Critical comparison of equations correlating valence and length of a chemical bond. Evaluation of the parameters R1 and B for the MoO bond in MoO6 octahedra

The most commonly used equations correlating bond valence and bond length have been critically compared. It has been shown that the Zachariasen equation is more accurate than the Brown–Shannon equation. Doubts already voiced about the universality of the constant B in the Brown–Altermatt equation with a value of 0.37 Å have been hereby confirmed. Moreover, by a method based on the comparison of formal oxidation states and valences of molybdenum in suitable oxides, the parameters relative to the Zachariasen equation have been accurately determined for the MoO bond in MoO₆ octahedra. Their values are R₁=1.8790 and B=0.3048 Å in the 3–6 v.u. range.     

Synthesis and crystal chemistry of NH3(MoO3)3

NH₃(MoO₃)₃ crystallizes with hexagonal symmetry, space group $\text{P6}{}_3\text{m}$, lattice constants a = 10.568 Å, c = 3.726 Å, and Z = 2. The crystal structure has been determined by Patterson synthesis and refined assuming isotropic temperature factors to a final conventional R value of 0.085. The structure shows a three-dimensional arrangement built up of double chains of distorted MoO₆ octahedra, parallel to the [001] direction. The octahedral double chains are linked among each other through common oxygen atoms. In addition to the shared oxygen atoms, each molybdenum is coordinated to one terminal oxygen. MoO distances range from 1.645 to 2.378 Å and OMoO angles from 74.3 to 114.3°. These results are consistent with the fact that molybdenum in high-valence states shows octahedral coordination with terminal oxygens.     

Structure determination of low-dimensional conductor sodium molybdenum purple bronze Na0.9Mo6O17

Structure determination of the molybdenum purple bronze Na_0.9Mo₆O₁₇ is carried out by single-crystal X-ray diffraction. The crystal is monoclinic with space group A2 and the lattice constants are a = 12.983(2), b = 5.518(1), c = 9.591(2) Å, β = 89.94(1)°, Z = 2. Full-matrix least-squares refinement gives the final values of R(F) = 0.028 and R_w(F) = 0.040 for 1484 independent reflections, in which the occupancy factor of the sodium atom becomes 0.899(12). The present structure is built up of the linkage of the MoO₄ and MoO₆ polyhedra. There are slabs which consist of four layers of distorted MoO₆ octahedra sharing corners. Both the structure and the molybdenum valence distribution estimated from the MoO bond lengths are considered to lead to the two-dimensional electronic transport. This structure is compared with those of other members of molybdenum purple bronzes, K_0.9Mo₆O₁₇ and Li_0.9Mo₆O₁₇. The difference of the electronic properties among these compounds can be well understood on the basis of their structural characteristics.     

Structure cristalline d'un conducteur métallique bidimensionnel: Le bronze violet de potassium et molybdene K0.9Mo6O17

Single crystals of the purple bronze K_0.9Mo₆O₁₇ have been grown by a electrolytic reduction technique. Measurements of the electrical resistivity show that this compound is a quasi two-dimensional metal. A crystal structure determination is used to explain the strongly anisotropic resistivity. K_0.9Mo₆O₁₇ is found to be trigonal with lattice parameters: a = 5.538 Å and c = 13.656 Å; Z = 1. The space group is $\text{P}\text{3}$. The K cations are surrounded by 12 oxygen anions which form icosahedral sites. One third of the Mo cations (Mo(1)) occupy tetrahedral sites, while the Mo(2) and Mo(3) cations have octahedral surroundings. The structure can be described as slabs of ReO₃-type connected by KO₁₂ icosahedra. Each slab is built up of 4 layers, parallel to the (001) plane, of Mo(2) and Mo(3) octahedra sharing corners. Two slabs are connected by K icosahedra which share 2 faces with the upper and lower neighboring Mo(3) octahedra. Each K icosahedron is edge linked to 3 upper and 3 lower Mo(1) tetrahedra. Each Mo(1) tetrahedron is itself corner linked to 3 Mo(3) octahedra of the neighboring layer. The deformations of the occupied polyhedra are a good illustration of the Pauling's third rule. There is no Mo(1)OMo(1) bonding, so that the MoOMo bonding, infinite in the a and b directions, is disrupted in the c direction. The Zachariasen's bond length-bond strength relation has been applied to the MoO bonds. The computed effective mean Mo valences are +6 for Mo(1) on tetrahedral sites and about 5.1 and 5.8, respectively, for Mo(2) and Mo(3) on octahedral sites. The 4d electrons of Mo atoms are so located in the two-dimensional infinite slabs of octahedra. The conduction band is expected to be an antibonding π1 band resulting from the hybridization of the Mo 4dt_2g and oxygen p_π states. Thus, the structural properties should lead to a very anisotropic Fermi surface and thus, to a quasi two-dimensional electrical conductivity.     

