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

2016 ◽  
Vol 72 (1) ◽  
pp. 51-66 ◽  
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.

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

2001 ◽  
Vol 57 (5) ◽  
pp. 652-664 ◽  
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.

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.

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

2015 ◽  
Vol 71 (1) ◽  
pp. 34-47 ◽  
Author(s):  
Jean-Guillaume Eon ◽  
Massimo Nespolo
Keyword(s):  
Charge Distribution ◽  
Mixed Valence ◽  
Theoretical Description ◽  
Oxidation Number ◽  
Acta Cryst ◽  
Coordination Polyhedra ◽  
Structural Details ◽  
Mixed Valence Compounds ◽  
Experimental Geometry ◽  
Insight Into

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.

Mathematical Knowledge and the Interplay of Practices

2015 ◽  
Author(s):  
José Ferreirós
Keyword(s):  
Mathematical Knowledge ◽  
A Priori ◽  
Philosophy Of Mathematics ◽  
Advanced Mathematics ◽  
New Approach ◽  
Agent Based ◽  
Epistemology Of Mathematics ◽  
Actual Experience ◽  
Elementary Math ◽  
Mathematical Tradition

This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, the book uses the crucial idea of a continuum to provide an account of the development of mathematical knowledge that reflects the actual experience of doing math and makes sense of the perceived objectivity of mathematical results. Describing a historically oriented, agent-based philosophy of mathematics, the book shows how the mathematical tradition evolved from Euclidean geometry to the real numbers and set-theoretic structures. It argues for the need to take into account a whole web of mathematical and other practices that are learned and linked by agents, and whose interplay acts as a constraint. It demonstrates how advanced mathematics, far from being a priori, is based on hypotheses, in contrast to elementary math, which has strong cognitive and practical roots and therefore enjoys certainty. Offering a wealth of philosophical and historical insights, the book challenges us to rethink some of our most basic assumptions about mathematics, its objectivity, and its relationship to culture and science.

Survey Data Quality in Analyzing Harmonized Indicators of Protest Behavior: A Survey Data Recycling Approach

2021 ◽  
pp. 000276422110216
Author(s):  
Kazimierz M. Slomczynski ◽  
Irina Tomescu-Dubrow ◽  
Ilona Wysmulek
Keyword(s):  
Data Processing ◽  
Data Quality ◽  
Survey Data ◽  
A Priori ◽  
Data Sets ◽  
New Approach ◽  
Survey Quality ◽  
Survey Error ◽  
Ex Post ◽  
The Impact

This article proposes a new approach to analyze protest participation measured in surveys of uneven quality. Because single international survey projects cover only a fraction of the world’s nations in specific periods, researchers increasingly turn to ex-post harmonization of different survey data sets not a priori designed as comparable. However, very few scholars systematically examine the impact of the survey data quality on substantive results. We argue that the variation in source data, especially deviations from standards of survey documentation, data processing, and computer files—proposed by methodologists of Total Survey Error, Survey Quality Monitoring, and Fitness for Intended Use—is important for analyzing protest behavior. In particular, we apply the Survey Data Recycling framework to investigate the extent to which indicators of attending demonstrations and signing petitions in 1,184 national survey projects are associated with measures of data quality, controlling for variability in the questionnaire items. We demonstrate that the null hypothesis of no impact of measures of survey quality on indicators of protest participation must be rejected. Measures of survey documentation, data processing, and computer records, taken together, explain over 5% of the intersurvey variance in the proportions of the populations attending demonstrations or signing petitions.

A New Approach to the Extraction of ANN Rules and to Their Generalization Capacity Through GP

2004 ◽  
Vol 16 (7) ◽  
pp. 1483-1523 ◽  
Author(s):  
Juan R. Rabuñal ◽  
Julián Dorado ◽  
Alejandro Pazos ◽  
Javier Pereira ◽  
Daniel Rivero
Keyword(s):  
Genetic Programming ◽  
Rule Extraction ◽  
Human Beings ◽  
Activation Functions ◽  
New Approach ◽  
Previous Algorithm ◽  
Internal Distribution

Various techniques for the extraction of ANN rules have been used, but most of them have focused on certain types of networks and their training. There are very few methods that deal with ANN rule extraction as systems that are independent of their architecture, training, and internal distribution of weights, connections, and activation functions. This article proposes a methodology for the extraction of ANN rules, regardless of their architecture, and based on genetic programming. The strategy is based on the previous algorithm and aims at achieving the generalization capacity that is characteristic of ANNs by means of symbolic rules that are understandable to human beings.

