scholarly journals The Principle of Maximal Simplicity for Modular Inorganic Crystal Structures

Crystals ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 1472
Author(s):  
Sergey V. Krivovichev
Keyword(s):  
Crystal Structures ◽  
Structure Prediction ◽  
Structural Information ◽  
Structural Complexity ◽  
Configurational Entropy ◽  
Sensu Stricto ◽  
Least Action ◽  
Inorganic Crystal ◽  
Principle Of Least Action ◽  
Structure Description

Modularity is an important construction principle of many inorganic crystal structures that has been used for the analysis of structural relations, classification, structure description and structure prediction. The principle of maximal simplicity for modular inorganic crystal structures can be formulated as follows: in a modular series of inorganic crystal structures, the most common and abundant in nature and experiments are those arrangements that possess maximal simplicity and minimal structural information. The latter can be quantitatively estimated using information-based structural complexity parameters. The principle is applied for the modular series based upon 0D (lovozerite family), 1D (biopyriboles) and 2D (spinelloids and kurchatovite family) modules. This principle is empirical and is valid for those cases only, where there are no factors that may lead to the destabilization of simplest structural arrangements. The physical basis of the principle is in the relations between structural complexity and configurational entropy sensu stricto (which should be distinguished from the entropy of mixing). It can also be seen as an analogy of the principle of least action in physics.

Crystal chemistry of natural layered double hydroxides: 4. Crystal structures and evolution of structural complexity of quintinite polytypes from the Kovdor alkaline-ultrabasic massif, Kola peninsula, Russia

2018 ◽  
Vol 82 (2) ◽  
pp. 329-346 ◽  
Author(s):  
Elena S. Zhitova ◽  
Sergey V. Krivovichev ◽  
Viktor N. Yakovenchuk ◽  
Gregory Yu. Ivanyuk ◽  
Yakov A. Pakhomovsky ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Structural Information ◽  
Structural Complexity ◽  
Configurational Entropy ◽  
Direct Methods ◽  
Stacking Sequence ◽  
Layer Stacking ◽  
Complete Layer ◽  
Double Hydroxide ◽  
Double Hydroxides

AbstractTwo quintinite polytypes, 3R and 2T, which are new for the Kovdor alkaline-ultrabasic complex, have been structurally characterized. The crystal structure of quintinite-2T was solved by direct methods and refined to R1 = 0.048 on the basis of 330 unique reflections. The structure is trigonal, P$\bar 3$c1, a = 5.2720(6), c = 15.113(3) Å and V = 363.76(8) Å3. The crystal structure consists of [Mg2Al(OH)6]+ brucite-type layers with an ordered distribution of Mg2+ and Al3+ cations according to the $\sqrt 3 $ × $\sqrt 3 $ superstructure with the layers stacked according to a hexagonal type. The complete layer stacking sequence can be described as …=Ab1C = Cb1A=…. The crystal structure of quintinite-3R was solved by direct methods and refined to R1 = 0.022 on the basis of 140 unique reflections. It is trigonal, R$\bar 3$m, a = 3.063(1), c = 22.674(9) Å and V = 184.2(1) Å3. The crystal structure is based upon double hydroxide layers [M2+,3+(OH)2] with disordered distribution of Mg, Al and Fe and with the layers stacked according to a rhombohedral type. The stacking sequence of layers can be expressed as …=АB = BC = CA=… The study of morphologically different quintinite generations grown on one another detected the following natural sequence of polytype formation: 2H → 2T → 1M that can be attributed to a decrease of temperature during crystallization. According to the information-based approach to structural complexity, this sequence corresponds to the increasing structural information per atom (IG): 1.522 → 1.706 → 2.440 bits, respectively. As the IG value contributes negatively to the configurational entropy of crystalline solids, the evolution of polytypic modifications during crystallization corresponds to the decreasing configurational entropy. This is in agreement with the general principle that decreasing temperature corresponds to the appearance of more complex structures.

scholarly journals Complexity Parameters for Molecular Solids

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1399
Author(s):  
Alexander M. Banaru ◽  
Sergey M. Aksenov ◽  
Sergey V. Krivovichev
Keyword(s):  
Crystal Structures ◽  
Degrees Of Freedom ◽  
Inorganic Compounds ◽  
Molecular Crystals ◽  
Structural Complexity ◽  
Molecular Solids ◽  
Complexity Measures ◽  
Inorganic Crystal ◽  
Shannon Information Entropy ◽  
Intermolecular Contacts

Structural complexity measures based on Shannon information entropy are widely used for inorganic crystal structures. However, the application of these parameters for molecular crystals requires essential modification since atoms in inorganic compounds usually possess more degrees of freedom. In this work, a novel scheme for the calculation of complexity parameters (HmolNet, HmolNet,tot) for molecular crystals is proposed as a sum of the complexity of each molecule, the complexity of intermolecular contacts, and the combined complexity of both. This scheme is tested for several molecular crystal structures.

