Ab Initio Study of the Lowest-Lying Electronic States of LuCl Molecules

Nov 12, 2012 - Faculty of Engineering III, Lebanese University, Campus Hadath, Lebanon. J. Phys. Chem. A , 2012, 116 (49), pp 12123–12128. DOI: 10.1...
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Ab Initio Study of the Lowest-Lying Electronic States of LuCl Molecules Y. Hamade,† H. Bazzi,‡ J. Sidawi,‡ F. Taher,*,‡ and Y. Monteil† †

Multimaterials and Interfaces Laboratory, LMI, University of Claude Bernard Lyon-1, Claude Bertollet Bldg, 43 Bd of 11 November, 69622 Villeurbanne, France ‡ Faculty of Engineering III, Lebanese University, Campus Hadath, Lebanon ABSTRACT: By using the CASSCF/MRCI methods, the theoretical electronic structure of the LuCl molecule has been investigated. These methods have been performed for 20 singlet and triplet electronic states in the representation 2s+1Λ(±). Calculated potential energy curves (PECs) are also displayed. Spectroscopic constants including the harmonic vibrational wavenumber ωe (cm−1), the relative electronic energy Te (cm−1) referred to the ground state, and the equilibrium internuclear distance Re (Å) have been predicted for all of the singlet and triplet electronic states situated below 43 000 cm−1. Spin−orbit effects have also been taken into consideration and calculated for the lowest-lying electronic states in the representation Ω(±).

state of the three isotopes 175Lu35Cl, 175Lu37Cl, and 176Lu35Cl. The measurements were made using the Fourier transform spectrometer (FTMW) type Flygare−Balle8 in the microwave region. Theoretically, S. Cooke et al.7 conducted a similar study to that performed on LuF, using both the DFT and the SAOP (statistical average of orbital potentials) methods.9 The centrifugal distortion constants, the internuclear distance at equilibrium, the dissociation energy, and the hyperfine constants for the ground state X 1Σ+ were determined. In 2007, A. Haiduk et al. determined the nuclear electric quadruple moment in these molecules. 10 In this paper, the theoretical LuCl electronic structure is investigated using the ab initio methods CASSCF (complete active space-self consistent field) and MRCI (multireference interaction of configuration) simple and double excitation with Davidson correction. On the basis of our previous work on the lutetium monofluoride,11 we compare the lowest-lying electronic structures obtained for LuF with the theoretically studied electronic structure of LuCl by analogy. Our objective is to carry out the theoretical calculations of all of the low-lying electronic structures of the LuCl molecule situated below 43 000 cm−1. In this study, 20 electronic states 2s+1Λ(±) (neglecting spin−orbit effect) are predicted with their PECs and their spectroscopic constants. Thirty three spin orbit components, in the representation Ω(±), that correspond to the first 15 electronic states are also investigated. The spin−orbit coupling (SOC) effects for the five remaining highest electronic states are not calculated because they are correlated to other highest states not considered in our calculations.

1. INTRODUCTION Knowledge of the spectroscopy of the lutetium monohalides LuX is significant in many areas, particularly in astrophysics.1,2 These molecules are also of special interest in catalysis and hightemperature chemistry.3,4 The electronic structure of LuX is challenging due to the correlation effect caused by the open d shell connected with the 4f orbital shell.5 Also, it is important to understand the role played by the d electrons in chemical bonds in these molecules. The lutetium monohalides LuX have been the subject of few experimental and theoretical studies. These kinds of molecules are produced experimentally in the gas phase at high temperatures. However, it has been very challenging to use furnaces that can withstand high temperatures for sufficient time to produce these molecules and observe their spectra. For this reason and because the f and open d shells in lanthanides make the spectra complex and dense, the theoretical studies will be a useful tool for the experimentalists to identify the observed electronic transition bands. The experimental work of Kramer6 has reported observations of the LuCl spectra at medium resolution in the visible region. The vibrational analysis of these spectra has led to the first spectroscopic information obtained from two electronic transition bands called systems A and B, without identifying the involved electronic states. Both transition systems A and B are red degraded, that is, ωe of the lower state is larger than that of the upper state. The system A was located at Te′ − Te″ = 20 844.9 ± 2.1 cm−1, with ωe′ = 323 ± 2.2 cm−1 for the highest state and ωe″ = 350.6 ± 2.6 cm−1 for the lowest state. The system B was located at T′e − T″e = 21 828.1 ± 2.2 cm−1, with ω′e = 369.2 ± 2.4 cm−1 for the highest state and ωe″ = 386.4 ± 256 cm−1 for the lowest state. Later in 2005, S. Cooke et al.7 studied the pure rotational spectrum of this molecule in its ground electronic state X1Σ+. This spectrum was reported for the ground electronic vibrational © 2012 American Chemical Society

