Theoretical prediction of bond-valence networks. II. Comparison of the graph-matrix and resonance-bond approaches. Erratum

1999 ◽  
Vol 55 (1) ◽  
pp. 131-131 ◽  
Author(s):  
John S. Rutherford

The correct version of Fig. 2 in the paper by Rutherford [Acta Cryst. (1998), B54, 204–210] is given. It shows that, assuming graph-equivalent bonds are equal, there are 57 possible bond-length sequences for β-Ga2O3 within the constraints of the Valence-Sum Rule.

Author(s):  
Vasyl Sidey

The oxidation-state independent `bond valence (s)versusbond length (r)' correlation curve for manganese–oxygen bonds has been closely approximated using the modified two-parameter Trömels=f(r) function [Trömel (1983).Acta Cryst.B39, 664–669],s= [(r0−l)/(r−l)]2, wherer0= 1.763 (2) Å andl= 1.148 (9) Å. Ther0andlrefinable parameters of the above function can be regarded as the alternative bond-valence parameters intended for use in the modern bond-valence model [Brown (2009).Chem. Rev.109, 6858–6919] in cases where the traditional bond-valence parameters (r0;n) and (r0;b) fail.


1998 ◽  
Vol 54 (3) ◽  
pp. 204-210 ◽  
Author(s):  
J. S. Rutherford

This paper provides a common framework for the bond-valence and resonance-bond-number methods, both of which explain the principal variations in inorganic bond lengths from the sum of radii, as arising from the connectivity of the structure, and therefore may apply graph information in conjunction with the Valence-Sum Rule. Under these constraints, possible predictions are limited to specific ranges of (M − N + 1) parameters, where M and N are the size and order of a multigraph describing the crystal motif. Further restrictions on these parameters may arise from non-crystallographic graph symmetries. Convenient graph-theoretical calculation schemes are described for both approaches. As it is possible to identify the best possible prediction within the limits described, which is that most closely corresponding to the experimental result, we have a means of making a direct comparison of the effectiveness of the various methods proposed, as well as being able to evaluate them against a statistically based prediction. The resonance-bond-number method proves to be the better predictor in most cases. Examples analysed in this way comprise KVO3 (potassium metavanadate), α-Ga2O3 (gallium oxide), TeI4 [tellurium(IV) iodide], Li2SiO3 (lithium metasilicate), Li2GeO3 (lithium metagermanate) and CaCrF5 (calcium chromium fluoride).


2004 ◽  
Vol 60 (2) ◽  
pp. 174-178 ◽  
Author(s):  
Agata Trzesowska ◽  
Rafal Kruszynski ◽  
Tadeusz J. Bartczak

The bond-valence method, especially the valence-sum rule, is very useful for checking if the structures formed by trivalent lanthanides are correct. In this work bond-valence parameters (R ij ), which connect bond valences and bond lengths, have been computed for a large number of bonds taken from the Cambridge Structural Database, Version 5.24 (2002) [Allen (2002). Acta Cryst. B58, 380–388]. The calculated values of bond-valence parameters for metal-organic compounds decrease with an increase in lanthanide atomic number; the R ij values are also smaller than bond-valence parameters calculated for inorganic compounds. A summary of bond-valence sums calculated for R ij given in this work and reported in the literature, and a functional correlation between lanthanide–oxygen distances and coordination number are presented.


