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.

Theoretical analysis of apical bonding in copper(II) chelates withN-substituted amino acids

2009 ◽  
Vol 43 (1) ◽  
pp. 42-47 ◽  
Author(s):  
Ante Miličević ◽  
Nenad Raos
Keyword(s):  
Amino Acids ◽  
Theoretical Analysis ◽  
Bond Length ◽  
Coordination Polyhedron ◽  
Naturally Occurring ◽  
Steric Crowding ◽  
Overlapping Spheres

The interdependence between the side of apical coordination of H2O and steric crowding at the apical positions was investigated on a set of 34 copper(II) bis-complexes withN- andN,N-substituted amino acids. As a measure of steric crowding, overlapping volumesV* were used, calculated using a modified overlapping spheres method. Steric crowding around the apically bonded ligand was the same for this set of complexes as for the copper(II) bis-complexes with naturally occurring amino acids, with the optimal occupied volume values between 1 and 1.5 Å3. The interdependence between the length of the apical bond and distortion of the coordination polyhedron was also studied. The apical bond length showed sigmoidal dependence on the magnitude of distortion.

Theoretical analysis of apical bonding in copper(II) chelates with amino acids

2009 ◽  
Vol 42 (5) ◽  
pp. 793-797 ◽  
Author(s):  
Ante Miličević ◽  
Nenad Raos
Keyword(s):  
Amino Acids ◽  
Theoretical Analysis ◽  
Bond Length ◽  
Dimethyl Sulfoxide ◽  
Coordination Polyhedron ◽  
Side Chain ◽  
Naturally Occurring ◽  
Steric Crowding ◽  
Overlapping Spheres

The interdependence between the side of apical coordination (H2O, >C=O, dimethyl sulfoxide and Cl−) and steric crowding at the apical positions was investigated for a set of 20 copper(II) bis complexes with naturally occurring amino acids. As a measure of steric crowding the overlapping volumes,V*, were used, calculated by the modified overlapping spheres method. It was found that the apically coordinated side of a complex is more hindered by the side-chain atoms. In addition, if both sides are apically coordinated, the apical bond is shorter at the more crowded side. The interdependence between the length of the apical bond and distortion of the coordination polyhedron was also studied. The apical bond length shows sigmoidal dependence on the magnitude of distortion, and is also dependent on the kind of distortion (square-pyramidal or tetrahedral).

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 STRUCTURAL STUDY OF BIS(2,6-BIS(PYRAZOL-3-YL)PYRIDINE)NICKEL(II) BY CALORIMETRY AND EXAFS SPECTROMETRY

2010 ◽  
Vol 3 (2) ◽  
pp. 74-79
Author(s):  
Kristian H Sugiyarto
Keyword(s):  
Complex Formation ◽  
Bond Length ◽  
Structural Study ◽  
Formation Constants ◽  
Exafs Analysis ◽  
The Mean

The main aim of this work is to reveal the complex formation of 2,6-bis(pyrazol-3-yl)pyridine, bpp, with nickel(II) perchlorate in DMF by calorimetric stepwise complex formation and then followed by EXAFS spectrometry. It was found that the complex formation follows two stepwise pathways namely the formation of mono pyrazolyl-pyridine, [Ni(DMF)3 bpp]2+, and bis pyrazolyl-pyridine, [Ni(bpp)2]2+;  the formation constants being  log β1 = 6.57, and log β2 = 5.02, and the total value of log β  = 11.58. The final formation of six-coordinated compound was confirmed by EXAFS analysis with the mean Ni-Nbpp bond length of 2.0646(0.0014) Å.   Keywords: nickel(II), bpp, EXAFS

scholarly journals Effects of Structure Boundary Conditions and Snow-Pack Properties on Snow-Creep Pressures

1989 ◽  
Vol 13 ◽  
pp. 175-179
Author(s):  
D.M. McClung ◽  
J.O. Larsen
Keyword(s):  
Theoretical Analysis ◽  
Field Data ◽  
Nonlinear Deformation ◽  
Design Consideration ◽  
Snow Pack ◽  
Deformation Law ◽  
Linear Creep ◽  
The Mean ◽  
Structure Boundary ◽  
Analytical Expressions

Structures placed in deep snow covers are subject to forces caused by interruption of the down-slope snow-pack deformation components. The resulting creep pressures are often the primary design consideration. In this paper, accurate field data (pressures) and theoretical analysis of the problem using a linear creep law to define snow deformation are presented. Results include analytical expressions for the pressures, and it is demonstrated that the resulting linear theory underestimates the mean pressures by about 20%. Higher accuracy will require that a nonlinear deformation law be formulated.

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.

