KMgCu4V3O13 crystallizes in the monoclinic P2_1/m space group. K(1) is bonded in a 10-coordinate geometry to one O(6), two equivalent O(5), three equivalent O(4), and four equivalent O(8) atoms. Mg(1) is bonded to one O(4), one O(7), two equivalent O(10), and two equivalent O(8) atoms to form MgO6 octahedra that share  a cornercorner with one V(3)O4 tetrahedra, corners with two equivalent V(2)O4 tetrahedra, corners with three equivalent V(1)O4 tetrahedra, edges with two equivalent Cu(1)O5 square pyramids, and  an edgeedge with one Cu(3)O5 trigonal bipyramid. There are three inequivalent V sites. In the first V site, V(1) is bonded to one O(7), one O(9), and two equivalent O(8) atoms to form VO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra and corners with four equivalent Cu(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 48-68°. In the second V site, V(2) is bonded to one O(3), one O(6), and two equivalent O(10) atoms to form VO4 tetrahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Cu(1)O5 square pyramids,  a cornercorner with one Cu(2)O5 trigonal bipyramid, and corners with three equivalent Cu(3)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 34°. In the third V site, V(3) is bonded to one O(1), one O(4), and two equivalent O(5) atoms to form VO4 tetrahedra that share  a cornercorner with one Mg(1)O6 octahedra, corners with two equivalent Cu(1)O5 square pyramids,  a cornercorner with one Cu(3)O5 trigonal bipyramid, and corners with three equivalent Cu(2)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 45°. There are three inequivalent Cu sites. In the first Cu site, Cu(1) is bonded to one O(10), one O(2), one O(5), one O(7), and one O(9) atom to form distorted CuO5 square pyramids that share  a cornercorner with one Cu(1)O5 square pyramid,  a cornercorner with one V(2)O4 tetrahedra,  a cornercorner with one V(3)O4 tetrahedra, corners with two equivalent V(1)O4 tetrahedra, corners with two equivalent Cu(3)O5 trigonal bipyramids,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Cu(1)O5 square pyramid, and  an edgeedge with one Cu(2)O5 trigonal bipyramid. In the second Cu site, Cu(2) is bonded to one O(1), one O(2), one O(6), and two equivalent O(5) atoms to form distorted CuO5 trigonal bipyramids that share  a cornercorner with one V(2)O4 tetrahedra, corners with three equivalent V(3)O4 tetrahedra, edges with two equivalent Cu(1)O5 square pyramids, and  an edgeedge with one Cu(3)O5 trigonal bipyramid. In the third Cu site, Cu(3) is bonded to one O(1), one O(2), one O(3), and two equivalent O(10) atoms to form CuO5 trigonal bipyramids that share corners with four equivalent Cu(1)O5 square pyramids,  a cornercorner with one V(3)O4 tetrahedra, corners with three equivalent V(2)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra, and  an edgeedge with one Cu(2)O5 trigonal bipyramid. There are ten inequivalent O sites. In the first O site, O(7) is bonded to one Mg(1), one V(1), and two equivalent Cu(1) atoms to form OMgVCu2 tetrahedra that share corners with two equivalent O(2)Cu4 trigonal pyramids and edges with two equivalent O(10)MgVCu2 tetrahedra. In the second O site, O(8) is bonded in a 4-coordinate geometry to two equivalent K(1), one Mg(1), and one V(1) atom. In the third O site, O(9) is bonded in a 3-coordinate geometry to one V(1) and two equivalent Cu(1) atoms. In the fourth O site, O(10) is bonded to one Mg(1), one V(2), one Cu(1), and one Cu(3) atom to form distorted OMgVCu2 tetrahedra that share  a cornercorner with one O(10)MgVCu2 tetrahedra, corners with two equivalent O(2)Cu4 trigonal pyramids,  an edgeedge with one O(10)MgVCu2 tetrahedra, and  an edgeedge with one O(7)MgVCu2 tetrahedra. In the fifth O site, O(1) is bonded in a distorted trigonal planar geometry to one V(3), one Cu(2), and one Cu(3) atom. In the sixth O site, O(2) is bonded to one Cu(2), one Cu(3), and two equivalent Cu(1) atoms to form distorted corner-sharing OCu4 trigonal pyramids. In the seventh O site, O(3) is bonded in a bent 120 degrees geometry to one V(2) and one Cu(3) atom. In the eighth O site, O(4) is bonded in a 2-coordinate geometry to three equivalent K(1), one Mg(1), and one V(3) atom. In the ninth O site, O(5) is bonded in a 4-coordinate geometry to one K(1), one V(3), one Cu(1), and one Cu(2) atom. In the tenth O site, O(6) is bonded in a distorted linear geometry to one K(1), one V(2), and one Cu(2) atom.
