Bond Constraint Research Articles

Newton's method revisited: How accurate do we have to be?

SummaryWe analyze the convergence of quasi‐Newton methods in exact and finite precision arithmetic using three different techniques. We derive an upper bound for the stagnation level and we show that any sufficiently exact quasi‐Newton method will converge quadratically until stagnation. In the absence of sufficient accuracy, we are likely to retain rapid linear convergence. We confirm our analysis by computing square roots and solving bond constraint equations in the context of molecular dynamics. In particular, we apply both a symmetric variant and Forsgren's variant of the simplified Newton method. This work has implications for the implementation of quasi‐Newton methods regardless of the scale of the calculation or the machine.

Optimal Bond Constraint Topology for Molecular Dynamics Simulations of Cholesterol.

We recently observed artificial temperature gradients in molecular dynamics (MD) simulations of phase-separating ternary lipid mixtures using the Martini 2 force field. We traced this artifact to insufficiently converged bond length constraints with typical time steps and default settings for the linear constraint solver (LINCS). Here, we systematically optimize the constraint scaffold of cholesterol. With massive virtual sites in an equimomental arrangement, we accelerate bond constraint convergence while preserving the original cholesterol force field and dynamics. The optimized model does not induce nonphysical temperature gradients even at relaxed LINCS settings and is at least as fast as the original model at the strict LINCS settings required for proper thermal sampling. We provide a python script to diagnose possible problems with constraint convergence for other molecules and force fields. Equimomental constraint topology optimization can also be used to boost constraint convergence in atomistic MD simulations of molecular systems.

Elasticity, hardness, and fracture toughness of sodium aluminoborosilicate glasses

AbstractDue to an increasing demand for oxide glasses with a better mechanical performance, there is a need to improve our understanding of the composition‐structure‐mechanical property relations in these brittle materials. At present, some properties such as Young's modulus can to a large extent be predicted based on the chemical composition, while others—in particular fracture‐related properties—are typically optimized based on a trial‐and‐error approach. In this work, we study the mechanical properties of a series of 20 glasses in the quartenary Na2O–Al2O3–B2O3–SiO2 system with fixed soda content, thus accessing different structural domains. Ultrasonic echography is used to determine the elastic moduli and Poisson's ratio, while Vickers indentation is used to determine hardness. Furthermore, the single‐edge precracked beam method is used to estimate the fracture toughness (KIc) for some compositions of interest. The compositional evolutions of Vickers hardness and Young's modulus are in good agreement with those predicted from models based on bond constraint density and strength. Although there is a larger deviation, the overall compositional trend in KIc can also be predicted by a model based on the strength of the bonds assumed to be involved in the fracture process.

Energy wave propogation in pristine and bi-crystal graphene

This study investigates the distribution and propagation of potential energy in graphene under tearing loads. Before crack extension, high potential energy accumulates at the crack tip. The distributions of the high potential energy are symmetrical and asymmetrical in pristine graphene and bi-crystal graphene with misorientation angle of [Formula: see text], respectively. When a C–C bond breaks during the fracture of graphene, numerous energy waves successively arise from the crack tip, i.e., the two atoms linked by the broken bond. These atoms lose one bond constraint and turn into unstable states, and they displace with high accelerations. In pristine graphene, the energy waves present as hexagonal geometries, while the waveforms near the loading areas are compressed to flatter geometries. In bi-crystal graphene, the refractions of potential energy waves are observed when the energy waves propagate to the grain boundary (GB) and interact with it, and the waveforms are changed after the wave crosses the GB. For both pristine graphene and bi-crystal graphene, wrinkles are generated when the crack tip extends to the site sufficiently close to the vertical free boundary, and the wrinkles are always nearly parallel to the horizontal free boundary and move along with the motion of the crack tip.

Modifier Interaction and Mixed-Alkali Effect in Bond Constraint Theory Applied to Ternary Alkali Metaphosphate Glasses

Introducing an interaction parameter γ, we implement modifier interaction and the mixed-alkali effect into bond constraint theory, and apply this extension for simplistic property prediction on ternary phosphate glasses. The severity of the mixed alkali effect results from the interplay of two simultaneous contributions: Bond constraints on the modifier species soften or stiffen with decreasing or increasing γ, respectively. When the modifier size is not too dissimilar the decrease in γ reflects that the alkali ions can easily migrate between different sites, forcing the network to continuously re-accommodate for any subsequent distortions. With increasing size difference, migration becomes increasingly difficult without considerable network deformation. This holds even for smaller ions, where the sluggish dynamics of the larger constituent result in blocking of the fast ion movement, leading to the subsequent increase in γ. Beyond a certain size difference in the modifier pair, a value of γ exceeding unity may indicate the presence of steric hindrance due to the large surrounding modifiers impeding the phosphate network to re-accommodate deformation.

