Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 124 (2014) 618–628

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Theoretical investigation of electronic states and spectroscopic properties of tellurium selenide molecule employing relativistic effective core potentials Surya Chattopadhyaya a,⇑, Abhijit Nath a, Kalyan Kumar Das b a b

Department of Physics, Tripura University, Suryamaninagar 799022, Tripura, India Department of Chemistry, Physical Chemistry Section, Jadavpur University, Kolkata 700032, India

h i g h l i g h t s

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

 Selection of basis sets and relativistic

Potential energy curves of low-lying bound K–S states of TeSe. 40000 3

3

3Π

4Π 3 − 3Σ

1

3

Te( Dg) + Se( Pg)

30000 3

CΠ 3 − BΣ Energy/cm-1

effective core potentials (RECP) of Te and Se atoms.  Computation of MRDCI calculations without and with considering effect of spin–orbit coupling.  Construction of potential energy curves without and with spin–orbit effect.  Computation of spectroscopic constants without and with spin– orbit effect.  Computation of transition probabilities of some transitions and dipole moments.

3

3

Te( Pg) + Se( Pg)

3

AΠ

20000

5

Π

3 +

Σ

1 -

3

cΣ 10000

Δ

1 +

bΣ

1

aΔ 0

3 -

XΣ

-5000 3

4

5

6

7

8

9

10

r/a0

a r t i c l e

i n f o

Article history: Received 24 June 2013 Received in revised form 17 December 2013 Accepted 10 January 2014 Available online 21 January 2014 Keywords: Tellurium selenide Configuration interaction Relativistic effective core potentials Spin–orbit coupling Potential energy curves Electronic states

a b s t r a c t Ab initio based relativistic configuration interaction calculations have been performed to study the electronic states and spectroscopic properties of tellurium selenide (TeSe) – the heaviest heteronuclear diatomic group 16–16 molecule. Potential energy curves of several spin-excluded (K–S) electronic states of TeSe have been constructed and spectroscopic constants of low-lying bound K–S states within 3.85 eV are reported in the first stage of calculations. The X3R, a1D and b1R+ are found as the ground, first excited and second excited state, respectively, at the K–S level and all these three states are mainly dominated by . . .p4p2 configuration. The computed ground state dissociation energy is in very good agreement with the experimental results. In the next stage of calculations, effects of spin–orbit coupling on the potential energy curves and spectroscopic properties of the species are investigated in details and compared with the existing experimental results. After inclusion of spin–orbit coupling the X31 R 0þ is found as the ground-state spin component of TeSe. The computed spin–orbit splitting between two components of X3R state is 1285 cm1. Also, significant amount of spin–orbit splitting are found between spin–orbit components (X-components) of several other excited states. Transition moments of some important spin-allowed and spin-forbidden transitions are calculated from configuration interaction 1 3  wave functions. The spin-allowed transition B3R–X3R and spin-forbidden transition b Rþ 0þ —X1 R0þ are found to be the strongest in their respective categories. Electric dipole moments of all the bound K–S states along with those of the two X-components of X3R are also calculated in the present study. Ó 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author. Tel.: +91 381 2375317 (O); fax: +91 381 2374802 (O). E-mail address: [email protected] (S. Chattopadhyaya). http://dx.doi.org/10.1016/j.saa.2014.01.032 1386-1425/Ó 2014 Elsevier B.V. All rights reserved.

S. Chattopadhyaya et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 124 (2014) 618–628

Introduction The tellurium selenide (TeSe) is a diatomic molecule containing atoms of group VIA and it is the heaviest heteronuclear diatomic group 16–16 molecule. It is one of the molecules belonging to the group VIA whose ground state 3R splits into two widely separated 3  components X31 R 0þ and X2 R1 by application of spin–orbit interaction. This intermetallic dimer is a photoconducting semimetal material and is widely used for preparation of optoelectronic devices such as liquid crystal light waves (LCLV) [1]. In recent years, researchers [2] are very much interested in preparation of nanowires, nanotubes and semiconductor heterojunction nanorods from this material as well as in their studies and applications. There are very few experimental spectroscopic studies [3–12] available for this species while no theoretical study has yet been performed to investigate the electronic states and spectroscopic properties of this molecule. The thermochemical data for the dissociation energy of few diatomic selenides (BiSe and TeSe) and tellurides (BiTe and SbTe) from the reaction M2(g) + Y2(g) = 2MY(g) was reported for the first time by Porter and Spencer [3] using mass spectrometric technique. In their study, M–Y systems were taken as Bi–Se, Bi–Te, Sb–Te and Te–Se. From their study, they have reported the ground-state dissociation energy for TeSe as 3.0 eV. Joshi and Sharma [4] have observed the violet degraded bands of this species in absorption in the quartz ultra-violet region 2520–2140 Å, classified most of the bands into two systems and found the vibrational constants such as transition energies (Te), vibrational frequencies (xe) and first anharmonicity constants (xexe) of these two systems. Ahmed and coworkers [5] have observed and analyzed the fluorescence spectra of gaseous, isotopically pure samples of TeSe by exciting it with five lines of argon ion laser. They photographed the D–X systems of 128Te78Se in absorption at moderate resolution and confirmed that the ground state of this molecule is mainly represented by . . .r2p4p2 (3R) configuration. They have analyzed twenty-one fluorescence series for B0+–X0+, A0+–X0+, B1–X1 c1–X1 and B0+–X1 systems of 128Te78Se, 128Te80Se, 130Te78Se, and 130 Te80Se isotopologues and reported molecular constants such as Te, xe and xexe for ground-state spin components (X10+ and X21) as well as for the excited states components A0+, B0+, B1 and c1 of these species. Their study has revealed the energy separation between the ground-state spin components of 128Te78Se as 1547.2 cm1. Study of laser induced fluorescence spectra of both natural and isotopically enriched samples of Te2, TeS, SeS and TeSe in their vapor phase and argon matrices have also been reported by Ahmed and Nixon [6]. They have observed nine band systems for each of the four molecules. They have reported molecular constants such as Te, xe and xexe for ground and some low-lying excited states of 130Te2, 130Te32S, 78Se32S and 128Te80Se in both their vapor phases and argon matrices. From their study, the energy splitting between the ground state spin components of 128Te80Se in its vapor phase is found to be almost similar to that of 128Te78Se reported by Ahmed and coworkers [5]. Drowart and Smoes [7] have derived the thermodynamic properties of TeSe from Knudsen-cell mass spectrometric experiments. From their study, they have reported the ground-state dissociation energy of TeSe as 3.0398 eV. Winter and coworkers [8] have observed near-infrared emissions of the b0+–X10+, X21 band systems of TeSe in a discharge flow system. From the analysis of the spectra, they have reported Te = 8794 ± 5 cm1 and xe = 294 ± 3 cm1 for b0+ state. They have also reported the energy splitting between the ground state spin components as 1235 ± 5 cm1. Fink and coworkers [9] have observed the rotationally resolved IR-chemiluminescence spectrum of TeSe in its gaseous state. They have recorded the 0–0 band of the b0+–X10+ subsystem at very high resolution using separated 130Te and 80Se isotopes and carried