The Monte Carlo method for finding missing atoms in solving crystal structures from powder diffraction data without applying a rigid-body approximation

2001 ◽  
Vol 16 (2) ◽  
pp. 65-70 ◽  
Author(s):  
Hisayoshi Nakamura ◽  
Satoru Yamazaki ◽  
Tomohiko Ohnishi ◽  
Takashi Ida ◽  
Hideo Toraya
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Rigid Body ◽  
Crystal Structures ◽  
Structural Information ◽  
Inorganic Crystal ◽  
The Monte Carlo Method ◽  
Structure Solution ◽  
Monte Carlo Search ◽  
Correct Structure

The Monte Carlo method is applied to finding missing atoms in solving inorganic crystal structures without applying a rigid-body approximation. Whole powder patterns of α-SiO2 and Mg2SiO4 were used for testing a procedure. Four atoms among the six in the asymmetric unit of Mg2SiO4 could be found in the present analysis. The use of well-refined profile parameters enhanced the frequency of correct structure configurations in the Monte Carlo search. Utilizing structural information available for constructing a trial configuration is also considered to be important for efficiently searching the structure solution. A procedure for assignment of equivalent positions to respective atoms is presented. The method can be used as a powerful tool for finding missing atoms in a partially solved structure. A histogram of weighted reliability index in Monte Carlo calculations is very informative for evaluating the performance of the method. ©

scholarly journals Kurchatovite and Clinokurchatovite, Ideally CaMgB2O5: An Example of Modular Polymorphism

Minerals ◽  
2018 ◽  
Vol 8 (8) ◽  
pp. 332 ◽  
Author(s):  
Yulia Pankova ◽  
Sergey Krivovichev ◽  
Igor Pekov ◽  
Edward Grew ◽  
Vasiliy Yapaskurt
Keyword(s):  
Crystal Structures ◽  
Structural Complexity ◽  
Structural Features ◽  
Geometrical Parameters ◽  
Modular Approach ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
X Ray ◽  
Least Action ◽  
Ideal Composition

Kurchatovite and clinokurchatovite, both of ideal composition CaMgB2O5, from the type localities (Solongo, Buryatia, Russia, and Sayak-IV, Kazakhstan, respectively) have been studied using electron microprobe and single-crystal X-ray diffraction methods. The empirical formulae of the samples are Ca1.01Mg0.87Mn0.11Fe2+0.02B1.99O5 and Ca0.94Mg0.91Fe2+0.10Mn0.04B2.01O5 for kurchatovite and clinokurchatovite, respectively. The crystal structures of the two minerals are similar and based upon two-dimensional blocks arranged parallel to the c axis in kurchatovite and parallel to the a axis in clinokurchatovite. The blocks are built up from diborate B2O5 groups, and Ca2+ and Mg2+ cations in seven- and six-fold coordination, respectively. Detailed analysis of geometrical parameters of the adjacent blocks reveals that symmetrically different diborate groups have different degrees of conformation in terms of the δ angles between the planes of two BO3 triangles sharing a common O atom, featuring two discrete sets of the δ values of ca. 55° (B’ blocks) and 34° (B” blocks). The stacking of the blocks in clinokurchatovite can be presented as …(+B’)(+B”)(+B’)(+B”)… or [(+B’)(+B”)], whereas in kurchatovite it is more complex and corresponds to the sequence …(+B’)(+B”)(+B’)(−B’)(−B”)(−B’)(+B’)(+B”)(+B’)(−B’)(−B”)(−B’)… or [(+B’)(+B”)(+B’)(−B’)(−B”)(−B’)]. The B’:B” ratios for clinokurchatovite and kurchatovite are 1:1 and 2:1, respectively. According to this description, the two minerals cannot be considered as polytypes and their mutual relationship corresponds to the term modular polymorphs. From the viewpoint of information-based measures of structural complexity, clinokurchatovite (IG = 4.170 bits/atom and IG,total = 300.235 bits/cell) is structurally simpler than kurchatovite (IG = 4.755 bits/atom and IG,total = 1027.056 bits/cell). The high structural complexity of kurchatovite can be inferred from the modular character of its structure. The analysis of structural combinatorics in terms of the modular approach allows to construct the whole family of theoretically possible “kurchatovite”-type structures that bear the same structural features common for kurchatovite and clinokurchatovite. However, the crystal structures of the latter minerals are the simplest and are the only ones that have been observed in nature. The absence of other possible structures is remarkable and can be explained by either the maximum-entropy of the least-action fundamental principles.

