MgV3P3O13 crystallizes in the monoclinic P2_1/m space group. Mg(1) is bonded in a 7-coordinate geometry to one O(9), two equivalent O(2), two equivalent O(4), and two equivalent O(8) atoms. There are three inequivalent V sites. In the first V site, V(1) is bonded to one O(1), one O(5), one O(6), one O(9), and two equivalent O(8) atoms to form distorted VO6 octahedra that share corners with two equivalent V(3)O6 octahedra,  a cornercorner with one P(1)O4 tetrahedra, corners with two equivalent P(2)O4 tetrahedra,  a cornercorner with one V(2)O5 trigonal bipyramid, and  an edgeedge with one P(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 55°. In the second V site, V(2) is bonded to one O(1), one O(3), one O(7), and two equivalent O(2) atoms to form distorted VO5 trigonal bipyramids that share  a cornercorner with one V(1)O6 octahedra,  a cornercorner with one P(2)O4 tetrahedra,  a cornercorner with one P(3)O4 tetrahedra, and corners with three equivalent P(1)O4 tetrahedra. The corner-sharing octahedral tilt angles are 50°. In the third V site, V(3) is bonded to two equivalent O(10), two equivalent O(4), and two equivalent O(6) atoms to form VO6 octahedra that share corners with two equivalent V(1)O6 octahedra, corners with two equivalent P(2)O4 tetrahedra, corners with two equivalent P(3)O4 tetrahedra, and edges with two equivalent V(3)O6 octahedra. The corner-sharing octahedral tilt angles are 55°. There are three inequivalent P sites. In the first P site, P(1) is bonded to one O(5), one O(7), and two equivalent O(2) atoms to form PO4 tetrahedra that share  a cornercorner with one V(1)O6 octahedra and corners with three equivalent V(2)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 34°. In the second P site, P(2) is bonded to one O(10), one O(3), and two equivalent O(8) atoms to form PO4 tetrahedra that share corners with two equivalent V(1)O6 octahedra, corners with two equivalent V(3)O6 octahedra, and  a cornercorner with one V(2)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 46-54°. In the third P site, P(3) is bonded to one O(1), one O(9), and two equivalent O(4) atoms to form PO4 tetrahedra that share corners with two equivalent V(3)O6 octahedra,  a cornercorner with one V(2)O5 trigonal bipyramid, and  an edgeedge with one V(1)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. There are ten inequivalent O sites. In the first O site, O(10) is bonded in a distorted trigonal planar geometry to two equivalent V(3) and one P(2) atom. In the second O site, O(1) is bonded in a distorted trigonal planar geometry to one V(1), one V(2), and one P(3) atom. In the third O site, O(2) is bonded in a 3-coordinate geometry to one Mg(1), one V(2), and one P(1) atom. In the fourth O site, O(3) is bonded in a linear geometry to one V(2) and one P(2) atom. In the fifth O site, O(4) is bonded in a distorted trigonal planar geometry to one Mg(1), one V(3), and one P(3) atom. In the sixth O site, O(5) is bonded in a bent 150 degrees geometry to one V(1) and one P(1) atom. In the seventh O site, O(6) is bonded in a trigonal planar geometry to one V(1) and two equivalent V(3) atoms. In the eighth O site, O(7) is bonded in a bent 150 degrees geometry to one V(2) and one P(1) atom. In the ninth O site, O(8) is bonded in a distorted trigonal planar geometry to one Mg(1), one V(1), and one P(2) atom. In the tenth O site, O(9) is bonded in a 3-coordinate geometry to one Mg(1), one V(1), and one P(3) atom.