619

out their rotational analysis. They have reported several molecular constants, mainly re, xe and xexe, of both the X10+ and b0+ states for the species 130Te80Se from the rotational analysis of the 0–0 band. The Fourier transform infrared magneto-optical spectrum of the Se2, Te2 and TeSe at a temperature 4 K in rare gas matrices have been studied by Li and coworkers [10]. They have observed the spectrum of the zero-field X1–X0+ band of TeSe molecule in raregas matrices at 4 K temperature with 0, 2 and 4 Tesla magnetic field strengths. From their study, they have and reported the energy splitting between the ground state spin components of TeSe as 1243 ± 2 cm1, 1248 ± 2 cm1 and 1234 ± 2 cm1 in krypton (Kr), argon (Ar) and neon (Ne) matrices, respectively, and compared them with the corresponding gas-phase value, reported by Winter and coworkers [8]. Banser and coworkers [11] have designed a new twin laserablation source and shown that the combination of supersonic jet Fourier transform microwave (FTMW) spectroscopy and the laser-ablation is a very powerful tool for research on intermetallic species. With this combination of techniques, they have investigated the spectroscopic parameters, structural information, internuclear potential, electronic structure and details of the chemical bond of TeSe from high-resolution multi-isotopologue pure rotational spectra. They have reported vibrational ground-state constants such as equilibrium bond length (re) and ground-state dissociation energy (De), vibrational frequency (xe) and first anharmonicity constant (xexe), of the main and most abundant isotopologue 130Te80Se considering Morse potential function. In a subsequent article [12], Banser and coworkers have analyzed the pure rotational spectrum of TeSe in its X0+ electronic ground state by a global multi-isotopologue Dunhum fit. From their analysis, they have derived the rotational and vibrational parameters for 43 TeSe isotopologues. They have reported isotopologue independent ground-state molecular constants such as equilibrium bond length (re) and ground-state dissociation energy (De) of TeSe using Morse potential function. They have also reported the fundamental vibrational frequencies (xe) and first anharmonicity constants (xexe) of 128Te78Se, 128Te80Se and 130Te80Se isotopologues. In this article, we have provided a detailed theoretical study of the electronic states and spectroscopic properties of TeSe using ab initio based configuration interaction (CI) methodology which includes relativistic effects and spin–orbit coupling. Potential energy curves of the ground and low-lying excited spin-excluded (K–S) and spin-included (X) states of TeSe are constructed. Spectroscopic parameters in both the cases are calculated and compared with the existing experimental data. Transition dipole moments of some important dipole-allowed and spin forbidden transitions are computed and from these data we have calculated radiative lifetimes of some excited states at the lowest three vibrational levels. In the present article, we have also computed the z-component of electric dipole moments (lz) of all the bound K–S states as well as two X-components (X = 0+, 1) of the ground state as a function of bond distance and reported their value (lz)eq at respective equilibrium of all these states.

Computational details As both the tellurium (Te) and selenium (Se) atoms are fairly heavy, the use of relativistic effective core potentials (RECP) is appropriate in the present configuration interaction (CI) calculations. The 4d105s25p4 electrons of Te are kept in valence space and allowed to take part in CI calculations while its 36 core electrons, described by 1s22s22p63s23p63d104s24p6, are substituted by semi-core type RECPs of LaJohn and coworkers [13]. The

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1s22s22p63s23p6 core electrons of Se atom are substituted by semicore type RECPs of Pacios and Christiansen [14] while the 3d104s24p4 electrons are retained in the valance space. Thus, for TeSe molecule, the total number of active electrons in the valence space is 32 only. The (3s3p4d) primitive Gaussian basis set of tellurium atom of LaJohn et al. [13] is enhanced with one diffuse s function of exponent 0:015 a2 0 ; a set of diffuse p functions of exponent 0:037 a2 0 ; and a set of d polarization functions of exponent 0:17 a2 0 : Exponents of the additional s, p and d basis functions are taken from Giri et al. [15]. We have also included a set of 10 component f polarization functions with exponent 2:5 a2 from 0 Setzer et al. [16] so that the final uncontracted AO basis set of Te atom becomes (4s4p5d1f). Similarly, the (3s3p4d) Gaussian basis set for Se atom, taken from Hurley et al. [17], is augmented with a couple of diffuse s functions of exponents 0.047 and 0:017 a2 0 ; a couple of p functions of exponents 0.037 and 0:011 a2 0 ; a pair 2 of d functions of exponents 0:489 a2 0 and 0:144 a0 ; and a set of 10 component f functions of exponent 0:4 a2 : The exponents of 0 these additional basis functions are taken from Balasubramanian and Liao [18]. First two d functions with larger exponents are contracted. Therefore, in the present calculations, the resulting AO basis set of Se atom becomes (5s5p6d1f)/[5s5p5d1f]. The calculations have been performed in the C2v subgroup of the C1v group keeping TeSe along the +z axis with Te atom at the origin of the Cartesian coordinate system. Self-consistent field (SCF) molecular orbital calculations are carried out for the . . .p4p2 3  R state under Börn-Oppenheimer approximation at each bond distance in the range 3.0–12.0 a0. As a result, a set of 106 optimized and symmetry adapted SCF-MOs is generated and these SCF-MOs are treated as one electron basis for generation of configurations in the CI calculations. The 4d10 inner d-electrons of Te atom and 3d10 inner d-electrons of Se atom are localized and hence do not participate in the chemical bonding. Therefore, the MOs, in which these d electrons are localized, are kept frozen in the CI space. Thus the number of active electrons of TeSe in the present calculations reduces to 12. In present study, we have focused our attention only on the low-lying electronic states of TeSe. Observing the orbital energies of the 106 generated SCF-MOs, we have found that the MOs having energies more than 10 a.u. leads to very high-lying states. Further analysis revealed that the probability of excitations of electrons from the lower occupied MOs to vacant higher orbitals having energies up to 10 a.u. are highly probable and contributes significantly to the CI calculations while the same to the vacant higher orbitals having energies above 10 a.u. are very less and the contribution of these excitations to the CI calculations are negligible. So, we have allowed 74 SCF-MOs having orbital energy up to 10 a.u. to take part in the CI calculations and discarded the 32 others having energies more than 10 a.u. The multireference singles and doubles configuration interaction (MRDCI) methodology with perturbative correction and energy extrapolation techniques of Buenker and co-workers [19–26] has been employed in the present study. The calculations of K–S states are carried out in the first step by introducing the relativistic massvelocity correction in the Hamiltonian but discarding the spin–orbit coupling. Details of these MRDCI calculations at the equilibrium bond length (re = 4.5 a0) of the ground state of TeSe are given in Table 1. The leading electronic configurations for the lowest roots of each symmetry are also listed in Table 1. For each spin multiplicity and spatial symmetry, a set of few reference configurations (2–5 nos.) are initially chosen as dominant configurations. Single and double excitations are carried out from these configurations which, in turn, generate more configurations. We have collected only the configurations having high value of square of CI-coefficient (c2) and included them in the set. By repeating the process for several times and including all the configurations up to c2 = 0.01, we have constructed finally a set of reference configurations (Nref) for each

