (1) R ; 0.% (3) R + (15)1/ 98.81% () R ; 0.6% 97.93% () D; 1.69% (5) P; 0.93% () R + (1) C; 0.38% (3) U (16)1/ 98.3% () R + ; 1.7% () R (11)5/ 97.7% (1) C, 0.% (3) U, 1.86% () D (17)1/ 98 % () R ; 1.78% () R + ; 0.% (5) P (1)5/ 99.7% (3) U; 0.6% (1) C; 0.13% () D (18)1/ 99.81% (6) P; 0.19(3) R + (1)7/ 98.19% (1) U; 1.81% (1) U (19)1/ 100% () D ()7/ 99.9% (1) U; 0.01% (1) U; 0.07% () U ()3/ 99.71% (1) P; 0.9% () D (3)7/ 99.5% (1) D; 0.55% () P (3)3/ 99.99% () P ()7/ 99.% () U; 0.38% (1) U; 0.% (1) R ()3/ 99.7% (1) P; 0.58% (5)7/ 99.6% () D; 0.38% (3) U (1) R + ; 0.15% (3) P (5)3/ 99.9% (1) U; 0.08% (1) D (6)7/ 96.03% (3) U; 3.63% (1) C (6)3/ 99.71% (3) P; 0.09% (7)7/ 96.03% (3) U; 3.63% (1) C (1) R + ; 0.% () P (7)3/ 97.93% (1) R + ; 0.7% (8)7/ 100% (3) U (3) P; 0.9% (1) R 0.15% (1) P (8)3/ 96.9% (1) D; 0.15% (1)9/ 97.88% (1) C,.08% (3) U (1) R ;.1% () P; 0.83% () D (9)3/ 98.56% () D; 0.99% () P; 0.5% (5) P; (10)3/ 91.% (1) R ; 7.0% () P; 0.79% (1) R + ; 0.77() P using three valence electrons. To the best of our knowledge, there are experimental values for the states A P 1/,A P 3/ and P ±1/ of YS molecule [,5,11]. The comparison between these values and those of the present work shows an excellent agreement. The transition energy T e and the rotational constant B e of the (1) P 1/ [] are very close to our calculated values with relative differences dt e /T e = 3.0% and db e /B e = 3.85% respectively. The comparison of our calculated value of r e for the (5) X = 1/ [(1) P] state with that of Steimle and Virgo [5] shows an excellent agreement with a relative difference dr e /r e =.71%. From the calculated energies, the SO splitting DE (E(X) E(X 0 )) evaluated at the well positions for the

5 A. Farhat et al. / Chemical Physics 1 (013) Table 3 Equilibrium internuclear distances re, transition energies Te, rotational constants B e and harmonic frequencies, x e, for X states of the molecule YS. (n)x[(k) S+1 K] T e (cm 1 ) dt e /T e r e (Å) dr e /r e B e (cm 1 ) db e /B e x e (cm 1 ) dx e /x e (%) (1)1/ [X R + ] 0.00 a.311 a a a.80 (DF) b 1.3% 61 (DF) b (Exp) b 1.% 9.7 d c 0.5% 508 c 1. ()1/ [(1) P] 1st Min 1908 a.356 a a a e 3.0% e 3.85% nd Min 1799 a.53 a a 60.1 a (3)1/[() R + ] 1105 a.370 a a 0.67 a d ()1/[() P] 1333 a.09 a a a (5)1/[(1) P] 1889 a.61 a.71% a 37.7 a b c (6)1/[(3) P] a.66 a a a (7)1/[(1) R + ] 0065 a.609 a a a (8)1/[(1) D] 0787 a.619 a a a (9)1/[(3) R + ] 1317 a.63 a a 5.6 a (10)1/[(1) R ] 118 a.619 a a a (11)1/[() P] 1755 a.66 a a a (1)1/[() P] 1 a.65 a a a (13)1/[(1) R ] 369 a.6 a a a (1)1/[(5) P] 905 a.616 a a 73.0 a (15)1/[() R ] 389 a.651 a a 39.8 a (16)1/[() R + ] 79 a.65 a a a (17)1/[() R ] 5679 a.558 a a a (18)1/[(6) P] 68 a.553 a a a (19)1/[() D] a.69 a a a (1)3/[(1) D] 1188 a.361 a a a ()3/[(1) P] 1st Min a.33 a a 53.8 a nd Min 1885 a.501 a a a (3)3/[() P] 133 a.09 a a a ()3/[(1) P] 1869 a.61 a a a (5)3/[(1) U] a.61 a a 9.76 a (6)3/[(3) P] 0088 a.636 a a 85.7 a (7)3/[(1) R + ] a.6 a a 00.5 a (8)3/[(1) D] 106 a.636 a a a (9)3/[() D] 10 a.615 a a a (10)3/[(1) R ] 1665 a.55 a a 09.3 a (11)3/[() P] 0 a.619 a a a (1) 3/ [() P] 53 a.599 a a a (13)3/[(5) P] 3073 a.75 a a a (1)3/[(6) P] 670 a.588 a a a (15)3/[() D] a.651 a a 6.55 a (1)5/[(1) D] 197 a.506 a a a ()5/[(1) P] 1875 a.61 a a a (3)5/[(1) U] 1819 a.68 a a a ()5/[(1) U] 181 a.60 a a a (5)5/[(1) D] 0857 a.616 a a 9.60 a (6)5/[() D] 1375 a.616 a a a (7)5/[() U] 1501 a.611 a a a (8)5/[() P] 1865 a.660 a a a (9)5/[(3) D] 6 a.69 a a a (10)5/[() D] a.65 a a 39.8 a (11)5/[(1) C] a.67 a a 3.53 a (1)5/[(3) U] 319 a.631 a a a (1)7/[(1) U] a.613 a a.57 a ()7/[(1) U] a.6 a a a (3)7/[(1) D] 116 a.66 a a a ()7/[() U] 1683 a.66 a a a (5)7/[() D] a.59 a a a (6)7/[(1) C] a.61 a a 33.7 a (8)7/[(3) U] 