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 A_ν^′ν, 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.