spin multiplicity and spatial symmetry. In the present study, the configuration spaces are generated from 54 to 166 reference configurations depending on the K–S symmetries as shown in Table 1. The number of roots in each symmetry and multiplicity is selected to be large enough to take into proper account the effects of higherlying states in the final spin–orbit CI treatment for the states of major interest in the present study. For each of the 3A1 and 3A2 symmetries, eight roots are calculated while six roots are considered for 3 B1/3B2. For singlet and quintet symmetries, the number of roots treated lies between three and five (Table 1). All single and double excitations are carried out from the selected set of main reference configurations. As a result of such excitations, a large number of configurations, about several millions, are generated for a given irreducible representation. For the symmetries with 6–8 roots, the generated configuration space is of the order of (28–38)  106 symmetry adapted functions (SAFs), while the corresponding order of the generated configuration space is (12–23)  106 SAFs for symmetries with 3–5 roots (Table 1). However, a configuration selection method is used to reduce the size of CI-space drastically. A configuration selection threshold of 0.75 micro-hartree is used to restrict the largest number of the selected configurations below 2  105. Table 1 shows that at the above threshold, 59,000– 130,000 SAFs are included in the final secular equations. The sums of squares of CI-coefficients for each root always remain above 0.90 as shown in Table 1. In our present calculations, we have used the Table-direct CI version of MRDCI code [26]. The energy extrapolation method is used to estimate the CI energies at zero-threshold. Multireference analogue of Davidson’s correction [27] has been introduced in our calculations to incorporate the neglected contributions of the higher order excitations from these reference configurations. Although effects of some higher order excitations are still missing, the calculations provide a good estimate of full-CI energies. Spectroscopic and transition properties of the K–S states of TeSe are determined from the computed full-CI energies and wave functions. In the subsequent calculations, the spin–orbit coupling is incorporated into the calculations through a two-step variational method, the details of which are discussed elsewhere [28]. All 18 K–S states, correlating with the lowest limit Te(3Pg) + Se(3Pg), are included in the spin–orbit CI treatment, but the nine triplet K–S states, correlating with the second dissociation channel Te(1Dg) + Se(3Pg), are not incorporated in the spin–orbit CI treatment. If these nine states correlating with second channel were included then after spin–orbit mixing they would lead to some very high-lying X states. But practically, calculations of such very high-lying X states are beyond the capability of the MRDCI code used here. According to the MRDCI methodology, the estimated full-CI energies of the K–S CI calculations are placed in the diagonals of the spin-included Hamiltonian matrix, while the off-diagonals are calculated from the K–S CI wave functions and RECP based spin–orbit operators [13,14]. Though initially the K–S full-CI energies are present in the diagonal elements of the SO matrix, but after its diagonalization, the effects of spin–orbit operators are incorporated in the diagonal elements of the SO matrix. To compute spin–orbit matrix elements, the Wigner–Eckart theorem and spin-projection methods are employed. After incorporating spin orbit coupling, the X-states are classified into A1, A2 and B1/B2 representations of the C22V and these representations consist of all X-components (0+, 0, 1, 2, 3, 4) of the low-lying states of the molecule. Diagonalization of the spin-included blocks provides energies and wave functions of spin–orbit states. It should be noted that in the two-step procedure for the inclusion of spin– orbit interaction [28], the resulting spin–orbit CI wave functions may be easily analyzed in terms of K–S eigenfunctions. Potential energy curves for both the spin-excluded (K–S) and spin-included (X) electronic states of TeSe are constructed and

621

S. Chattopadhyaya et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 124 (2014) 618–628 Table 1 Details of the MRDCI calculations of TeSe at equilibrium of the ground state.a C2v

Nref/Nroot

SAFtotal/SAFselected

1

93/5

19,526,607/63,850

1

54/5

1

C1v 1

Leading configuration 4

Rc2p

1 D 11R+ 21D 21R+ 31D

2

. . .p p . . .p4p2 . . .p3p3 . . .p3p3 . . .p2p4

0.962 0.955 0.927 0.911 0.903

13,538,495/81,130

11D 11R 21D 21R 31D

. . .p4p2 . . .p3p3 . . .p3p3 . . .p4p2 . . .p2p4

0.958 0.967 0.935 0.914 0.908

58/5

22,603,832/86,883

11P 21P 31P 41P 51P

. . .p4p . . .p4p3 . . .p3p2 . . .p3p2 . . .p3p2

0.927 0.922 0.924 0.929 0.918

3

166/8

37,453,603/129,986

13D 13R+ 23D 23R+ 33D 33R+ 43D 43R+

. . .p3p3 . . .p3p3 . . .p4p2 . . .p4p2 . . .p3p3 . . .p4p2 . . .p3p3 . . .p4p2

0.964 0.967 0.933 0.919 0.922 0.937 0.902 0.901

3

131/8

32,152,277/118,531

13R 13D 23R 33R 23D 43R 53R 33D

. . .p4p2 . . .p3p3 . . .p4p2 . . .p3p3 . . .p4p2 . . .p2p4 . . .p4p2 . . .p3p3

0.983 0.959 0.937 0.903 0.925 0.912 0.901 0.906

3

82/6

28,017,768/97,123

13P 23P 33P 43P 53P 63P

. . .p3p2 . . .p4p . . .p4p3 . . .p3p2 . . .p3p2 . . .p3p2

0.926 0.922 0.903 0.929 0.908 0.901

5

91/4

17,137,604/701,191

15D 15R+ 25R+ 25D

. . .p3p3 . . .p3p3 . . .p2p2 . . .p4p2

0.916 0.920 0.905 0.917

5

84/3

15,579,520/59,731

15R 15D 25R

. . .p4p2 . . .p3p3 . . .p4p2

0.921 0.908 0.904

5

90/3

12,961,301/91,368

15P 25P 35P

. . .p3p2 . . .p2p3 . . .p3p2

0.933 0.916 0.905

A1

A2

B1/1B2

A1

A2

B1/3B2

A1

A2

B1/5B2

a The number of selected SAFs and the Rc2p values over the reference configurations are presented for r = 4.5 a0. Nref and Nroot refer to the number of initially chosen reference configurations and number of roots treated, respectively. SAFtotal and SAFselected denote the total number of generated and the number of selected SAFs, respectively.