Neue Chalkogenometallate mit binuklearen Anionen, I: Darstellung und Kristallstruktur von Rb6Sn2S7 / New Chalcogenometallates with Binuclear Anions, I: Preparation and Crystal Structure of Rb6Sn2S7

1999 ◽  
Vol 54 (12) ◽  
pp. 1505-1509 ◽  
Author(s):  
Kurt O. Klepp ◽  
Ferdinand Fabian
Keyword(s):  
Crystal Structure ◽  
Bond Length ◽  
Sulfur Atom ◽  
Bond Angle ◽  
The Mean

Colorless crystals of the new thiostannate Rb6Sn2S7 were obtained by reacting a stoichiometric melt of Rb2S, Sn and S at 700°C. The compound is orthorhombic, oP60, s.g. P212121 (No. 19) with a = 9.982(4), b = 13.45(1), c = 15.20(1) Å; Z = 4. The crystal structure was determined from diffractometer data and refined to a conventional R of 0.043 (1380 Fo's, 137 variables). The crystal structure contains dimeric anions, [Sn2S7]2 -, which are built up by slightly distorted SnS4 tetrahedra sharing a common sulfur atom. The mean Sn-S bond length calculates as 2.384 Å, the bond angle on the bridging S is 110.4°. The structure contains six independent Rb-cations which are coordinated to 5-6 sulfur atoms in irregular configurations.

Bond lengths in organic and metal-organic compounds revisited: X—H bond lengths from neutron diffraction data

2010 ◽  
Vol 66 (3) ◽  
pp. 380-386 ◽  
Author(s):  
Frank H. Allen ◽  
Ian J. Bruno
Keyword(s):  
Bond Length ◽  
Data Availability ◽  
General Level ◽  
Mean Values ◽  
Bond Lengths ◽  
Transition Metal Hydrides ◽  
Order Of Magnitude ◽  
Metal Organic ◽  
Structural Database ◽  
The Mean

The number of structures in the Cambridge Structural Database (CSD) has increased by an order of magnitude since the preparation of two major compilations of standard bond lengths in mid-1985. It is now of interest to examine whether this huge increase in data availability has implications for the mean bond-length values published in the late 1980s. Those compilations reported mean X—H bond lengths derived from rather sparse information and for rather few chemical environments. During the intervening years, the number of neutron studies has also increased, although only by a factor of around 2.25, permitting a new analysis of X—H bond-length distributions for (a) organic X = C, N, O, B, and (b) a variety of terminal and homometallic bridging transition metal hydrides. New mean values are reported here and are compared with earlier results. These new overall means are also complemented by an analysis of X—H distances at lower temperatures (T ≤ 140 K), which indicates the general level of librational effects in X—H systems. The study also extends the range of chemical environments for which statistically acceptable mean X—H bond lengths can be obtained, although values from individual structures are also collated to further extend the chemical range of this compilation. Updated default `neutron-normalization' distances for use in hydrogen-bond and deformation-density studies are also proposed for C—H, N—H and O—H, and the low-temperature analysis provides specific values for certain chemical environments and hybridization states of X.

P3Se4I: 5-Iodo-2,3,6,7-tetraselena-1,4,5-triphosphabicyclo[221]heptan, ein neues Phosphorselenaiodid / P3Se4I: 5-Iodo-2,3,6,7-tetraselena-1,4,5-triphosphabicyclo[221]heptan, a New Phosphorus Selena Iodide

1987 ◽  
Vol 42 (1) ◽  
pp. 47-51 ◽  
Author(s):  
Roger Blachnik ◽  
Willi Buchmeier ◽  
Claudia Schneider ◽  
Ulrike Wickel
Keyword(s):  
Bond Length ◽  
Nmr Spectra ◽  
Lattice Parameters ◽  
Monoclinic Space Group ◽  
Space Group ◽  
Bond Lengths ◽  
The Mean

P3Se4I is formed by the reaction of molten P4Se3 and I2. P3Se4I is monoclinic, space group P21/c with the lattice parameters of a = 1130.3(3) pm, b = 654.5(2) pm, c =1420.5(4) pm, β - 117.64(2)°. d = 3.87 g cm-3 and dx = 3.82 g cm-3 for Z = 4. The structure of the molecule is derived from the structure of α-or β-P4Se3I2 by the substitution of a P−I group by a Se-atom. The P−I, P−P and Se−Se bond lengths are 249.9, 219.2 and 236.9 pm. resp. The mean P−Se bond length is 225.0 pm. The molecule is stabilized by two weak intramolecular P−Se and P−I bonds, comparable to the bonding situation in α-P4Se3I2 . The 31P NMR spectra reveal a coalescence effect, due to equilibrium between two isomeric forms of the molecules.

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