cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.17188/1654177
title: Materials Data on LaTiNiO4 by Materials Project

description: LaTiNiO4 crystallizes in the tetragonal P4/nmm space group. The structure is three-dimensional. La3+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of La–O bond distances ranging from 2.35–2.75 Å. Ti4+ is bonded in a 5-coordinate geometry to six O2- atoms. There are a spread of Ti–O bond distances ranging from 1.83–2.60 Å. Ni1+ is bonded to four equivalent O2- atoms to form a mixture of distorted edge and corner-sharing NiO4 trigonal pyramids. All Ni–O bond lengths are 2.06 Å. There are three inequivalent O2- sites. In the first O2- site, O2- is bonded in a 1-coordinate geometry to five equivalent La3+ and one Ti4+ atom. In the second O2- site, O2- is bonded in a 5-coordinate geometry to one Ti4+ and four equivalent Ni1+ atoms. In the third O2- site, O2- is bonded in a 4-coordinate geometry to two equivalent La3+ and two equivalent Ti4+ atoms.
DOI: 10.17188/1654178
title: Materials Data on Tb3Mg by Materials Project

description: MgTb3 crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. Mg is bonded in a body-centered cubic geometry to eight equivalent Tb atoms. All Mg–Tb bond lengths are 3.33 Å. There are two inequivalent Tb sites. In the first Tb site, Tb is bonded in a 12-coordinate geometry to four equivalent Mg and four equivalent Tb atoms. All Tb–Tb bond lengths are 3.52 Å. In the second Tb site, Tb is bonded to twelve Tb atoms to form a mixture of corner and face-sharing TbTb12 cuboctahedra. All Tb–Tb bond lengths are 3.62 Å.
DOI: 10.17188/1654179
title: Materials Data on SmInPt4 by Materials Project

description: SmPt4In is Cubic Laves-derived structured and crystallizes in the cubic F-43m space group. The structure is three-dimensional. Sm3+ is bonded in a 12-coordinate geometry to twelve equivalent Pt1- atoms. All Sm–Pt bond lengths are 3.19 Å. Pt1- is bonded to three equivalent Sm3+, six equivalent Pt1-, and three equivalent In1+ atoms to form a mixture of edge, face, and corner-sharing PtSm3In3Pt6 cuboctahedra. There are three shorter (2.71 Å) and three longer (2.73 Å) Pt–Pt bond lengths. All Pt–In bond lengths are 3.19 Å. In1+ is bonded in a 12-coordinate geometry to twelve equivalent Pt1- atoms.
DOI: 10.17188/1654182
title: Materials Data on Ge(SbTe2)2 by Materials Project

description: Ge(SbTe2)2 crystallizes in the tetragonal I-4m2 space group. The structure is three-dimensional. Ge4+ is bonded to six Te2- atoms to form GeTe6 octahedra that share corners with two equivalent SbTe6 octahedra, corners with four equivalent GeTe6 octahedra, and edges with eight SbTe6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are two shorter (3.00 Å) and four longer (3.06 Å) Ge–Te bond lengths. There are two inequivalent Sb2+ sites. In the first Sb2+ site, Sb2+ is bonded to six Te2- atoms to form SbTe6 octahedra that share corners with two equivalent GeTe6 octahedra, corners with four equivalent SbTe6 octahedra, edges with four equivalent GeTe6 octahedra, and edges with four equivalent SbTe6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are two shorter (3.05 Å) and four longer (3.06 Å) Sb–Te bond lengths. In the second Sb2+ site, Sb2+ is bonded to six Te2- atoms to form SbTe6 octahedra that share corners with four equivalent SbTe6 octahedra, edges with four equivalent GeTe6 octahedra, and edges with four equivalent SbTe6 octahedra. The corner-sharing octahedral tilt angles are 1°. There are two shorter (3.05 Å) and four longer (3.06 Å) Sb–Te bond lengths. There are two inequivalent Te2- sites. In the first Te2- site, Te2- is bonded to two equivalent Ge4+ and three Sb2+ atoms to form a mixture of edge and corner-sharing TeGe2Sb3 square pyramids. In the second Te2- site, Te2- is bonded in a square co-planar geometry to one Ge4+ and three Sb2+ atoms.
DOI: 10.17188/1654183
title: Materials Data on Pr2Fe2Se2O3 by Materials Project

