Na4Mn2C4SO16 crystallizes in the orthorhombic F222 space group. There are four inequivalent Na sites. In the first Na site, Na(1) is bonded to two equivalent O(2), two equivalent O(4), and two equivalent O(8) atoms to form distorted NaO6 octahedra that share corners with two equivalent Na(3)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, and  an edgeedge with one S(1)O4 tetrahedra. The corner-sharing octahedral tilt angles are 61°. In the second Na site, Na(2) is bonded to two equivalent O(5), two equivalent O(6), and two equivalent O(7) atoms to form distorted NaO6 octahedra that share corners with two equivalent Na(3)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, and  an edgeedge with one S(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 83°. In the third Na site, Na(3) is bonded to two equivalent O(1), two equivalent O(4), and two equivalent O(5) atoms to form distorted NaO6 octahedra that share corners with two equivalent Na(1)O6 octahedra, corners with two equivalent Na(2)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, and  an edgeedge with one S(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 61-83°. In the fourth Na site, Na(4) is bonded in a distorted hexagonal planar geometry to two equivalent O(3), two equivalent O(4), and two equivalent O(6) atoms. Mn(1) is bonded to one O(1), one O(2), one O(3), one O(5), one O(6), and one O(8) atom to form MnO6 octahedra that share  an edgeedge with one Na(1)O6 octahedra,  an edgeedge with one Na(2)O6 octahedra, and  an edgeedge with one Na(3)O6 octahedra. There are two inequivalent C sites. In the first C site, C(1) is bonded in a trigonal planar geometry to one O(2), one O(3), and one O(5) atom. In the second C site, C(2) is bonded in a trigonal planar geometry to one O(1), one O(6), and one O(8) atom. There are two inequivalent S sites. In the first S site, S(1) is bonded to four equivalent O(4) atoms to form SO4 tetrahedra that share edges with two equivalent Na(1)O6 octahedra and edges with two equivalent Na(3)O6 octahedra. In the second S site, S(2) is bonded to four equivalent O(7) atoms to form SO4 tetrahedra that share edges with two equivalent Na(2)O6 octahedra. There are eight inequivalent O sites. In the first O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Na(2), one Na(4), one Mn(1), and one C(2) atom. In the second O site, O(7) is bonded in an L-shaped geometry to one Na(2) and one S(2) atom. In the third O site, O(8) is bonded in a 3-coordinate geometry to one Na(1), one Mn(1), and one C(2) atom. In the fourth O site, O(1) is bonded in a 3-coordinate geometry to one Na(3), one Mn(1), and one C(2) atom. In the fifth O site, O(2) is bonded in a 3-coordinate geometry to one Na(1), one Mn(1), and one C(1) atom. In the sixth O site, O(3) is bonded in a 3-coordinate geometry to one Na(4), one Mn(1), and one C(1) atom. In the seventh O site, O(4) is bonded to one Na(1), one Na(3), one Na(4), and one S(1) atom to form distorted edge-sharing ONa3S trigonal pyramids. In the eighth O site, O(5) is bonded in a 4-coordinate geometry to one Na(2), one Na(3), one Mn(1), and one C(1) atom.
