Li4Ti3Cr2Mn3O16 is Spinel-derived structured and crystallizes in the monoclinic Cm space group. There are four inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(12), one O(3), and two equivalent O(9) atoms to form LiO4 tetrahedra that share  a cornercorner with one Mn(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra, and corners with four equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-63°. In the second Li site, Li(2) is bonded to one O(5), one O(7), and two equivalent O(11) atoms to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Ti(2)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra,  an edgeedge with one Mn(1)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 62-66°. In the third Li site, Li(3) is bonded to one O(4), one O(8), and two equivalent O(1) atoms to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Mn(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with three equivalent Cr(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 62-65°. In the fourth Li site, Li(4) is bonded to one O(10), one O(2), and two equivalent O(6) atoms to form LiO4 tetrahedra that share  a cornercorner with one Ti(2)O6 octahedra, corners with two equivalent Mn(1)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with three equivalent Cr(1)O6 octahedra, and corners with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-65°. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(11), one O(2), one O(3), one O(4), one O(6), and one O(7) atom to form TiO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Cr(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 48-51°. In the second Ti site, Ti(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form TiO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Cr(2)O6 octahedra, edges with four equivalent Mn(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 51°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with two equivalent Ti(2)O6 octahedra, corners with four equivalent Mn(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Li(3)O4 trigonal pyramids,  an edgeedge with one Mn(1)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-53°. In the second Cr site, Cr(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form CrO6 octahedra that share corners with two equivalent Mn(1)O6 octahedra, corners with four equivalent Ti(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-53°. There are two inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form MnO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Cr(1)O6 octahedra, edges with four equivalent Ti(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 53°. In the second Mn site, Mn(2) is bonded to one O(1), one O(10), one O(12), one O(5), one O(8), and one O(9) atom to form MnO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Cr(2)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 51-53°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Li(3), one Ti(2), one Cr(1), and one Mn(2) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Ti(1), and one Cr(1) atom to form distorted OLiTi2Cr tetrahedra that share corners with two equivalent O(4)LiTi2Mn tetrahedra,  a cornercorner with one O(10)LiTiMn2 trigonal pyramid, corners with two equivalent O(6)LiTiMnCr trigonal pyramids,  an edgeedge with one O(3)LiTi2Mn trigonal pyramid, and edges with two equivalent O(6)LiTiMnCr trigonal pyramids. In the third O site, O(3) is bonded to one Li(1), two equivalent Ti(1), and one Mn(1) atom to form distorted OLiTi2Mn trigonal pyramids that share corners with two equivalent O(9)LiTiMnCr tetrahedra, corners with three equivalent O(4)LiTi2Mn tetrahedra,  an edgeedge with one O(2)LiTi2Cr tetrahedra, and edges with two equivalent O(6)LiTiMnCr trigonal pyramids. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Ti(1), and one Mn(1) atom to form distorted OLiTi2Mn tetrahedra that share corners with two equivalent O(2)LiTi2Cr tetrahedra, corners with three equivalent O(3)LiTi2Mn trigonal pyramids, and corners with four equivalent O(6)LiTiMnCr trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), one Ti(2), and two equivalent Mn(2) atoms to form OLiTiMn2 tetrahedra that share corners with four equivalent O(9)LiTiMnCr tetrahedra and corners with three equivalent O(10)LiTiMn2 trigonal pyramids. In the sixth O site, O(6) is bonded to one Li(4), one Ti(1), one Cr(1), and one Mn(1) atom to form distorted OLiTiMnCr trigonal pyramids that share  a cornercorner with one O(2)LiTi2Cr tetrahedra, corners with two equivalent O(4)LiTi2Mn