Mean bond-length variation in crystal structures: a bond-valence approach

2014 ◽  
Vol 70 (4) ◽  
pp. 697-704 ◽  
Author(s):  
Ferdinando Bosi
Keyword(s):  
Bond Length ◽  
Crystal Structures ◽  
Coordination Sphere ◽  
Distortion Theorem ◽  
Bond Valence ◽  
Algebraic Expression ◽  
Length Variation ◽  
Bond Lengths ◽  
Valence Theory ◽  
New Equation

The distortion theorem of the bond-valence theory predicts that the mean bond length 〈D〉 increases with increasing deviation of the individual bond lengths from their mean value according to the equation 〈D〉 = (D′ + ΔD), whereD′ is the length found in a polyhedron having equivalent bonds and ΔDis the bond distortion. For a given atom,D′ is expected to be similar from one structure to another, whereas 〈D〉 should vary as a function of ΔD. However, in several crystal structures 〈D〉 significantly varies without any relevant contribution from ΔD. In accordance with bond-valence theory, 〈D〉 variation is described here by a new equation: 〈D〉 = (DRU + ΔDtop + ΔDiso + ΔDaniso + ΔDelec), whereDRUis a constant related to the type of cation and coordination environment, ΔDtopis the topological distortion related to the way the atoms are linked, ΔDisois an isotropic effect of compression (or stretching) in the bonds produced by steric strain and represents the same increase (or decrease) in all the bond lengths in the coordination sphere, ΔDanisois the distortion produced by compression and stretching of bonds in the same coordination sphere, ΔDelecis the distortion produced by electronic effects. If present, ΔDeleccan be combined with ΔDanisobecause they lead to the same kind of distortions in line with the distortion theorem. EachD-index, in the new equation, corresponds to an algebraic expression containing experimental and theoretical bond valences. On the basis of this study, the ΔDindex defined in bond valence theory is a result of both the bond topology and the distortion theorem (ΔD= ΔDtop + ΔDaniso + ΔDelec), andD′ is a result of the compression, or stretching, of bonds (D′ =DRU + ΔDiso). The deficiencies present in the bond-valence theory in explaining mean bond-length variations can therefore be overcome, and the observed variations of 〈D〉 in crystal structures can be described by a self-consistent model.

scholarly journals Survey of Bond Lengths in the Solid State for Oxides: Results and Applications

2014 ◽  
Vol 70 (a1) ◽  
pp. C1103-C1103
Author(s):  
Olivier Gagne ◽  
Frank Hawthorne
Keyword(s):  
Solid State ◽  
Bond Length ◽  
Crystal Structures ◽  
A Priori ◽  
Bond Valence ◽  
Inorganic Crystal Structure Database ◽  
Ionic Radii ◽  
Coordination Polyhedra ◽  
Coordination Numbers ◽  
Bond Lengths

A complete survey of bond lengths from the Inorganic Crystal Structure Database (ICSD) is presented for all atoms of the Periodic Table of Elements, bonded to oxygen and in different oxidation states and coordination numbers. From over 135,000 crystal structures, a total of 33,343 coordination polyhedra and 188,462 bond distances were collected after passing a rigorous filtering process. One hundred thirty-six (136) ions in four hundred seventy-three (473) different configurations (coordination numbers) resulted. First, the bondlength distributions are visually inspected. This leads to (1) the observation and visual interpretation of known phenomena (e.g. Jahn-Teller effect), and (2) the isolation of new phenomena, as trends that are less obvious in smaller case-studies become more noticeable. Next, different applications of the data are investigated. The completeness of the survey allows the reassessment of important parameters of the solid state: ionic radii, and bond-valence parameters. Of the 473 ionic radii derived in this study, 329 revisions are made to Shannon's list of radii [1] (of which 176 were estimates), and 144 new ionic radii are derived. Next, a systematic evaluation of all bond-valence parameters published to date is done for oxides. Furthermore, using a new method of derivation, 136 new pairs of bond-valence parameters are obtained. In comparison to the previous-best published bond-valence parameters, an overall average decrease in the r.m.s.d. to the valence-sum rule of 20.7% (12.6% when weighted) is observed for the 33,343 coordination polyhedra, using the new parameters. New equations to describe the bond-length to bond-valence relation are also investigated. From an optimization between the experimental and a priori bond-valences of 54 carefully-selected crystal structures, roughly 20 relatively simple equations were selected for testing. Following a rigorous evaluation, the current exponential equation was found to be a viable choice in describing the relation. Finally, bond-length and bond-valence ranges are assigned to the 473 configurations of the atoms. Whereas the bondlength ranges are a useful aid in structure refinement, the assignment of a bond-valence range to ions allows a priori analysis of site occupancy in crystal structures.

