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We report state-of-the-art ab initio calculations of the potential energycurve for the $a^3\Sigma_u^+$ state of the lithium dimer conducted to achievespectroscopic accuracy ($<$1cm$^{-1}$) without any prior adjustment to fit thecorresponding experimental data. The nonrelativistic clamped-nuclei componentof the interaction energy is calculated with a composite method involvingsix-electron coupled cluster and full configuration interaction theoriescombined with basis sets of Slater-type orbitals ranging in quality fromdouble- to sextuple-zeta. To go beyond the nonrelativistic Born-Oppenheimerpicture we include both the leading-order relativistic and adiabaticcorrections, and find both of these effects to be non-negligible within thepresent accuracy standards. The potential energy curve developed by us allowedto calculate molecular parameters ($D_e$, $D_0$, $\omega_e$ etc.) for thissystem, as well as the corresponding vibrational energy levels, with an errorof only a few tenths of a wavenumber ($0.2-0.4\,$cm$^{-1}$). We also report anab initio value for the scattering length of two $^2S$ lithium atoms whichdetermines the stability of the related Bose-Einstein condensate.

Potential energy curve for the $a^3\Sigma_u^+$ state of lithium dimer with Slater-type orbitals