  We build the first analytic empirical potential for the most deeply bound
$\mbox{Li}_{2}$ state: $b\left(1^{3}\Pi_{u}\right)$. Our potential is based on
experimental energy transitions covering $v=0-34$, and very high precision
theoretical long-range constants. It provides high accuracy predictions up to
$v=100$ which pave the way for high-precision long-range measurements, and
hopefully an eventual resolution of the age old discrepancy between experiment
and theory for the $\mbox{Li}\left(2^{2}S\right)+\mbox{Li}\left(2^{2}P\right)$
$C_{3}$ value. State of the art ab initio calculations predict vibrational
energy spacings that are all in at most 0.8 cm$^{-1}$ disagreement with the
empirical potential.
