Charge distribution as a tool to investigate structural details. III. Extension to description in terms of anion-centred polyhedra

The charge distribution (CHARDI) method is a self-consistent generalization of Pauling's concept of bond strength which does not make use of empirical parameters but exploits the experimental geometry of the coordination polyhedra building a crystal structure. In the two previous articles of this series [Nespoloet al.(1999).Acta Cryst.B55, 902–916; Nespoloet al.(2001).Acta Cryst.B57, 652–664], we have presented the features and advantages of this approach and its extension to distorted and heterovalent polyhedra and to hydrogen bonds. In this third article we generalize CHARDI to structures based on anion-centred polyhedra, which have drawn attention in recent years, and we show that computations based on both descriptions can be useful to obtain a deeper insight into the structural details, in particular for mixed-valence compounds where CHARDI is able to give precise indications on the statistical distribution of atoms with different oxidation number. A graph-theoretical description of the structures rationalizes and gives further support to the conclusions obtainedviathe CHARDI approach.

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Charge distribution as a tool to investigate structural details. II. Extension to hydrogen bonds, distorted and hetero-ligand polyhedra

Acta Crystallographica Section B Structural Science ◽

10.1107/s0108768101009879 ◽

2001 ◽

Vol 57 (5) ◽

pp. 652-664 ◽

Cited By ~ 65

Author(s):

Massimo Nespolo ◽

Giovanni Ferraris ◽

Gabriella Ivaldi ◽

Rudolf Hoppe

Keyword(s):

Hydrogen Bonds ◽

Charge Distribution ◽

Empirical Parameter ◽

Coordination Polyhedra ◽

Scale Factors ◽

Iterative Calculation ◽

Structural Details ◽

Contraction Parameter ◽

Bond Strengths ◽

Dynamic Structures

It is shown that one of the main reasons for most failures of the methods for calculating distance-dependent bond strengths is related to the distortion of the coordination polyhedra. The charge distribution (CD) method which depends on only one universal empirical parameter (contraction parameter) is modified to include: (i) an iterative calculation of the effective coordination number (ECoN), to deal with structures containing very distorted coordination polyhedra; (ii) a specific contraction parameter to treat structures containing any type of hydrogen bond; (iii) scale factors for coordination subshells, to treat structures with hetero-ligand polyhedra. The contraction parameter for the hydrogen bonds was obtained from 119 well refined structures based on neutron diffraction data. Examples of the application of the iterative charge distribution (CD-IT) are presented to show the efficiency of the new method in dealing with distorted (including hydrogen bonding) and hetero-ligand polyhedra. In particular, analysis of a series of 74 structures with pentacoordinated cations shows that deviations from overall trends are related to structure instability. The possible failure of the method with polyionic structures and `dynamic' structures is discussed.

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Probing the localized-to-delocalized transition

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2007.2148 ◽

2007 ◽

Vol 366 (1862) ◽

pp. 163-175 ◽

Cited By ~ 39

Author(s):

Javier J Concepcion ◽

Dana M Dattelbaum ◽

Thomas J Meyer ◽

Reginaldo C Rocha

Keyword(s):

Transition Metal Complexes ◽

Classification Scheme ◽

Mixed Valence ◽

Spin Orbit Coupling ◽

Energy Bands ◽

Coupled Vibrations ◽

Orbital Interactions ◽

Experimental Protocols ◽

Mixed Valence Compounds ◽

Insight Into

Detailed understanding of the transition between localized and delocalized behaviour in mixed valence compounds has been elusive as evidenced by many interpretations of the Creutz–Taube ion, [(NH 3 ) 5 Ru(pz)Ru(NH 3 ) 5 ] 5+ . In a review in 2001, experimental protocols and a systematic model to probe this region were proposed and applied to examples in the literature. The model included: (i) multiple orbital interactions in ligand-bridged transition metal complexes, (ii) inclusion of spin-orbit coupling which, for dπ 5 –dπ 6 complexes, leads to five low-energy bands, two from interconfigurational (dπ→dπ) transitions at the dπ 5 site and three from intervalence transfer transitions, (iii) differences in time scale between coupled vibrations and solvent modes which can result in solvent averaging with continued electronic asymmetry defining ‘class II–III’, an addition to the Robin–Day classification scheme, and (iv) delineation of coupled vibrations into barrier vibrations and ‘spectator’ vibrations. The latter provide direct insight into localization or delocalization and time scales for electron transfer. In this paper, the earlier model is applied to a series of mixed-valence molecules.

