Hf5N5O2 crystallizes in the monoclinic Cm space group. There are five inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to one N(3), one N(5), two equivalent N(1), and two equivalent N(2) atoms to form HfN6 octahedra that share  a cornercorner with one Hf(5)N3O3 octahedra, corners with two equivalent Hf(4)N5O octahedra, edges with two equivalent Hf(1)N6 octahedra, and edges with three equivalent Hf(4)N5O octahedra. The corner-sharing octahedral tilt angles range from 7-57°. In the second Hf site, Hf(2) is bonded in a 8-coordinate geometry to one N(1), two equivalent N(3), two equivalent N(4), one O(2), and two equivalent O(1) atoms. In the third Hf site, Hf(3) is bonded in a 7-coordinate geometry to one N(4), two equivalent N(2), two equivalent N(5), and two equivalent O(2) atoms. In the fourth Hf site, Hf(4) is bonded to one N(2), two equivalent N(1), two equivalent N(3), and one O(1) atom to form HfN5O octahedra that share  a cornercorner with one Hf(5)N3O3 octahedra, corners with two equivalent Hf(1)N6 octahedra, edges with two equivalent Hf(4)N5O octahedra, and edges with three equivalent Hf(1)N6 octahedra. The corner-sharing octahedral tilt angles range from 7-61°. In the fifth Hf site, Hf(5) is bonded to one N(5), two equivalent N(4), one O(1), and two equivalent O(2) atoms to form HfN3O3 octahedra that share  a cornercorner with one Hf(4)N5O octahedra,  a cornercorner with one Hf(1)N6 octahedra, and edges with two equivalent Hf(5)N3O3 octahedra. The corner-sharing octahedral tilt angles range from 57-61°. There are five inequivalent N sites. In the first N site, N(1) is bonded in a distorted rectangular see-saw-like geometry to one Hf(2), two equivalent Hf(1), and two equivalent Hf(4) atoms. In the second N site, N(2) is bonded to one Hf(4), two equivalent Hf(1), and two equivalent Hf(3) atoms to form NHf5 trigonal bipyramids that share  a cornercorner with one O(1)Hf4 tetrahedra, corners with four equivalent N(5)Hf4 tetrahedra, corners with two equivalent N(4)Hf5 trigonal bipyramids, corners with two equivalent O(2)Hf5 trigonal bipyramids,  an edgeedge with one N(5)Hf4 tetrahedra,  an edgeedge with one O(2)Hf5 trigonal bipyramid, edges with two equivalent N(2)Hf5 trigonal bipyramids, and edges with two equivalent N(3)Hf5 trigonal bipyramids. In the third N site, N(3) is bonded to one Hf(1), two equivalent Hf(2), and two equivalent Hf(4) atoms to form NHf5 trigonal bipyramids that share  a cornercorner with one N(5)Hf4 tetrahedra, corners with four equivalent O(1)Hf4 tetrahedra, corners with two equivalent N(4)Hf5 trigonal bipyramids, corners with two equivalent O(2)Hf5 trigonal bipyramids,  an edgeedge with one O(1)Hf4 tetrahedra,  an edgeedge with one N(4)Hf5 trigonal bipyramid, edges with two equivalent N(2)Hf5 trigonal bipyramids, and edges with two equivalent N(3)Hf5 trigonal bipyramids. In the fourth N site, N(4) is bonded to one Hf(3), two equivalent Hf(2), and two equivalent Hf(5) atoms to form distorted NHf5 trigonal bipyramids that share corners with four equivalent O(1)Hf4 tetrahedra, corners with two equivalent N(2)Hf5 trigonal bipyramids, corners with two equivalent N(3)Hf5 trigonal bipyramids, corners with two equivalent O(2)Hf5 trigonal bipyramids,  an edgeedge with one O(1)Hf4 tetrahedra, edges with two equivalent N(5)Hf4 tetrahedra,  an edgeedge with one N(3)Hf5 trigonal bipyramid, edges with two equivalent N(4)Hf5 trigonal bipyramids, and edges with three equivalent O(2)Hf5 trigonal bipyramids. In the fifth N site, N(5) is bonded to one Hf(1), one Hf(5), and two equivalent Hf(3) atoms to form NHf4 tetrahedra that share  a cornercorner with one O(1)Hf4 tetrahedra, corners with two equivalent N(5)Hf4 tetrahedra,  a cornercorner with one N(3)Hf5 trigonal bipyramid, corners with four