Received: June 2, 2012 Revised: November 12, 2012 Published: November 12, 2012 12123

dx.doi.org/10.1021/jp305409e | J. Phys. Chem. A 2012, 116, 12123−12128

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Table 1. Theoretical Energy Levels of Lu+ Using ECP28 Lu+

term

without spin−orbit effect

1

S

3

D

1

D

3

P

energy (cm−1) 0.00a 0.00b 12 810.21a 12 993.25b 17 332.58a 17 276.36b 29 406.94a 30 651.94b

Lu+ with spin− orbit effect

term 1

S

energy (cm−1)

J

0.00a

0

3

D

1 2 3

1

2

3

0

P

1 2

Lu (2D) + Cl (2P) Lu (2P) + Cl (2P) Lu+ (1S) + Cl− (1S) Lu (4F) + Cl (2P) Lu (4F) + Cl (2P) Lu (2D) + Cl (2P) Lu (4D) + Cl (2P) Lu (4P) + Cl (2P) Lu (2S) + Cl (2P) Lu (2D) + Cl (2P) Lu (4P) + Cl (2P) Lu (2G) + Cl (2P)

1490 6657 14 624 20 382 20 662 22 021 22 686 24 292 24 420 24 928 25 011 26 921

Lu+ (3D) + Cl−(1S) Lu+ (1D) + Cl−(1S) Lu+ (3P) + Cl−(1S) Lu+ (3F) + Cl−(1S)

27 086 31 984 43 154 45 540

ωe (cm−1)

ωe χ e (cm−1)

2.38 2.37 2.38

(1)3Δ (1)3Π (1)3Σ+ (1)1Δ (1)1Π

2.42 2.43 2.43 2.44 2.45

(2)1Σ+

2.43

(2)3Π (1)3Φ (2)3Δ (2)1Π (1) 3Σ− (3)3Π (2)1Δ (2)3Σ− (3)1Σ+ (1)1Γ (1)1Φ (4)3Π (3)1Π

2.44 2.45 2.45 2.43 2.46 2.46 2.42 2.47 2.43 2.44 2.46 2.47 2.45

0 0 0 0 13 223 14 573 15 831 17 491 19 803 20 844e 22 210 21 828g 29 178 32 510 33 272 34 491 33 777 33 876 37 341 38 843 39 420 39 636 41 471 42 196 42 415

348 337 329 350−387 323 318 315 319 306 323f 307 369.3h 331 307 305 332 300 301 321 302 315 311 303 294 309

1.07 1.05 3.01 0.78−1.76 0.9 1.1 1.2 0.9 1.0 1.1 1.7 1.8 0.9 0.9 0.8 1.0 0.8 0.9 1.1 1.0 1.2 1.0 0.9 1.1 1.0

c d

Table 2. Correlation between Atomic States and Molecular States in LuCl energy averaged (cm−1)

Te (cm−1)

b

0.00b 11 796.24a 11 214.21b 12 435.32a 12 113.65b 14 199.08a 14 674.74b 17 332.58a 17 649.75b 27 264.40a 26 029.24b 28 503.16a 28 044.93b 32 453.26a 32 059.01b

