Maximum filling principle and sublattice characteristics for the atoms of period 2 elements

The most important characteristics of the Voronoi-Dirichlet polyhedra (VDP) of 7195542 atoms A (A = Li, Be, B, C, N, O, or F) in sublattices containing only chemically identical A atoms in the crystal structures of inorganic, coordination, and organoelement compounds were determined. The VDP of Li, Be, B, N, O, or F atoms in these sublattices have most often 14 faces and those of C atoms, 16 faces. The Fedorov cuboctahedron is the most abundant combinatorial topologic type of VDP in all cases. The effect of the nature of the A atoms on the A-A interatomic distances in the homoatomic sublattices of the crystal structures was considered.     

Maximum filling principle and sublattice characteristics for the atoms of period 3 elements

The most important characteristics of the Voronoi-Dirichlet polyhedra (VDP) of A atoms (A = Na, Mg, Al, Si, P, S, Cl, or Ar) were determined. The sublattices contain chemically identical A atoms in the crystal structures of 232006 inorganic, coordination, and organoelement compounds. The VDP of A atoms have most often 14 faces, the Fedorov cuboctahedron being the most abundant VDP type. The effect of the nature of the A atoms on the characteristic A-A interatomic distances in the homoatomic sublattices of the crystal structures was considered.     

Maximum filling principle and sublattices of actinide atoms in crystal structures

The most important characteristics of the Voronoi-Dirichlet polyhedra (VDP) of A atoms (A is actinide) in chemically homogeneous sublattices in the crystal structures of 3479 inorganic, coordination, and organometallic compounds are determined. The effect of the actinide nature on the A-A interatomic distances in the crystal structures is considered. In the Th, U, Np, or Pu sublattices, VDP have most often 14 faces and the Fedorov cuboctahedron is the most abundant type of VDP, whereas in Ac, Pa, Am, Cm, Bk, or Cf sublattices, the VDP have mainly 12 faces and are shaped like rhomobododecahedra. In A sublattices that typically form VDP with 14 faces, the actinide atoms occupy, most often, sites with C ₁ symmetry (47 to 59% of the sample size). In the case of actinides whose A sublattices tend to form VDP with 12 faces, the C ₁ site symmetry is found either very rarely (Pa, Am, Cf) or not at all (Ac, Cm, Bk).     

Topology features of chemically homogeneous sublattices in crystal structures

Using Voronoi-Dirichlet polyhedra, the principle of maximum space filling in sublattices containing atoms of a particular element (from H to Cf) is tested in the structures of all crystalline compounds studied so far. It is found that atoms of the overwhelming majority of elements are most often surrounded by 14 neighboring atoms in these sublattices. Anomalous features of H- and C-sublattices, in which hydrogen and carbon atoms most commonly have 15 and 16 neighboring atoms respectively, and sublattices consisting of Ar, Ac, Pa, Am, Cm, Bk, or Cf atoms, in which the number of nearest neighboring atoms is usually 12, are discovered. The main reasons for the revealed differences are discussed.     

Maximum filling principle and sublattices of lanthanide atoms in crystal structures

The most important characteristics of the Voronoi-Dirichlet polyhedra (VDP) were determined for 20526 Ln atoms (Ln = La?Lu) in sublattices containing chemically identical lanthanide atoms in the crystal structures of 14659 inorganic, coordination, and organoelement compounds. The number of lanthanide VDP faces in the sublattice can vary from 4 to 36 and, irrespective of the lanthanide nature, the VDP have most often 14 faces. The Fedorov cuboctahedron is the most abundant type of VDP. In the crystal structures, Ln atoms were found to have, most often, C ₁ site symmetry (～49% of cases) and also C _s (16), C _2v (7%), or C ₂ (6%) site symmetries.     

Maximum filling principle and sublattice characteristics for the atoms of period 4 elements

The most important characteristics of the Voronoi-Dirichlet polyhedra (VDP) of A atoms (A = K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge, As, Se, Br, or Kr) were determined. The sublattices contain chemically identical A atoms in the crystal structures of 136395 inorganic and organoelement compounds. Irrespective of the nature of period 4 element, the VDP of A atoms have most often 14 faces, the Fedorov cuboctahedron being the most abundant VDP type. In the crystals, A atoms were found to have, most often, C ₁ site symmetry (75% of cases) and also C _s , C _i , and C ₂ site symmetries (6 to 4%). Certain relationships were shown to exist between the nature of the A atom and the preferred symmetry of the site it occupies in the crystal structures.     