spectroscopic constants of the bound K–S and X states are estimated by fitting the curves into polynomials. Employing Numerov–Cooley numerical integration procedure [29], onedimensional nuclear Schrödinger equations are solved to obtain the corresponding vibrational energies and wave functions. Subsequently, these are used to calculate transition dipole moments for a pair of vibrational functions in a particular transition. Einstein spontaneous emission coefficients and the transition probabilities are calculated in the following way. The Einstein spontaneous emission coefficients Av 0 v 00 (in s1) between vibrational levels (v0 ) of the upper state and vibrational levels (v00 ) of the lower electronic states are written as

h i Av 0 v 00 ¼ g e0 e00 2:1416  1010 ðDEÞ3 Sv 0 v 00 where

  2 Sv 0 v 00 ¼  vv 00 ðrÞRe0 e00 ðrÞvv 0 ðrÞ 

and DE is the transition energy value in a.u. The term Sv 0 v 00 is obtained from a polynomial fit to the set of data for the electronic transition moment Re0 e00 and vibrational wave functions vv ðrÞ generated for the respective pairs of electronic states. The term g e0 e00 is the degeneracy factor. The radiative lifetime (s) of an upper electronic state for each vibrational level are obtained by summing the Einstein spontaneous emission coefficients for each of its downward transitions and inverting them, i.e.

s¼P

1 v 00 Av 0 v 00

It is worthwhile to be mentioned in this context that we have not used any standard software package or code for various curve fittings and radiative life time calculations. For these purposes, we have carried our computations by using the computer programs which were developed by us i.e. these are our in-house codes. In the present work, using MRDCI wave functions, we have also

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computed z-component of dipole moments (lz) of all the bound K–S states as well as those of two X-components of the ground state as a function of internuclear distance by employing expectation value approach.

Results and discussion Potential energy curves and spectroscopic constants of low-lying K–S states Eighteen low-lying singlet, triplet and quintet states of the K–S symmetry of TeSe correlate with the lowest dissociation limit Te(3Pg) + Se(3Pg). The first excited state (1Dg) of Te atom combines with the ground state (3Pg) of the Se atom to form the second asymptote and it correlates with nine triplet K–S states of R+, R(2), P(3), D(2) and U symmetries. The third dissociation limit Te(3Pg) + Se(1Dg) also correlates with nine triplets of the same symmetries as those correlate with the second limit. The relative energies of the lowest three dissociation limits are computed and compared with the observed J-averaged (J = total angular momentum of each energy level) atomic energy levels [31] in Table 2. The computed relative energy of the second and third dissociation limit are in excellent agreement with the experimental data [31]. Potential energy curves of all the singlet, triplet and quintet states correlating with the lowest dissociation limit are displayed in Fig. 1a–c. Several potential energy curves of triplet excited states, correlate with the second dissociation limit, are also shown in Fig. 1b. There are 12 bound K–S states while the remaining states are either repulsive or predissociative. Spectroscopic constants, such as transition energy (Te), equilibrium bond length (re), and equilibrium vibrational frequency (xe) of the ground state and eleven low-lying bound excited K–S states within 3.85 eV of energy are presented in Table 3. It is should be noted in this context that no experimentally or other theoretically estimated molecular constants for these K–S states are yet available in literature for comparison. The ground state (X3R), first excited state (a1D) and the second excited state (b1R+) in the K–S level are mainly characterized by the same electronic configuration . . .p4p2 (c2  0.86) at the potential minima. Another configuration . . .p3p3, arising from the single excitation p ? p, also contributes considerably (c2  0.08) at the potential minima of these three states. Analyzing the molecular orbitals (MOs) in the Franck–Condon (FC) region of all the three states, it is found that p is bonding MO while p MO is anti-bonding in nature. From the analysis, it is also found that in FC region of the above three states, p MO is mainly localized on px/y atomic orbitals of Se atom while p MO is mainly concentrated on px/y atomic orbitals of Te atom and these observations are in accordance with the outcome from electronegativity consideration. In the present study, the ground-state dissociation energy (De), computed without incorporating spin–orbit coupling is 3.1 eV which is in very good agreement with the D00 value of 3.0 eV reported by Porter and Spencer [3] from thermochemical data. Drowart and Smoes [7] have reported the dissociation energy of the

Table 2 Dissociation correlation between the molecular states and atomic states of TeSe. Atomic states (Te + Se) 3

Te(1Dg) + Se(3Pg) Te(3Pg) + Se(1Dg) Ref. [31].

Expt.a

(K–S states) 3

Te( Pg) + Se( Pg)

a

Relative energy (cm1)

Molecular states

1

+

1

1

1

R (2), R , P(2), D 3 + R (2), 3R,3P(2),3D 5 + R (2), 5R,5P(2),5D 3 + 3  R , R (2),3P(3),3D(2), 3U 3 + 3  R , R (2),3P(3),3D(2), 3U

Calc.

0

0

8975 9107

9095 9172

ground state as 3.0398 eV (293.3 kJ/mol) from Knudsen-cell mass spectrometric experiments and it is also in excellent agreement with our calculated value. Our calculated value and other two experimental values [3,7] of dissociation energy are about 25% lower than the dissociation energy of 4.0825 eV (393.9 kJ/mol), derived by Banser and coworkers [11,12] considering Morse potential function. Because of the heavier mass of the molecule, the spin– orbit interaction is expected to have considerable effect on the dissociation energy of the ground state. The first excited (a1D) state has a strongly bound potential energy curve with dissociation energy of 2.55 eV. The transition energy of the second excited state (b1R+) is 2810 cm1 larger than that of the first excited state. Its strongly bound potential energy curve has dissociation energy of 2.2 eV. The potential minimum of c1R state exists above b1R+ state. The dissociation energy of this state is about 1.46 eV. At the potential minima, this state is almost entirely dominated by the singly excited (p ? p) electronic configuration . . .p3p3 (c2  0.94). The next two higher excited states are 3D and 3R+. They are nearly degenerate with Te(3R+) > Te(3D). Dissociation energy of the 3D is 1.29 eV while it is 1.23 eV for 3R+. Minimum in the potential energy curve of these two states have been located at a distance very close to 2.65 Å and the xe for these two states are around 220 cm1. Both the states, at their equilibrium, are mainly characterized by the . . .p3p3 configuration and the contribution of this configuration to the wave functions of 3D and 3R+ are 93.9% and 94.5%, respectively. The next excited state is 5P and it correlates with the groundstate dissociation limit. From Fig. 1c, it is clear that 5P is a very weakly bound state with dissociation energy only 0.52 eV. At the equilibrium, the dominating electronic configuration to the wave function of this state is . . .p3p2 (c2 = 0.87). The equilibrium bond length of this state is the longest among all the bound K–S states reported in the present study. All other quintet states, namely, 5  R , 25P, 5D, 5R+ and 25R+ are repulsive in nature as shown in Fig. 1c and correlate with the lowest dissociation limit. The next excited state is designated by A3P and it is the lowest root of 3P symmetry. This state has a shallow potential well and dissociation energy of this state is 0.49 eV only. The dominant configurations at the equilibrium of this state are represented by . . .p3p2 (56.6%) and . . .p2p3 (33.6%). The next spectroscopically important excited K–S state is 23R and it is designated as B3R. The B3R state undergoes a symmetry allowed and fairly strong transition to the ground state X3R, details of which will be discussed later. This state dissociates to the second limit Te(1Dg) + Se(3Pg). Dissociation energy of this state in the present study is 1.51 eV. At equilibrium, this state is represented mainly by . . .p4p2 (66.5%) and p3p3 (24.8%) configurations. Looking into Fig. 1b, it is clear that near the bond distance 5.3 a0, an avoided crossing is observed between the curves of C3P (23P) and 33P. The existence of the avoided crossing is confirmed by analyzing the compositions of CI wave functions of the 23P and 33P states at different bond lengths around r = 5.3 a0. From the analyses, it is found that at bond distances longer than 5.3 a0 the 33P is dominated by . . .p4 p (c2 > 0.90) which is the dominant configuration of the 23P state at shorter bond lengths. Therefore, we have to consider the diabatic potential energy curve of 23P to compute the spectroscopic parameters of the C3P state. At the potential minimum, the dominant configuration representing the C3P is . . .p4p (c2 = 0.91). It is also to be noted in this context that the diabatic consideration makes the potential energy curve of 33P repulsive in nature and it correlates to the lowest dissociation limit, as shown in Fig. 1b. As shown in Fig. 1b, the potential energy curves of both the 43P and 33R dissociate to the second limit. Both the two states are

