Electronic Structure Studies with Spin-Orbit Coupling Effect of the

Molecule TlI

GHINA CHAMIEH, LOKMAN AWAD, MAHMOUD KOREK*

Faculty of Science,

Beirut Arab University,

P. O. Box 11-5020 Riad El Solh, Beirut 1107 2809,

LEBANON

*Corresponding Author

Abstract: - To study the low–lying electronic states of the TlI molecule, the electronic structure of this molecule

has been investigated via an ab initio Complete Active Space Self Consistent Field and the Multireference

Configuration Interaction with Davidson correction calculation (CASSCF/MRCI+Q). In the representations of

2s+1Λ(+/−) and (±), the adiabatic potential energy curves (PECs) along with static and transition dipole moment

(DM) curves for 19 low-lying electronic states for TlI molecule have been investigated. For the low-lying

electronic states of this molecule, the spectroscopic constants Re, Te, ωe, and Be, are provided. Based on the

data obtained, this molecule is not a candidate for a Doppler laser cooling study.

Key-Words: - ab initio calculation, electronic structure, spin-orbit coupling, potential energy curves, dipole

moment, spectroscopic constants, diatomic molecule.

Received: March 15, 2023. Revised: October 17, 2023. Accepted: November 29, 2023. Published: December 31, 2023.

1 Introduction

With a spin-orbit splitting of 7793 cm-1, thallium

exhibits strong relativistic effects as a heavy metal

belonging to the GIII-A group, which are

anticipated to be significant for chemical bonding,

[1]. It is well known that thallium compounds make

valuable materials, such as high-temperature

superconducting materials and catalysts for organic

synthesis, [2], [3]. Thallium halides have drawn

much attention from researchers because they are

among the earliest thallium compounds to be

produced. The spectra and dynamics of the

electronic states of these compounds have been the

subject of several experimental and theoretical

studies.

Here, we use gaseous thallium mono-halide as

straightforward representations of thallium

compounds. Both theorists and experimentalists

have long been drawn to these systems. For TlX (X

= F, Cl, Br, and I), several spectroscopic

measurements have been made up to this point, [4].

However, most excited states' geometrical and

spectroscopic characteristics are yet unknown. The

ground state and some excited electronic states of

TlI were investigated, [4]. Spin-orbit coupling

(SOC) significantly impacts spectroscopy and

dynamics. The SOC effect can cause pre-

dissociations between S states with various spin

multiplicities and multiple avoided crossings of Ω

(±) states, [5].

The present work on the molecule TlI is a part of

our research project on iodine compounds such

as CaI, [6], BaI, [7], MgI, [8] and BeI, [9]. Since

there is some available data for electronic states

in the literature on the molecule TlI, we expect to

supply pleasant details for theoretical studies

of this molecule, [4]. Our powerful motive is to

profoundly analyze the molecule's ground with

excited states with their complete spectroscopic

and spin-orbit studies in the current work.

Because of this absence, an ab initio method

with a Complete Active Space Self Consistent Field

has been used with Davidson correction (CASSCF/

MRCI+Q) to calculate the potential energy (PECs),

the static and transition dipole moment curves

(DMCs), the Franck-Condon factor FCF, and the

radiative lifetime. In the representations, 2s+1Λ(+/−)

and Ω(±), 19 low-lying electronic states have been

investigated for the molecule of TlI where most of

the investigated data are presented here for the first

time.

2 Computational Methods

The state average Complete Active Self

Consistent Field (CASSCF)/Multireference

Configuration

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Interaction (MRCI + Q) has been used to investigate

the singlet and triplet electronic states of the TlI

molecule. With the graphical interface GABEDIT,

[10]. The computational chemistry program

MOLPRO (a software package developed for

accurate ab initio quantum chemistry calculations) is

used to accomplish these calculations, [11].

The Born-Oppenheimer approximation was

used to obtain the potential energy curves. Using the

customized core polarization potentials (CPP) and

energy-consistent effective core potentials (ECP)

from the Stuttgart/Cologne Group, the relativistic

effects and core electrons were treated. The MRCI

and CASSCF methods, along with selected basis

sets, were used to describe the valence electrons.

