Electronic Structure of the Cesium Oxide Molecule CsO ()

Diana Kaeen^{1}, Mahmoud Korek^{1*}, Saleh Nabhan Abdulal^{2}

^{1}Physics Department, Faculty of Science, Beirut Arab University, Beirut, Lebanon.

^{2}Physics Department, Lebanese International University, Beirut, Lebanon.

**DOI: **10.4236/jmp.2015.613194
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Adiabatic potential energy curves of 12 doublet and quartet lowest spinless electronic states of the molecule CsO have been investigated via ab initio CASSCF and MRCI (doublet and quartet excitations with Davidson correction) calculations. The spectroscopic constants such as vibrational harmonic frequency *ω*_{e}, the internuclear distance at equilibrium R_{e}, the rotational constant B_{e}, and the electronic transition energy T_{e} of the ground and the excited electronic states have been calculated by fitting the energy values around the equilibrium position to a polynomial in terms of the internuclear distance. The comparison of these values to those available in the literature shows a good agreement.

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Kaeen, D. , Korek, M. and Abdulal, S. (2015) Electronic Structure of the Cesium Oxide Molecule CsO. *Journal of Modern Physics*, **6**, 1889-1894. doi: 10.4236/jmp.2015.613194.

1. Introduction

The alkali metal oxides have been the subject of different theoretical and experimental studies in order to specify their electronic ground state. These studies focused on the transition between the 2 electronic states ^{2}Π and ^{2}Σ^{+} [1] -[3] . This change in ground state symmetry is due to the hole in oxygen that will lead either to a ^{2}Π (LiO and NaO) or to a ^{2}Σ^{+} (KO, RbO and CsO). The nature of ground state depends on the competing effects. When the terms are attractive, we expect to have ^{2}Π as ground state due to quadrupole interactions while we expect to have ^{2}Σ^{+} as ground state due to Pauli repulsion. There is a great concern in studying the spectra of this molecule which is shown in different papers written on its ground state ^{2}Π and the first excited state ^{2}Π. Using an ab initio method, Langhoff et al. [4] studied the ground states of alkali oxides and determined the values of spectroscopic constants for the two states ^{2}Σ^{+} and ^{2}Π. Lindsay et al. [5] demonstrated that CsO had ^{2}Σ^{+} ground state by using ESR matrix experiments. Allison and Goddard III [2] explained the change in ground state symmetry from LiO (^{2}Π) to CsO (^{2}Σ^{+}). Yamada and Hirota [6] investigated systematically CsO by using microwave and infrared diode laser spectroscopy. The observed spectra showed that the ground state of CsO was ^{2}Σ^{+}. Woodward et al. [7] showed that the ground state of CsO was ^{2}Σ^{+}. It was demonstrated that RbO and CsO had ^{2}Σ^{+} ground states using ESR experiments [2] [5] which was indicated previously for CsO through reactive scattering experiments [8] . By using a high-level RCCSD(T) ab initio method, Lee et al. [9] calculated the spectroscopic constants of the two lying electronic states ^{2}Σ^{+} and ^{2}Π.

In the present work 12 low-lying doublet and quartet electronic states of CsO molecule have been investigated by using the ab initio method. The potential energy curves (PECs) together with the transition energy with respect to the minimum energy for the ground state T_{e}, the equilibrium internuclear distance R_{e}, the harmonic frequency ω_{e}, and the rotational constant B_{e} have been obtained for the considered electronic states. Ten electronic states have been investigated here for the first time.

2. Method of Calculations

In the present work we study the low-lying doublet and quartet electronic states of the molecule CsO using state averaged complete active space self consistent field (CASSCF) procedure followed by a multireference configuration interaction (MRDSCI with Davidson correction) treatment for the electron correlation. The entire CASSCF configuration space was used as the reference in the MRDSCI calculations, which were done via the computational chemistry program MOLPRO [10] taking advantage of the graphical user interface GABEDIT [11] . For this purpose five different basis sets were used in our theoretical study for cesium monoxide molecule. In the first basis set the 55 electrons of the cesium atom are considered using a contracted ECP46MWB basis set for s and p functions, while the oxygen species is treated as a system of 8 electrons by using the aug-cc-pCV5Z basis set for s, p, and d functions. In the second basis set, the 55 electrons of the cesium atom are considered using a contracted ECP46MWB basis set for s and p functions, while the oxygen species is treated as a system of 8 electrons by using the 6-311++G basis set for s, p, and d functions. This basis is developed by optimizing exponents and coefficients at the Möller-Plesset second-order level. It has a triple split in the valence s and p shells together with a single set of uncontracted polarization functions on each atom. In the third basis set, the 55 electrons of the cesium atom are considered using a contracted Hay-Wadt VDZ (n+1) ECP basis set for s and p functions, while the oxygen species is treated as a system of 8 electrons by using the aug-cc-pCV5Z basis set for s, p, and d functions.