Experimental values for Lu+ levels.19 bOur theoretical values

atomic states

Re (Å)

1 +a

states XΣ

D

a

Table 3. Theoretical Spectroscopic Constants, by (MRCI+Q), in the Case of 22 Valence Electrons, Of the Electronic States of 175Lu35Cl

molecular states 21,3Σ+, 31,3Π, 21,3Δ, 11,3Φ, 11,3Σ− 21,3Σ+, 21,3Π, 11,3Δ, 11,3Σ− 11Σ+ 13,5Σ+, 33,5Π, 33,5Δ, 23,5Φ, 13,5Γ, 13,5Σ− 13,5Σ+, 33,5Π, 33,5Δ, 23,5Φ, 13,5Γ, 13,5Σ− 11,3Σ+, 31,3Π, 21,3Δ, 11,3Φ, 21,3Σ− 13,5Σ+, 23,5Σ−, 33,5Π, 23,5Δ, 13,5Φ 13,5Σ+, 23,5Σ−, 23,5Π, 13,5Δ 11,3Σ+, 11,3Π 11,3Σ+, 31,3Π, 21,3Δ, 11,3Φ, 21,3Σ− 13,5Σ+, 23,5Σ−, 23,5Π, 13,5Δ 11,3Σ+, 11,3Σ+, 31,3Π, 31,3Δ, 31,3Φ, 2 1,3Γ, 11,3Λ = 5 13Σ+, 13Π, 13Δ 11Σ+, 11Π, 11Δ 13Σ+, 13Π 13Σ−, 13Π, 13Δ, 13Φ

a

Theoretical values (MRCI+Q) given by our calculations. bExperimental values given by S. A. Cooke et al.7 cCalculation by a DFT method given by S. A. Cooke et al.7 dInterval of experimental values given by J. Kramer.6 eTe′ − Te″ value of system A given by J. Kramer.6 f ́ ωe value of system A given by J. Kramer.6 gT′e − T″e value of system B given by J. Kramer.6 hωe′ value of system B given by J. Kramer.6

Table 4. Theoretical Spectroscopic Constants, by (MRCI+Q), in the Case of 16 Valence Electrons of the Electronic States of 175Lu35Cl states

Re (Å)

Te (cm−1)

ωe (cm−1)

ωe χ e (cm−1)

XΣ (1)3Δ (1)3Π (1)3Σ+ (1)1Δ (1)1Π (2)1Σ+ (2)3Π (1)3Φ (2)3Δ (2)1Π (1) 3Σ− (3)3Π (2)1Δ (2)3Σ− (3)1Σ+ (1)1Γ (1)1Φ (4)3Π (3)1Π

2.388 2.425 2.431 2.431 2.439 2.455 2.425 2.449 2.449 2.447 2.432 2.459 2.463 2.424 2.472 2.431 2.439 2.459 2.467 2.450

0.00 13 792 14 922 16 005 17 895 20 322 22 314 29 011 33 426 34 057 34 734 34 747 34 769 38 006 39 855 40 241 40 676 42 354 42 675 42 934

338.25 317.38 314.45 311.86 313.63 302.57 308.55 322.09 303.66 303.41 325.81 296.44 297.56 313.89 296.68 308.76 305.52 298.59 292.49 303.02

1.096 1.039 1.025 1.089 1.091 0.911 1.025 0.957 0.885 0.933 1.239 0.843 0.883 1.081 0.836 1.015 0.959 0.834 0.913 0.929