Unique effects of thermal and pressure histories on glass hardness: Structural and topological origin.

The properties of glass are determined not only by temperature, pressure, and composition, but also by their complete thermal and pressure histories. Here, we show that glasses of identical composition produced through thermal annealing and through quenching from elevated pressure can result in samples with identical density and mean interatomic distances, yet different bond angle distributions, medium-range structures, and, thus, macroscopic properties. We demonstrate that hardness is higher when the density increase is obtained through thermal annealing rather than through pressure-quenching. Molecular dynamics simulations reveal that this arises because pressure-quenching has a larger effect on medium-range order, while annealing has a larger effect on short-range structures (sharper bond angle distribution), which ultimately determine hardness according to bond constraint theory. Our work could open a new avenue towards industrially useful glasses that are identical in terms of composition and density, but with differences in thermodynamic, mechanical, and rheological properties due to unique structural characteristics.

Floppy Mode Degeneracy and Decoupling of Constraint Predictions in Super-Cooled Borate and Silicate Liquids

The theory of temperature-dependent topological constraints has been used to successfully explain the compositional dependence of glass properties for oxide and non-oxide compositions. It relates the number of topological degrees of freedom with the glass transition temperature through the configurational entropy of the system. Based on this, we estimated the number of degrees of freedom directly from viscosity measurements of binary alkali borate and silicate glasses. Both approaches exhibit a strong decoupling, which we suggest can be traced to the presence of medium- and long-range constraints that are not taken into account by bond constraint counting. The observed variation of the energy barrier for structural rearrangement and floppy mode degeneracy also corroborate our interpretation. We provide evidence that the degeneracy of floppy modes changes with chemical composition and that the parameter K(x) of the MYEGA viscosity equation could be used to assess changes in the medium-range order.

Modifier constraints in alkali ultraphosphate glasses

In applying the recently introduced concept of cationic constraint strength [J. Chem. Phys. 140, 214501 (2014)] to bond constraint theory (BCT) of binary phosphate glasses in the ultraphosphate region of xR2O-(1−x)P2O5 (with x≤0.5 and R={Li, Na, Cs}), we demonstrate that a fundamental limitation of BCT can be overcome. The modifiers are considered to exist in either “isolated” or “crosslinking” sites, in line with the so-called modifier sub-network [J. Chem. Phys. 140, 154501 (2014)] and each site is associated with a certain number of constraints. We estimate the compositional dependence of the modifier sites and then use this to calculate the glass transition temperature as a function of chemical composition. A statistical distribution of sites achieves a remarkable agreement with experimental data for all tested glasses and greatly improves upon previously published work.

Cationic constraint effects in metaphosphate glasses.

Temperature-dependent bond constraint theory (BCT) relies on counting the number of atomic degrees of freedom for a given topology of a glass network. It has been proven useful as a simplistic approach towards the prediction of glass properties. However, it breaks down at the inclusion of ionic bonds and is therefore presently unable to distinguish the effects of varying cationic species with predominantly ionic bonding. Here, we consider the treatment of modifier ions in the scope of BCT. Using the example of metaphosphate glasses with a broad range of modifier cation species, we find that the theory fails to predict the glass properties because of the specific contribution of each modifier species to the rigidity of the glass network. We therefore introduce the concept of constraint strength, which is a simplistic measure of how strongly the modifiers are bound to the surrounding oxygens through columbic forces.

Importance of hydrophobic parameters in identifying appropriate pose of CYP substrates in cytochromes

Cytochromes are catalytic enzymes which perform oxidative metabolic reactions on drugs. To determine the primary binding forces of CYP-substrate complex, molecular docking studies were carried out. Molecular docking analysis of several drugs with the enzymes CYP2C9, CYP2D6 and CYP3A4 revealed that hydrophobic interactions play a major role in determining the pose selection between substrates and enzymes. GOLD software with hydrophobic and hydrogen bond constraint was employed to identify the specific interactions which play deterministic role in the pose selection.

