  The precision of the photoassociation spectroscopy of Yb dimer in degenerate
gases is enough to improve the constraints on the new short-range gravity-like
forces if the theoretical knowledge of the Born-Oppenheimer interatomic
potential and non-Born-Oppenheimer interactions is refined [M. Borkowski et al.
Sci. Rep. A {\bf 9}, 14807 (2019)]. The ground-state interaction potential of
ytterbium dimer is investigated at the eXact 2-component core-correlated
CCSD(T) level of {\it ab initio} theory in the complete basis set limit with
extensive augmentation by diffuse functions. For the small basis set the
comparison is made with the four-component relativistic finite-nuclei CCSD(T)
calculations to identify the contraction of the dimer bond length as the main
unrecoverable consequence of the scalar-relativistic approximation. Empirical
constraint on the number of bound vibrational energy levels of the
$^{174}$Yb$_2$ dimer is accounted for by representing the global {\it ab
initio}-based Born-Oppenheimer potential with the model semianalytical function
containing the scale and shift parameters. The results support the previous
evaluation of the Yb dimer potentials from the photoassociation spectroscopy
data and provide an accurate and flexible reference for future refinement of
the constraints on the short-range gravity-like forces by ultracold atomic
spectroscopy.