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(a) 50000

Λ-S Singlets

(b) 50000

Λ-S Triplets

3

2Δ

(c) 50000

Λ-S Quintets

3

1 +

2Σ

40000

3Δ 3 5Π 3 − 3Σ 3 4Π

40000

5 +

Σ

40000

1

5

2Π

Π 3

3

Te( Pg) + Se( Pg)

20000 1 -

cΣ

3Π

30000

3 −

BΣ

3

AΠ 3 +

Σ

10000

5 -

Σ

3

Π

3 -

3 −

XΣ

XΣ

1

0

3 -

XΣ

5

3

Te( Pg) + Se( Pg)

5

20000

10000

aΔ

4

3

Te( Pg) + Se( Pg)

3

5 +

30000

2Σ

Δ

1 +

3

2Σ

3

CΠ

20000

2Π

3

Te( Dg) + Se( Pg)

3

bΣ

0

3 +

Energy/cm-1

1

Energy/cm-1

Energy/cm-1

30000

10000

5

Δ

1

3

6

7

8

9

10

0

3

4

5

r/a0

6

7

8

9

10

3

4

5

r/a0

6

7

8

9

10

r/a0

Fig. 1. Computed potential energy curves of low-lying K–S states of TeSe for (a) singlet (b) triplet and (c) quintet spin multiplicities.

Table 3 Spectroscopic constants of K–S states of TeSe. State 3



X R a1D b1R+ c1R 3 D 3

R+ P A3P B3R C3P 43P 33R

5

Table 4 Dissociation correlation between X states of TeSe.

Te (cm1)

re (Å)

xe (cm1)

(lz)eq (D)

0 4422 7232 13,254 14,563 15,104 20,782 21,015 22,115 28,212 30,172 30,998

2.378 2.401 2.426 2.657 2.646 2.651 3.047 2.732 2.707 2.627 2.941 3.028

320 303 285 223 222 219 167 161 193 169 209 173

1.685 1.304 1.158 0.999 1.043 1.037 1.071 2.167 3.245 2.017 1.181 2.232

X states

Potential energy curves and spectroscopic constants of low-lying X states Spin orbit coupling has been incorporated in the molecular Hamiltonian through spin–orbit operators of both Te and Se atoms in the next stage of our calculations. These spin–orbit operators, derived from RECPs, are also available in literatures [13,14]. The ground-state dissociation limit Te(3Pg) + Se(3Pg) splits into nine asymptotes as a result of inclusion of spin–orbit effect. These nine asymptotes correlate with fifty X states of 0+, 0, 1, 2, 3 and 4 symmetries within 7500 cm1 of energy and we allow all of them to interact in the spin–orbit CI calculations. Table 4 displays the observed [31] and computed splitting among these nine asymptotes and their correlations with the fifty X states of TeSe. The calculated results are in very good agreement with the observed data. Computed potential energy curves of some of the low-lying X states of 0+, 0, 1, 2 and 3 symmetries are displayed in Fig. 2a–d. Our computed spectroscopic constants (Te, re and xe) of 18 bound X states within 23,750 cm1 of energy are listed and compared with available experimental data in Table 5. Table 5 also contains the composition (%) of K–S states at the respective equilibrium (re)

Relative energy (cm1) Expt.

+

+

+



4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 0 , 0 , 0 , 0 , 0 3, 2, 2, 1, 1, 1, 0+, 0, 0 2, 1, 0+ 2, 1, 0+ 3, 2, 2, 1, 1, 1, 0+, 0, 0 1, 0 2, 1, 1, 0+, 0+, 0 0+ 1, 0 a

very weakly bound having dissociation energies only 0.51 eV and 0.41 eV, respectively. At the potential minima, the 43P is represented mainly by . . .p3p2 (c2 = 0.91) while the 33R is characterized by mainly by . . .p3p3 (c2 = 0.89) electronic configuration. The transition energy of the 33R state is larger than that of 43P by 826 cm1.

Atomic states (Te + Se)

a

3

3

0

3

3

1989.49 2534.35 4707 4751 6696.49 6740.49 7241.35 7285.35

P2 + P2

P2 + P1 P2 + 3P0 3 P0 + 3 P2 3 P1 + 3P2 3 P0 + 3 P1 3 P1 + 3P1 3 P0 + 3 P0 3 P1+3P0 3

Calc. 0 1854 2809 4433 4550 6462 6546 7362 7437

Ref. [31].

of all the X states. The effect of spin–orbit coupling does not modify greatly the general appearance of the potential energy curves of TeSe obtained in the K–S level. The main distinctions are simply the result of splitting the pure spin-states into their Xcomponents. The ground state (X3R) has two spin components X31 R 0þ and 3  3  X32 R 1 with X1 R0þ lying below the other. Therefore, the X1 R0þ is found as the ground-state spin component of TeSe after incorporation of spin orbit coupling. The two spin components of X3R are separated by 1285 cm1. The experimental fine structure splitting between the ground state spin components, reported from laser induced fluorescence experiments by Ahmed and coworkers [5] for 128 Te78Se in its gas phase and by Ahmed and Nixon [6] for 128Te80Se in its vapor phase, are about 262 cm1 larger than our theoretically estimated value. Winter and coworkers [8] have reported the fine structure splitting between the ground state spin components from their experimental study of near-infrared emission spectrum of the b0+–X10+, X21 band systems and it is only about 50 cm1 smaller than our computed result. Also our computed energy splitting between the ground-state spin components is about 37– 50 cm1 larger than those reported by Li and coworkers [10] from their study of Fourier transform infrared magnetooptical spectra of TeSe in rare-gas matrices. From Table 5 it is also clear that at the 3  potential minima of X31 R is perturbed 0þ component, the X R slightly by b1R+, while the minima of the other component X32 R 1 is characterized by almost pure X3R state.