Molecular structure of two dicyclopentadienylmolybdenum derivatives containing a four-membered ring [Mo(η5-C5H5)2(2-NHNC5H4)][PF6] and [Mo(η5C5H5)2(2-ONC5H4)][PF6]

The structure of the new compound [Mo(η⁵-C₅H₅)₂(2-NHNC₅H₄)][PF₆] (1) has been determined. The crystals are orthorhombic, space group Pca2₁ with a 20.807(1), b 8.0030(8), c 10.056(3) Å, V 1674.5 ų, Z = 4. The structure of [Mo(η⁵-C₅H₅)₂(2-ONC₅H₄)][PF₆] (2) has also been determined. The crystals are orthorhombic, space group Pnma with a 12.727(3), b 10.174(2), c 12.918(1) Å, V 1672.8 ų, Z = 4. The structures were solved by Patterson and difference electron density syntheses and refined by least-squares to R of 0.028 for 1287 reflections for 1 and 0.059 for 1178 reflections for 2.Although not isostructural the two cationic complexes have equivalent geometries with the normal bent bismetallocene structure. For 1 the MoN bond lengths are 2.160(8) and 2.142(9) Å, with a NMoN bond angle of 59.8(3)°, whereas for 2 MoO is 2.142(10), MoN is 2.138(11) Å, the NMoO angle is 61.2(4)°. These parameters are discussed and compared with the corresponding data for similar biscyclopentadienyl complexes of molybdenum(IV). Extended Hückel molecular orbital calculations have been carried out to throw light on the nature of the bonding between the metal and the bidentate ligand.     

The crystal structure of ammonium β-octamolybdate pentahydrate

X-ray structure analysis (film data, R = 0.080 for 1568 reflections) has confirmed the structure of the anion in (NH₄)₄[Mo₈O₂₆], 5H₂O, deduced by Lindqvist in 1950 from the Mo coordinates alone. The compound is triclinic, P$\text{1}$, a = 9.769(16), b = 9.832(13), c = 7.848(11) Å, α = 99.11(4), β = 101.03(11), γ = 97.40(4)°, Z = 1. Eight MoO₆ octahedra share edges in a compact grouping, with short terminal MoO bonds (1.69 to 1.75 Å), longer bonds (1.88–2.00 Å) to bicoordinate O atoms, and long bonds (2.18–2.39 Å) to multiply-shared interior atoms.     

The crystal structure of a complex cerium(III) molybdate; Ce6(MoO4)8(Mo2O7)

Ce₆Mo₁₀O₃₉ crystallizes in the triclinic system with unit-cell dimensions (from single-crystal data) a = 10.148(5), Å, b = 18.764(6), Å, c = 9.566(5), Å, α = 103.12(7)°, β = 78.07(7)°, γ = 107.69(7)°, and space group $\text{P}\text{1}\text{, z = 2}$. The structure was solved using direct methods with 3113 countermeasured reflections (MoKα radiation), and refined using Fourier and least-squares techniques to a conventional R of 0.039 (ωR = 0.047). Ce₆Mo₁₀O₃₉ has a structure that consists of isolated MoO₄ tetrahedra together with one corner-shared pair of tetrahedra, linked to irregular eight-coordinate Ce(III) polyhedra. The average MoO distance of 1.77 Å, and average CeO distance of 2.52 Å are in good agreement with previously reported values.     