For the TlI molecule, the ECP60MDF basis set

is used for the Tl atom with 21 valence electrons

distributed as 5s2 5p6 5d10 6s2 6p1, [12]. For the I

atom, the basis set ECP46MDF is considered with

seven valence electrons distributed as 5s2 5p5, [13].

For the considered molecule TlI, 9 occupied shells

are investigated in symmetry 1, 4 in symmetries (2

and 3), and only 1 shell in symmetry 4. For the

closed shells, five are considered in symmetry 1, 2

in symmetries (2 and 3), and 1 shell in symmetry 4.

We chose ECP as a basis for Tl and I atoms by

referring to many papers on these atoms published

in the literature, [14], [15], [16].

The diatomic molecules belong to C∞v, and

because of the limitation of the MOLPRO, it turns

to its subgroup C2v, which has four irreducible

representations (a1, b1, b2, a2). The active space for

the TlI molecule is 4σ (Tl: 6p0, 7s; I: 5p0, 6s), 2π

(Tl: 6p±1; I: 5p ±1;) and 0δ, with the irreducible

representation 7a1, 3b1, 3b2, and 1a2 noted by

[4, 2, 2, 0]. To obtain the potential energy curves,

the estimated energy points are connected using the

avoided-crossing rule for electronic states that

belong to the same irreducible representation of the

single/double point group C∞v. The one-

dimensional Born-Oppenheimer Schrödinger

equation is used to obtain the spectroscopic

constants including Re (equilibrium bond length), Te

(transition energy), ωe (harmonic constant), and Be

(rotational constant).

3 Results and Discussion

3.1 Spectroscopic Constants

With and without spin-orbit coupling, the singlet

and triplet electronic states of the molecule TlI are

investigated. The spectroscopic constants

(Transition energies, internuclear distances,

harmonic vibrational frequencies) for the bound

states can be computed using the X-Poly or X-min

programs. The PECs are first fitted to a polynomial

function (U(r) = a0 + a1r + a2r2 +...) to reproduce the

ab initio values. After that, the constants are

computed analytically by their definitions.

The operating system that is being used

determines which program is selected. The

Windows operating system is used with X-poly, and

the Ubuntu operating system is used with X-min.

However, both provide the same reliability and

accuracy. Table 1 and Table 2 present the PECs

spectroscopic constants that we computed using the

X-poly program for the different electronic states.

Table 1. Spectroscopic constants Te, Re, e, and Be

of the molecule TlI (with spin-orbit coupling)

Table 2. Spectroscopic constants Te, Re, e and Be

of the molecule TlI (without spin-orbit coupling)

By comparing our outcomes of spectroscopic

constant ωe with those given in the literature, we

obtain a good agreement with the relative

differences Δωe/ωe= 7.13%, ΔRe/Re =9.7%, and

ΔBe/Be =0.08% for the ground electronic state X1Σ+

of TlI molecule, [4]. These relative differences

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DOI: 10.37394/232017.2023.14.15

Ghina Chamieh, Lokman Awad, Mahmoud Korek

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130

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become larger for Δωe/ωe = 12.7 %, ΔRe/Re =12.0%,

and in very good agreement with ΔBe/Be =0.29% by

comparing our values with those of the excited

electronic state (1)3Σ+, [4].

Similarly, for (1)3electronic state, a strong

agreement is obtained between our obtained results

and published data for the given spectroscopic

constants Δωe/ωe= 5.12%, ΔRe/Re =1.12%, and

ΔBe/Be =4.50%. The spectroscopic constants for the

other electronic states are not calculated here since

they are unbound states, [4].

3.2 Potential Energy Curves

Based on the 21 valence electrons of the Tl atom

using the ECP 60 MDF basis set, and the seven

valence electrons of the Iodine atom using the

ECP46MDF basis set, 16 singlet and triplet

electronic states are investigated and plotted in

Figure 1 and Figure 2 as a function of internuclear

distance R in the ranges 1.8Å ≤ R ≤ 6.80Å and 2Å ≤

R ≤ 6Å, respectively. The potential energy curves,

including spin-orbital coupling, are presented in

Figure 3 and Figure 4.