tetrahedra,  a cornercorner with one O(10)LiTiMn2 trigonal pyramid,  a cornercorner with one O(6)LiTiMnCr trigonal pyramid,  an edgeedge with one O(2)LiTi2Cr tetrahedra,  an edgeedge with one O(3)LiTi2Mn trigonal pyramid, and  an edgeedge with one O(6)LiTiMnCr trigonal pyramid. In the seventh O site, O(7) is bonded in a distorted rectangular see-saw-like geometry to one Li(2), two equivalent Ti(1), and one Cr(2) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one Cr(1), and two equivalent Mn(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Ti(2), one Cr(2), and one Mn(2) atom to form distorted OLiTiMnCr tetrahedra that share  a cornercorner with one O(9)LiTiMnCr tetrahedra, corners with two equivalent O(5)LiTiMn2 tetrahedra,  a cornercorner with one O(3)LiTi2Mn trigonal pyramid,  an edgeedge with one O(9)LiTiMnCr tetrahedra, and  an edgeedge with one O(10)LiTiMn2 trigonal pyramid. In the tenth O site, O(10) is bonded to one Li(4), one Ti(2), and two equivalent Mn(2) atoms to form distorted OLiTiMn2 trigonal pyramids that share  a cornercorner with one O(2)LiTi2Cr tetrahedra, corners with three equivalent O(5)LiTiMn2 tetrahedra, corners with two equivalent O(6)LiTiMnCr trigonal pyramids, and edges with two equivalent O(9)LiTiMnCr tetrahedra. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(1), one Cr(2), and one Mn(1) atom. In the twelfth O site, O(12) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Cr(2), and two equivalent Mn(2) atoms.
Li4Ti3Cr2Mn3O16 is Spinel-derived structured and crystallizes in the monoclinic Cm space group. There are four inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(12), one O(3), and two equivalent O(9) atoms to form LiO4 tetrahedra that share  a cornercorner with one Mn(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra, and corners with four equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-63°. The Li(1)-O(12) bond length is 1.95 Å. The Li(1)-O(3) bond length is 2.07 Å. Both Li(1)-O(9) bond lengths are 1.99 Å. In the second Li site, Li(2) is bonded to one O(5), one O(7), and two equivalent O(11) atoms to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Ti(2)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra,  an edgeedge with one Mn(1)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 62-66°. The Li(2)-O(5) bond length is 1.79 Å. The Li(2)-O(7) bond length is 2.00 Å. Both Li(2)-O(11) bond lengths are 1.96 Å. In the third Li site, Li(3) is bonded to one O(4), one O(8), and two equivalent O(1) atoms to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Mn(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with three equivalent Cr(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 62-65°. The Li(3)-O(4) bond length is 1.80 Å. The Li(3)-O(8) bond length is 1.92 Å. Both Li(3)-O(1) bond lengths are 1.98 Å. In the fourth Li site, Li(4) is bonded to one O(10), one O(2), and two equivalent O(6) atoms to form LiO4 tetrahedra that share  a cornercorner with one Ti(2)O6 octahedra, corners with two equivalent Mn(1)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with three equivalent Cr(1)O6 octahedra, and corners with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-65°. The Li(4)-O(10) bond length is 2.03 Å. The Li(4)-O(2) bond length is 1.98 Å. Both Li(4)-O(6) bond lengths are 1.98 Å. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(11), one O(2), one O(3), one O(4), one O(6), and one O(7) atom to form TiO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Cr(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 48-51°. The Ti(1)-O(11) bond length is 1.94 Å. The Ti(1)-O(2) bond length is 2.00 Å. The Ti(1)-O(3) bond length is 2.00 Å. The Ti(1)-O(4) bond length is 1.98 Å. The Ti(1)-O(6) bond length is 1.95 Å. The Ti(1)-O(7) bond length is 2.01 Å. In the second Ti site, Ti(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form TiO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Cr(2)O6 octahedra, edges with four equivalent Mn(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 51°. The Ti(2)-O(10) bond length is 1.96 Å. The Ti(2)-O(5) bond length is 1.96 Å. Both Ti(2)-O(1) bond lengths are 1.98 Å. Both Ti(2)-O(9) bond lengths are 2.01 Å. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with two equivalent Ti(2)O6 octahedra, corners with four equivalent Mn(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Li(3)O4 trigonal pyramids,  an edgeedge with one Mn(1)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-53°. The Cr(1)-O(2) bond length is 2.08 Å. The Cr(1)-O(8) bond length is 2.02 Å. Both Cr(1)-O(1) bond lengths are 2.10 Å. Both Cr(1)-O(6) bond lengths are 2.03 Å. In the second Cr site, Cr(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form CrO6 octahedra that share corners with two equivalent Mn(1)O6 octahedra, corners with four equivalent Ti(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-53°. The Cr(2)-O(12) bond length is 2.00 Å. The Cr(2)-O(7) bond length is 2.13 Å. Both Cr(2)-O(11) bond lengths are 2.04 Å. Both Cr(2)-O(9) bond lengths are 2.06 Å. There are two inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form MnO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Cr(1)O6 octahedra, edges with four equivalent Ti(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 53°. The Mn(1)-O(3) bond length is 1.92 Å. The Mn(1)-O(4) bond length is 1.92 Å. Both Mn(1)-O(11) bond lengths are 2.11 Å. Both Mn(1)-O(6) bond lengths are 2.11 Å. In the second Mn site, Mn(2) is bonded to one O(1), one O(10), one O(12), one O(5), one O(8), and one O(9) atom to form MnO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Cr(2)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 51-53°. The Mn(2)-O(1) bond length is 1.99 Å. The Mn(2)-O(10) bond length is 1.97 Å. The Mn(2)-O(12) bond length is 2.03 Å. The Mn(2)-O(5) bond length is 1.97 Å. The Mn(2)-O(8) bond length is 2.05 Å. The Mn(2)-O(9) bond length is 1.97 Å. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Li(3), one Ti(2), one Cr(1), and one Mn(2) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Ti(1), and one Cr(1) atom to form distorted OLiTi2Cr tetrahedra that share corners with two equivalent O(4)LiTi2Mn tetrahedra,  a cornercorner with one O(10)LiTiMn2 trigonal pyramid, corners with two equivalent O(6)LiTiMnCr trigonal pyramids,  an edgeedge with one O(3)LiTi2Mn trigonal pyramid, and edges with two equivalent O(6)LiTiMnCr trigonal pyramids. In the third O site, O(3) is bonded to one Li(1), two equivalent Ti(1), and one Mn(1) atom to form distorted OLiTi2Mn trigonal pyramids that share corners with two equivalent O(9)LiTiMnCr tetrahedra, corners with three equivalent O(4)LiTi2Mn tetrahedra,  an edgeedge with one O(2)LiTi2Cr tetrahedra, and edges with two equivalent O(6)LiTiMnCr trigonal pyramids. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Ti(1), and one Mn(1) atom to form distorted OLiTi2Mn tetrahedra that share corners with two equivalent O(2)LiTi2Cr tetrahedra, corners with three equivalent O(3)LiTi2Mn trigonal pyramids, and corners with four equivalent O(6)LiTiMnCr trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), one Ti(2), and two equivalent Mn(2) atoms to form OLiTiMn2 tetrahedra that share corners with four equivalent O(9)LiTiMnCr tetrahedra and corners with three equivalent O(10)LiTiMn2 trigonal pyramids. In the sixth O site, O(6) is bonded to one Li(4), one Ti(1), one Cr(1), and one Mn(1) atom to form distorted OLiTiMnCr trigonal pyramids that share  a cornercorner with one O(2)LiTi2Cr tetrahedra, corners with two equivalent O(4)LiTi2Mn tetrahedra,  a cornercorner with one O(10)LiTiMn2 trigonal pyramid,  a cornercorner with one O(6)LiTiMnCr trigonal pyramid,  an edgeedge with one O(2)LiTi2Cr tetrahedra,  an edgeedge with one O(3)LiTi2Mn trigonal pyramid, and  an edgeedge with one O(6)LiTiMnCr trigonal pyramid. In the seventh O site, O(7) is bonded in a distorted rectangular see-saw-like geometry to one Li(2), two equivalent Ti(1), and one Cr(2) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one Cr(1), and two equivalent Mn(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Ti(2), one Cr(2), and one Mn(2) atom to form distorted OLiTiMnCr tetrahedra that share  a cornercorner with one O(9)LiTiMnCr tetrahedra, corners with two equivalent O(5)LiTiMn2 tetrahedra,  a cornercorner with one O(3)LiTi2Mn trigonal pyramid,  an edgeedge with one O(9)LiTiMnCr tetrahedra, and  an edgeedge with one O(10)LiTiMn2 trigonal pyramid. In the tenth O site, O(10) is bonded to one Li(4), one Ti(2), and two equivalent Mn(2) atoms to form distorted OLiTiMn2 trigonal pyramids that share  a cornercorner with one O(2)LiTi2Cr tetrahedra, corners with three equivalent O(5)LiTiMn2 tetrahedra, corners with two equivalent O(6)LiTiMnCr trigonal pyramids, and edges with two equivalent O(9)LiTiMnCr tetrahedra. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(1), one Cr(2), and one Mn(1) atom. In the twelfth O site, O(12) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Cr(2), and two equivalent Mn(2) atoms.