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(a) 40000

+

Ω=0

(b) 40000

30000

Energy/cm-1

Energy/cm-1

30000

-

Ω=0

20000 3

A1 Π0

3 -

B1 Σ 0

+

10000

+

3 +

5

Σ

Π0

-

3

-

A2 Π0

0

-

1 −

cΣ

-

0

10000

1 +

bΣ

20000

+

0

3 -

X1 Σ 0

+

0

0

3 -

X1 Σ 0

+

3

4

5

6

7

8

9

10

3

4

5

r/a0

7

8

9

10

r/a0

(c) 40000

Ω = 1, 3

(d) 40000

Ω=2

30000

Energy/cm-1

30000

Energy/cm-1

6

3

Δ1

20000

3 -

B2 Σ 1

3

A3 Π1

5

Π3

3

Δ3

3

A4 Π2

20000

3

Δ2

3 +

Σ

10000

1

10000

1

a Δ2

3 -

X2 Σ 1

0

0

3 -

X1 Σ 0

3 -

X1 Σ 0

+

+

3

4

5

6

7

8

9

10

r/a0

3

4

5

6

7

8

9

10

r/a0

Fig. 2. Computed potential energy curves of low-lying X states of TeSe for (a) X = 0+ (b) X = 0 (c) X = 1, 3 and (d) X = 2.

The computed re and xe of both the spin components of X3R remain almost unchanged after the inclusion of spin–orbit coupling. Our computed re for the ground-state component X31 R 0þ is only 0.013 Å longer than the experimentally observed result for 128 Te78Se [30]. Fink and coworkers [9] have reported re for this component from their study of rotationally resolved IR-chemiluminescence spectrum of 130Te80Se in its gaseous state and it is about 0.024 Å shorter than the value computed in our present work. They have also reported [9] an equilibrium bond length for this component from the mean of re values for the homonuclear diatomic molecules Te2 and Se2 and it is about 0.022 Å shorter than the result computed in our present study. Banser and coworkers [11,12] have reported re as about 2.359 Å which is about 0.026 Å shorter than the value calculated in the present work. The computed xe for this component is in excellent agreement with the experimental data

reported by Fink and coworkers [9] for 130Te80Se, Joshi and Sharma [4] for 128Te78Se, Ahmed and coworkers [5] for 128Te78Se, Ahmed and Nixon [6] for 128Te80Se and Banser and coworkers [11,12] for 128 Te78Se, 128Te80Se and 130Te80Se as shown in Table 5. Because of the heavier mass of the molecule, the spin–orbit interaction is found to have considerable effect on the dissociation energy of the ground-state component X31 R 0þ : After the inclusion of spin orbit coupling, the computed dissociation energy for this component becomes 0.25 eV (24.12 kJ/mol) smaller than that of X3R obtained in the K–S level. The computed re for the other component X32 R 1 is only 0.011 Å longer than the experimental data [30] while our calculated xe for this component is in well agreement with the observed values [5,6]. After the application of spin orbit coupling, the transition energy (Te) for the spin–orbit state a1D2 becomes 1147 cm1 larger

S. Chattopadhyaya et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 124 (2014) 618–628

625

Table 5 Spectroscopic constants of X states of TeSe. State

Te (cm1) Calc.

X31 R 0þ

0

X32 R 1

1285

xe (cm1)

re (Å) Expt.

Calc.

Expt.

Calc.

Expt.

0

2.385

2.372a 2.361b* 2.364b# 2.359c,d

316

1547.2f

2.383

2.372a

322

313.08b* 318e 316.24f 313.8g* 309.71g# 313h* 314h# 316h$ 317.39f 314.9g* 311.27g#

2.405 2.427

2.389b*

299 283

1547g* 1235 ± 5i 1243.2 ± 2j* 1248.5 ± 2j# 1234.8 ± 2j$ a1D2 1

b Rþ 0þ c1 R 0 3 D3 3 D2

5569 9717

Composition at re (%)

8794 ± 5i

289.86b* 294 ± 3i

X3R (88), b1R+ (12)

X3R (99)

a1D (99) b1R+ (87), X3R (12) c1R (78), 3R+ (22)

12,479

2.651

221

3

12,822 15,960 16,473

2.648 2.639 2.656

221 221 217

3

18,573

2.659

215

18,920 20,741

2.642 2.733

227 183

D (98) D (98) 3 + R (99) 3 + R (78), c1R (21) 3 D (98) A3P (72), B3R (21), 5P (6)

Rþ 1 Rþ 0 3 D1 A31 P0þ

22,210f 22,000g* 20,477g#

3 3

A32 P0

21,054

2.731

180

A3P (91), 5R (4), 5P (2)

A33 P1 A34 P2 5 P3 5 P0 B31 R 0þ

21,530

2.734

169

A3P (85), B3R (7), 1P (5)

21,710

2.731

173

A3P (74), 5P (24)

21,984 22,117 23,553

2.951 2.949 2.662

5

2.647a

194 189 195

189f

P (99) P (89), A3P (8) B3R (66), A3P (21), 1P (11)

B32 R 1

23,719

2.683

2.69a

198

191.5f

B3R (73), 5P (17), A3P (8)

23,393 a 23,487 f 23,596a 23,692f

5

a

Ref. [30]. Ref. [9]. b# Mean of the values for the homonuclear diatomic molecules Te2 and Se2; Ref. [9]. c Morse potential parameter for main isotopologue 130Te80Se; Ref. [11]. d Isotopologue independent Morse potential parameter for TeSe; Ref. [12]. e Ref. [4]. f Ref. [5]. g* Values for 128Te80Se in vapor; Ref. [6]. g# Values for 128Te80Se in Ar matrix; Ref. [6]. h* Value for 130Te80Se; Ref. [11,12]. h# Value for 128Te80Se; Ref. [11,12]. h$ Values for 128Te78Se; Ref. [11,12]. i Ref. [8]. j* Values from Fourier transform magnetooptical spectra in Kr matrix; Ref. [10]. j# Values from Fourier transform magnetooptical spectra in Ar matrix; Ref. [10]. j$ Values from Fourier transform magnetooptical spectra in Ne matrix; Ref. [10]. b*

than that of its K–S counterpart a1D. From Tables 3 and 5, it is clear that the computed re and xe for a1D state remain almost unchanged after application of spin–orbit interaction. The a1D2 component is not perturbed due to absence of any nearby X = 2 component and hence it remains almost as a pure a1D in the Franck–Condon region. No experimental or other theoretical data for this component is available for comparison. 1 The next higher excited state is b Rþ 0þ : The effect of spin orbit interaction enhances the transition energy of the b1R+ significantly by 2485 cm1, while the changes in re and xe of this state are negligible. In the Franck–Condon region, this state is perturbed slightly by X3R. There are few experimental spectroscopic data 1 available for b Rþ 0þ state. The experimental Te value for this state, reported by Winter and coworkers [8], is about 923 cm1 smaller than that computed in our present study. The computed re for this state is about 0.037 Å longer than the experimental data reported

