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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 onexperimental energy transitions covering $v=0-34$, and very high precisiontheoretical long-range constants. It provides high accuracy predictions up to$v=100$ which pave the way for high-precision long-range measurements, andhopefully an eventual resolution of the age old discrepancy between experimentand 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 vibrationalenergy spacings that are all in at most 0.8 cm$^{-1}$ disagreement with theempirical potential.

State of the art for ab initio vs empirical potentials for predicting  6e$^{-}$ excited state molecular energies: Application to  Li$_{2}\left(b,1^{3}\Pi_{u}\right)$