Electronic structure with spin-orbit coupling effect of HfH molecule for laser cooling investigations

The electronic structure, including the spin-orbit coupling effect of the HfH molecule, has been studied to determine if it can be cooled through Doppler and Sysphus laser cooling techniques. The multi-reference configuration interaction plus Davidson correction (MRCI + Q) method has been used to calculate its potential energy curves (P.E.C.s) in the Ω^(±) and ^2s+1Ʌ^(+/-) representation. The spectroscopic constants T_e, R_e, ω_e, B_e, α_e, the dipole moment µ_e, and the dissociation energies D_e agree very well with previously published work. In addition, we present in this work twenty new doublet and quartet states in the Ω^(±) representation. The electronic transition dipole moment curves (TDMCs) between the lowest-lying electronic states have been investigated for the Δ - Π, Π - ∑⁺ and Δ - Φ transitions among specific Ω^(±) states. The Franck-Condon factors (FCFs), the Einstein coefficient of spontaneous emission [Formula: see text] , and the radiative lifetime τ have been computed for the investigated transitions. In addition, properties of the molecules' electronic and vibrational states, such as the static dipole moment curves (D.M.C.s), the ionic character f_ionic, and the rovibrational constants are calculated. We deduce from our results that the HfH molecule is indeed a laser-cooling candidate that can reach a temperature as low as the nK regime. We present a complementary scheme with suitable experimental parameters. These results can be of great interest to experimental spectroscopists interested in ultracold diatomic molecules and their applications.