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The NL-eEDM collaboration is building an experimental setup to search for thepermanent electric dipole moment of the electron in a slow beam of cold bariumfluoride molecules [Eur. Phys. J. D, 72, 197 (2018)]. Knowledge of molecularproperties of BaF is thus needed to plan the measurements and in particular todetermine an optimal laser-cooling scheme. Accurate and reliable theoreticalpredictions of these properties require incorporation of both high-ordercorrelation and relativistic effects in the calculations. In this worktheoretical investigations of the ground and the lowest excited states of BaFand its lighter homologues, CaF and SrF, are carried out in the framework ofthe relativistic Fock-space coupled cluster (FSCC) and multireferenceconfiguration interaction (MRCI) methods. Using the calculated molecularproperties, we determine the Franck-Condon factors (FCFs) for the $A^2\Pi_{1/2}\rightarrow X^2\Sigma^{+}_{1/2}$ transition, which was successfully used forcooling CaF and SrF and is now considered for BaF. For all three species, theFCFs are found to be highly diagonal. Calculations are also performed for the$B^2\Sigma^{+}_{1/2} \rightarrow X^2\Sigma^{+}_{1/2}$ transition recentlyexploited for laser-cooling of CaF; it is shown that this transition is notsuitable for laser-cooling of BaF, due to the non-diagonal nature of the FCFsin this system. Special attention is given to the properties of the$A'^2\Delta$ state, which in the case of BaF causes a leak channel, in contrastto CaF and SrF species where this state is energetically above the excitedstates used in laser-cooling. We also present the dipole moments of the groundand the excited states of the three molecules and the transition dipole moments(TDMs) between the different states.

High accuracy theoretical investigations of CaF, SrF, and BaF and implications for laser-cooling