Reaktionen von Azacoronanden mit Quecksilber(II)iodid: Kristallstrukturen zweier Komplexe von Hgl2 mit Diaza-15-krone-5 und Diaza-18-krone-6 /Reactions of Azacoronands with Mercury(II) Iodide: Crystal Structures of Two Complexes of Hgl2 with Diaza-15-crown-5, and Diaza-18-crown-6

1997 ◽  
Vol 52 (7) ◽  
pp. 847-850 ◽  
Author(s):  
Joachim Pickardt ◽  
Sven Wiese
Keyword(s):  
Bond Length ◽  
Crystal Structures ◽  
Iodine Atom ◽  
Bond Lengths ◽  
The Mean ◽  
Iodide Crystal

The reactions of diaza-15-crown-5 (“2.1”), and diaza-18-crown-6 (“2.2”), resp., with HgI2 in methanol afford the compounds [Hg(2.1)I][Hg2I6] (1) and [Hg(2.2)I][Hg2I6] (2), the crystal structures of which were determined. 1 consists of isolated cations [Hg(2.1)I]+ and anions [Hg2I6]2-. In the cations Hg is coordinated by one iodine atom, the two N atoms and the three O atoms of the ligand; the Hg-I distance is 262.1(3) pm, the Hg-N bond lengths are 221(2) and 238(2) pm; they are significantly shorter than the Hg-O distances, which are in the range between 262 and 271 pm. 2 consists of cations [Hg(2.2)I]+, which are bridged by the anions. In the cations of 2 Hg is coordinated by an iodine atom and by the two N atoms of the ligand, but by only three of the four O atoms. The Hg-I distance is 275.8(5) pm, the mean Hg-N bond length 234(4) pm, and the Hg-O distances vary between 285 and 304 pm. The Hg-I distance to the bridging I atom of the anion is 388.6(6) pm. The Hg-I bond lengths within the anions are slightly widened by this coordination.

scholarly journals Bond-length distributions for ions bonded to oxygen: metalloids and post-transition metals

2018 ◽  
Vol 74 (1) ◽  
pp. 63-78 ◽  
Author(s):  
Olivier Charles Gagné ◽  
Frank Christopher Hawthorne
Keyword(s):  
Transition Metal ◽  
Metal Ions ◽  
Bond Length ◽  
Coordination Number ◽  
Lone Pair ◽  
Transition Metal Ions ◽  
Length Variation ◽  
Coordination Polyhedra ◽  
Bond Lengths ◽  
Lone Pair Electrons

Bond-length distributions have been examined for 33 configurations of the metalloid ions and 56 configurations of the post-transition metal ions bonded to oxygen, for 5279 coordination polyhedra and 21 761 bond distances for the metalloid ions, and 1821 coordination polyhedra and 10 723 bond distances for the post-transition metal ions. For the metalloid and post-transition elements with lone-pair electrons, the more common oxidation state between n versus n+2 is n for Sn, Te, Tl, Pb and Bi and n+2 for As and Sb. There is no correlation between bond-valence sum and coordination number for cations with stereoactive lone-pair electrons when including secondary bonds, and both intermediate states of lone-pair stereoactivity and inert lone pairs may occur for any coordination number > [4]. Variations in mean bond length are ∼0.06–0.09 Å for strongly bonded oxyanions of metalloid and post-transition metal ions, and ∼0.1–0.3 Å for ions showing lone-pair stereoactivity. Bond-length distortion is confirmed to be a leading cause of variation in mean bond lengths for ions with stereoactive lone-pair electrons. For strongly bonded cations (i.e. oxyanions), the causes of mean bond-length variation are unclear; the most plausible cause of mean bond-length variation for these ions is the effect of structure type, i.e. stress resulting from the inability of a structure to adopt its characteristic a priori bond lengths.