3150 a.59 a a a (1)9/[(1) C] a.60 a a a Note: DF(c); Density Functional calculations in Ref. (c), (v = 0) (c) results are for the zero vibrational level in Ref. c, Exp(c); Experimental results in Ref. (c). a First entry is for the values of the present work with 3 valence electrons. b Ref. [5]. c Ref. []. d Ref. [7]. e Ref. [9]. quartet states R ±, P, U, C, for which we were able to identify, are listed in Table and Fig. 5. The summation of the splitting in each of the considered is represented by DE tot. No comparison of these values with other results since they are calculated here for the first time. Knowledge of the components of the dipole moment l along the molecular fixed axis is essential for relative intensity predictions of pure rotational transitions [1]. Its utility is also in the construction of the molecular orbital based models of bonding and its variation with changes in geometry enters into the description of

6 11 A. Farhat et al. / Chemical Physics 1 (013) Table Calculation of the spin orbit splitting (in cm 1 ) at the energy minima for the quartet states of the molecule YS. Parent state s+1 K X X 0 DE = E(X) E(X 0 ) DE tot = R DE (1) P 1/ 3/ 0 6 3/ 5/ 6 (1) R + 1/ 3/ (1) D 1/ 3/ / 5/ 189 5/ 7/ 68 (1) R 1/ 3/ 6 6 () P 1/ 3/ / 5/ 388 () D 1/ 3/ / 5/ 355 5/ 7/ 9 (1) U 3/ 5/ / 7/ 65 (1) C 5/ 7/ / 9/ 71 9/ 11/ 113 light-matter interaction in resonant spectroscopy [1]. Recently, the availability of experimentally well determined values for l has become increasingly more important in the assessment of ab initio and semi empirical electronic structure calculations for molecules. The quantum mechanical operator is a simple sum of one-electron operator; its expectation value is sensitive to the nature of the least energetic and most chemically relevant valence electrons [1]. Accordingly, a comparison of the experimental and theoretical values of l is a sensitive test of the general predictive quality of the computational methodology. Yttrium monosulfide is a particularly apt candidate in this respect, since the metal ligand bond is expected to contain both covalent and ionic contributions to a significant extent [5]. The permanent dipole moment curves for the investigated states s+1 K ±, X of the YS molecule have been drawn in Figs. 6 8, within the internuclear distance range of.1 Å 6 r 6.8 Å. The calculated permanent dipole moments l, with three valence electrons, at the equilibrium internuclear distance of these states are given in Table 5 along with the available theoretical and experimental values in literature (the values of the dipole moments calculated using seven valence electrons are given in supplementary material). The comparison of our calculated values with those obtained experimentally by James and Simard [7] shows very good agreement with relative differences Dl/l =.6% and.3% respectively for the ground X R + and () R + states. The agreement is always good by comparing these values with those calculated by DFT techniques [] with relative differences of 3.5% and 1.8% for the ground X R + and (1) U states. The calculated values of dipole moment by Langhoff et al. [6] compared to our values shows a very good agreement for the states (1) D and (1) Q 1st Min with relative differences 0.5% and 3.9% respectively while this difference becomes larger for the ground Δ 5/ 197 (1) 1331 cm -1 3/ ΔE = 1685 (1) Δ cm -1 Δ 3/ / 1907 Δ 7/ 115 Δ 3/ 106 () 185 cm -1 3/ 53 (1) Δ 0876 cm -1 Δ 1/ 0857 ΔE = 338 1/ 1865 ΔE = 99 Δ 5/ / 175 Δ 1/ Δ 3/ () cm -1 3/ () 305 cm -1 Δ 5/ ΔE =600 1/ ΔE =389 Δ 7/ Φ 7/ / ) Φ 1855cm -1 ΔE =90 (3) cm -1 ΔE =1189 Φ 5/ / Fig. 5. Spin orbit splitting occurring in the electronic states of the YS molecule in cm 1.

