The sodium–sulfur (NAS) battery is a candidate for energy storage and load leveling in power systems, by using the reversible reduction of elemental sulfur by sodium metal to give a liquid mixture of polysulfides (Na2Sn) at approximately 320 °C. We investigated a large number of reactions possibly occurring in such sodium polysulfide melts by using density functional calculations at the G3X(MP2)/B3LYP/6-31+G(2df,p) level of theory including polarizable continuum model (PCM) corrections for two polarizable phases, to obtain geometric and, for the first time, thermodynamic data for the liquid sodium–sulfur system. Novel reaction sequences for the electrochemical reduction of elemental sulfur are proposed on the basis of their Gibbs reaction energies. We suggest that the primary reduction product of S8 is the radical anion , which decomposes at the operating temperature of NAS batteries exergonically to the radicals and together with the neutral species S6 and S5, respectively. In addition, is predicted to disproportionate exergonically to S8 and followed by the dissociation of the latter into two radical ions. By recombination reactions of these radicals various polysulfide dianions can in principle be formed. However, polysulfide dianions larger than are thermally unstable at 320 °C and smaller dianions as well as radical monoanions dominate in Na2Sn (n=2–5) melts instead. The reverse reactions are predicted to take place when the NAS battery is charged. We show that ion pairs of the types , , and Na2Sn can be expected at least for n=2 and 3 in NAS batteries, but are unlikely in aqueous sodium polysulfide except at high concentrations. The structures of such radicals and anions with up to nine sulfur atoms are reported, because they are predicted to play a key role in the electrochemical reduction process. A large number of isomerization, disproportionation, and sulfurization reactions of polysulfide mono- and dianions have been investigated in the gas phase and in a polarizable continuum, and numerous reaction enthalpies as well as Gibbs energies are reported.