scholarly journals On the security of $\alpha\eta$: response to 'some attacks on quantum-based cryptographic protocols'

2006 ◽  
Vol 6 (7) ◽  
pp. 561-582
Author(s):  
H.P. Yuen ◽  
R. Nair ◽  
E. Corndorf ◽  
G.S. Kanter ◽  
P. Kumar
Keyword(s):  
Coherent State ◽  
Optical Communications ◽  
A Priori ◽  
Key Generation ◽  
Generation System ◽  
New Approach ◽  
Security Proof ◽  
Grover Search ◽  
Channel Loss ◽  
Key Length

Lo and Ko have developed some attacks on the cryptosystem called $\alpha \eta$}, claiming that these attacks undermine the security of $\alpha\eta$ for both direct encryption and key generation. In this paper, we show that their arguments fail in many different ways. In particular, the first attack in [1] requires channel loss or length of known-plaintext that is exponential in the key length and is unrealistic even for moderate key lengths. The second attack is a Grover search attack based on `asymptotic orthogonality' and was not analyzed quantitatively in [1]. We explain why it is not logically possible to "pull back'' an argument valid only at $n=\infty$ into a limit statement, let alone one valid for a finite number of transmissions n. We illustrate this by a `proof' using a similar asymptotic orthogonality argument that coherent-state BB84 is insecure for any value of loss. Even if a limit statement is true, this attack is a priori irrelevant as it requires an indefinitely large amount of known-plaintext, resources and processing. We also explain why the attacks in [1] on $\alpha\eta$ as a key-generation system are based on misinterpretations of [2]. Some misunderstandings in [1] regarding certain issues in cryptography and optical communications are also pointed out. Short of providing a security proof for $\alpha\eta$, we provide a description of relevant results in standard cryptography and in the design of $\alpha\eta$ to put the above issues in the proper framework and to elucidate some security features of this new approach to quantum cryptography.

scholarly journals Bond-Length Distributions for Ions Bonded to Oxygen: Results for the Transition Metals and Quantification of the Factors Underlying Bond-Length Variation in Inorganic Solids

2020 ◽  
Author(s):  
Olivier Charles Gagné ◽  
Frank Christopher Hawthorne
Keyword(s):  
Transition Metal ◽  
Bond Length ◽  
A Priori ◽  
Bond Formation ◽  
Length Variation ◽  
Electronic Effects ◽  
Coordination Polyhedra ◽  
Jahn Teller ◽  
Jahn Teller Effect ◽  
Non Local