MgV3P3O13 crystallizes in the monoclinic P2_1/m space group. Mg(1) is bonded in a 7-coordinate geometry to one O(9), two equivalent O(2), two equivalent O(4), and two equivalent O(8) atoms. The Mg(1)-O(9) bond length is 2.13 Å. Both Mg(1)-O(2) bond lengths are 2.53 Å. Both Mg(1)-O(4) bond lengths are 2.49 Å. Both Mg(1)-O(8) bond lengths are 2.21 Å. There are three inequivalent V sites. In the first V site, V(1) is bonded to one O(1), one O(5), one O(6), one O(9), and two equivalent O(8) atoms to form distorted VO6 octahedra that share corners with two equivalent V(3)O6 octahedra,  a cornercorner with one P(1)O4 tetrahedra, corners with two equivalent P(2)O4 tetrahedra,  a cornercorner with one V(2)O5 trigonal bipyramid, and  an edgeedge with one P(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 55°. The V(1)-O(1) bond length is 2.07 Å. The V(1)-O(5) bond length is 1.99 Å. The V(1)-O(6) bond length is 1.96 Å. The V(1)-O(9) bond length is 2.20 Å. Both V(1)-O(8) bond lengths are 2.03 Å. In the second V site, V(2) is bonded to one O(1), one O(3), one O(7), and two equivalent O(2) atoms to form distorted VO5 trigonal bipyramids that share  a cornercorner with one V(1)O6 octahedra,  a cornercorner with one P(2)O4 tetrahedra,  a cornercorner with one P(3)O4 tetrahedra, and corners with three equivalent P(1)O4 tetrahedra. The corner-sharing octahedral tilt angles are 50°. The V(2)-O(1) bond length is 1.97 Å. The V(2)-O(3) bond length is 1.93 Å. The V(2)-O(7) bond length is 1.89 Å. Both V(2)-O(2) bond lengths are 2.04 Å. In the third V site, V(3) is bonded to two equivalent O(10), two equivalent O(4), and two equivalent O(6) atoms to form VO6 octahedra that share corners with two equivalent V(1)O6 octahedra, corners with two equivalent P(2)O4 tetrahedra, corners with two equivalent P(3)O4 tetrahedra, and edges with two equivalent V(3)O6 octahedra. The corner-sharing octahedral tilt angles are 55°. Both V(3)-O(10) bond lengths are 2.14 Å. Both V(3)-O(4) bond lengths are 2.09 Å. Both V(3)-O(6) bond lengths are 2.00 Å. There are three inequivalent P sites. In the first P site, P(1) is bonded to one O(5), one O(7), and two equivalent O(2) atoms to form PO4 tetrahedra that share  a cornercorner with one V(1)O6 octahedra and corners with three equivalent V(2)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 34°. The P(1)-O(5) bond length is 1.54 Å. The P(1)-O(7) bond length is 1.55 Å. Both P(1)-O(2) bond lengths are 1.55 Å. In the second P site, P(2) is bonded to one O(10), one O(3), and two equivalent O(8) atoms to form PO4 tetrahedra that share corners with two equivalent V(1)O6 octahedra, corners with two equivalent V(3)O6 octahedra, and  a cornercorner with one V(2)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 46-54°. The P(2)-O(10) bond length is 1.55 Å. The P(2)-O(3) bond length is 1.51 Å. Both P(2)-O(8) bond lengths are 1.56 Å. In the third P site, P(3) is bonded to one O(1), one O(9), and two equivalent O(4) atoms to form PO4 tetrahedra that share corners with two equivalent V(3)O6 octahedra,  a cornercorner with one V(2)O5 trigonal bipyramid, and  an edgeedge with one V(1)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. The P(3)-O(1) bond length is 1.57 Å. The P(3)-O(9) bond length is 1.56 Å. Both P(3)-O(4) bond lengths are 1.55 Å. There are ten inequivalent O sites. In the first O site, O(10) is bonded in a distorted trigonal planar geometry to two equivalent V(3) and one P(2) atom. In the second O site, O(1) is bonded in a distorted trigonal planar geometry to one V(1), one V(2), and one P(3) atom. In the third O site, O(2) is bonded in a 3-coordinate geometry to one Mg(1), one V(2), and one P(1) atom. In the fourth O site, O(3) is bonded in a linear geometry to one V(2) and one P(2) atom. In the fifth O site, O(4) is bonded in a distorted trigonal planar geometry to one Mg(1), one V(3), and one P(3) atom. In the sixth O site, O(5) is bonded in a bent 150 degrees geometry to one V(1) and one P(1) atom. In the seventh O site, O(6) is bonded in a trigonal planar geometry to one V(1) and two equivalent V(3) atoms. In the eighth O site, O(7) is bonded in a bent 150 degrees geometry to one V(2) and one P(1) atom. In the ninth O site, O(8) is bonded in a distorted trigonal planar geometry to one Mg(1), one V(1), and one P(2) atom. In the tenth O site, O(9) is bonded in a 3-coordinate geometry to one Mg(1), one V(1), and one P(3) atom.