equivalent N(2)Hf5 trigonal bipyramids, corners with four equivalent O(2)Hf5 trigonal bipyramids,  an edgeedge with one N(2)Hf5 trigonal bipyramid,  an edgeedge with one O(2)Hf5 trigonal bipyramid, and edges with two equivalent N(4)Hf5 trigonal bipyramids. There are two inequivalent O sites. In the first O site, O(1) is bonded to one Hf(4), one Hf(5), and two equivalent Hf(2) atoms to form OHf4 tetrahedra that share  a cornercorner with one N(5)Hf4 tetrahedra, corners with two equivalent O(1)Hf4 tetrahedra,  a cornercorner with one N(2)Hf5 trigonal bipyramid, corners with four equivalent N(3)Hf5 trigonal bipyramids, corners with four equivalent N(4)Hf5 trigonal bipyramids,  an edgeedge with one N(3)Hf5 trigonal bipyramid,  an edgeedge with one N(4)Hf5 trigonal bipyramid, and edges with two equivalent O(2)Hf5 trigonal bipyramids. In the second O site, O(2) is bonded to one Hf(2), two equivalent Hf(3), and two equivalent Hf(5) atoms to form distorted OHf5 trigonal bipyramids that share corners with four equivalent N(5)Hf4 tetrahedra, corners with two equivalent N(2)Hf5 trigonal bipyramids, corners with two equivalent N(3)Hf5 trigonal bipyramids, corners with two equivalent N(4)Hf5 trigonal bipyramids,  an edgeedge with one N(5)Hf4 tetrahedra, edges with two equivalent O(1)Hf4 tetrahedra,  an edgeedge with one N(2)Hf5 trigonal bipyramid, edges with two equivalent O(2)Hf5 trigonal bipyramids, and edges with three equivalent N(4)Hf5 trigonal bipyramids.
Hf5N5O2 crystallizes in the monoclinic Cm space group. There are five inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to one N(3), one N(5), two equivalent N(1), and two equivalent N(2) atoms to form HfN6 octahedra that share  a cornercorner with one Hf(5)N3O3 octahedra, corners with two equivalent Hf(4)N5O octahedra, edges with two equivalent Hf(1)N6 octahedra, and edges with three equivalent Hf(4)N5O octahedra. The corner-sharing octahedral tilt angles range from 7-57°. The Hf(1)-N(3) bond length is 2.30 Å. The Hf(1)-N(5) bond length is 2.10 Å. Both Hf(1)-N(1) bond lengths are 2.17 Å. Both Hf(1)-N(2) bond lengths are 2.23 Å. In the second Hf site, Hf(2) is bonded in a 8-coordinate geometry to one N(1), two equivalent N(3), two equivalent N(4), one O(2), and two equivalent O(1) atoms. The Hf(2)-N(1) bond length is 2.81 Å. Both Hf(2)-N(3) bond lengths are 2.28 Å. Both Hf(2)-N(4) bond lengths are 2.28 Å. The Hf(2)-O(2) bond length is 2.48 Å. Both Hf(2)-O(1) bond lengths are 2.20 Å. In the third Hf site, Hf(3) is bonded in a 7-coordinate geometry to one N(4), two equivalent N(2), two equivalent N(5), and two equivalent O(2) atoms. The Hf(3)-N(4) bond length is 2.45 Å. Both Hf(3)-N(2) bond lengths are 2.31 Å. Both Hf(3)-N(5) bond lengths are 2.15 Å. Both Hf(3)-O(2) bond lengths are 2.36 Å. In the fourth Hf site, Hf(4) is bonded to one N(2), two equivalent N(1), two equivalent N(3), and one O(1) atom to form HfN5O octahedra that share  a cornercorner with one Hf(5)N3O3 octahedra, corners with two equivalent Hf(1)N6 octahedra, edges with two equivalent Hf(4)N5O octahedra, and edges with three equivalent Hf(1)N6 octahedra. The corner-sharing octahedral tilt angles range from 7-61°. The Hf(4)-N(2) bond length is 2.21 Å. Both Hf(4)-N(1) bond lengths are 2.17 Å. Both Hf(4)-N(3) bond lengths are 2.19 Å. The Hf(4)-O(1) bond length is 2.18 Å. In the fifth Hf site, Hf(5) is bonded to one N(5), two equivalent N(4), one O(1), and two equivalent O(2) atoms to form HfN3O3 octahedra that share  a cornercorner with one Hf(4)N5O octahedra,  a cornercorner with one Hf(1)N6 octahedra, and edges with two equivalent Hf(5)N3O3 octahedra. The corner-sharing octahedral tilt angles range from 57-61°. The Hf(5)-N(5) bond length is 2.05 Å. Both Hf(5)-N(4) bond lengths are 2.15 Å. The