2017 ◽  
Vol 73 (8) ◽  
pp. 1202-1207
Author(s):  
Agata Gapinska ◽  
Alan J. Lough ◽  
Ulrich Fekl

Two coordination compounds containing tetra-n-butylammonium cations and bis-tfd-chelated molybdenum(IV) [tfd2− = S2C2(CF3)2 2−] and oxalate (ox2−, C2O4 2−) in complex anions are reported, namely bis(tetra-n-butylammonium) bis(1,1,1,4,4,4-hexafluorobut-2-ene-2,3-dithiolato)oxalatomolybdate(IV)–chloroform–oxalic acid (1/1/1), (C16H36N)2[Mo(C4F6S2)2(C2O4)]·CHCl3·C2H2O4 or (N n Bu4)2[Mo(tfd)2(ox)]·CHCl3·C2H2O4, and bis(tetra-n-butylammonium) μ-oxalato-bis[bis(1,1,1,4,4,4-hexafluorobut-2-ene-2,3-dithiolato)molybdate(IV)], (C16H36N)2[Mo2(C4F6S2)4(C2O4)] or (N n Bu4)2[(tfd)2Mo(μ-ox)Mo(tfd)2]. They contain a terminal oxalate ligand in the first compound and a bridging oxalate ligand in the second compound. Anion 1 2− is [Mo(tfd)2(ox)]2− and anion 2 2−, formally generated by adding a Mo(tfd)2 fragment onto 1 2−, is [(tfd)2Mo(μ-ox)Mo(tfd)2]2−. The crystalline material containing 1 2− is (N n Bu4)2-1·CHCl3·oxH2, while the material containing 2 2− is (N n Bu4)2-2. Anion 2 2− lies across an inversion centre. The complex anions afford a rare opportunity to compare terminal oxalate with bridging oxalate, coordinated to the same metal fragment, here (tfd)2MoIV. C—O bond-length alternation is observed for the terminal oxalate ligand in 1 2−: the difference between the C—O bond length involving the metal-coordinating O atom and the C—O bond length involving the uncoordinating O atom is 0.044 (12) Å. This bond-length alternation is significant but is smaller than the bond-length alternation observed for oxalic acid in the co-crystallized oxalic acid in (N n Bu4)2-1·CHCl3·oxH2, where a difference (for C=O versus C—OH) of 0.117 (14) Å was observed. In the bridging oxalate ligand in 2 2−, the C—O bond lengths are equalized, within the error margin of one bond-length determination (0.006 Å). It is concluded that oxalic acid contains a localized π-system in its carboxylic acid groups, that the bridging oxalate ligand in 2 2− contains a delocalized π-system and that the terminal oxalate ligand in 1 2− contains an only partially localized π-system. In (N n Bu4)2-1·CHCl3·oxH2, the F atoms of two of the –CF3 groups in 1 2− are disordered over two sets of sites, as are the N and eight of the C atoms of one of the N n Bu4 cations. In (N n Bu4)2-2, the whole of the unique N n Bu4 + cation is disordered over two sets of sites. Also, in (N n Bu4)2-2, a region of disordered electron density was treated with the SQUEEZE routine in PLATON [Spek (2015). Acta Cryst. C71, 9–18].


2018 ◽  
Author(s):  
Olivier Charles Gagné ◽  
Patrick H.J. Mercier ◽  
Frank Christopher Hawthorne

<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.


2003 ◽  
Vol 59 (2) ◽  
pp. 190-208 ◽  
Author(s):  
Fumihito Mohri

The bond-valence sum rule has been examined by molecular-orbital methods related to spin-coupling matrix theory [Okada & Fueno (1976). Bull. Chem. Soc. Jpn, 49, 1524–1530], to give a new formulation of the Lewis-electron pair concept. It is shown that the `pair-coupling population' between atoms M and X exhibits the same behaviour as the bond valence between them. A quantum chemical definition for bond valence is proposed and successfully applied to Al2Cl6, Te4Cl16 and Al2Be3(SiO3)6 (beryl). Using an alternative bond-valence definition it is shown that for oxides the bond valence can possibly be taken as the double pair-coupling population.


Author(s):  
M. S. Nickolsky

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.


2009 ◽  
Vol 65 (3) ◽  
pp. 401-402 ◽  
Author(s):  
Vasyl Sidey

Systematic variations of the bond-valence sums calculated from the poorly determined bond-valence parameters [Sidey (2008), Acta Cryst. B64, 515–518] have been illustrated using a simple graphical scheme.


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