Fig. 1: The potential energy curves of the singlet

electronic states of the TlI molecule without spin-

orbit coupling

Fig. 2: The potential energy curves of the triplet

electronic states of the TlI molecule without spin-

orbit coupling

Fig. 3: The potential energy curves of the singlet

electronic states of the TlI molecule with spin-

orbital

Fig. 4: The potential energy curves of the triplet

electronic states of the TlI molecule with spin-

orbital

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The ground state of the considered molecule TlI

has a deep well, while the other investigated

electronic states are shallow or unbound. Mainly

most of the studied electronic states reach their

dissociation limit at around 5Å. The potential

energy curve's deepness indicates the molecule's

stability, while small forces bind the two atoms for a

shallow potential energy curve.

To prove the credibility of our investigated

values of the TlI molecule, we show in Table 3 the

trend of the spectroscopic parameters between the

TlBr molecule and our obtained values for the TlI

molecule, [4]. From bromine to iodine in the

Periodic Table, the rotational constant Be decreases

as the reduced mass increases. This Table also

confirms the increase in bond length Re and the

decrease of harmonic frequency e with the

decrease of the electronegativity for all the

considered electronic states, which can confirm the

reliability of our work.

Table 3. The trend study of the spectroscopic

constants of the different electronic states of the

molecules TlBr and TlI

a [4], bPresent work

3.3 Permanent Dipole Moment Curves

By taking the iodine atom at the origin, the curves

with and without the spin-orbit of the static dipole

moment (DMCs) of the TlI molecule are plotted as a

function of internuclear distance R in Figure 5,

Figure 6, Figure 7 and Figure 8. These DMCs are

essential in constructing the molecular orbit bonding

model, specifying the polarity and the interaction of

electronic states, [17], [18], [19]. One can notice

that all the investigated DMCs tend to zero at a large

internuclear distance, resulting in a neutral fragment

Figure 5 and Figure 8 except for the two electronic

states and. Thesecurves tend to have

negative values in the negative region within 5.20Å

≤ R ≤ 7.20 Å (Figure 5 and Figure 7) where the

molecule dissociates in the ionic fragment.

Fig. 5: The dipole moment curves as a function of

internuclear distance for the singlet electronic states

of TlI without spin-orbit coupling

Fig. 6: The dipole moment curves as a function of

internuclear distance for the triplet electronic states

of TlI without spin-orbit coupling

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Fig. 7: The dipole moment curves as a function of

internuclear distance for the singlet spin-orbit

coupling electronic states of the TlI molecule

Fig. 8: The dipole moment curves as a function of

internuclear distance for the triplet spin-orbit

coupling electronic states of the TlI molecule

4 Conclusion

Using an ab initio calculation (CASSCF/MRCI + Q)

we investigated in the present work the PECs and

the DMCs for 19 and 10 electronic states (singlet

and triplet) states of TlI molecule. In this

calculation, the used basis sets are the ECP60MDF

[12] and ECP46MDF [13] for Tl and I atoms,

respectively. The ground state is confirmed as X1Σ+

with deep potential energy curves for the molecule

TlI. A good agreement can be noticed by comparing

our calculated spectroscopic constants in Table 1

with those in the literature. Our previous work on

the iodine compounds confirmed the candidacy of

the two molecules CaI and BaI for Doppler laser

cooling. This study of laser cooling for the molecule

TlI has not been done since the first condition,

which is that the small difference between the Re of

the ground and one bound excited state is not

verified.

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Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

- Ghina Chamieh: Conception, design, calculation,

and writing the paper.

- Lokman Awad: Revising the paper critically for

important intellectual content.

- Mahmoud Korek: Supervised and approved the

final version.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

No funding for this manuscript.

Conflict of Interest

The authors declare no competing interests.

Data availability

All data generated or analyzed during this study are

included in this published article.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

Creative Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en

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WSEAS TRANSACTIONS on ELECTRONICS

DOI: 10.37394/232017.2023.14.15

Ghina Chamieh, Lokman Awad, Mahmoud Korek

E-ISSN: 2415-1513

134

Volume 14, 2023