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Analytic potentials are built for all four $^{2S+1}\Pi_{u/g}$ states ofLi$_{2}$ dissociating to Li$(2S)$ + Li$(3P)$: $3b(3^{3}\Pi_{u})$,$3B(3^{1}\Pi_{u})$, $3C(3^{1}\Pi_{g}),$ and $3d(3^{3}\Pi_{g})$. Thesepotentials include the effect of spin-orbit coupling for large internucleardistances, and include state of the art long-range constants. This is the firstsuccessful demonstration of fully analytic diatomic potentials that capturefeatures that are usually considered too difficult to capture without apoint-wise potential, such as multiple minima, and shelves. Vibrationalenergies for each potential are presented for the isotopologues$^{6,6}$Li$_{2}$, $^{6,7}$Li$_{2}$, $^{7,7}$Li$_{2}$, and the elusive `halonucleonic molecule' $^{11,11}$Li$_{2}$. These energies are claimed to beaccurate enough for new high-precision experimental setups such as the onepresented in {[}Sebastian \emph{et al.} Phys. Rev. A, \textbf{90}, 033417(2014){]} to measure and assign energy levels of these electronic states, allof which have not yet been explored in the long-range region. Measuringenergies in the long-range region of these electronic states may be significantfor studying the \emph{ab initio} vs experiment discrepancy discussed in{[}Tang \emph{et al.} Phys. Rev. A, \textbf{84}, 052502 (2014){]} for the$C_{3}$ long-range constant of Lithium, which has significance for improvingthe SI definition of the second.

Analytic potentials and vibrational energies for Li$_{2}$ states  dissociating to $\mbox{Li}\left(2S\right)+\mbox{Li}\left(3P\right)$. Part 1:  The $^{2S+1}\Pi_{u/g}$ states