A Priori Bond-Valence and Bond-Length Calculations in Rock-Forming Minerals

2018 ◽  
Author(s):  
Olivier Charles Gagné ◽  
Patrick H.J. Mercier ◽  
Frank Christopher Hawthorne
Keyword(s):  
Bond Length ◽  
A Priori ◽  
Bond Valence ◽  
Bond Lengths ◽  
Structural Strain

<i>A priori </i>bond-valences and bond-lengths are calculated for a series of rock-forming minerals. Comparison of <i>a priori </i>and observed bond-lengths allows structural strain to be assessed for those minerals.

Über die Reaktion von Bis(t-butylamino)dimethylsilan mit Titantetrachlorid. Kristallstrukturen des Imido-Komplexes [TiCl2(N-CMe3)(H2 N-CMe3)(CH3CN)]2 und des Ketimido-Komplexes [TiCl3 {NC(Me)N(H)CMe3}(CH3CN)2]/ On the Reaction of Bis(t-butylamino)dimethylsilane with Titanium Tetrachloride. Crystal Structures of the Imido Complex [TiCl2(N-CMe3)(H2N-CMe3)(CH3CN)]2 and of the Ketimido Complex [TiCl3{NC(Me)N(H)CMe3}(CH3CN)2]

1998 ◽  
Vol 53 (8) ◽  
pp. 887-892 ◽  
Author(s):  
Andreas Mommertz ◽  
Roland Leo ◽  
Werner Massa ◽  
Kurt Dehnicke
Keyword(s):  
Crystal Structure ◽  
Bond Length ◽  
Crystal Structures ◽  
Titanium Tetrachloride ◽  
Titanium Atom ◽  
Double Bonds ◽  
Dichloromethane Solution ◽  
Bond Lengths ◽  
Monomeric Complex ◽  
Structure Determinations

Abstract The reaction of bis(t-butylamino)dimethylsilane with titanium tetrachloride in dichloromethane solution leads to a mixture of compounds from which the imido complex (H3NCMe3)2[TiCl3(N-CMe3)]2 (1) and by extraction of the residue with acetonitrile the imido complex [TiCl2(N-CMe3)(H2N-CMe3)(CH3CN)]2 (2) can be isolated. 1 reacts with acetonitrile to give the ketimido complex [TiCl3{NC(Me)N(H)CMe3}(CH3CN)2] (3). According to crystal structure determinations 2 consists of centrosymmetric dimeric molecules containing TiCl2Ti bridges, the N-CMe32- ligands being in equatorial positions with TiN bond lengths of 168.8(4) pm which corresponds to double bonds. In the monomeric complex 3 the chloro ligands are in meridional positions of the distorted octahedrally coordinated titanium atom with a TiN bond length of 175.7(2) pm of the ketimido ligand.

A note on the distortion theorem

2017 ◽  
Vol 73 (5) ◽  
pp. 874-878
Author(s):  
M. S. Nickolsky
Keyword(s):  
Theoretical Analysis ◽  
Bond Length ◽  
Coordination Polyhedron ◽  
Distortion Theorem ◽  
Bond Valence ◽  
Conditional Statement ◽  
The Mean

The distortion theorem is a conditional statement that establishes the certain relations between the variation of the mean bond length and the variation of the valence of a central ion of a coordination polyhedron. It was found that in some principal cases the conditional part of the distortion theorem is not necessary. A combinatorial evaluation of the distortion theorem and a theoretical analysis of the bond length–bond valence correlation were performed. An extension of the distortion theorem is proposed.