7 A. Farhat et al. / Chemical Physics 1 (013) r(ǻ) () Σ + (3) Δ (3) Σ + () Δ μ(dbye) (X) (1) Δ -.5 Fig. 6. Permanent dipole moment curves for the states (1) D,X P+, () P+, () D, (3) P+, (3) D of the molecule YS. (6) Π (5) Π () Φ () Π (1) Φ (3) Π (3) Φ (1) Π () Π Fig. 7. Permanent dipole moment curves for the states (1) P, () P, (3) P, () P, (5) P, (6) P, (1) U, () U, (3) U of the molecule YS. Fig. 8. Permanent dipole moment curves for the spin orbit state (1) 1/, () 1/, () 1/, (5)5/, () 5/, () 7/ of the molecule YS.

8 116 A. Farhat et al. / Chemical Physics 1 (013) Table 5 The permanent dipole moment for the lowest 5 electronic states of YS at the equilibrium internuclear distance of the ground state r =.3 Å. State s+1 K l (Debye) dl=l (%) r (Å) X P a b DFc d 9.0 (1) D 9.73 a.363 (1) Q 1st Min d a e d 3.9 (1) Q nd Min.369 a.51 () Q.56 a.9 () P a b.3 (1) U a.615 (1) Q 3.5 DFc a.618 (1) U.157 a.633 (3) Q.103 a.68 (1) P +.50 a.68 (1) D.9 a.615 () U.019 a.63 () Q 0.85 a.66 () D 6.81 a.66 (1) P -.6 a.63 (3) P a.6 (1) P.535 a.630 () Q a.61 (5) Q 3.89 a.631 (3) D.7 a.661 () P.7 a.671 (6) Q 3.36 a.6 (1) C 5.16 a.66 () D a.660 (3) U a.68 a First entry is for the values of the present work with three valence electrons. b Ref. [10]. c Ref. [5]. d Ref. []. e Ref. [11]. states which is equal 9.0%. An excellent agreement is obtained for the state (1) Q 1st Min by comparing our value with that obtained experimentally by Steimle and Virgo [5] with relative difference of 0.5%. The canonical functions approach [ 6] have been used to calculate, for the ab initio potentials curves of the molecule YS, the vibrational energies E v, the rotational constants B v and the centrifugal distortion constants D v for the 5 bound states in the representation S+1 K (±) and 51 electronic states in the representation X (±). Then by using the calculated vibrational eigenvalues of energy and the potential energy curves of the investigated states, the turning points r min and r max for each vibrational level were determined. The values of these constants for six states in the representation s+1 K (±) and seven states in the representation X (±) are reported in Tables 6 9 (as example and given in supplementary materials). The remaining vibrational energy values for the other electronic states in YS are available upon request with the authors. The comparison of our results with the available data of James et al. [] in literature shows a very good agreement for the rotational constant B v with a relative difference db v /B v equal.1% and 3.9% for v =0of the X P+ and () P+ states respectively. The agreement is also good for the centrifugal distortion constant D v with relative difference.9% for v = 0 of the ground state. James et al. [] calculated also the eigenvalues of the states () P+ for the three vibrational levels v = 0, 1,. The comparison of these values with our results shows again a very good agreement with average relative difference.1%. The vibration rotation of the four states (1) D, (1) P, (5) Q, () D have not been investigated due to the lack in the literature of the extrapolation study of the potential energy curves for these states. Conclusion A theoretical investigation of the lowest states of YS molecule have been performed via CASSCF/MRCI calculations for 55 electronic states in the representation X (±) with spin orbit effect. To the best of our knowledge, the only X R +, B R, A P 1/, A P 3/ and P ±1/ states have been observed experimentally. The potential energy curves, the spectroscopic constants, the permanent dipole moment and the rovibrational data have been obtained for the investigated states where the comparison with the available experimental data shows very good agreement which may confirm the validity and the accuracy of the newly studied states. The investigation of these new valid excited electronic states with spin orbit effect may leads to the investigation of new experimental works on this molecule. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at References [1] J.M. Thompsen, L.M. Ziurys, Chem. Phys. Lett. 3 (001) 75. [] J. Jonsson, B. Lindgren, A.G. Taklif, Astron. Astrophys. 6 (1991) L67. [3] C.W. Bauschlicher, P. Maitre, Theor. Chim. Acta 90 (1995) 189. [] A.M. James, R. Fournier, B. Simard, M.D. Campbell, Can. J. 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