Bond-length distributions are examined for 63 transition-metal ions bonded to O2- in 147 configurations, for 7522 coordination polyhedra and 41,488 bond distances, providing baseline statistical knowledge of bond lengths for transi-tion metals bonded to O2-. A priori bond valences are calculated for 140 crystal structures containing 266 coordination poly-hedra for 85 transition-metal ion configurations with anomalous bond-length distributions. Two new indices, Δ𝑡𝑜𝑝𝑜𝑙 and Δ𝑐𝑟𝑦𝑠𝑡, are proposed to quantify bond-length variation arising from bond-topological and crystallographic effects in extended solids. Bond-topological mechanisms of bond-length variation are [1] non-local bond-topological asymmetry, and [2] multi-ple-bond formation; crystallographic mechanisms are [3] electronic effects (with inherent focus on coupled electronic-vibra-tional degeneracy in this work), and [4] crystal-structure effects. The Δ𝑡𝑜𝑝𝑜𝑙 and Δ𝑐𝑟𝑦𝑠𝑡 indices allow one to determine the primary cause(s) of bond-length variation for individual coordination polyhedra and ion configurations, quantify the dis-torting power of cations via electronic effects (by subtracting the bond-topological contribution to bond-length variation), set expectation limits regarding the extent to which functional properties linked to bond-length variations may be optimized in a given crystal structure (and inform how optimization may be achieved), and more. We find the observation of multiple bonds to be primarily driven by the bond-topological requirements of crystal structures in solids. However, we sometimes observe multiple bonds to form as a result of electronic effects (e.g. the pseudo Jahn-Teller effect); resolution of the origins of multiple-bond formation follows calculation of the Δ𝑡𝑜𝑝𝑜𝑙 and Δ𝑐𝑟𝑦𝑠𝑡 indices on a structure-by-structure basis. Non-local bond-topological asymmetry is the most common cause of bond-length variation in transition-metal oxides and oxysalts, followed closely by the pseudo Jahn-Teller effect (PJTE). Non-local bond-topological asymmetry is further suggested to be the most widespread cause of bond-length variation in the solid state, with no a priori limitations with regard to ion identity. Overall, bond-length variations resulting from the PJTE are slightly larger than those resulting from non-local bond-topological asym-metry, comparable to those resulting from the strong JTE, and less than those induced by π-bond formation. From a compar-ison of a priori and observed bond valences for ~150 coordination polyhedra in which the strong JTE or the PJTE is the main reason underlying bond-length variation, the Jahn-Teller effect is found not to have a symbiotic relation with the bond-topo-logical requirements of crystal structures. The magnitude of bond-length variations caused by the PJTE decreases in the fol-lowing order for octahedrally coordinated d0 transition metals oxyanions: Os8+ > Mo6+ > W6+ >> V5+ > Nb5+ > Ti4+ > Ta5+ > Hf4+ > Zr4+ > Re7+ >> Y3+ > Sc3+. Such ranking varies by coordination number; for [4], it is Re7+ > Ti4+ > V5+ > W6+ > Mo6+ > Cr6+ > Os8+ >> Mn7+; for [5], it is Os8+ > Re7+ > Mo6+ > Ti4+ > W6+ > V5+ > Nb5+. We conclude that non-octahedral coordinations of d0 ion configurations are likely to occur with bond-length variations that are similar in magnitude to their octahedral counterparts. However, smaller bond-length variations are expected from the PJTE for non-d0 transition-metal oxyanions.<br>

Transuranium Element Incorporation into the β-U3O8 Uranyl Sheet

1996 ◽  
Vol 465 ◽  
Author(s):  
M. L. Miller ◽  
P. C. Burns ◽  
R. J. Finch ◽  
R. C. Ewing
Keyword(s):  
Crystal Structure ◽  
Spent Nuclear Fuel ◽  
Chemical Characteristics ◽  
Transuranium Element ◽  
Limited Data ◽  
Charge Balance ◽  
Coordination Polyhedra ◽  
Structural Details ◽  
Structure Determinations ◽  
Shared Edge

ABSTRACTSpent nuclear fuel (SNF) is unstable under oxidizing conditions. Although recent studies have determined the paragenetic sequence for uranium phases that result from the corrosion of SNF, there are only limited data on the potential of alteration phases for the incorporation of transuranium elements. The crystal chemical characteristics of transuranic elements (TUE) are to a certain extent similar to uranium; thus TUE incorporation into the sheets of uranyl oxide hydrate structures can be assessed by examination of the structural details of the β-U3O8 sheet type.The sheets of uranyl polyhedra observed in the crystal structure of β-U3O8 also occur in the mineral billietite (Ba[(UO2)3O2(OH)3]2(H2O)4), where they alternate with α-U3O8 type sheets. Preliminary crystal structure determinations for the minerals ianthinite, ([U24+(HO2)4O6(HO)4(H2O)4](H2O)5), and “wyartite II” (mineral name not approved by IMA committee on mineral names), {CaCo3}[U4+(UO2)2O3(OH)2](H2O)4, indicate that these phases also contain β-U3O8 type sheets. The β-U3O8sheet anion topology contains triangular, rhombic, and pentagonal sites in the proportions 2: 1:2. In all structures containing β-U3O8 type sheets, the triangular sites are vacant. The pentagonal sites are filled with U6+O2 forming pentagonal bipyramids. The rhombic dipyramids filling the rhombic sites contain U6+O2 in billietite, U4+O2 in β-U3O8U4+(H2O)2 in ianthinite, and U4+O3 in “wyartite-II” (in which one apical anion is replaced by two O atoms forming a shared edge with a carbonate triangle of the interlayer). Interlayer species include: H2O (billietite, “wyartite II”, and ianthinite), Ba2+ (billietite) Ca2+ (”wyartite II”), and CO3−2 (”wyartite II”); there is no interlayer in β-U3O8. The similarity of known TUE coordination polyhedra with those of U suggests that the β-U3O8 sheet will accommodate TUE substitution coupled with variations in apical anion configuration and interlayer population providing the required charge balance.

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