Electronic Structure and Dipole Moment Calculations of the Electronic States of the Molecule BeCl

The electronic structure of the molecule BeCl have been investigated by using the Complete Active Space Self Consistent Field (CASSCF) with Multireference Configuration Interaction MRCI+Q (singly and doubly excitation with Davidson corrections). The potential energy curves, in terms of the internuclear distance R, have been calculated for 13 doublet and 14 quartet electronic states in the representation Λ of the molecule BeCl. The internuclear distance at equilibrium Re, the electronic energy with respect to the ground state Te, the harmonic frequency ωe, the rotational constants Be and the permanent dipole moment have been calculated for the bound electronic states. The Franck-Condon factor is calculated for the electronic transition between the two electronic states XΣ-(1)Π. Since there is limited data are published in literature, twenty-two new electronic states have been investigated here for the first time for the molecule BeCl. The comparison between our calculated values and those available in the literature shows a very good good agreement.


Introduction
The alkaline-earth monohalide received a considerable attention from experimentalists since the early thirties (Fredrickson and Hogan Jr 1934).A reinvestigation, and further refinement, of the spectroscopic data of the molecule BeCl have been provided by (Novikov and Tunitskii 1960), (Hildenbrand 1969) and (Colin, Carleer, & Prevot 1972).Recently more experimental data on this molecule has been provided by (Farber & Srivastava 1974), (Carleer, Burtin, & Colin 1977), (Subbaram, Vasudeo, & Jones 1975), (Varma & Jha 1979), and (Knight Jr., Wise, Childers, Daasch, & Davidson, 1981).In an Early attempts, a limited number of low-lying electronic states of the molecule BeCl has been calculated along with the radiative lifetimes and the Franck-Condon factors (Singh & Prabhuram 1975), (Varma & Jha 1981), (Montagnani, Riani, & Salvetti 1983), (Langhoff, Bauschlicher Jr., & Partridge 1986), (Langhoff, Bauschlicher Jr., Partridge, & Ahlrichs 1986), (Bruna & Grein 2001), (Behere, Saksena, Deo, & Jadhav 2006), (Vasiliu, Feller, Gole,& Dixon 2010).Shuman et al. (Shuman, Barry, & DeMille 2010) introduce the first direct cooling of a polar molecule (SrF) by using an optical cycling scheme with Doppler and Sisyphus cooling forces.This significant innovation needs a deep knowledge of the electronic structure and its ro-vibrational energy levels of the ultracold candidate molecule.Moreover, highly diagonally distributed Franck-Condon factors (FCFs) and the short radiative lifetimes (between 10 -6 and10 -9 s ) are needed for these ultracold molecules.While the FCF calculation is based on the accurate potential energy curve of two electronic states, the radiative lifetimes needs the calculation of the dipole moment.DeMille (DeMille2002) has detailed a prototype design for quantum computation using ultracold polar molecules, trapped in a one-dimensional optical lattice, partially oriented in an external electric field, and coupled by the dipole-dipole interaction.This offers a promising platform for quantum computing because scale-up appears feasible to obtain large networks of coupled qubits.
In order to provide an accurate global picture of a manifold of electronic states of BeCl molecule and quantitatively account of the observed spectra we present in this work, the theoretical electronic structure of BeCl molecule.By using ab-initio method 13 doublet and 14 quartet electronic states have been investigated.The Potential energy curves (PECs) have been plotted, the spectroscopic constants T e , ω e , ω e x e , B e , the internuclear distances R e and the electronic static dipole moments have been calculated.The Franck-Condon factors have been calculated for electronic transitions with the discussion on the feasibility of laser cooling of the BeCl molecule

Method
By using Complete Active Space Self Consistent Field (CASSCF) procedure followed by a multireference configuration interaction (MRCI+Q with Davidson correction), we investigated the low-lying double and quartet electronic states of the molecule BeCl.These calculations have been performed by the computational chemistry program MOLPRO (Molpro) using the graphical user interface GABEDIT (Allouche 2011).The berilium and the chlorine atoms are treated in all electrons schemes by using the basis sets cc-pVTZ;c and aug-cc-pVQZ;c for Be and Cl atoms repespectively with the s, p, d orbitals for the 2 atoms.The active space has been identified in the C 2v symmetry: 10σ (Be: 1s, 2s, 2p 0 , 3s; Cl:1s, 2s, 2p 0 , 3s, 3p 0 , 4s), 3π (Be: 2p ±1; Na: 2p ±1, 3p ±1 ) distributed into irreducible representation of the C 2v group: noted by [10,3,3,0].Being an heteronuclear diatomic molecule, BeCl is of C ∞v point group symmetry; however, MOLPRO software can only make use of Abelian point groups which means that C ∞v will be treated using the C 2v point group placing the molecule along the + z-axis and keeping Be at the origin.