1 +

2. COMPUTATIONAL APPROACH For the lutetium atom (Lu), the basis set is treated as a system of the ECP method, choosing 28 inner electrons in the ECP28MWB,12 including the spin−orbit pseudopotential for determining the spin− orbit splitting of the multiplet correlated states. The chlorine atom basis set is an all-electrons scheme (17s, 12p, 5d, 4f)/ [6s, 5p, 3d, 2f], developed by Widmark et al.13 Among the 60 electrons of the LuCl, 38 inner electrons are frozen, so that 22 valence electrons are explicitly considered in the treatment. The active space contains nine active orbitals corresponding to 3σ[Lu:6s,6p0,5d0], 4π[Lu: 6p±1, 5d±1], and 2δ[Lu: 5d±2] distributed as 4a1, 2b1, 2b2, and 1a2, noted [4221] in the irreducible representations of the C2v. The valence occupied orbitals of chlorine are considered as inactive at the CASSCF level of calculations. Energy calculations for the low-lying electronic states of the LuCl employ molecular orbitals that are determined using the state-averaged CASSCF and the MRCI methods. The MRCI 12124

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Figure 1. PECs for the lowest singlet states including the ground state X1Σ+ of 175Lu35Cl.

Figure 3. (a) The electronic transition dipole moments from singlet states to the ground state (in au) at Re = 2.38 Å. The stronger transitions are denoted by the bolder lines. (b) The electronic transition dipole moments between the upper singlet excited states (in au) at Re = 2.38 Å. The stronger transitions are denoted by the bolder lines.

calculated using the ECP28 basis set for Lu with the spin−orbit effect. Table 1 lists these values and compares them with the experimental results.19 The comparison shows the accuracy of our results, which reflects the adequacy of our basis set choice. Table 2 presents the increasing averaged energy order of all atomic states located between 1490 and 45540 cm−1 at dissociation16,17,19−22 and all of the possible corresponding molecular electronic states associated with these atomic states. Around the equilibrium internuclear distance, LuCl is considered to have ionic behavior. Hence, the molecular states are highly correlated to the first lowest levels of Lu+ + Cl− (1S). The prediction of the lowest-lying electronic states of the LuCl molecule has been obtained by calculating energies in a range of internuclear distances R varying from 1.80 to 3.63 Å. The theoretical prediction included the ground state, which is of type X1Σ+, and the lowest excited states as follows: (2,3)1Σ+, (1,2,3)1Π, (1,2,3,4)3Π, (1)3Σ+, (1,2)1Δ, (1,2)3Δ, (1,2)3Σ−, (1)1,3Φ, and (1)1Γ, which are all located below 43 000 cm−1. The obtained spectroscopic constants for these electronic states, using (MRCI + Davidson correction) with 22 valence electrons, are listed in Table 3. The spectroscopic constants obtained at the case of 16 valence electrons are also given in Table 4. The case of 16 valence electrons is not considered for the SOC calculations because the f orbital has an important role in the spin−orbit interaction effect in the electronic states. In the literature, precise data are provided only for the ground state X1Σ+.7 By comparing our results with the limited experimental and theoretical values,7 an error of less than 1% on the internuclear distance at equilibrium is found. This value is close to that found by S. A. Cooke calculated using the DFT method.7

Figure 2. PECs for the lowest triplet states of 175Lu35Cl.

(single and double excitations) method including the Davidson correction14 is performed taking into account the correlation effects for the 22 valence electrons. These calculations are carried out by using the computational chemistry program MOLPRO.15 As a first step in our calculation, 44 electrons are frozen, including the f shell of lutetium, to keep the 16 remaining electrons as valence electrons in the computational treatment. These calculations are performed for few points only around the internuclear distance of X1Σ+. However, in the active natural orbitals, the f shell is placed as the highest valence shell in Lu+. For this reason, we decide to take 22 valence electrons, including the 14 electrons of the f shell, as free electrons.

3. RESULTS AND DISCUSSION The LuCl molecule is assumed to be ionic Lu+Cl−, as in the case of all Lu+X− (X = F, Cl, Br, and I). The ionization potential (IP) of Lu is of 5.43 eV,16 and the electronic affinity (EA) of Cl is of 3.6135 eV.17 The dissociation energy De of LuCl is at 31 800 cm−1, and its IP is at 60 500 cm−1.18 The Lu+ energy levels have been 12125

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Figure 4. The electronic transition dipole moments between triplet electronic states (in au) at Re = 2.38 Å. The stronger transitions are denoted by the bolder lines.