KMgCu4V3O13 crystallizes in the monoclinic P2_1/m space group. K(1) is bonded in a 10-coordinate geometry to one O(6), two equivalent O(5), three equivalent O(4), and four equivalent O(8) atoms. The K(1)-O(6) bond length is 2.99 Å. Both K(1)-O(5) bond lengths are 2.92 Å. There is one shorter (2.91 Å) and two longer (3.20 Å) K(1)-O(4) bond lengths. There are two shorter (2.80 Å) and two longer (2.90 Å) K(1)-O(8) bond lengths. Mg(1) is bonded to one O(4), one O(7), two equivalent O(10), and two equivalent O(8) atoms to form MgO6 octahedra that share  a cornercorner with one V(3)O4 tetrahedra, corners with two equivalent V(2)O4 tetrahedra, corners with three equivalent V(1)O4 tetrahedra, edges with two equivalent Cu(1)O5 square pyramids, and  an edgeedge with one Cu(3)O5 trigonal bipyramid. The Mg(1)-O(4) bond length is 2.04 Å. The Mg(1)-O(7) bond length is 2.12 Å. Both Mg(1)-O(10) bond lengths are 2.27 Å. Both Mg(1)-O(8) bond lengths are 2.08 Å. There are three inequivalent V sites. In the first V site, V(1) is bonded to one O(7), one O(9), and two equivalent O(8) atoms to form VO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra and corners with four equivalent Cu(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 48-68°. The V(1)-O(7) bond length is 1.94 Å. The V(1)-O(9) bond length is 1.69 Å. Both V(1)-O(8) bond lengths are 1.72 Å. In the second V site, V(2) is bonded to one O(3), one O(6), and two equivalent O(10) atoms to form VO4 tetrahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Cu(1)O5 square pyramids,  a cornercorner with one Cu(2)O5 trigonal bipyramid, and corners with three equivalent Cu(3)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 34°. The V(2)-O(3) bond length is 1.73 Å. The V(2)-O(6) bond length is 1.70 Å. Both V(2)-O(10) bond lengths are 1.82 Å. In the third V site, V(3) is bonded to one O(1), one O(4), and two equivalent O(5) atoms to form VO4 tetrahedra that share  a cornercorner with one Mg(1)O6 octahedra, corners with two equivalent Cu(1)O5 square pyramids,  a cornercorner with one Cu(3)O5 trigonal bipyramid, and corners with three equivalent Cu(2)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 45°. The V(3)-O(1) bond length is 1.78 Å. The V(3)-O(4) bond length is 1.70 Å. Both V(3)-O(5) bond lengths are 1.77 Å. There are three inequivalent Cu sites. In the first Cu site, Cu(1) is bonded to one O(10), one O(2), one O(5), one O(7), and one O(9) atom to form distorted CuO5 square pyramids that share  a cornercorner with one Cu(1)O5 square pyramid,  a cornercorner with one V(2)O4 tetrahedra,  a cornercorner with one V(3)O4 tetrahedra, corners with two equivalent V(1)O4 tetrahedra, corners with two equivalent Cu(3)O5 trigonal bipyramids,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Cu(1)O5 square pyramid, and  an edgeedge with one Cu(2)O5 trigonal bipyramid. The Cu(1)-O(10) bond length is 1.99 Å. The Cu(1)-O(2) bond length is 1.94 Å. The Cu(1)-O(5) bond length is 1.95 Å. The Cu(1)-O(7) bond length is 1.96 Å. The Cu(1)-O(9) bond length is 2.32 Å. In the second Cu site, Cu(2) is bonded to one O(1), one O(2), one O(6), and two equivalent O(5) atoms to form distorted CuO5 trigonal bipyramids that share  a cornercorner with one V(2)O4 tetrahedra, corners with three equivalent V(3)O4 tetrahedra, edges with two equivalent Cu(1)O5 square pyramids, and  an edgeedge with one Cu(3)O5 trigonal bipyramid. The Cu(2)-O(1) bond length is 1.99 Å. The Cu(2)-O(2) bond length is 2.01 Å. The Cu(2)-O(6) bond length is 1.91 Å. Both Cu(2)-O(5) bond lengths are 2.08 Å. In the third Cu site, Cu(3) is bonded to one O(1), one O(2), one O(3), and two equivalent O(10) atoms to form CuO5 trigonal bipyramids that share corners with four equivalent Cu(1)O5 square pyramids,  a cornercorner with one V(3)O4 tetrahedra, corners with three equivalent V(2)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra, and  an edgeedge with one Cu(2)O5 trigonal bipyramid. The Cu(3)-O(1) bond length is 1.99 Å. The Cu(3)-O(2) bond length is 1.98 Å. The Cu(3)-O(3) bond length is 1.95 Å. Both Cu(3)-O(10) bond lengths are 2.21 Å. There are ten inequivalent O sites. In the first O site, O(7) is bonded to one Mg(1), one V(1), and two equivalent Cu(1) atoms to form OMgVCu2 tetrahedra that share corners with two equivalent O(2)Cu4 trigonal pyramids and edges with two equivalent O(10)MgVCu2 tetrahedra. In the second O site, O(8) is bonded in a 4-coordinate geometry to two equivalent K(1), one Mg(1), and one V(1) atom. In the third O site, O(9) is bonded in a 3-coordinate geometry to one V(1) and two equivalent Cu(1) atoms. In the fourth O site, O(10) is bonded to one Mg(1), one V(2), one Cu(1), and one Cu(3) atom to form distorted OMgVCu2 tetrahedra that share  a cornercorner with one O(10)MgVCu2 tetrahedra, corners with two equivalent O(2)Cu4 trigonal pyramids,  an edgeedge with one O(10)MgVCu2 tetrahedra, and  an edgeedge with one O(7)MgVCu2 tetrahedra. In the fifth O site, O(1) is bonded in a distorted trigonal planar geometry to one V(3), one Cu(2), and one Cu(3) atom. In the sixth O site, O(2) is bonded to one Cu(2), one Cu(3), and two equivalent Cu(1) atoms to form distorted corner-sharing OCu4 trigonal pyramids. In the seventh O site, O(3) is bonded in a bent 120 degrees geometry to one V(2) and one Cu(3) atom. In the eighth O site, O(4) is bonded in a 2-coordinate geometry to three equivalent K(1), one Mg(1), and one V(3) atom. In the ninth O site, O(5) is bonded in a 4-coordinate geometry to one K(1), one V(3), one Cu(1), and one Cu(2) atom. In the tenth O site, O(6) is bonded in a distorted linear geometry to one K(1), one V(2), and one Cu(2) atom.