Maximum filling principle and sublattice characteristics for the atoms of period V elements

The most important characteristics of the Voronoi-Dirichlet polyhedra (VDP) were determined for the 146 493 crystallographically different A atoms (A = Rb, Sr, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, In, Sn, Sb, Te, I, or Xe) in sublattices containing chemically identical atoms in the crystal structures of 82093 inorganic and organoelement compounds. Irrespective of the nature of the element of period 5, the VDP have most often 14 faces, the Fedorov cuboctahedron being the most abundant VDP type. The metal atoms A were found to have, most often, C ₁ site symmetry (79% of cases) and also C _s, C ₂, and C _i site symmetries (7 to 2%). Certain relationships were shown to exist between the nature of the metal atom and the preferred symmetry of the site it occupies in the crystal structure.     

Maximum filling principle and sublattice characteristics for the atoms of period 6 elements

The most important characteristics of the Voronoi-Dirichlet polyhedra (VDP) were determined for the 88223 crystallographically different A atoms (A = Cs, Ba, La, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, Tl, Pb, or Bi) in sublattices containing chemically identical atoms in the crystal structures of 52370 inorganic and organoelement compounds. Irrespective of the nature of the A element, the VDP have most often 14 faces, the Fedorov cuboctahedron being the most abundant VDP type. The metal atoms A were found to have, most often, C ₁ site symmetry (76% of cases) and also C _s , C ₂, C _i , and C _2v site symmetries (7 to 2%). Certain relationships were shown to exist between the nature of the metal atom and the preferred symmetry of the sites it occupies in the crystal structures.     

Interrelation between the spatial structure of unsaturated hydrocarbon molecules and heats of their adsorption

The total area (s ^m) of Voronoi-Dirichlet polyhedron faces corresponding to all intermolecular contacts of one molecule in the structure of crystals and the total volume of pyramids (V ^m) built on such faces and containing the nuclei of atoms participating in intermolecular contacts in their vertices were determined for 19 unsaturated hydrocarbons. The differential molar heat of adsorption of the hydrocarbons on graphitized thermal carbon black was found to be linearly related to the s ^m or V ^m integral parameters of their Voronoi-Dirichlet polyhedra. Aromatic hydrocarbons on the one hand and saturated hydrocarbons, olefins, and acetylene on the other are characterized by different dependences because of the special shapes of their molecular Voronoi-Dirichlet polyhedra.     

Stereochemistry of vanadium in oxygen-containing compounds

Using Voronoi-Dirichlet (VD) polyhedra and the method of overlapping spheres, we analyze the coordination of 714 crystallographically different vanadium atoms in the structure of compounds containing VO _n polyhedra. Vanadium atoms are found to be bonded to 4, 5, 6, or 7 oxygen atoms. The effect of the valence state and coordination number of vanadium atoms on the main parameters of their VD polyhedra is considered. A unified linear dependence between the solid angles of VD polyhedron faces corresponding to V-O bonds and the respective interatomic distances varying in a range of 1.55 Å to 2.79 Å is stated to exist. It is shown that the parameters of VD polyhedra can be used to determine the valence state of vanadium atoms.     

Coordination polyhedra PbO n in crystal structures

Voronoi-Dirichlet polyhedra and the intersecting spheres method were used to analyze the oxygen surroundings of Pb(II) and Pb(IV) atoms in the crystal structures of 433 compounds. The stereochemical activity of the lone electron pair of Pb(II) atoms was quantified. This effect is responsible for the asymmetry of the coordination sphere of Pb(II) atoms and is manifested in a considerable (on average by 0.3 Å) displacement of these atoms from the centroids of their Voronoi-Dirichlet polyhedra.     

The coordination polyhedra GaS<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> in crystal structures

Voronoi-Dirichlet polyhedra (VDP) and the intersecting sphere method were used to perform coordination analysis of 204 crystallographically different gallium atoms in the structures of all known compounds containing GaS _n polyhedra. The Ga(III) atoms in crystal structures were found to be linked to 6, 4, or three sulfur atoms to form coordination octahedra, tetrahedra, and triangles, respectively, whereas Ga(II) atoms are bound only to three sulfur atoms and a gallium atom. The effect of the valence state and the coordination number of gallium atoms on the key parameters of the VDP is considered. A common linear dependence of the solid angles of the VDP faces corresponding to the Ga-S bonds on the corresponding interatomic distances, which vary from 2.09 to 2.53 Å, was established to exist.     

The Coordination Polyhedra OsN n in Crystal Structures

Characteristics of the Voronoi-Dirichlet polyhedra were used to perform the crystal-chemical analysis of 53 compounds containing osmium atoms surrounded by nitrogen atoms. Depending on the metal oxidation state, which varies from Os(II) to Os(VII), the coordination polyhedra formed by osmium atoms can be octahedra or trigonal prisms (OsN₆), square pyramids (OsN₄Os), tetrahedra (OsN₄), or triangles (OsN₃). The parameters of the Voronoi-Dirichlet polyhedra allow one to estimate quantitatively the main stereochemical features of Os atoms, depending on their oxidation state, and in controversial cases, they can be used to determine the oxidation state of osmium in the crystal structures.     