Table 5. Composition of Ω-State Wave Functions in Terms of S−Λ Terms (in percentage) (1)0 +X1Σ+ (1)1 [(1)3Δ] (1)2 [(1)3Δ] (1)0− [(1)3Π] (2)0+ [(1)3Π] (2)1 (1)3 (1)3Δ (2)2 [(1)3Π] (3)1 (2)0− [(1)3Σ+] (3)2 [(1)1Δ] (4)1 [(1)1Π] (3)0+ [(2)1Σ+] (3)0− (2)3Π (4)0+ [(2)3Π] (5)1 [(2)3Π] (4)2 [(1)3Φ] (5)2 [(2)3Π] (6)1 (5)0+ (2)3 [(1)3Φ] (6)2 (7)1 (4)0− (3)3Π (1)4 [(1)3Φ] (8)1 (3)3 [(2)3Δ] (7)2 (6)0+ (9)1 (8)2 [(2)1Δ] (7)0+ [(2)3Σ−] (10)1 [(2)3Σ−]

100% X1Σ+ 92% (1)3Δ 85% (1)3Δ 76% (1)3Π 97% (1)3Π 59% (1)3Π 100% (1)3Δ 87% (1)3Π 64% (1)3Σ+ 76% (1)3Σ+ 91% (1)1Δ 94% (1)1Π 95% (2)1Σ+ 100% (2)3Π 99% (2)3Π 90% (2)3Π 79% (1)3Φ 98% (2)3Π 55% (2)3Δ 55% (3)3Π 81% (1)3Φ 51% (2)3Δ 57% (1)3Σ− 100% (3)3Π 100% (1)3Φ 62% (2)1Π 81% (2)3Δ 63% (3)3Π 55% (1)3Σ− 52% (3)3Π 95% (2)1Δ 98% (2)3Σ− 97% (2)3Σ−

7% (1)3Π 9% (1)3Π 24% (1)3Σ+ 3% (2)1Σ+ 31% (1)3Σ+

6% (1)1Δ

6% (1)3Δ

11% (2)3Δ 33% (1)3Π 24% (1)3Π 5% (1)3Π 4% (1)3Σ+ 3% (1)3Π

2% (1)1Δ 1% (1)3Δ

4% (1)1Π

4% (1)3Δ 1% (1)3Π 1% (2)3Π

1% (1) 3Σ−

2% (2)3Δ 4% (2)1Δ

1% (3)3Π 1% (3)3Π

27% (3)3Π 44% (1)3Σ− 19% (2)3Δ 33% (3)3Π 28% (2)3Δ

6% (1) 3Σ− 1% (2)1Σ+

6% (2)3Π

16% (1)3Σ− 19% (1)3Φ 28% (2)3Δ 43% (3)3Π 24% (2)1Π 2% (3)3Π 2% (3)3Π 2% (2)1Π

12% (2)3Δ

5% (3)3Π

5% (1)1Δ 1% (2)3Σ− 20% (1)3Σ− 2% (1)3Φ

4% (1)3Φ

1% (2)1Σ+ 6% (2)1Π 15% (2)3Δ

15% (1)3Φ 15% (3)3Π

Also, the ωe value of X1Σ+ is in good agreement with the experimental value, with a small error of 3%. For the first excited states (1)1Π and (2)1Σ+, the results are compared to the

3% (2)3Δ

2% (2)3Σ− 3% (2)3Π

1% (2)3Π

experimental values of the upper states in systems A and B observed by Kramer,6 considering that the lowest state in both systems A and B is the ground state X1Σ+. The prediction of 12126