description: Pr2Fe2Se2O3 crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. Pr3+ is bonded in a 4-coordinate geometry to four equivalent Se2- and four equivalent O2- atoms. All Pr–Se bond lengths are 3.36 Å. All Pr–O bond lengths are 2.37 Å. Fe2+ is bonded in a distorted linear geometry to four equivalent Se2- and two equivalent O2- atoms. All Fe–Se bond lengths are 2.78 Å. Both Fe–O bond lengths are 2.06 Å. Se2- is bonded in a 12-coordinate geometry to four equivalent Pr3+ and four equivalent Fe2+ atoms. There are two inequivalent O2- sites. In the first O2- site, O2- is bonded to four equivalent Pr3+ atoms to form a mixture of edge and corner-sharing OPr4 tetrahedra. In the second O2- site, O2- is bonded in a square co-planar geometry to four equivalent Fe2+ atoms.
DOI: 10.17188/1654184
title: Materials Data on MgBi by Materials Project

description: MgBi crystallizes in the monoclinic Cm space group. The structure is three-dimensional. there are three inequivalent Mg sites. In the first Mg site, Mg is bonded to five Mg and seven Bi atoms to form a mixture of distorted corner and face-sharing MgMg5Bi7 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 3.19–3.37 Å. There are a spread of Mg–Bi bond distances ranging from 3.34–3.62 Å. In the second Mg site, Mg is bonded in a 6-coordinate geometry to one Mg and six Bi atoms. There are a spread of Mg–Bi bond distances ranging from 3.16–3.30 Å. In the third Mg site, Mg is bonded in a 5-coordinate geometry to two equivalent Mg and five Bi atoms. There are a spread of Mg–Bi bond distances ranging from 3.19–3.44 Å. There are three inequivalent Bi sites. In the first Bi site, Bi is bonded in a 5-coordinate geometry to five Mg and three equivalent Bi atoms. There are one shorter (3.26 Å) and two longer (3.63 Å) Bi–Bi bond lengths. In the second Bi site, Bi is bonded in a 12-coordinate geometry to six Mg and six Bi atoms. There are two shorter (3.37 Å) and one longer (3.63 Å) Bi–Bi bond lengths. In the third Bi site, Bi is bonded in a 6-coordinate geometry to seven Mg and one Bi atom.
DOI: 10.17188/1654185
title: Materials Data on CsZn4P3 by Materials Project

description: CsZn4P3 is alpha bismuth trifluoride-derived structured and crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. Cs1+ is bonded in a body-centered cubic geometry to eight equivalent P3- atoms. All Cs–P bond lengths are 3.76 Å. Zn2+ is bonded to four P3- atoms to form a mixture of corner and edge-sharing ZnP4 tetrahedra. There are two shorter (2.43 Å) and two longer (2.59 Å) Zn–P bond lengths. There are two inequivalent P3- sites. In the first P3- site, P3- is bonded in a 8-coordinate geometry to four equivalent Cs1+ and four equivalent Zn2+ atoms. In the second P3- site, P3- is bonded in a body-centered cubic geometry to eight equivalent Zn2+ atoms.
DOI: 10.17188/1654186
title: Materials Data on Y8In3Co by Materials Project