In the fourth basis set the 55 electrons of the cesium atom are considered using a contracted ECP46MWB basis set for s and p functions, while the oxygen species is treated as a system of 8 electrons by using the VDZ basis set for s, p, and d functions. In the fifth basis set, the 55 electrons of the cesium atom are considered using a contracted ECP46MWB basis set for s and p functions, while the oxygen species is treated as a system of 8 electrons by using the aug-cc-pCVDZ basis set for s, p, and d functions.

Among the 63 electrons explicitly considered for CsO (55 electrons for Cs and 8 for O) 46 inner electrons were frozen in subsequent calculations so that 17 valence electrons were explicitly treated. All computations were performed in the C_{2v} point group. Using the first basis set ECP46MWB, the potential energy curves of 12 low-lying electronic states of the molecule CsO were generated using the MRSDCI for 350 internuclear distances calculations in the range 1.5Å ≤ R_{e} ≤ 5Å in the representation ^{2s+1}Λ^{(±)} where we assumed that, the CsO molecule is mainly ionic around the equilibrium position. These PECs for the different symmetries are given in Figure 1 and Figure 2.

The spectroscopic constant ω_{e}, r_{e}, B_{e}, and T_{e} have been calculated by fitting the energy values around the equilibrium position to a polynomial in terms of the internuclear distance. These values are given in Table 1 with the available values in the literature. The comparison of our results for the constants ω_{e} with those available in literature [3] [4] [6] [9] [12] [13] shows a very good agreement by using the second basis for the states X^{2}Σ^{+} with the relative difference 2.6% ([4] ) ≤ Δω_{e}/ω_{e} ≤ 4.4% ([9] ); while the best agreement for the state (1)^{2}Π is obtained by using the basis one with the relative difference 4.8% ([12] ) ≤ Δω_{e}/ω_{e} ≤ 6.8% ([4] ). By comparing our calculated values of R_{e} with those found in literature for the 2 electronic states X^{2}Σ^{+} and (1)^{2}Π, one can find an

Figure 1. Potential energy curves of the lowest doublet electronic states of the molecule CsO using the first basis set.

Figure 2. Potential energy curves of the lowest quartet electronic states of the molecule CsO using the first basis set.

excellent agreement is obtained by using the first, fourth and fifth used basis sets with the relative differences 0.32% ([12] ) ≤ ΔR_{e}/R_{e} ≤ 0.37% ([4] ).

Our calculated values of T_{e} by using basis one are in very good agreement with those given in [4] [6] [9] with the relative differences 1.04% ([6] ) ≤ ΔT_{e}/T_{e} ≤ 6.1% ([9] ). This agreement deteriorates by using third and fifth basis sets. There is no comparison of our calculated values for B_{e} and for the investigated spectroscopic constants of the electronic states (1)^{4}Σ^{−}, (2)^{2}Π, (2)^{4}Σ^{−} since they are given here for the first time. These spectroscopic constants are also absent for other investigated electronic states either because of the crossing or avoiding

Table 1. Spectroscopic constants for the lowest doublet and quartet electronic states of the molecule CsO.

^{a}Present work using for the 55 electrons of the cesium atom a contracted ECP46MWB basis set for s and p functions, while the oxygen species is treated as a system of 8 electrons by using the aug-cc-pCV5Z basis set for s, p, and d functions. ^{b}Present work using for the 55 electrons of the cesium atom a contracted ECP46MWB basis set for s and p functions ,while the oxygen species is treated as a system of 8 electrons by using the 6-311++G basis set for s, p, and d functions. ^{c}Present work using for the 55 electrons of the cesium atom a contracted Hay-Wadt VDZ (n+1) ECP basis set for s and p functions ,while the oxygen species is treated as a system of 8 electrons by using the aug-cc-pCV5Z basis set for s, p, and d functions. ^{d}Present work using for the 55 electrons of the cesium atom a contracted ECP46MWB basis set for s and p functions ,while the oxygen species is treated as a system of 8 electrons by using the VDZ basis set for s, p, and d functions. ^{e}Present work using for the 55 electrons of the cesium atom a contracted ECP46MWB basis set for s and p functions ,while the oxygen species is treated as a system of 8 electrons by using the aug-cc-pCVDZ basis set for s, p, and d functions. ^{k}Ref. [3] , ^{f}Ref. [4] , ^{g}Ref. [6] , ^{h}Ref. [9] , ^{l}Ref. [12] , ^{i}Ref. [13] .

^{*}Corresponding author.

3. Conclusion

In the present work, the ab initio investigation for the low-lying doublet and quartet electronic states of the CsO molecule has been performed via CASSCF/MRCI method using five different basis sets. The potential energy curves have been determined along with the spectroscopic constants T_{e}, R_{e}, ω_{e} and the rotational constant B_{e} for these states. The calculation has been done by using 5 different basis sets. The comparison of our results with those obtained theoretically in literature shows a very good accuracy. Ten new electronic states have been investigated in the present work for the first time.

NOTES

^{*}Corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

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