A DPF analysis yields accurate analytic potentials for Li${}_2(a{}^3{\mathrm{\Sigma }}_u^{+})$ and Li${}_2(1{}^3{\mathrm{\Sigma }}_g^{+})$ that incorporate 3-state mixing near the $1{}^3{\mathrm{\Sigma }}_g^{+}$-state asymptote

A combined-isotopologue direct-potential-fit (DPF) analysis of optical and photoassociation spectroscopy data for the $a{}^3{\mathrm{\Sigma }}_u^{+}$ and $1{}^3{\mathrm{\Sigma }}_g^{+}$ states of Li${}_2$ has yielded accurate analytic potential energy functions for both states. The recommended M3LR${}_{5,3}^{8.0}(3)$ potential for the $a{}^3{\mathrm{\Sigma }}_u^{+}$ of ${}^{7,7}$Li${}_2$ has a well depth of ${\mathfrak{D}}_e=333.758(7)\mathrm{c}{\mathrm{m}}^{-1}$ and equilibrium distance of $r_e=4.17005(3)$\AA, and the associated scattering lengths are $,a_{\rm SL}= -14.759(9),$\mathring{A}for$^{7,7}$Li$_2$and$-1906(50),$\mathring{A}for$^{6,6}$Li$_2$\mathrm{.}Forthe$1,^3\Sigma_g^+$state,inspiteofagapof$,\sim 5200,{\rm cm}^{-1}$(from$,v(1,^3\Sigma_g^+)= 8-61$) for which there are no data, the DPF procedure has no difficulty determining an accurate overall potential. The $1{}^3{\mathrm{\Sigma }}_g^{+}$ state of the ${}^{7,7}$Li${}_2$ isotopologue has a well depth of ${\mathfrak{D}}_e=7092.417(33)\mathrm{c}{\mathrm{m}}^{-1}$ and equilibrium distance of $r_e=3.06524(9)$\AA. The long-range tail of the recommended M3LR${}_{6,3}^{3.6}(9)$ potential energy function for the $1{}^3{\mathrm{\Sigma }}_g^{+}$ state is defined by the lowest eigenvalue of a $3\times 3$ long-range interstate coupling matrix to take into account the 3-state mixing near its asymptote.