description: Y8CoIn3 crystallizes in the hexagonal P6_3mc space group. The structure is three-dimensional. there are four inequivalent Y sites. In the first Y site, Y is bonded in a 3-coordinate geometry to one Co and four equivalent In atoms. The Y–Co bond length is 2.84 Å. There are two shorter (3.28 Å) and two longer (3.82 Å) Y–In bond lengths. In the second Y site, Y is bonded in a 4-coordinate geometry to one Co and four equivalent In atoms. The Y–Co bond length is 2.84 Å. There are a spread of Y–In bond distances ranging from 3.09–3.83 Å. In the third Y site, Y is bonded to one Co and three equivalent In atoms to form distorted corner-sharing YIn3Co tetrahedra. The corner-sharing octahedra tilt angles range from 14–48°. The Y–Co bond length is 2.70 Å. All Y–In bond lengths are 3.22 Å. In the fourth Y site, Y is bonded to six equivalent In atoms to form distorted YIn6 octahedra that share corners with six equivalent YIn3Co tetrahedra and faces with two equivalent YIn6 octahedra. There are three shorter (3.38 Å) and three longer (3.48 Å) Y–In bond lengths. Co is bonded in a 7-coordinate geometry to seven Y atoms. In is bonded in a 11-coordinate geometry to eleven Y atoms.
DOI: 10.17188/1654187
title: Materials Data on DyFe3(BO3)4 by Materials Project

description: DyFe3(BO3)4 is Calcite-derived structured and crystallizes in the trigonal R32 space group. The structure is three-dimensional. Dy3+ is bonded to six equivalent O2- atoms to form distorted DyO6 pentagonal pyramids that share corners with six equivalent FeO6 octahedra. The corner-sharing octahedral tilt angles are 59°. All Dy–O bond lengths are 2.36 Å. Fe3+ is bonded to six O2- atoms to form FeO6 octahedra that share corners with two equivalent DyO6 pentagonal pyramids and edges with two equivalent FeO6 octahedra. There are two shorter (2.01 Å) and four longer (2.05 Å) Fe–O bond lengths. There are two inequivalent B3+ sites. In the first B3+ site, B3+ is bonded in a trigonal planar geometry to three O2- atoms. There is one shorter (1.38 Å) and two longer (1.39 Å) B–O bond length. In the second B3+ site, B3+ is bonded in a trigonal planar geometry to three equivalent O2- atoms. All B–O bond lengths are 1.38 Å. There are three inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted trigonal planar geometry to two equivalent Fe3+ and one B3+ atom. In the second O2- site, O2- is bonded in a distorted trigonal planar geometry to one Dy3+, one Fe3+, and one B3+ atom. In the third O2- site, O2- is bonded in a distorted trigonal planar geometry to two equivalent Fe3+ and one B3+ atom.
DOI: 10.17188/1654188
title: Materials Data on LiV2OF7 by Materials Project

description: Computed materials data using density functional theory calculations. These calculations determine the electronic structure of bulk materials by solving approximations to the Schrodinger equation. For more information, see https://materialsproject.org/docs/calculations
DOI: 10.17188/1654189
title: Materials Data on LaMg14Co by Materials Project

description: Mg14LaCo crystallizes in the orthorhombic Amm2 space group. The structure is three-dimensional. there are seven inequivalent Mg sites. In the first Mg site, Mg is bonded to twelve Mg atoms to form MgMg12 cuboctahedra that share corners with four equivalent LaMg10Co2 cuboctahedra, corners with six equivalent MgMg12 cuboctahedra, edges with two equivalent MgMg12 cuboctahedra, and faces with two equivalent MgMg12 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 3.03–3.38 Å. In the second Mg site, Mg is bonded to twelve Mg atoms to form MgMg12 cuboctahedra that share corners with six equivalent MgMg12 cuboctahedra, edges with two equivalent MgMg12 cuboctahedra, faces with two equivalent MgMg12 cuboctahedra, and faces with two equivalent LaMg10Co2 cuboctahedra. There are a spread of Mg–Mg bond distances ranging from 3.10–3.33 Å. In the third Mg site, Mg is bonded in a distorted single-bond geometry to four Mg, two equivalent La, and one Co atom. There are two shorter (3.05 Å) and two longer (3.37 Å) Mg–Mg bond lengths. There are one shorter (3.27 Å) and one longer (3.31 Å) Mg–La bond lengths. The Mg–Co bond length is 2.85 Å. In the fourth Mg site, Mg is bonded in a 12-coordinate geometry to ten Mg atoms. There are a spread of Mg–Mg bond distances ranging from 3.00–3.15 Å. In the fifth Mg site, Mg is bonded in a 12-coordinate geometry to ten Mg, one La, and one Co atom. There are a spread of Mg–Mg bond distances ranging from 2.97–3.49 Å. The Mg–La bond length is 3.29 Å. The Mg–Co bond length is 3.13 Å. In the sixth Mg site, Mg is bonded in a distorted single-bond geometry to seven Mg and one Co atom. Both Mg–Mg bond lengths are 3.09 Å. The Mg–Co bond length is 2.89 Å. In the seventh Mg site, Mg is bonded in a 12-coordinate geometry to eleven Mg and one La atom. The Mg–La bond length is 3.25 Å. La is bonded to ten Mg and two equivalent Co atoms to form distorted LaMg10Co2 cuboctahedra that share corners with four equivalent MgMg12 cuboctahedra, corners with six equivalent LaMg10Co2 cuboctahedra, and faces with two equivalent MgMg12 cuboctahedra. Both La–Co bond lengths are 3.06 Å. Co is bonded in a 10-coordinate geometry to eight Mg and two equivalent La atoms.
DOI: 10.17188/1654190
title: Materials Data on CaMn3O4 by Materials Project