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(1)1Π as the upper state in system A and of (2)1Σ+ as the upper state in system B is confirmed by our calculated transition dipolar moments from these states toward X1Σ+, showing the most intensive terms. The assumption of X1Σ+ as the lowest state of systems A and B could be true if the difference in values of ωe″ = 350.6 ± 2.6 cm−1 in system A and of ω″e = 386.4 ± 256 cm−1 in system B is justified. Following the theoretical results and the experimental techniques used by Kramer, in the reached visible regions, X1Σ+ is the only possible state having the highest ωe. Furthermore, the spectroscopic experimental results are based on the head of bands analysis and not on the origin of bands observation because the spectra are obtained at medium resolution, assuming also that Lu37Cl isotopes spectra could be obtained in this region. It is clear that ωe′ and ωe″ in system B are both of high values in comparison with those in system A. Moreover, the values of ωe″ of the lowest states in systems A and B for LuBr and LuI do not differ as much as those in the case of LuCl. This implies that we are probably dealing with the same lowest electronic structure. For the other calculated states included in Table 3 and that have not been experimentally unobserved, the energy shifts between some of these states are compared with those in Lu+ levels. We find that the experimental energy shift in Lu+ between (1)1D and (1)3D2 having the value of 4897.26 cm−119 is close to the energy difference between (1)1Δ and (1)3Δ having a value of 4268 cm−1 in LuCl (Table 3). Similarly, the energy shift of (1)3F3 − (1)3D2 of 18454.57 cm−1 in Lu+19 is comparable to the shift (1)3Φ − (1)3Δ of 19287 cm−1 in LuCl. Moreover, the shift (1)3P1 − (1)1D = 11 170.58 cm−1 is very close to that of (2)3Π − (1)1Δ of 11 617 cm−1, and the shift (1)3P1 − (1)3D2 = 16 067.84 cm−1 is of the same order as the energy difference (2)3Π − (1)3Δ = 15 219 cm−1. This confirms the high contribution of Lu+ in the lowest electronic structure of LuCl, as previously found in the case of LuF.11 The potential energy curves (PECs) using MRCI+Q methods in the case of 22 valence electrons of the set of the singlet electronic states and the set of the triplet electronic states are illustrated in Figures 1 and 2, respectively. The polynomial evolution of these curves does not show any avoided crossing between the electronic states. The calculations of the transition dipole moments between electronic states, respecting the selection rules ΔΛ = 0 and ±1 and ΔS= 0, determine the possible intense electronic transitions in this molecule. The energy diagram in Figure 3a shows the transition dipole moments from the upper singlet excited states to the ground state X1Σ+ at Re = 2.38 Å. Figure 3b illustrates the transition dipole moments between the upper singlet states also at Re = 2.38 Å. The intensive possible transition bands between electronic states of spin multiplicity S = 3 are deduced from Figure 4, which represents the electric dipole moment between these states at Re = 2.38 Å. The strongest transitions found for ((1)1Π − X1Σ+), ((2)1Σ+ − X1Σ+), ((2)1Π − X1Σ+), ((3)1Π − X1Σ+), ((2)1Δ − (1)1Δ), ((3)1Π − (2)1Σ+), and ((1)1Φ − (3)1Σ+) in LuCl are also of the same order in the LuF molecule.11 Similarly, the strongest triplet transitions ((1)3Φ − (1)3Δ), ((2)3Δ − (1)3Δ), ((1)3Σ− − (1)3Π), ((3)3Π − (1)3Δ), ((4)3Π − (1)3Δ), ((4)3Π − (1)3Π), ((4)3Π − (1)3Σ+), and ((2)3Σ− − (1)3Σ−) are analogous to those calculated for LuF.11 The SOC, using MRCI + Davidson correction, calculated for the different Λ−S states leads to common components Ω. The percentage contribution at Re = 2.38 Å, of the components to the Ω state-wave functions, is shown in Table 5. A significant mixing

of S−Λ components for the states (5)0+ and (6)0+ between (3)3Π and (1)3Σ− is predicted. Table 6 presents the calculated values of the spectroscopic constants Te, ωe, Re, and ωexe for the first 33 Ω(±) components, Table 6. Spectroscopic Constants for the Lowest-Lying Molecular States Ω(±) of LuCl states