by Fink and coworkers [9]. Our calculated xe differs from the experimental values [8,9] by about 7–11 cm1 only. 1 þ The spin–orbit state c1 R 0 lies above b R0þ and the energy gap 1 between b and c state is 2762 cm . In the Franck–Condon region, this state is perturbed significantly by X = 0 component of the 3R+ state. Incorporation of spin–orbit interaction lowers the transition energy of c1R state by 775 cm1. The computed re and xe for 1  c1 R 0 are found to be very close to those of c R state in absence of spin–orbit coupling. We cannot compare these results due to unavailability of any kind of data for this state in literature. After incorporation of spin–orbit coupling, the 3D state splits into three spin-components X = 1, 2 and 3. The transition energies of these components are arranged in inverted order i.e. Te(3D3) < Te(3D2) < Te(3D1). These components of 3D are not perturbed due to absence of any respective nearby X = 1, 2 and 3 components. Therefore, all these three spin-components remain as almost pure

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3

D at their potential minima. The components are nearly equally spaced and the spin–orbit splitting between the components of 3 D are considerably large. The fine structure splitting between the 3D3 and 3D2 components is 3138 cm1 while it is 2960 cm1 between the 3D2 and 3D1. From Tables 3 and 5, it is found that the transition energy of 3D3 is 1741 cm1 smaller while that of 3 D2 and 3D1 are 1397 cm1 and 4357 cm1, respectively, larger than that of 3D calculated in K–S level. The equilibrium bond lengths (re) and the vibrational frequencies (xe) of the 3D and its three spin–orbit components are almost similar. Due to unavailability of any kind of data in literature, we are not in a position to compare our computed results for the X-components of 3D. It is interesting to be noted in this context that the two spin– orbit components (X = 1 and 0) of 3R state are sandwiched between the 3D2 and 3D1 components. Both the spin components 3 þ R1 and 3 Rþ0 exhibit bound potential energy curve. At equilibrium, 3 + the 3 Rþ 1 is characterized by almost pure R while it is perturbed significantly by c1R at the potential minima of 3 Rþ 0 An appreciable amount of splitting is observed between two spin components of 3  R . The transition energy of the 3 Rþ1 is lower than that of 3 Rþ0 by 2100 cm1. After the application of spin–orbit coupling the transi3 þ tion energies of 3 Rþ 1 and R0 components are found to be increased by 1369 cm1 and 3469 cm1, respectively, compared to that of their K–S counterpart. It is also found that the differences between the computed re and xe values of 3R and its spin–orbit components are very small. Due to unavailability of any experimental or other theoretical result, we could not compare our results for two spin components of 3R. It is also to be mentioned that in the K–S level, the transition energy of the 5P was lower than that of A3P. But, due to the effect of spin–orbit interaction, enhancement in transition energies in case of spin–orbit components 5P is more appreciable compared to the changes in Te of the X components of A3P. As a result, the transition energies of all the X components of A3P are now become lower than that of X-components of the 5P as shown in Table 5. The transition energies of four spin–orbit components (X = 0+, 0, 1 and 2) of A3P state are arranged in a regular order       i.e. T e A31 P0þ < T e ðA32 P0 Þ < T e A33 P1 < T e A34 P2 . The potential energy curves of all the four spin-components of A3P show shallow potential well. These X components are closely spaced within the energy spread of 969 cm1. At all the potential minima of X = 0+, 0, 1 and 2 of A3P, this state is perturbed by several other states as shown in Table 5. The transition energy of X = 0+ component is 274 cm1 smaller while that of X = 0, 1 and 2 components of A3P are 39 cm1, 515 cm1 and 695 cm1, respectively, larger than that of A3P obtained in the K–S level. The equilibrium bond lengths of A3P in the K–S level and all of its spin-components of are almost similar while the vibrational frequencies of spin-components of A3P are enhanced by 8–22 cm1 after the application of spin–orbit coupling. The A31 P0þ component is important from the experimental point of view. Only the transition energy for A31 P0þ component is experimentally measured and reported in a couple of articles [5,6], but we cannot find any experimental data regarding re and xe for this component. The experimentally observed transition energy for this component, reported by Ahmed and coworkers [5], is 1469 cm1 larger than the Te computed in our present work. Also, our calculated Te for A31 P0þ is 1259 cm1 lower than that reported by Ahmed and Nixon [6] from their study of laser induced fluorescence spectra of TeSe in its vapor phase while it is only 264 cm1 larger than that reported by the same authors [6] when they made the same study in Argon matrix. Among the six components of the 5P state, we are able to present the spectroscopic constants for only two components 5P3 and

P0 in Table 5. Due to very strong spin–orbit mixing of 5 P0 , 5P1,1 and 5P2 with number of respective nearby X = 0+, 1 and 2 components, we cannot fit the potential energy curves of 5 P0þ and 5P1,1 and 5P2 into polynomial to compute the spectroscopic constants 5

for these components and hence they are absent in Table 5. Analyzing compositions at several points throughout the Franck–Condon region of the curve of 5P3, it is found that this component remains unaffected due to absence of any nearby component with X = 3. Therefore, at the potential minima, this spin component remains as a pure 5P state. At the equilibrium of the 5 P0 component, the 5P state is perturbed slightly by A3P. The transition energy of 5 P0 is found to be slightly greater than that of 5P3 and the energy gap between these two components is only 133 cm1. After the application of spin–orbit interaction, it is found that the transition energies of 5P3 and 5 P0 are 1202 cm1 and 1335 cm1, respectively, larger compared to that of 5P calculated in the K–S level. Also, the equilibrium bond lengths of 5P3 and 5 P0 are found to be 0.096 Å and 0.098 Å, respectively, smaller while their vibrational frequencies are found to be 27 cm1 and 22 cm1, respectively, larger than that of 5P in absence of spin–orbit interaction. No experimental or other theoretical data for 5P3 and 5 P0 are available for comparison. 3  The B3R has two spin-components B31 R 0þ and B2 R1 with     3  3  T e B2 R1 > T e B1 R0þ . The computed energy gap between these two components is only 166 cm1. Both the two components are weakly bound having shallow potential well. From Table 5, it is clear that at re of both the spin components of B3R, this state is coupled strongly with A3P and 5P states. From Tables 3 and 5, it is clear that after the incorporation of spin–orbit effect, the Te for 3  1 B31 R and 1604 cm1, 0þ and B2 R1 components become 1438 cm respectively, larger than that of B3R calculated in absence of spin–orbit interaction. Moreover, application of the spin orbit effect reduce the bond lengths of two components by 0.045 Å and 0.024 Å, respectively, while negligible amount of changes in xe are observed between B3R and its two spin components. Spectro3  þ and B R scopic parameters of both the B31 R components are ob0  2 1   3  and T e B32 R are in served experimentally. The T e B1 R0þ 1