Lineare oligophosphaalkane: XVIII. Addition Ph-funktioneller methylenbisphosphane an die MoMo-Dreifachbindun in (η5-C5H5)2Mo2(CO)4

By means of the addition of the PH-functional methylenebisphosphanes R¹R²-PCH₂PR³H (PCP) to the MoMo triple bond in (η⁵-C₅H₅)₂Mo₂(CO)₄(MoMo) the complexes (η⁵-C₅H₅)₂Mo₂(CO)₄(PCP) containing a five-membered ring system Mo₂P₂C are obtained. Starting with unsymmetrically substituted methylenebisphosphanes R′₂PCH₂PRH only one isomer is formed, while the disecondary derivatives RHPCH₂PHR (as the diastereomeric mixture) gave two isomers of (η⁵-C₅H₅)₂Mo₂(CO)₄(PCP) (A₂ and AB) as indicated by the ³¹P{¹H} and ¹³C{¹H} NMR spectra.X-ray structural analysis of the derivative of the racemate of t-BuHPCH₂PH(t-Bu) space group C2/c, monoclinic, a 18.034(2), b 14.909(1), c 11.106(1) Å, α 90, β 99.788(8), γ 90°) reveals a puckered Mo₂P₂C five-membered ring system (dihedral angle PMoMo′P′ 54.4(2)°) with square-pyramidal coordination geometry at the Mo atoms. Two of the CO ligands (C(6)O(1) and C(6′)O(1′)) are almost coplanar with the molybdenum atoms, while the terminal CO groups (C(7)O(2) and C(7′)O(2′)) are about orthogonal (dihedral angle C(7)MoMo′C(7′) 88.4(3), MoMo′ 3.2109(4), MoP 2.4567(8), PC(8) 1.834(3), PH(P) 1.37(3) Å).     

Structure and properties of La2Mo2O7: A quasi-two-dimensional metallic oxide with strong MoMo bonds

Single crystals of La₂Mo₂O₇, prepared by fused salt electrolysis, were used for structural and electronic characterization. La₂Mo₂O₇ is orthorhombic with a = 6.034Å, b = 12.236 Å, and c = 3.888 Å. The dominant feature of the structure, which was refined in space group Pnnm, is Mo₂O₁₀ units formed by edge-sharing MoO₆ octahedra which contain MoMo distances of only 2.478 Å. These groups then share corners in two dimensions to give rise to MoO layers which are held together by the lanthanum ions. The relationship of the La₂Mo₂O₇ structure to those of other reduced oxides is discussed. La₂Mo₂O₇ is a metallic conductor down to 125 K where a phase transition takes place. A similar transition is seen in the magnetic susceptibility. The anomalous electric and magnetic behavior of this compound may be associated with a charge density wave instability of the type often found in quasi-two-dimensional materials.     

The molybdenum-molybdenum triple bond—XVII. Syntheses,spectroscopic and structural characterizations of Mo4F4(O—t-Bu)8 and Mo2F2(O—t-Bu)4(PMe3)2 (MoMo)

