Electronic structure calculation of the MgAlk (Alk = K, Rb, Cs) molecules for laser cooling experiments

Laser Cooling with an Intermediate State and Electronic Structure Studies of the Molecules CaCs and CaNa

The ground and excited electronic states of the diatomic molecules CaCs and CaNa have been investigated by implementing the ab initio CASSCF/(MRCI + Q) calculation. The potential energy curves of the doublet and quartet electronic low energy states in the representation ^2s+1Λ^(±) have been determined for the two considered molecules, in addition to the spectroscopic constants T _e, ω_e, B _e, R _e, and the values of the dipole moment μ_e and the dissociation energy D _e. The determination of vibrational constants E _v, B _v, D _v, and the turning points R _min and R _max up to the vibrational level v = 100 was possible with the use of the canonical functions schemes. Additionally, the transition and the static dipole moments curves, Einstein coefficients, the spontaneous radiative lifetime, the emission oscillator strength, and the Franck-Condon factors are computed. These calculations showed that the molecule CaCs is a good candidate for Doppler laser cooling with an intermediate state. A "four laser" cooling scheme is presented, along with the values of Doppler limit temperature T _D = 55.9 μK and the recoil temperature T _r = 132 nK. These results should provide a good reference for experimental spectroscopic and ultra-cold molecular physics studies.

Laser Cooling and Electronic Structure of Be Halides Anions BeX- (X=Cl, Br, F, and I)

The adiabatic potential energy curves of the low lying electronic states of the Be halides anions BeX- (Cl, Br, F, and I) have been investigated in the representation 2s+1Ʌ(+/−) by using the complete active space self-consistent field (CASSCF) with multireference configuration interaction (MRCI+Q) method. The spectroscopic parameters Te,, Re, ωe, and Be, the static and transition dipole moment μe, and a rovibrational study of the investigated electronic states have been performed. New electronic states were investigated here for the first time. The highly diagonal FCF and the short radiative lifetime for the molecular anion BeF- prove its candidacy for direct Doppler laser cooling. The experimental proof of the stability and the calculated experimental parameters such as the vibrational branching ratio, the slowing distance, the recoil and Doppler temperatures with the experimental conditions of the buffer gas cell of this anion open the route for experimental work on the BeF- molecular ion.

Electronic Structure with Dipole Moment and Rovibrational Calculation of Cadmium Chalcogenide Molecules CdX (X = Se, Te)

Ab initio calculations of 51 electronic states in the representation 2s+1Λ(±) of CdX (X = Se, Te) molecules have been carried out by using the complete active space self-consistent field and multireference configuration interaction (single and double excitations with the Davidson correction). The potential energy along with the static and transition dipole moment curves for the investigated electronic states of the CdX molecules has been mapped. Consequently, the spectroscopic constants R e, ωe, B e, and T e have been computed for the bound states. The spectroscopic dissociation energy D e, the zero-point energy, and the ionicity are also calculated for the bound electronic states X3Π, (1)1Σ+, (1)1Π, and (1)3Σ+. Rovibrational calculation is performed for the X3Π, (1)1Σ+, (1)1Π, and (1)3Σ+ states of CdSe together with the X3Π, (1)1Σ+, and (1)1Π states of a CdTe molecule. The Einstein coefficients of spontaneous and induced emissions, A 21 and B 21, are computed for the transition between the electronic states (1)3Σ+ and X3Π. In the present work, the values are well-consistent with those available in the literature.

Solution of the Rovibrational Schrödinger Equation of a Molecule Using the Volterra Integral Equation

By using the Rayleigh-Schrödinger perturbation theory the rovibrational wave function is expanded in terms of the series of functions ϕ0,ϕ1,ϕ2,…ϕn, where ϕ0 is the pure vibrational wave function and ϕι are the rotational harmonics. By replacing the Schrödinger differential equation by the Volterra integral equation the two canonical functions α0 and β0 are well defined for a given potential function. These functions allow the determination of (i) the values of the functions ϕι at any points; (ii) the eigenvalues of the eigenvalue equations of the functions ϕ0,ϕ1,ϕ2,…ϕn which are, respectively, the vibrational energy Ev, the rotational constant Bv, and the large order centrifugal distortion constants Dv,Hv,Lv….. Based on these canonical functions and in the Born-Oppenheimer approximation these constants can be obtained with accurate estimates for the low and high excited electronic state and for any values of the vibrational and rotational quantum numbers v and J even near dissociation. As application, the calculations have been done for the potential energy curves: Morse, Lenard Jones, Reidberg-Klein-Rees (RKR), ab initio, Simon-Parr-Finlin, Kratzer, and Dunhum with a variable step for the empirical potentials. A program is available for these calculations free of charge with the corresponding author.