description: CaMn3O4 is Caswellsilverite-like structured and crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. Ca2+ is bonded to six O2- atoms to form CaO6 octahedra that share corners with two equivalent MnO6 octahedra, corners with four equivalent CaO6 octahedra, edges with four equivalent CaO6 octahedra, and edges with eight equivalent MnO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are four shorter (2.32 Å) and two longer (2.36 Å) Ca–O bond lengths. There are two inequivalent Mn2+ sites. In the first Mn2+ site, Mn2+ is bonded to six O2- atoms to form MnO6 octahedra that share corners with six equivalent MnO6 octahedra, edges with four equivalent CaO6 octahedra, and edges with eight MnO6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mn–O bond distances ranging from 2.21–2.35 Å. In the second Mn2+ site, Mn2+ is bonded to six O2- atoms to form MnO6 octahedra that share corners with two equivalent CaO6 octahedra, corners with four equivalent MnO6 octahedra, and edges with twelve MnO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are two shorter (2.19 Å) and four longer (2.32 Å) Mn–O bond lengths. There are three inequivalent O2- sites. In the first O2- site, O2- is bonded to one Ca2+ and five Mn2+ atoms to form a mixture of edge and corner-sharing OCaMn5 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. In the second O2- site, O2- is bonded to four equivalent Ca2+ and two equivalent Mn2+ atoms to form OCa4Mn2 octahedra that share corners with six OCa4Mn2 octahedra and edges with twelve OCaMn5 octahedra. The corner-sharing octahedral tilt angles are 0°. In the third O2- site, O2- is bonded to six Mn2+ atoms to form OMn6 octahedra that share corners with six OCa4Mn2 octahedra and edges with twelve OCaMn5 octahedra. The corner-sharing octahedral tilt angles are 0°.
DOI: 10.17188/1654191
title: Materials Data on Zr2PtRh by Materials Project

description: Zr2RhPt crystallizes in the orthorhombic Immm space group. The structure is one-dimensional and consists of two Zr2RhPt ribbons oriented in the (1, 0, 0) direction. Zr is bonded in a linear geometry to one Rh and one Pt atom. The Zr–Rh bond length is 2.36 Å. The Zr–Pt bond length is 2.51 Å. Rh is bonded in a linear geometry to two equivalent Zr atoms. Pt is bonded in a linear geometry to two equivalent Zr atoms.
DOI: 10.17188/1654192
title: Materials Data on Ba by Materials Project

description: Ba is Tungsten structured and crystallizes in the monoclinic C2/m space group. The structure is three-dimensional. Ba is bonded in a distorted body-centered cubic geometry to eight equivalent Ba atoms. There are a spread of Ba–Ba bond distances ranging from 4.35–4.42 Å.
DOI: 10.17188/1654193
title: Materials Data on CoSiW by Materials Project