Results
Figure 1.Potential energy curves of the 2 Σ ± , 2 Π and 2 ∆ states of the molecule BeCl

Potential Energy Curves and Spectroscopic Constants
The potential energy curves (PECs) for the 27 doublet and quartet electronic states, in the representation , of the molecule BeCl were generated using the MRCI+Q for 303 internuclear distances calculations in the range 1.442Ǻ≤ R e ≤4.452Ǻ (Figs. (1-2)).The spectroscopic constants ω e , T e , and B e have been obtained by fitting the calculated points around the internuclear distance at equilibrium R e of the investigated electronic states into a polynomial in R. The comparison of these values with those available in literature (Barreto de Lima & Ornellas 2013), (Vasiliu, Feller, Gole, & Dixon 2010), (Colin, Carleer, & Prevot 1972), and (Carleer, Burtin, & Colin 1977) are given in Table 1.(Colin, Carleer, & Prevot 1972), and e (Carleer, Burtin, & Colin 1977).

Permanent Dipole Moment
Figure 3. Permanent dipole cuves of the electronic states 2 Σ ± , 2 ∆ and 2 Π of the molecule BeCl The permanent dipole moment (PMD) is a fundamental electrostatic property of a neutral molecule.Its importance is lying in the accurate predictions of transition dipoles and the description of numerous physical phenomena.By taking the Be atom at the origin and chlorine atom along the internuclear Z-axis, we present in Figs ( 1-2) the calculated values of the permanent dipole moment in term of the internuclear distance R. The polarity of the states with their interactions and the bond nature are discussed by the investigation of these PDM curves.One can notice that, as the internuclear distance increases there are two types of curves: i) dipole moment curves in the positive region which are corresponding to an ionic structure of Be δ-Cl δ+ type, ii) curves passing from one region to another by changing the ionic structure.At large internuclear distance R there are also two types of curves: i) dipole moment curves tend smoothly to zero where the molecule is dissociating into (1) 4 Σ + (1) 4 ∆ (3) 4 Σ + (4) 4 Σ + (5) 4 (1) 4 Σ − (1) 4 ∆ (3) 4 Σ − (1) 4 Π (2) 4 Π (3) 4 Π (4) 4 Π natural fragments, ii) dipole moment curves, for the other electronic states, increase in the negative region which point out polarized states that dissociate into ionic fragments.The sharp change in the directions of the PDM curves indicates a reverse in the polarity of the atoms where we can find an avoided crossing of the energy curves at the same position of the internuclear distance.From this agreement, we can confirm the validity and the accuracy of the calculation of the studied excited electronic states.

Franck-Condon Factor
The overlap of the vibrational wave functions is described by the calculation of the Franck-Condon Factor (FCF).For a spontaneous radiative transition, the calculation of this factor is essential to identify the optimal electronic transition for laser cooling.The calculated values of the FCF for the electronic transion X 2 Σ + -(1) 2 Π have been done by using the LEVEL8.2program (A computer program).These values are given in Table 2 and represented in Fig. 5 Table 2. Values of the Franck-Condon Factor for the electronic transion X The large diagonal values of the Franck-Condon factor for the transition X 2 Σ + (v'=0) ↔ (1) 2 Π (v=0) show that the molecule BeCl can be considered as a good candidate for laser cooling through X 2 Σ + -(1) 2 Π electronic transition.

Conclusion
From an initio calculation the potential energy curves of 27 electronic states have investigated by using the complete active space self-consistent field (CASSCF) with multireference configuration cnteraction MRCI+Q (singly and doubly excitation with Davidson corrections).The spectroscopic constants R e , ω e , T e , and B e are determined for the investigated bound electronic states.The permanent dipole moment have been calculated for the investigated electronic states and poltted in terms of the internucluar distance R. The calculated values of the FCF for the transition X 2 Σ + -(1) 2 Π shows that the molecule BeCl is a good candidate for a laser cooling for this transition.Twenty-three new electronic states have been investigated in the present work for th e first time.The confirmation of these theoretical investigated data can be done by a future experiment for these electronic states of the molecule BeCl.