Hydrocarbon solutions of Mo₂(O—t-Bu)₆ and PF₃ (2 equiv) yield Mo₄F₄(O—t-Bu)₈, I, and PF₂(O—t-Bu). Compound I contains a bisphenoid of molybdenum atoms with two short MoMo distances, 2.26 Å, and four long MoMo distances, 3.75 Å, corresponding to localized MoMo triple bonding and non-bonding distances, respectively. The tetranuclear compound may be viewed as a dimer, [Mo₂(μ₂-F)₂(O-t-Bu)₄]₂, and addition of PMe₃ to hydrocarbon solutions of I yields Mo₂F₂(O—t-Bu)₄(PMe₃)₂, II, which contains an unbridged MoMo triple bond of distance 2.27 Å. Each molybdenum atom is coordinated to two oxygen atoms, one fluorine atom and the phosphorus atom of the PMe₃ ligand in a roughly square planar manner. The overall central Mo₂O₄F₂P₂ skeleton has C₂ symmetry and NMR studies (¹H, ¹⁹F and ³¹P) are consistent with the maintenance of this type of structure in solution. Infrared and electronic absorption spectral data are reported. These are the first compounds containing fluorine ligands attached to the (MoMo)⁶⁺ unit.     

K4MoV8P12O52, a tunnel structure characterized by an unusual valence of molybdenum

A new phosphate of molybdenum (V) K₄Mo^v₈P₁₂O₅₂ has been isolated and its structure solved from a single crystal X-ray diffraction study. It crystallizes in a monoclinic cell, space groupC2–c, with the parametersa = 10.7433(16)Å,b = 14.0839(9)Å,c = 8.8519(7)Å, and β = 126.42(1)°. After refinement of the different parameters, the reliability factors were lowered toR = 0.026 and_w = 0.029. The framework “Mo₈P₁₂O₅₂” can be described as corner-sharing PO₄ tetrahedra,P₂O₇groups, and MoO₆ octahedra. Although the “O₆” octahedron surrounding the molybdenum ion is almost regular, the metal ion is strongly off center so that its coordination is better described as a MoO₅ pyramid. This particular coordination, which characterizes Mo(V), is discussed.     

Synthese und Röntgenstrukturanalyse von Bis(2,2,6,6-tetramethylpiperidin-1-oxidato-O,N)-molybdän(VI)-dioxid

Synthesis and X-Ray Structure Analysis of Bis(2,2,6,6-tetramethylpiperidine-1-oxidato-O,N)molybdenum (VI) Dioxide The title compound ( 1 ) was synthesized by a photoreaction of the 2,2,6,6-tetramethylpiperidin-1-oxyl [TMPO] radical with Mo(CO)₆ and characterized by an X-ray structure analysis as (TMPO)₂MoO₂ complex. In the coordinatively unsaturated 16 electron compound of mm2 symmetry the Mo^VI is coordinated nearly tetrahedrally by the four ligands, the TMPO^? ligands being O,N coordinated. The Mo? O, Mo? N, and Mo?O distances are 1.972(3), 2.198(3), and 1.711(2) Å respectively; the N? O distances are 1.436(4) Å. The stereochemistry of the Mo coordination is the same as in other (R₂NO)₂MoO₂ complexes.     

Etudes electrique et Raman de borotungstates et de boromolybdates de lithium vitreux

Conductivity studies of glasses obtained from the B₂O₃Li₂OLi₂MoO₄ and B₂O₃Li₂OLi₂WO₄ systems have been carried out. The presence of the transition element in tetrahedral coordination and with two different oxidation states is discussed. A Raman spectroscopy study shows that the MoO₄ or WO₄ tetrahedra are slightly compressed by the network forming lattice.     

Variation of mean SiO bond lengths in silicon-oxygen octahedra

The mean bond length SiO in silicon-oxygen octahedra is a function of the mean coordination number of the oxygen atoms (CN) in the octahedron: (SiO)_mean = 1.729 + 0.013CN. The radius of Si in six coordination against oxygen is 0.407 Å.     

A large-angle X-ray scattering study of two amorphous inorganic polymers,Ru(SPh)3 and Mo(SPh)3

The two inorganic polymers Ru(SPh)₃ and Mo(SPh)₃ were examined by large-angle X-ray scattering, showing in both cases chains of face-sharing octahedra with alternating metal-metal distances (RuRu: 3.25 and 2.65 Å; MoMo: 3.30 and 2.70 Å).     