Torsional vibration and central bond length of N-benzylideneanilines

2004 ◽  
Vol 60 (5) ◽  
pp. 578-588 ◽  
Author(s):  
Jun Harada ◽  
Mayuko Harakawa ◽  
Keiichiro Ogawa
Keyword(s):  
Temperature Dependence ◽  
Bond Length ◽  
Crystal Structures ◽  
Torsional Vibration ◽  
Room Temperature ◽  
X Ray Diffraction ◽  
Static Disorder ◽  
X Ray ◽  
Bond Lengths ◽  
Central Bond

The crystal structures of N-benzylideneaniline (1), N-benzylidene-4-carboxyaniline (2), N-(4-methylbenzylidene)-4-nitroaniline (3), N-(4-nitrobenzylidene)-4-methoxyaniline (4), N-(4-nitrobenzylidene)-4-methylaniline (5), N-(4-methoxybenzylidene)aniline (6) and N-(4-methoxybenzylidene)-4-methylaniline (7) were determined by X-ray diffraction analyses at various temperatures. In the crystal structures of all the compounds, an apparent shortening of the central C=N bond was observed at room temperature. As the temperature was lowered, the observed bond lengths increased to approximately 1.28 Å at 90 K, irrespective of substituents in the molecules. The shortening and the temperature dependence of the C=N bond length are interpreted in terms of an artifact caused by the torsional vibration of the C—Ph and N—Ph bonds in the crystals. In the crystal structures of (1) and (7), a static disorder around the C=N bond was observed, which is also responsible for the apparent shortening of the C=N bond.

scholarly journals Syntheses and crystal structures of 2-methyl-1,1,2,3,3-pentaphenyl-2-silapropane and 2-methyl-1,1,3,3-tetraphenyl-2-silapropan-2-ol

2019 ◽  
Vol 75 (9) ◽  
pp. 1339-1343
Author(s):  
Alexandra Williams ◽  
Michelle Brown ◽  
Richard J. Staples ◽  
Shannon M. Biros ◽  
William R. Winchester
Keyword(s):  
Hydrogen Bond ◽  
Bond Length ◽  
Crystal Structures ◽  
Trifluoromethanesulfonic Acid ◽  
Silicon Compound ◽  
Geometric Features ◽  
Axis Direction ◽  
Bond Lengths ◽  
Π Interactions ◽  
Sterically Hindered

The sterically hindered silicon compound 2-methyl-1,1,2,3,3-pentaphenyl-2-silapropane, C33H30Si (I), was prepared via the reaction of two equivalents of diphenylmethyllithium (benzhydryllithium) and dichloromethylphenylsilane. This bisbenzhydryl-substituted silicon compound was then reacted with trifluoromethanesulfonic acid, followed by hydrolysis with water to give the silanol 2-methyl-1,1,3,3-tetraphenyl-2-silapropan-2-ol, C27H26OSi (II). Key geometric features for I are the Si—C bond lengths that range from 1.867 (2) to 1.914 (2) Å and a τ4 descriptor for fourfold coordination around the Si atom of 0.97 (indicating a nearly perfect tetrahedron). Key geometric features for compound II include Si—C bond lengths that range from 1.835 (4) to 1.905 (3) Å, a Si—O bond length of 1.665 (3) Å, and a τ4 descriptor for fourfold coordination around the Si atom of 0.96. In compound II, there is an intramolecular C—H...O hydrogen bond present. In the crystal of I, molecules are linked by two pairs of C—H...π interactions, forming dimers that are linked into ribbons propagating along the b-axis direction. In the crystal of II, molecules are linked by C—H...π and O—H...π interactions that result in the formation of ribbons that run along the a-axis direction.

A Priori Bond-Valence and Bond-Length Calculations in Rock-Forming Minerals

2018 ◽  
Author(s):  
Olivier Charles Gagné ◽  
Patrick H.J. Mercier ◽  
Frank Christopher Hawthorne
Keyword(s):  
Bond Length ◽  
A Priori ◽  
Bond Valence ◽  
Bond Lengths ◽  
Structural Strain

<i>A priori </i>bond-valences and bond-lengths are calculated for a series of rock-forming minerals. Comparison of <i>a priori </i>and observed bond-lengths allows structural strain to be assessed for those minerals.

A Priori Bond-Valence and Bond-Length Calculations in Rock-Forming Minerals

2018 ◽  
Author(s):  
Olivier Charles Gagné ◽  
Patrick H.J. Mercier ◽  
Frank Christopher Hawthorne
Keyword(s):  
Bond Length ◽  
A Priori ◽  
Bond Valence ◽  
Bond Lengths ◽  
Structural Strain

<i>A priori </i>bond-valences and bond-lengths are calculated for a series of rock-forming minerals. Comparison of <i>a priori </i>and observed bond-lengths allows structural strain to be assessed for those minerals.

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