Re (Å)

Te (cm−1)

ωe (cm−1)

ωe χ e (cm−1)

(1)0+ X1Σ+ (1)1 [(1)3Δ] (1)2 [(1)3Δ] (1)0− [(1)3Π] (2)0+ [(1)3Π] (2)1 (1)3 (1)3Δ (2)2 [(1)3Π] (3)1 (2)0− [(1)3Σ+] (3)2 [(1)1Δ] (4)1 [(1)1Π] (3)0+ [(2)1Σ+] (3)0− (2)3Π (4)0+ [(2)3Π] (5)1 [(2)3Π] (4)2 [(1)3Φ] (5)2 [(2)3Π] (6)1 (5)0+ (2)3 [(1)3Φ] (6)2 (7)1 (4)0− (3)3Π (1)4 [(1)3Φ] (8)1 (3)3 [(2)3Δ] (7)2 (6)0+ (9)1 (8)2 [(2)1Δ] (7)0+ [(2)3Σ−] (10)1 [(2)3Σ−]

2.38 2.43 2.43 2.43 2.43 2.43 2.42 2.43 2.43 2.43 2.43 2.45 2.43 2.45 2.45 2.45 2.45 2.44 2.46 2.47 2.45 2.46 2.46 2.47 2.45 2.43 2.45 2.45 2.46 2.45 2.43 2.47 2.47

0.00 11 814 12 694 12 739 13 493 13 780 14 447 15 730 16 665 16 895 17 855 20 135 22 393 28 066 28 154 28 872 29 585 30 395 30 963 31 824 31 951 32 815 33 157 33 435 34 702 34 863 35 127 35 377 35 478 35 818 37 930 38 982 39 048

348 321 320 318 319 317 324 319 316 316 320 307 308 328 327 329 307 333 304 292 307 304 301 300 308 320 307 306 304 313 321 301 304

1.07 1.05 1.05 1.03 1.05 1.08 0.97 1.02 1.12 1.15 1.03 0.98 1.69 1.04 1.03 1.05 0.88 1.00 0.92 0.79 0.80 1.01 0.98 0.98 1.05 1.25 1.02 1.02 1.03 0.81 1.04 0.99 0.94

including the identification of the main parent S−Λ for each component. These results show that the spin−orbit splitting between two consecutive components of all triplet states is unequally spaced. This behavior is similar to the spin−orbit splitting in the triplet components of Lu+.

4. CONCLUSION This paper is concerned with the theoretical study of the electronic structure of lutetium monochloride. Ab initio calculation methods CASSCF/MRCI with single and double excitations with Davidson correction have been employed in a range of points around the equilibrium internuclear distance of X1Σ+. The theoretical spectroscopic constants, for the set of the singlet and triplet electronic states in the representation (2s+1)Λ±, below 43 000 cm−1 have been obtained. The achieved theoretical results compared to the few available experimental values have been found to be accurate and of good agreement with experiment. The PECs and the transition electric dipole moments have been presented in this work. Spin−orbit calculations have been performed for 33 components in the representation Ω(±). Also, the 12127

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spectroscopic constants and the percentage contribution have been obtained for these components. By comparing the results of the LuCl molecule with those already published for the LuF molecule,11 we have found similar lowest electronic states. However, the energy of these states decreases when going to the heaviest halide due to the decrease in the electronegativity from fluorine to chlorine.

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AUTHOR INFORMATION

Corresponding Author

*Author to whom correspondence should be addressed. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to thank Prof. Monique FRECON, professor at LASIM- Claude Bernard Lyon 1-University, France, for the helpful discussions.

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REFERENCES

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