Etude du système SbMoO à 500°C: Mise en évidence de deux nouveaux oxydes de molybdène-antimoine

The ternary system SbMoO has been investigated by reduction using $\text{H}{}_2\text{H}{}_2\text{O}$ gas mixtures and direct synthesis under vacuum. The products were studied by X-ray diffraction, electron diffraction, and high-resolution electron microscopy. Two new compounds were characterized: Sb_0.2MoO_3.1, which is orthorhombic, with an average oxidation state for molybdenum of 5,5; and Sb_0.4MoO_3.1, which is hexagonal and in which the average oxidation state of molybdenum is 5. These two phases can be considered in some ways as molybdenum bronzes, but without possessing all the related bronze characteristics.     

The X-ray crystal structure of di-η5-cyclopentadienylthiophenolatoamminemolybdenum(IV) hexafluorophosphate solvate [Mo(η5-C5H5)2(NH3)(SC6H5)][PF6] · (CH32CO

Crystals of [Mo(η⁵-C₅H₅)₂(NH₃)(SC₆H₅)][PF₆] · (CH₃)₂CO solvate are monoclinic, space group P2₁/n, a 9.777(1), b 11.6343(2), c 19.656(4) Å, β 93.60(1)°, V 2231-46 ų, Z  D_c 1.617 g cm⁻³, μ(Mo-K_α) 7.21 cm⁻¹. The structure was solved by Patterson and difference Fourier electron density synthesis and refined to R (F)  0.047 and R_w(F)  0.057 for 3293 observed reflections. The molybdenum atom has the usual distorted tetrahedral geometry comprising the two MoCp (Cp  η⁵-C₅H₅) ring normals (MoCp 1.988(13), 1.989(15) Å), one Mo-NH₃ (MoN 2.226(12) Å), and one MoSc₆H₅ (MoS 2.465(5) Å). Extended HMO and steric energy calculations were made in order to account for the geometry adopted by the thiolato ligand in this complex.     

Pentaguanidinium monohydrogendiphosphopentamolybdate(VI) 2.5‐hydrate, (CH6N3)5[HP2Mo5O23]·2.5H2O: hydrogen bonding and π‐stacking in guanidinium cations

The asymmetric unit of the title compound consists of two crystallographically independent, but structurally identical, [HP₂Mo₅O₂₃]⁵⁻ anions, ten guanidinium cations and five water molecules. Each singly protonated diphosphopentamolybdate(VI) anion retains the typical geometry of a ring of five edge‐sharing MoO₆ octahedra [Mo...Mo = 3.3265 (8)–3.4029 (10) Å], except for one corner‐sharing link [Mo...Mo = 3.6642 (7) and 3.6826 (8) Å]. Two capping PO₄ tetrahedra share corners with the five octahedra. Despite being surrounded by an extensive network of hydrogen bonds, predominantly from the guanidinium cations, short P—O—H...O=P contacts [O...O = 2.519 (7) and 2.457 (7) Å] associate the anions into infinite columns generated by the c‐glide. In addition to their heavy involvement in hydrogen bonding, with all N—H donors being utilized, the guanidinium cations assemble into extensive π‐stacked columns with an average interplanar spacing of 3.53 Å.     

Studies of alkylmetal alkoxides of aluminium,gallium and indium : IV. The molecular structure of dimethylaluminium t-butoxide dimer by gas phase electron diffraction

The electron diffraction data for gaseous dimethylaluminium t-butoxide dimer are consistent with a molecular model of effective D_2h symmetry. The Al₂O₂ ring is planar and the three valencies of the O atoms are lying in a plane. The t-butyl groups undergo nonhindered or slightly hindered internal rotation. The most important bond distances and valence angles are: AlO = 1.864(6), AlC = 1.962(15), OC = 1.419(12), CC = 1.533(5) Å, ∠AlOAl = 98.1(0.7), ∠CAlC = 121.7(1.7) and ∠OCC = 110.4(0.5)°.