Analytic empirical potential and its comparison to state of the art ab initio calculations for the 6e_ excited b(13_u)-state of Li2.

Despite only having 6$e^-$, the most sophisticated Li$_2(b,1^3Pi_u)$ calculationfootnote{Musial & Kucharski (2014) textit{J. Chem. Theor. Comp.} textbf{10}, 1200.} has an $r_e$ that disagrees with the empirical value by over 1500% of the latter's uncertainty, and energy spacings that disagree with those of the empirical potential by up to over 1.5cm$^{-1}$. The discrepancy here is far more than for the ground state of the 5$e^-$ system BeH, for which the best textit{ab initio} calculation gives an $r_e$ which disagrees with the empirical value by less than 200% of the latter's uncertaintyfootnote{Dattani N. S. (2015) textit{J. Mol. Spec.} http://dx.doi.org/10.1016/j.jms.2014.09.005 }. In addition to this discrepancy, other reasons motivating the construction of an analytic empirical potential for Li$_2(b,1^3Pi_u)$ include (1) the fact that it is the most deeply bound Li$_2$ state, (2) it is the only Li$_2$ state out of the lowest five, for which no analytic empirical potential has yet been built, (3) the state it mixes with, the $A(1^1Sigma_u)$-state, is one of the most thoroughly characterized molecular states, but has a small gap of missing data in part of the region where it mixes with the $b$-state, and (4) it is one of the states accessible by new ultra-high precision techniques based on photoassociationfootnote{Semczuk M., Li X., Gunton W., Haw M., Dattani N. S., Witz J., Mills A., Jones D. J., Madison K. W. (2013) textit{Phys. Rev. A} textbf{87}, 052505 }$^,$footnote{Gunton W., Semczuk M., Dattani N. S., Madison K. W. (2013) textit{Phys. Rev. A} textbf{88}, 062510}. Finally (5) there is currently a discrepancy between the most sophisticated 3$e^{-}$ textit{ab initio} calculationfootnote{Tang L.-Y., Yan Z.-C., Shi T.-Y., Mitroy J (2011) textit{Phys. Rev. A} textbf{84}, 052502.}, and the most current empirical valuefootnote{Le$,$Roy R. J., Dattani N. S., Coxon J. A., Ross A. J., Crozet P., Linton C. (2009) textit{J. Chem Phys.} textbf{131}, 204309}, for the first Li$(^2S)-$Li$(^2P)$ interaction term ($C_3$), despite the latter being the most precise experimentally determined oscillator strength for any system, by an order of magnitude$^e$. The $b$-state is one of the states that has this exact $C_3$ interaction term