excellent agreement with the experimental data [30,5]. Our com    puted re B31 R and r e B32 R are larger than the experimental 0þ 1 data [30] by 0.015 Å and 0.007 Å only, respectively. Also the differences between the calculated and the observed [5] vibrational frequencies for these two components are very small (6 cm1). Dipole moments, transition moments and radiative lifetimes Employing the expectation value approach, we have computed z-component of dipole moments (lz) of twelve low lying bound K–S states at different bond distances using the computed CI wave functions. All the computed dipole moments tends to zero value as r ? 1 indicating that the atomic transitions are dipole forbidden and atoms are neutral. At the respective equilibrium bond distances of all these bound K–S states, we have also computed the z-component of dipole moment [(lz)eq] and presented in Table 3. All the computed dipole moments appear negative and the negative sign of dipole moments indicate Te+–Se polarity. The computed (lz)eq ground state is 1.685 D while it is maximum for B3R state in absence of any spin–orbit mixing. After the inclusion of spin orbit coupling, the calculated (lz)eq of the ground-state component X31 R 0þ remains almost unchanged (1.689 D) while that of X32 R is reduced slightly to 1.674 D. 1 Using estimated CI energies and wave functions, we have computed transition moments of some dipole-allowed and spin-forbidden transitions of TeSe. The transition dipole moment

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S. Chattopadhyaya et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 124 (2014) 618–628 1

comparatively larger transition moments compared to b Rþ 0þ – X32 R 1 so that the former is comparatively stronger than the later 1 one and partial lifetimes of the b Rþ 0þ state are of the order of microseconds and milliseconds, respectively. In case of another spin forbidden transition a1D2–X32 R 1 ; the computed transition moments are found to be small enough with computed partial lifetimes of a1D2 of the order of milliseconds. It should be noted in this connection that we are not in a position to compare the calculated dipole moments and lifetimes due to unavailability of any such kind of experimental or other theoretical data.

1.5

3 -

3 -

B Σ -X Σ

Transition moment/ea0

1.0

0.5 3

3 -

1 +

b Σ 0 -X1 Σ 0

3 -

A Π-X Σ

+

Conclusion

+

0.0 1

3

3 -

1 +

b Σ 0 -X2 Σ 1

3 -

a Δ2-X2 Σ 1

3 -

C Π-X Σ

+

-0.5 3

4

5

6

7

r/a0 Fig. 3. Transition moments of some dipole-allowed and spin-forbidden transitions of TeSe as a function of internuclear distance.

functions of these transitions are plotted as a function of internuclear distance in Fig. 3. In absence of any spin–orbit interaction, three triplets, namely A3P, B3R and C3P undergo symmetry-allowed transitions to the ground state X3R. We have also studied transition probabilities of some spin-forbidden transitions from some 0+ and 2 components to the spin–orbit components of the X3R. The partial radiative lifetimes of the excited states involved in all these transitions at lowest three vibrational levels (v0 = 0, 1 and 2) as well as their total radiative lifetimes at the lowest vibrational level (v0 = 0) are shown in Table 6. In the Franck–Condon region, the transition B3R–X3R has sufficiently large transition moments (>1.0 ea0) compared to others as shown in Fig. 3. Therefore, the B–X transition is found to have sufficient intensities with partial lifetimes of the order of microseconds. In the Franck–Condon region, although the transition moments of the transition A3P–X3R are larger than those of the C3P–X3R, the Franck–Condon overlap factor for the former transition is smaller due to the larger equilibrium bond length of its upper state (A3P). So, the later transition is comparatively stronger than the former one. It is worthwhile to be mentioned in this context that the transition between the ground state components i.e. X2–X1 is found to be extremely weak and the radiative lifetime of the X2 state are of the order of 1 seconds. The b Rþ 0þ component is found to undergo spin-forbidden transitions to both the components X10+ and X21 of the ground 1 3  state. It has been found that the transition b Rþ 0þ –X1 R0þ has

Potential energy curves and spectroscopic features of the low-lying electronic states of tellurium selenide have been studied theoretically by using ab initio based configuration interaction (CI) calculations which include relativistic effective core potentials and large Gaussian basis sets of both the Te and Se atoms. The computed relative energies of the lowest three dissociation limits are in excellent agreement with the observed data. Potential energy curves of several states correlating with the lowest two dissociation limits are constructed. There are only 12 bound K–S states. In the K–S level, the ground state (X3R), first excited state (a1D) and the second excited state (b1R+) are mainly represented by . . .p4p2 electronic configuration. We have reported the transition energies (Te), equilibrium bond lengths (re), vibrational frequencies (xe) of all the 12 bound K–S states within 3.85 eV of energy and their dissociation energies. Except ground-state dissociation energy, we cannot compare our results in the K–S level due to unavailability of any experimental as well as other theoretical data. The computed ground-state dissociation energy is slightly larger than the experimentally observed data and it is within the accuracy of the MRDCI methodology. The overall effects of the spin–orbit coupling do not significantly change the shapes of potential energy curves as well as re and xe of most of the spin–orbit states. The main differences are simply the result of significant amount of splitting the pure spin-states into their X components. After inclusion of spin–orbit coupling, X31 R 0þ is found as ground-state spin component. The effect of spin orbit coupling reduces the calculated dissociation energy of the ground state component by about 0.25 eV. The computed fine structure splitting of the ground state of TeSe is 1285 cm1 and it is very close to the results obtained from several experimental studies. A large number of spin–orbit states for this species have been studied here and very good agreements between our theoretically calculated and experimentally observed spectroscopic parameters have been found. Potential energy curves of several X states show some avoided crossings. We have also computed the z-component of dipole moments (lz) of all the 12 bound K–S states as a function of internuclear distance and reported the same at their respective equilibrium [(lz)eq]. The negative sign of all the dipole moments ensures Te+–Se polarity. It is also to be noted that the differences between

Table 6 Radiative lifetimes (s) of some excited states at the lowest three vibrational levels of TeSe. Numbers in the parentheses refer to the powers to the base 10. Transition

Total lifetime of the upper state at v0 = 0

Partial lifetime of the upper state at 0

0

0

v =0

v =1

v =2

4.04(3) 11.01(6) 18.04(5) 5.71

9.88(3) 8.7(6) 24.15(5) 7.37

17.62(3) 13.6(6) 47.54(5) 9.62

s(A3P) = 4.04(3) s(B3R) = 11.01(6) s(C3P) = 18.04(5)

1

27.21(6)

35.32(6)

34.83(6)

s b1 Rþ0þ ¼ 27:18ð6Þ

–X32 R b Rþ 1 0þ

1

26.76(3)

23.22(3)

24.11(3)

a1 D2 —X32 R 1

21.31(3)

17.84(3)

14.67(3)

A3P–X3R B3R–X3R C3P–X3R 3  X32 R 1 –X1 R0þ

–X31 R b Rþ 0þ 0þ









s X32 R1 ¼ 5:71

s(a1D2) = 21.31(3)

628

S. Chattopadhyaya et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 124 (2014) 618–628

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