  Present-day state-of-the-art ab initio many-body calculations on f-block
containing cold molecules heavily focus on perturbative approaches for
spin-orbit coupling and exclude a substantial part of the atomic transitions in
the $f$- and $d$-shell. Here, we demonstrate the cruciality of a proper
relativistic treatment of the $f$- and $d$-shell in Yb-containing diatomics and
the inclusion of $f\rightarrow d$ transitions to obtain physically sound
elastic scatterings and pre-dissociation lifetimes. We focus on
state-of-the-art relativistic many-body calculations for the Yb atom's ground-
and excited-state and the YbLi$^+$ potential energy surface. For that purpose,
we exploit various quantum many-body methods, namely a spin-free and
four-component implementation of the coupled cluster singles and doubles (CCSD)
model and its equation of motion extensions, spin-free complete active space
self-consistent field, and internally contracted multi-reference (MR)
configuration interaction approaches, and spin-free MRCCSD with a perturbative
and full triples correction. We oppose scalar relativistic calculations to
four-component variants to support the reliability of our EOM-CCSD study and
shed new light on the interplay between these systems' spin-orbit coupling and
the proper treatment of relativistic effects. Most importantly, we observe a
significant shift in the electronic spectra of the $f\rightarrow d$ excitation
block. We also provide new reference potential energy surfaces for ground and
excited states for which theoretically sound elastic scattering and
pre-dissociation lifetimes are calculated.