The coordination polyhedra CdS<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> in crystal structures

Voronoi-Dirichlet polyhedra (VDP) and the intersecting sphere method were used to perform analysis of coordination of cadmium atoms in the structures of all known compounds containing CdS _n polyhedra. The Cd(II) atoms were found to coordinate 6, 5, 4, or 3 sulfur atoms to form coordination octahedra or trigonal prisms, trigonal bipyramids, tetrahedra, or triangles, respectively. The effect of the coordination number of cadmium atoms on the key parameters of Cd VDP was considered. A common linear dependence of the solid angles of the VDP faces corresponding to both valence and non-valence Cd-S contacts on the corresponding interatomic distances was established to exist. Although the Cd-S bond varies over a broad range, from 2.39 to 3.29 Å, the Cd VDP volume almost does not depend on its C.N. with respect to sulfur.     

Analysis of nonvalent interactions in the crystals of conformational polymorphs of the composition CaHbNcOdSe by means of molecular voronoi-dirichlet polyhedra

Nonvalent interactions in crystals of compounds of the composition C _a H _b N _c O _d S _e that exhibit conformational polymorphism and have no fewer than four structurally characterized modifications are analyzed using molecular Voronoi-Dirichlet polyhedrals. A unique combination of the types of occurring intra- and intermolecular nonvalent contacts is shown to correspond to each conformational polymorph. Nonvalent interactions involving hydrogen atoms are found to occur most often in crystal structures, and least often those involving S, N, and O atoms.     

18-Electron rule and structure of uranyl sulfate complexes

Characteristics of the Voronoi-Dirichlet polyhedra were used to perform the crystal-chemical analysis of all known sulfate-containing uranyl compounds. The effect of the type of coordination of sulfate ions by U(VI) atoms on the characteristics of S-O and U-O bonds in the crystal structure is considered. The electrondonor properties of sulfate ions were estimated quantitatively on the basis of the 18-electron rule. Some predictive properties of the stereoatomic crystal structure model were demonstrated in relation to tri-and tetrasulfatouranylates.     

Coordination polyhedra LnFn (Ln = La-Lu) in crystal structures

Voronoi-Dirichlet (VD) polyhedra and the intersecting spheres method are used to study stereochemical features of lanthanides (Ln) surrounded by fluorine atoms in the structures of 118 compounds. The coordination numbers of Ln atoms range from 6 to 12. Nine types of coordination polyhedra LnF_n are found; depending on the CN of Ln, the Ln-F bond length can change by 0.2–0.7 Å. Despite the considerable differences in bond lengths, the volume of the VD polyhedra of Ln atoms depends only on their nature and oxidation state. The change in the radii of the spherical domains whose volume is equal to that of the VD polyhedra of Ln atoms shows the tetrad effect.     

Stereochemical features of bromine- and iodine-containing compounds of lanthanides

The Voronoi-Dirichlet (VD) polyhedra and the intersecting spheres method have been used to analyze the features of the environment of lanthanide (Ln) atoms consisting of bromine and iodine atoms in the structures of 94 compounds containing 96 LnBr _n complexes and 41 LnI _n complexes. The lanthanum CN with respect to halogen atoms varies from 6 to 9. The volume of the VD polyhedra of Ln atoms depends only on the oxidation state of the metal atom and the nature of the surrounding atoms.     

Coordination polyhedra TeO n in crystal structures

The Voronoi-Dirichlet (VD) polyhedra and the intersecting spheres method have been used to analyze the coordination of Te(IV) and Te(VI) atoms by oxygen atoms in the crystal structures of 317 compounds. The quantitative estimation of the steric effect of the Te(IV) lone electron pair, giving rise to the asymmetry of the coordination sphere and manifesting itself as a substantial (on average, by 0.5(1) Å) displacement of Te(IV) atoms from the centroids of their VD polyhedra, is presented.     

The coordination polyhedra KCl<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> in the crystal structures

The Voronoi-Dirichlet polyhedra (VDP) and the method of intersecting spheres were used to carry out crystal chemical analysis of 141 chlorides containing 245 crystallographic sorts of potassium atoms in the KCl_n coordination polyhedra. The potassium atoms in the crystal structures can coordinate 6 to 12 chlorine atoms, the K-Cl bond lengths varying from 2.81 to 3.91 Å. The radius of spherical domains whose volume coincides with the volume of potassium VDP was found to be virtually independent of the coordination number or the shape of the coordination polyhedron, being equal to 1.93(4) Å. The VDP characteristics were used to analyze the stereochemical features of potassium in the crystal structures.Translated from Koordinatsionnaya Khimiya, Vol. 31, No. 1, 2005, pp. 72–80.Original Russian Text Copyright © 2005 by Bikanina, Shevchenko, Serezhkin