description: CoWSi crystallizes in the orthorhombic Amm2 space group. The structure is three-dimensional. there are two inequivalent W2+ sites. In the first W2+ site, W2+ is bonded in a 7-coordinate geometry to seven Si4- atoms. There are a spread of W–Si bond distances ranging from 2.69–2.84 Å. In the second W2+ site, W2+ is bonded in a 5-coordinate geometry to five Si4- atoms. There are a spread of W–Si bond distances ranging from 2.70–2.81 Å. There are three inequivalent Co2+ sites. In the first Co2+ site, Co2+ is bonded in a 6-coordinate geometry to four equivalent Co2+ and two equivalent Si4- atoms. There are two shorter (2.28 Å) and two longer (2.44 Å) Co–Co bond lengths. Both Co–Si bond lengths are 2.27 Å. In the second Co2+ site, Co2+ is bonded in a 6-coordinate geometry to three Co2+ and two equivalent Si4- atoms. The Co–Co bond length is 2.32 Å. Both Co–Si bond lengths are 2.26 Å. In the third Co2+ site, Co2+ is bonded in a distorted hexagonal planar geometry to six Si4- atoms. There are a spread of Co–Si bond distances ranging from 2.32–2.38 Å. There are two inequivalent Si4- sites. In the first Si4- site, Si4- is bonded to six W2+, two equivalent Co2+, and four Si4- atoms to form a mixture of edge, corner, and face-sharing SiCo2Si4W6 cuboctahedra. There are a spread of Si–Si bond distances ranging from 2.34–2.54 Å. In the second Si4- site, Si4- is bonded to six W2+, four Co2+, and two equivalent Si4- atoms to form distorted SiCo4Si2W6 cuboctahedra that share corners with four equivalent SiCo2Si4W6 cuboctahedra, edges with six equivalent SiCo4Si2W6 cuboctahedra, and faces with eight SiCo2Si4W6 cuboctahedra.
DOI: 10.17188/1654194
title: Materials Data on CoSeO5 by Materials Project

description: CoSeO5 crystallizes in the monoclinic P2_1/c space group. The structure is three-dimensional. Co4+ is bonded to six O2- atoms to form distorted edge-sharing CoO6 octahedra. There are a spread of Co–O bond distances ranging from 1.67–2.40 Å. Se6+ is bonded in a distorted trigonal non-coplanar geometry to three O2- atoms. There are a spread of Se–O bond distances ranging from 1.72–1.77 Å. There are five inequivalent O2- sites. In the first O2- site, O2- is bonded in a bent 120 degrees geometry to one Co4+ and one Se6+ atom. In the second O2- site, O2- is bonded in a 3-coordinate geometry to two equivalent Co4+ and one Se6+ atom. In the third O2- site, O2- is bonded in a bent 120 degrees geometry to one Co4+ and one Se6+ atom. In the fourth O2- site, O2- is bonded in a single-bond geometry to one Co4+ atom. In the fifth O2- site, O2- is bonded in a single-bond geometry to one Co4+ atom.
DOI: 10.17188/1654195
title: Materials Data on Li2TiVO4 by Materials Project

description: Computed materials data using density functional theory calculations. These calculations determine the electronic structure of bulk materials by solving approximations to the Schrodinger equation. For more information, see https://materialsproject.org/docs/calculations
DOI: 10.17188/1654196
title: Materials Data on MgSc5 by Materials Project