Structural complexity of minerals: information storage and processing in the mineral world

2013 ◽  
Vol 77 (3) ◽  
pp. 275-326 ◽  
Author(s):  
S. V. Krivovichev
Keyword(s):  
Crystal Structure ◽  
Crystal Structures ◽  
Information Content ◽  
High Pressures ◽  
Structural Information ◽  
Structural Complexity ◽  
Information Storage ◽  
Inorganic Crystal Structure Database ◽  
Complexity Measures ◽  
Geological Processes

AbstractStructural complexity of minerals is characterized using information contents of their crystal structures calculated according to the modified Shannon formula. The crystal structure is considered as a message consisting of atoms classified into equivalence classes according to their distribution over crystallographic orbits (Wyckoff sites). The proposed complexity measures combine both size- and symmetry-sensitive aspects of crystal structures. Information-based complexity parameters have been calculated for 3949 structure reports on minerals extracted from the Inorganic Crystal Structure Database. According to the total structural information content, IG, total, mineral structures can be classified into very simple (0–20 bits), simple (20–100 bits), intermediate (100–500 bits), complex (500–1000 bits), and very complex (> 1000 bits). The average information content for mineral structures is calculated as 228(6) bits per structure and 3.23(2) bits per atom. Twenty most complex mineral structures are (IG, total in bits): paulingite (6766.998), fantappieite (5948.330), sacrofanite (5317.353), mendeleevite-(Ce) (3398.878), bouazzerite (3035.201), megacyclite (2950.928), vandendriesscheite (2835.307), giuseppetite (2723.097), stilpnomelane (2483.819), stavelotite-(La) (2411.498), rogermitchellite (2320.653), parsettensite (2309.820), apjohnite (2305.361), antigorite (m = 17 polysome) (2250.397), tounkite (2187.799), tschoertnerite (2132.228), farneseite (2094.012), kircherite (2052.539), bannisterite (2031.017), and mutinaite (2025.067). The following complexity-generating mechanisms have been recognized: modularity, misfit relationships between structure elements, and presence of nanoscale units (clusters or tubules). Structural complexity should be distiguished from topological complexity. Structural complexity increases with decreasing temperature and increasing pressure, though at ultra-high pressures, the situation may be different. Quantitative complexity measures can be used to investigate evolution of information in the course of global and local geological processes involving formation and transformation of crystalline phases. The information-based complexity measures can also be used to estimate the 'ease of crystallization' from the viewpoint of simplexity principle proposed by J.R. Goldsmith (1953) for understanding of formation of simple and complex mineral phases under both natural and laboratory conditions. According to the proposed quantitative approach, the crystal structure can be viewed as a reservoir of information encoded in its complexity. Complex structures store more information than simple ones. As erasure of information is always associated with dissipation of energy, information stored in crystal structures of minerals must have an important influence upon natural processes. As every process can be viewed as a communication channel, the mineralogical history of our planet on any scale is a story of accumulation, storage, transmission and processing of structural information.

scholarly journals Data-driven learning and prediction of inorganic crystal structures

2018 ◽  
Vol 211 ◽  
pp. 45-59 ◽  
Author(s):  
Volker L. Deringer ◽  
Davide M. Proserpio ◽  
Gábor Csányi ◽  
Chris J. Pickard
Keyword(s):  
Crystal Structure ◽  
Machine Learning ◽  
Crystal Structures ◽  
Structure Prediction ◽  
Data Driven ◽  
Interatomic Potentials ◽  
Crystal Structure Prediction ◽  
Energy Landscapes ◽  
Inorganic Crystal

Machine learning-based interatomic potentials, fitting energy landscapes “on the fly”, are emerging and promising tools for crystal structure prediction.