Hf(5)-O(1) bond length is 2.17 Å. Both Hf(5)-O(2) bond lengths are 2.25 Å. There are five inequivalent N sites. In the first N site, N(1) is bonded in a distorted rectangular see-saw-like geometry to one Hf(2), two equivalent Hf(1), and two equivalent Hf(4) atoms. In the second N site, N(2) is bonded to one Hf(4), two equivalent Hf(1), and two equivalent Hf(3) atoms to form NHf5 trigonal bipyramids that share  a cornercorner with one O(1)Hf4 tetrahedra, corners with four equivalent N(5)Hf4 tetrahedra, corners with two equivalent N(4)Hf5 trigonal bipyramids, corners with two equivalent O(2)Hf5 trigonal bipyramids,  an edgeedge with one N(5)Hf4 tetrahedra,  an edgeedge with one O(2)Hf5 trigonal bipyramid, edges with two equivalent N(2)Hf5 trigonal bipyramids, and edges with two equivalent N(3)Hf5 trigonal bipyramids. In the third N site, N(3) is bonded to one Hf(1), two equivalent Hf(2), and two equivalent Hf(4) atoms to form NHf5 trigonal bipyramids that share  a cornercorner with one N(5)Hf4 tetrahedra, corners with four equivalent O(1)Hf4 tetrahedra, corners with two equivalent N(4)Hf5 trigonal bipyramids, corners with two equivalent O(2)Hf5 trigonal bipyramids,  an edgeedge with one O(1)Hf4 tetrahedra,  an edgeedge with one N(4)Hf5 trigonal bipyramid, edges with two equivalent N(2)Hf5 trigonal bipyramids, and edges with two equivalent N(3)Hf5 trigonal bipyramids. In the fourth N site, N(4) is bonded to one Hf(3), two equivalent Hf(2), and two equivalent Hf(5) atoms to form distorted NHf5 trigonal bipyramids that share corners with four equivalent O(1)Hf4 tetrahedra, corners with two equivalent N(2)Hf5 trigonal bipyramids, corners with two equivalent N(3)Hf5 trigonal bipyramids, corners with two equivalent O(2)Hf5 trigonal bipyramids,  an edgeedge with one O(1)Hf4 tetrahedra, edges with two equivalent N(5)Hf4 tetrahedra,  an edgeedge with one N(3)Hf5 trigonal bipyramid, edges with two equivalent N(4)Hf5 trigonal bipyramids, and edges with three equivalent O(2)Hf5 trigonal bipyramids. In the fifth N site, N(5) is bonded to one Hf(1), one Hf(5), and two equivalent Hf(3) atoms to form NHf4 tetrahedra that share  a cornercorner with one O(1)Hf4 tetrahedra, corners with two equivalent N(5)Hf4 tetrahedra,  a cornercorner with one N(3)Hf5 trigonal bipyramid, corners with four equivalent N(2)Hf5 trigonal bipyramids, corners with four equivalent O(2)Hf5 trigonal bipyramids,  an edgeedge with one N(2)Hf5 trigonal bipyramid,  an edgeedge with one O(2)Hf5 trigonal bipyramid, and edges with two equivalent N(4)Hf5 trigonal bipyramids. There are two inequivalent O sites. In the first O site, O(1) is bonded to one Hf(4), one Hf(5), and two equivalent Hf(2) atoms to form OHf4 tetrahedra that share  a cornercorner with one N(5)Hf4 tetrahedra, corners with two equivalent O(1)Hf4 tetrahedra,  a cornercorner with one N(2)Hf5 trigonal bipyramid, corners with four equivalent N(3)Hf5 trigonal bipyramids, corners with four equivalent N(4)Hf5 trigonal bipyramids,  an edgeedge with one N(3)Hf5 trigonal bipyramid,  an edgeedge with one N(4)Hf5 trigonal bipyramid, and edges with two equivalent O(2)Hf5 trigonal bipyramids. In the second O site, O(2) is bonded to one Hf(2), two equivalent Hf(3), and two equivalent Hf(5) atoms to form distorted OHf5 trigonal bipyramids that share corners with four equivalent N(5)Hf4 tetrahedra, corners with two equivalent N(2)Hf5 trigonal bipyramids, corners with two equivalent N(3)Hf5 trigonal bipyramids, corners with two equivalent N(4)Hf5 trigonal bipyramids,  an edgeedge with one N(5)Hf4 tetrahedra, edges with two equivalent O(1)Hf4 tetrahedra,  an edgeedge with one N(2)Hf5 trigonal bipyramid, edges with two equivalent O(2)Hf5 trigonal bipyramids, and edges with three equivalent N(4)Hf5 trigonal bipyramids.