Na4Mn2C4SO16 crystallizes in the orthorhombic F222 space group. There are four inequivalent Na sites. In the first Na site, Na(1) is bonded to two equivalent O(2), two equivalent O(4), and two equivalent O(8) atoms to form distorted NaO6 octahedra that share corners with two equivalent Na(3)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, and  an edgeedge with one S(1)O4 tetrahedra. The corner-sharing octahedral tilt angles are 61°. Both Na(1)-O(2) bond lengths are 2.39 Å. Both Na(1)-O(4) bond lengths are 2.42 Å. Both Na(1)-O(8) bond lengths are 2.52 Å. In the second Na site, Na(2) is bonded to two equivalent O(5), two equivalent O(6), and two equivalent O(7) atoms to form distorted NaO6 octahedra that share corners with two equivalent Na(3)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, and  an edgeedge with one S(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 83°. Both Na(2)-O(5) bond lengths are 2.49 Å. Both Na(2)-O(6) bond lengths are 2.41 Å. Both Na(2)-O(7) bond lengths are 2.36 Å. In the third Na site, Na(3) is bonded to two equivalent O(1), two equivalent O(4), and two equivalent O(5) atoms to form distorted NaO6 octahedra that share corners with two equivalent Na(1)O6 octahedra, corners with two equivalent Na(2)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, and  an edgeedge with one S(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 61-83°. Both Na(3)-O(1) bond lengths are 2.51 Å. Both Na(3)-O(4) bond lengths are 2.44 Å. Both Na(3)-O(5) bond lengths are 2.44 Å. In the fourth Na site, Na(4) is bonded in a distorted hexagonal planar geometry to two equivalent O(3), two equivalent O(4), and two equivalent O(6) atoms. Both Na(4)-O(3) bond lengths are 2.46 Å. Both Na(4)-O(4) bond lengths are 2.51 Å. Both Na(4)-O(6) bond lengths are 2.44 Å. Mn(1) is bonded to one O(1), one O(2), one O(3), one O(5), one O(6), and one O(8) atom to form MnO6 octahedra that share  an edgeedge with one Na(1)O6 octahedra,  an edgeedge with one Na(2)O6 octahedra, and  an edgeedge with one Na(3)O6 octahedra. The Mn(1)-O(1) bond length is 2.02 Å. The Mn(1)-O(2) bond length is 2.18 Å. The Mn(1)-O(3) bond length is 2.03 Å. The Mn(1)-O(5) bond length is 2.12 Å. The Mn(1)-O(6) bond length is 2.23 Å. The Mn(1)-O(8) bond length is 2.07 Å. There are two inequivalent C sites. In the first C site, C(1) is bonded in a trigonal planar geometry to one O(2), one O(3), and one O(5) atom. The C(1)-O(2) bond length is 1.27 Å. The C(1)-O(3) bond length is 1.31 Å. The C(1)-O(5) bond length is 1.32 Å. In the second C site, C(2) is bonded in a trigonal planar geometry to one O(1), one O(6), and one O(8) atom. The C(2)-O(1) bond length is 1.31 Å. The C(2)-O(6) bond length is 1.29 Å. The C(2)-O(8) bond length is 1.29 Å. There are two inequivalent S sites. In the first S site, S(1) is bonded to four equivalent O(4) atoms to form SO4 tetrahedra that share edges with two equivalent Na(1)O6 octahedra and edges with two equivalent Na(3)O6 octahedra. All S(1)-O(4) bond lengths are 1.50 Å. In the second S site, S(2) is bonded to four equivalent O(7) atoms to form SO4 tetrahedra that share edges with two equivalent Na(2)O6 octahedra. All S(2)-O(7) bond lengths are 1.49 Å. There are eight inequivalent O sites. In the first O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Na(2), one Na(4), one Mn(1), and one C(2) atom. In the second O site, O(7) is bonded in an L-shaped geometry to one Na(2) and one S(2) atom. In the third O site, O(8) is bonded in a 3-coordinate geometry to one Na(1), one Mn(1), and one C(2) atom. In the fourth O site, O(1) is bonded in a 3-coordinate geometry to one Na(3), one Mn(1), and one C(2) atom. In the fifth O site, O(2) is bonded in a 3-coordinate geometry to one Na(1), one Mn(1), and one C(1) atom. In the sixth O site, O(3) is bonded in a 3-coordinate geometry to one Na(4), one Mn(1), and one C(1) atom. In the seventh O site, O(4) is bonded to one Na(1), one Na(3), one Na(4), and one S(1) atom to form distorted edge-sharing ONa3S trigonal pyramids. In the eighth O site, O(5) is bonded in a 4-coordinate geometry to one Na(2), one Na(3), one Mn(1), and one C(1) atom.