Static Dipole Moments and Electronic Structure Calculations of the Low-Lying Electronic States of the Molecule Zinc Selinum ZnSe

Zinc selenide is a compound that has many applications in optoelectrical systems. An understanding of its properties as an individual molecule can be of great help for its use at the nanoscale. Correspondingly, twenty two lowest electronic states of ZnSe have been studied in the 2s+1Λ± representation in this paper. The potential energy curves, the harmonic frequency ωe, the electronic energy Te, the static dipole moment and the internuclear distance re have been investigated. These calculations have been performed by using the multi-reference configuration interaction (MRCI+Q) method with Davidson correction. A very good agreement is obtained by comparing the present results with those available in literature. New electronic states have studied in the present work for the first time.


Introduction
Zinc is one of the essential elements for humans by its effects as cofactor for a very large number of enzymes, zinc-finger proteins and matrix metalloproteinases.The calculations of the dipole moment and the bond dissociation of Zn compounds provide critical data for biological simulations and industrial applications (Auld 2001), and (Silva, & Williams 2001).Zinc Chalcogenides have large iconicity of chemical bond with small values of energy for the formation of vacancies.From a stoichiometric ratio of Zn and Se powder, ZnSe molecule can be obtained by microwave irradiation technique (2.8 GHz).These compounds are very promising in optoelectronic applications, i.e in the domains of infrared optics and electro-optic, lenses, laser diodes and electric diodes, beam expanders, semiconductors, and solar cells (Wu, Qiu, Cai, Xu, Chen, & Cryst 2002), and (Porento, & Hirva 2002).The study of the structure and the electronic properties of these compounds at a small scale are needed to understand the applications of these materials.For example, ZnSe nanocluster represents the link between molecules and the bulk of these materials.At the molecular scale, theoretical investigations of the electronic structure of ZnSe are valuable in order to understand their experimentally observed properties.However, no systematic theoretical investigation on the potential energy, the static dipole moment, and the spectroscopic constants of ZnSe molecules have been conducted thus far.In the present work and in order to get further insight into various properties of ZnSe molecule, we extend our investigation to their highly excited electronic states with a rovibrational calculation using the canonical function approach.

Method
By using an ab initio calculation, we investigate in the present work the low-lying electronic states of ZnSe molecule.The calculation has been performed via CASSCF method.In order to determine the correlation effect, multireference CI calculations were performed using Davidson correction with singly and doubly excitations.In the MRCI calculation, all the CASSCF configuration space has been used as a reference.These calculations have been performed by using the computational chemistry program MOLPRO (MOLPRO 2015) with the graphical user gabedit interface (Allouche 2011).The Zn atom is treated by using the ECP10MDF basis set for the s, p, and d orbitals while the ECP28MWB basis is used for Se atom for the s and p orbitals; the d orbital for this atom is added from the aug-cc-PVDZ;C basis.Among the 24 electrons explicitly considered for the molecule ZnSe, 4 electrons were frozen in our calculation so that 9 valence electrons were explicitly treated.Around the equilibrium position, the molecule ZnSe can be considered ionic as many other transition metals.

Potential Energy Curves and Spectroscopic Constants
In the representation 2s+1 Λ (+/-) , the calculation of the eleven singlet and eleven triplet potential energy curves (PECs) of the ZnSe molecule has been performed up to 96 internuclear distances in the range of 1.49 Å< r < 4.5Å.These curves for the electronic states 1,3 Σ ± , 1,3 Π, and 1,3 Δ in the considered range of R are given respectively in Figures 1-5.One can notice that some avoided crossings have been obtained between the potential energy curves (2) 1 Σ + /(3) 1 Σ + , (1) 1 Π/(2) 1 Π, (2) 1 Π/(3) 1 Π, (3) 1 Π/(4) 1 Π, (2) 3 Π/(3) 3 Π and (4) 3 Π/(5) 3 Π.At these avoided crossing the corresponding wave functions will mix with each other to give two adiabatic solutions.These solutions of the Schrödinger equation are obtained by linear combinations of the diabatic ones where the variation method is used.Such crossings or avoided crossings can dramatically alter the stability of the molecule.Because crossing or avoided crossing is near the minima of some of the investigating potential energy curves, the spectroscopic constants for these curves have not been calculated.For each investigated electronic state, the relative energy with respect to the ground state Te, the harmonic frequencies ωe, the rotational constants Be, and the internuclear distance at equilibrium Re for the singlet and triplet electronic states of the ZnSe molecule have been calculated by fitting the calculated energy values of the different investigated electronic states into a polynomial in R around the equilibrium values Re.These values along with those found in literature, either theoretical or experimental, are given in Table 1.The comparison of our calculated value of the internuclear distance Re with those given in literature for the ground state (Peterson, Shepler, & Singleton 2007) showed a very good agreement with the average relative difference ΔRe/Re=1.5%;this relative difference becomes 3.4% for the first excited electronic state (1) 3 Π.In literature, there are only 2 theoretical published values for the harmonic vibrational frequency ωe for the ground state where the difference between them is 90.4 cm -1 (Peterson, Shepler, & Singleton 2007).Our calculated value for this constant is closer to that given by (Peterson, Shepler, & Singleton-CCSD(T) 2007), with the relative difference Δωe/ωe=9.1% while it is in disagreement with the value given by (Peterson, Shepler, & Singleton -MRCI+Q 2007), where the relative difference is 25.2%.Our calculated value of these constants for the first excited state is smaller than that given by (Peterson, Shepler, & Singleton 2007).There is no comparison of our calculated values of the spectroscopic constants with other data in literature since they are given here for the first time.

Static Dipole Moment
The vibrational excitation of a molecule depends on the variation of the dipole moment in terms of the internuclear distance.These static dipole moment curves can help in the transition intensities.By taking the atom Zn at the origin, we plot in Figures 6-7 the static dipole moment curves versus the internuclear R for singlet and triplet electronic states of the molecule ZnSe.Within the Born-Oppenheimer approximation, the radial Schrödinger equation can be replaced, by using the canonical functions approach (Kobeissi, Korek, & Dagher 1989), and (Korek 1999) where the eigenvalues Ev, the rotational constants Bv, and the centrifugal distortion constants Dv have been calculated for the electronic state (1) 1 Σ + .These values are given in Table 2.

Figure 1 .
Figure 1.Potential Energy Curves of the Singlet 1 Σ ± and 1 Δ Electronic States of the Molecule ZnSe

Figure 3 .
Figure 3. Potential Energy Curves of the Triplet 3 Σ + and 3 Δ Electronic States of the Molecule ZnSe

Figure 4 .
Figure 4. Potential Energy Curves of the Triplet 3 Σ -and 3 Δ Electronic States of the Molecule ZnSe

Figure 6 .
Figure 6.Static Dipole Moment Curves of Triplet Electronic States of the Molecule ZnSe.

Figure 7 .
Figure 7. Static Dipole Moment Curves of Singlet Electronic States of the Molecule ZnSe

Table 1 .
Spectroscopic Constants of the Zinc Selinum Molecule ZnSe

Table 2 .
The Eigenvalue Ev, the Rotational Constant Bv and the Centrifugal Distortion Constant Dv of the