description: MgSc5 is Magnesium-derived structured and crystallizes in the orthorhombic Amm2 space group. The structure is three-dimensional. Mg is bonded to two equivalent Mg and ten Sc atoms to form MgMg2Sc10 cuboctahedra that share corners with six equivalent MgMg2Sc10 cuboctahedra, corners with twelve ScMg2Sc10 cuboctahedra, edges with eighteen ScSc12 cuboctahedra, faces with four equivalent MgMg2Sc10 cuboctahedra, and faces with sixteen ScSc12 cuboctahedra. Both Mg–Mg bond lengths are 3.30 Å. There are a spread of Mg–Sc bond distances ranging from 3.22–3.34 Å. There are five inequivalent Sc sites. In the first Sc site, Sc is bonded to twelve Sc atoms to form ScSc12 cuboctahedra that share corners with eighteen ScSc12 cuboctahedra, edges with eight equivalent MgMg2Sc10 cuboctahedra, edges with ten ScMg4Sc8 cuboctahedra, faces with two equivalent MgMg2Sc10 cuboctahedra, and faces with eighteen ScSc12 cuboctahedra. There are a spread of Sc–Sc bond distances ranging from 3.23–3.33 Å. In the second Sc site, Sc is bonded to four equivalent Mg and eight Sc atoms to form ScMg4Sc8 cuboctahedra that share corners with eighteen ScSc12 cuboctahedra, edges with four equivalent MgMg2Sc10 cuboctahedra, edges with fourteen ScSc12 cuboctahedra, faces with four equivalent MgMg2Sc10 cuboctahedra, and faces with sixteen ScSc12 cuboctahedra. There are four shorter (3.27 Å) and two longer (3.30 Å) Sc–Sc bond lengths. In the third Sc site, Sc is bonded to two equivalent Mg and ten Sc atoms to form ScMg2Sc10 cuboctahedra that share corners with eighteen ScSc12 cuboctahedra, edges with eighteen ScSc12 cuboctahedra, faces with six equivalent MgMg2Sc10 cuboctahedra, and faces with fourteen ScSc12 cuboctahedra. There are four shorter (3.24 Å) and two longer (3.30 Å) Sc–Sc bond lengths. In the fourth Sc site, Sc is bonded to two equivalent Mg and ten Sc atoms to form ScMg2Sc10 cuboctahedra that share corners with six equivalent MgMg2Sc10 cuboctahedra, corners with twelve ScMg2Sc10 cuboctahedra, edges with three equivalent MgMg2Sc10 cuboctahedra, edges with fifteen ScSc12 cuboctahedra, faces with two equivalent MgMg2Sc10 cuboctahedra, and faces with eighteen ScSc12 cuboctahedra. There are two shorter (3.27 Å) and two longer (3.30 Å) Sc–Sc bond lengths. In the fifth Sc site, Sc is bonded to two equivalent Mg and ten Sc atoms to form ScMg2Sc10 cuboctahedra that share corners with six equivalent MgMg2Sc10 cuboctahedra, corners with twelve ScMg2Sc10 cuboctahedra, edges with three equivalent MgMg2Sc10 cuboctahedra, edges with fifteen ScMg4Sc8 cuboctahedra, faces with two equivalent MgMg2Sc10 cuboctahedra, and faces with eighteen ScSc12 cuboctahedra. Both Sc–Sc bond lengths are 3.30 Å.
DOI: 10.17188/1654197
title: Materials Data on Ni3H2Se3O10 by Materials Project

description: Computed materials data using density functional theory calculations. These calculations determine the electronic structure of bulk materials by solving approximations to the Schrodinger equation. For more information, see https://materialsproject.org/docs/calculations
DOI: 10.17188/1654198
title: Materials Data on Co6O5F7 by Materials Project

description: Computed materials data using density functional theory calculations. These calculations determine the electronic structure of bulk materials by solving approximations to the Schrodinger equation. For more information, see https://materialsproject.org/docs/calculations
DOI: 10.17188/1654199
title: Materials Data on LiV3O4 by Materials Project

description: Computed materials data using density functional theory calculations. These calculations determine the electronic structure of bulk materials by solving approximations to the Schrodinger equation. For more information, see https://materialsproject.org/docs/calculations
DOI: 10.17188/1654200
title: Materials Data on Cs2BrCl by Materials Project

description: Cs2BrCl is Heusler-like structured and crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. Cs1+ is bonded in a body-centered cubic geometry to four equivalent Br1- and four equivalent Cl1- atoms. All Cs–Br bond lengths are 3.74 Å. All Cs–Cl bond lengths are 3.74 Å. Br1- is bonded in a body-centered cubic geometry to eight equivalent Cs1+ atoms. Cl1- is bonded in a body-centered cubic geometry to eight equivalent Cs1+ atoms.
DOI: 10.17188/1654201
title: Materials Data on LiCrBO3 by Materials Project

description: Computed materials data using density functional theory calculations. These calculations determine the electronic structure of bulk materials by solving approximations to the Schrodinger equation. For more information, see https://materialsproject.org/docs/calculations