Interest in Na-S compounds stems from their use in battery materials at 1 atm, as well as the potential for superconductivity under pressure. Evolutionary structure searches coupled with Density Functional Theory calculations were employed to predict stable and low-lying metastable phases of sodium poor and sodium rich sulfides at 1 atm and within 100–200 GPa. At ambient pressures, four new stable or metastable phases with unbranched sulfur motifs were predicted: Na2
. Van der Waals interactions were shown to affect the energy ordering of various polymorphs. At high pressure, several novel phases that contained a wide variety of zero-, one-, and two-dimensional sulfur motifs were predicted, and their electronic structures and bonding were analyzed. At 200 GPa,
was predicted to become superconducting below 15.5 K, which is close to results previously obtained for the
-Po phase of elemental sulfur. The structures of the most stable M3
S and M4
S, M = Na, phases differed from those previously reported for compounds with M = H, Li, K.
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