  Ultracold polar and magnetic ${}^{23}$Na${}^6$Li molecules in the
rovibrational ground state of the lowest triplet $a^3\Sigma^+$ electronic state
have been recently produced. Here, we calculate the electronic and
rovibrational structure of these 14-electron molecules with spectroscopic
accuracy ($<0.5\,$cm$^{-1}$) using state-of-the-art ab initio methods of
quantum chemistry. We employ the hierarchy of the coupled-cluster wave
functions and Gaussian basis sets extrapolated to the complete basis set limit.
We show that the inclusion of higher-level excitations, core-electron
correlation, relativistic, QED, and adiabatic corrections is necessary to
reproduce accurately scattering and spectroscopic properties of alkali-metal
systems. We obtain the well depth, $D_e=229.9(5)\,$cm$^{-1}$, the dissociation
energy, $D_0=208.2(5)\,$cm$^{-1}$, and the scattering length,
$a_s=-84^{+25}_{-41}\,$bohr, in good agreement with recent experimental
measurements. We predict the permanent electric dipole moment in the
rovibrational ground state, $d_0=$0.167(1)$\,$debye. These values are obtained
without any adjustment to experimental data, showing that quantum chemistry
methods are capable of predicting scattering properties of many-electron
systems, provided relatively weak interaction and small reduced mass of the
system.
