The YbF molecule is a sensitive system for measuring the electron’s electric dipole moment. The precision of
this measurement can be improved by direct laser cooling of the molecules to ultracold temperature. However,
low-lying electronic states arising from excitation of a 4f electron may hinder laser cooling. One set of these ‘‘4f
hole’’ states lies below the 𝐴2𝛱1∕2 excited state used for laser cooling, and radiative decay to these intermediate
levels, even with branching ratios as small as 10−5, can be a hindrance. Other 4f hole states lie very close to
the 𝐴2𝛱1∕2 state, and a perturbation results in states of mixed character that are involved in the laser cooling
cycle. This perturbation may enhance the loss of molecules to states outside of the laser cooling cycle. We
model the perturbation of the 𝐴2𝛱1∕2 state to determine the strength of the coupling between the states, the
de-perturbed potential energy curves, and the radiative branching ratios to various vibrational levels of the
ground state, 𝑋2𝛴+. We use electronic structure calculations to characterize the 4f hole states and the strengths
of transitions between these states and the 𝐴2𝛱1∕2 and 𝑋2𝛴+ states. We identify a leak out of the cooling cycle
with a branching ratio of roughly 5 × 10−4, dominated by the contribution of the ground state configuration
in a 4f hole state. Finally, we assess the impact of these results for laser cooling of YbF and molecules with
similar structure.