Crystal structures of Magnaporthe oryzae trehalose-6-phosphate synthase (MoTps1) suggest a model for catalytic process of Tps1

2019 ◽  
Vol 476 (21) ◽  
pp. 3227-3240 ◽  
Author(s):  
Shanshan Wang ◽  
Yanxiang Zhao ◽  
Long Yi ◽  
Minghe Shen ◽  
Chao Wang ◽  
...  
Keyword(s):  
Crystal Structures ◽  
Conformational Changes ◽  
Magnaporthe Oryzae ◽  
Structural Information ◽  
Complex Structure ◽  
Critical Role ◽  
Catalytic Process ◽  
Structural Basis ◽  
Salt Bridges ◽  
Terminal Domain

Trehalose-6-phosphate (T6P) synthase (Tps1) catalyzes the formation of T6P from UDP-glucose (UDPG) (or GDPG, etc.) and glucose-6-phosphate (G6P), and structural basis of this process has not been well studied. MoTps1 (Magnaporthe oryzae Tps1) plays a critical role in carbon and nitrogen metabolism, but its structural information is unknown. Here we present the crystal structures of MoTps1 apo, binary (with UDPG) and ternary (with UDPG/G6P or UDP/T6P) complexes. MoTps1 consists of two modified Rossmann-fold domains and a catalytic center in-between. Unlike Escherichia coli OtsA (EcOtsA, the Tps1 of E. coli), MoTps1 exists as a mixture of monomer, dimer, and oligomer in solution. Inter-chain salt bridges, which are not fully conserved in EcOtsA, play primary roles in MoTps1 oligomerization. Binding of UDPG by MoTps1 C-terminal domain modifies the substrate pocket of MoTps1. In the MoTps1 ternary complex structure, UDP and T6P, the products of UDPG and G6P, are detected, and substantial conformational rearrangements of N-terminal domain, including structural reshuffling (β3–β4 loop to α0 helix) and movement of a ‘shift region' towards the catalytic centre, are observed. These conformational changes render MoTps1 to a ‘closed' state compared with its ‘open' state in apo or UDPG complex structures. By solving the EcOtsA apo structure, we confirmed that similar ligand binding induced conformational changes also exist in EcOtsA, although no structural reshuffling involved. Based on our research and previous studies, we present a model for the catalytic process of Tps1. Our research provides novel information on MoTps1, Tps1 family, and structure-based antifungal drug design.

A Systematic Review on Popularity, Application and Characteristics of Protein Secondary Structure Prediction Tools

2019 ◽  
Vol 16 (2) ◽  
pp. 159-172 ◽  
Author(s):  
Elaheh Kashani-Amin ◽  
Ozra Tabatabaei-Malazy ◽  
Amirhossein Sakhteman ◽  
Bagher Larijani ◽  
Azadeh Ebrahim-Habibi
Keyword(s):  
Systematic Review ◽  
Secondary Structure ◽  
Structure Prediction ◽  
Web Of Science ◽  
Secondary Structure Prediction ◽  
Structural Information ◽  
Protein Secondary Structure ◽  
Structural Features ◽  
Prediction Tools ◽  
Insight Into

Background: Prediction of proteins’ secondary structure is one of the major steps in the generation of homology models. These models provide structural information which is used to design suitable ligands for potential medicinal targets. However, selecting a proper tool between multiple Secondary Structure Prediction (SSP) options is challenging. The current study is an insight into currently favored methods and tools, within various contexts. Objective: A systematic review was performed for a comprehensive access to recent (2013-2016) studies which used or recommended protein SSP tools. Methods: Three databases, Web of Science, PubMed and Scopus were systematically searched and 99 out of the 209 studies were finally found eligible to extract data. Results: Four categories of applications for 59 retrieved SSP tools were: (I) prediction of structural features of a given sequence, (II) evaluation of a method, (III) providing input for a new SSP method and (IV) integrating an SSP tool as a component for a program. PSIPRED was found to be the most popular tool in all four categories. JPred and tools utilizing PHD (Profile network from HeiDelberg) method occupied second and third places of popularity in categories I and II. JPred was only found in the two first categories, while PHD was present in three fields. Conclusion: This study provides a comprehensive insight into the recent usage of SSP tools which could be helpful for selecting a proper tool.

On the Shoulders of Giants

2018 ◽  
Author(s):  
David D. Nolte
Keyword(s):  
Eighteenth Century ◽  
Robert Hooke ◽  
New Approach ◽  
Isaac Newton ◽  
Least Action ◽  
New Science ◽  
Principle Of Least Action ◽  
Parabolic Trajectory ◽  
Leonhard Euler ◽  
New Generation

Galileo’s parabolic trajectory launched a new approach to physics that was taken up by a new generation of scientists like Isaac Newton, Robert Hooke and Edmund Halley. The English Newtonian tradition was adopted by ambitious French iconoclasts who championed Newton over their own Descartes. Chief among these was Pierre Maupertuis, whose principle of least action was developed by Leonhard Euler and Joseph Lagrange into a rigorous new science of dynamics. Along the way, Maupertuis became embroiled in a famous dispute that entangled the King of Prussia as well as the volatile Voltaire who was mourning the death of his mistress Emilie du Chatelet, the lone female French physicist of the eighteenth century.

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