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Charge distribution as a tool to investigate structural details. IV. A new route to heteroligand polyhedra

Acta Crystallographica Section B Structural Science Crystal Engineering and Materials ◽

10.1107/s2052520615019472 ◽

2016 ◽

Vol 72 (1) ◽

pp. 51-66 ◽

Cited By ~ 13

Author(s):

Massimo Nespolo

Keyword(s):

Charge Distribution ◽

A Priori ◽

Total Charge ◽

Ionic Radii ◽

Empirical Parameter ◽

Coordination Polyhedra ◽

New Approach ◽

Bonding Effect ◽

Structural Details ◽

Previous Algorithm

A new route to apply the charge distribution (CHARDI) method to structures based on heteroligand coordination polyhedra is presented. The previous algorithm used scale factors computed in an iterative way based on the assumption (which turned out to be not always correct) that a real over–under bonding effect affects mainly the anionic charges of each single anion, without grossly modifying the total charge of each type of anion. The new, more general approach is not based on anya prioriassumption but treats separately the homoligand sub-polyhedra and attributes to each type of atom a fraction of the charge of the atom coordinated to it, computed in a self-consistent iterative way. The distinction between the bonding and non-bonding contact is also redefined in terms of the mean fictive ionic radii (MEFIR), without the need of an empirical parameter, used in the previous algorithm. CHARDI equations are generalized in terms of the new approach and a series of examples is presented.

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Charge Distribution in Arylhydrazine-Centered Mixed Valence Compounds with Smaller Bridges (Five to Nine Bonds between Closest Nitrogens)

The Journal of Physical Chemistry A ◽

10.1021/jp810645q ◽

2009 ◽

Vol 113 (18) ◽

pp. 5324-5332 ◽

Cited By ~ 5

Author(s):

Stephen F. Nelsen ◽

Kevin P. Schultz

Keyword(s):

Charge Distribution ◽

Mixed Valence ◽

Mixed Valence Compounds

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Charge distribution as a tool to investigate structural details: meaning and application to pyroxenes

Acta Crystallographica Section B Structural Science ◽

10.1107/s0108768199008708 ◽

1999 ◽

Vol 55 (6) ◽

pp. 902-916 ◽

Cited By ~ 55

Author(s):

Massimo Nespolo ◽

Giovanni Ferraris ◽

Haruo Ohashi

Keyword(s):

Bond Strength ◽

Bond Length ◽

Charge Distribution ◽

Integer Number ◽

Oxidation Number ◽

Structural Details ◽

Temperature And Pressure ◽

First Time ◽

Oxygen Bond ◽

Cation Ratio

The charge distribution (CD) method, previously introduced as a development of the bond-valence (BV) approach, is applied for the first time to mineral structures, and specifically to pyroxenes. CD essentially involves the distribution of the Effective Coordination Number (ECoN) of a cation among all the neighboring anions. This distribution is then interpreted in terms of distribution of `charges', where `charge' represents the formal oxidation state. Differently from BV, the CD description depends upon the geometry of each coordination polyhedron, which is characterized through ECoN (a non-integer number). The contribution of each cation–oxygen bond to ECoN, labelled `bond weight', corresponds to the bond strength in the BV method, but it is defined in terms of bond-length ratio in each polyhedron and not as a function of the cation–oxygen pair. The ratio q/Q of the formal oxidation number to the computed charge can be interpreted as a measure of the correctness of the structure (cation ratio) and of the degree of over- or under-bonding (anion ratio). A similar interpretation is not possible for the analogous quantities obtained through the BV approach. The analysis in terms of CD of the pyroxene chains (from 101 structures) shows different trends as a function of composition, temperature and pressure; in particular it shows a different behaviour of the two crystallographically independent chains of orthopyroxenes and of P21/c clinopyroxenes.

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Borohydride - Oxide Isomorphism in Design of Energy Storage Materials

Acta Crystallographica Section A Foundations and Advances ◽

10.1107/s205327331409055x ◽

2014 ◽

Vol 70 (a1) ◽

pp. C944-C944

Author(s):

Radovan Černý ◽

Pascal Schouwink

Keyword(s):

Solid State ◽

Mixed Valence ◽

Close Packing ◽

Energy Storage Materials ◽

Coordination Polyhedra ◽

High Hydrogen ◽

Storage Materials ◽

Structural Distortions ◽

Mixed Valence Compounds

An increasing number of novel single, double and triple cation borohydrides has been structurally characterized in the last few years as hydrogen storage materials and solid state electrolytes for battery applications [1,2]. It is interesting to note that the majority of these novel metal borohydrides resemble structures of various metal oxides. This is not altogether surprising considering the fact that [BH4]-and O2-anions are isoelectronic. The particularity of the borohydride-oxide analogy is the double negative charge of O2-vs. the simply charged borohydride [BH4]-, this providing a superior structural flexibility in oxides with respect to mixed valence compounds. Though somewhat handicapped by its lower charge regarding this issue, the borohydride anion obtains its versatility as a building block due to being a non-spherical anion with a tetrahedral shape as opposed to the oxide, which is approximately spherical. This commonly results in a lower symmetry of the borohydride when compared to the related oxide, the prototype very often showing a close packing of a readily polarisable soft oxide anion. We will show by means of in-situ synchrotron X-ray powder diffraction and ab initio calculations in the solid state that structural distortions in metal borohydrides compared to oxide prototypes have their origin in close hydridic di-hydrogen contacts of repulsive nature. These contacts may be suggested as a tool to tailor the crystal symmetry in complex metal hydrides in the future. Nearly twice as big as the oxide, the borohydride anion allows for connectivities of the coordination polyhedra rarely observed among the oxides such as tetrahedral edge sharing. We will show how the borohydride-oxide isomorphism, and cationic heterovalent substitution allow the prediction and design of novel borohydrides with high hydrogen content or high cation mobility.

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