Influence of network bond percolation on the thermal, mechanical, electrical and optical properties of high and low-k a-SiC:H thin films

As demand for lower power and higher performance nano-electronic products increases, the semiconductor industry must adopt insulating materials with progressively lower dielectric constants (i.e. low-k) in order to minimize capacitive related power losses in integrated circuits. However in addition to a lower dielectric constant, low-k materials typically exhibit many other reduced material properties that have limited the ability of the semiconductor industry to implement them. In this article, we demonstrate that the reduced material properties exhibited by low-k materials can be understood based on bond constraint and percolation theory. Using a-SiC:H as a case study material, we utilize nuclear reaction analysis, Rutherford backscattering, nuclear magnetic resonance and transmission Fourier transform infra-red spectroscopy measurements to determine the average coordination (〈r〉) for these materials. Correlations of 〈r〉 to Young's modulus, hardness, thermal conductivity, resistivity, refractive index, intrinsic stress, mass density and porosity show that an extremely wide range in material properties (in some cases several orders of magnitude) can be achieved through reducing 〈r〉 via the controlled incorporation of terminal SiHx and CHx groups. We also demonstrate that the critical point at 〈r〉≤2.4 predicted by constraint theory exists in this material system and places limitations on the range of properties that can be achieved for future low-k a-SiC:H materials.

Durability of rewritable phase-change Ge X Sb Y Te1 − X − Y memory devices

The bond constraint theory (BCT) dealing with the rigidity caused by bond constraints and the long-range potential fluctuations (LRPF) arising from the defects and heterogeneities in the disordered semiconductors are important for understanding the atomic and electronic properties of amorphous semiconductors. Here, they are applied to the already commercialized Ge X Sb Y Te1 − X − Y (GST) chalcogenide glasses used in the rewritable phase change memory (PCM) devices. The main concern at present is to improve their ability to withstand a large number of phase change cycles, by choosing the right composition. The two considerations (BCT and LRPF) are briefly described and tested on the most commonly used Ge2Sb2Te5 and the nearby compositions. While these considerations provide significant insight into their atomic and electronic structures, the ansatz linking them with the durability of the PCM devices need to be justified by more work.

Enumerating tree-like chemical graphs with given upper and lower bounds on path frequencies

BackgroundEnumeration of chemical graphs satisfying given constraints is one of the fundamental problems in chemoinformatics and bioinformatics since it leads to a variety of useful applications including structure determination of novel chemical compounds and drug design.ResultsIn this paper, we consider the problem of enumerating all tree-like chemical graphs from a given set of feature vectors, which is specified by a pair of upper and lower feature vectors, where a feature vector represents the frequency of prescribed paths in a chemical compound to be constructed. This problem can be solved by applying the algorithm proposed by Ishida et al. to each single feature vector in the given set, but this method may take much computation time because in general there are many feature vectors in a given set. We propose a new exact branch-and-bound algorithm for the problem so that all the feature vectors in a given set are handled directly. Since we cannot use the bounding operation proposed by Ishida et al. due to upper and lower constraints, we introduce new bounding operations based on upper and lower feature vectors, a bond constraint, and a detachment condition.ConclusionsOur proposed algorithm is useful for enumerating tree-like chemical graphs with given upper and lower bounds on path frequencies.

Amorphous materials: Properties, structure, and durability: Constrained interactions, rigidity, adaptative networks, and their role for the description of silicates

Silicate glasses can be seen as connectivity networks where specific tools are used for the understanding of the behavior with composition of their chemical and physical properties. These tools make use of the effective interatomic interactions and mechanical constraints such as those used for analyzing the stability of macroscopic trusses. We first describe how complex interactions and coordination numbers can be efficiently handled within a general framework. The ingredients of the general framework, also known as mean-field bond constraint theory, are then presented. The theory predicts flexible to stressed-rigid elastic phase transitions at threshold compositions (or mean-coordination numbers). Applications to alkali- and alkaline-earth-silicates are considered and experimental signatures of the phase transition identified. Finally, we focus on the latest development in the field, namely the appearance of a new self-organized intermediate phase between flexible and stressed-rigid phases. Experimental signatures of these phases are reviewed, and the tools of adaptative silicate networks used to understand their features.

HingeMaster: Normal mode hinge prediction approach and integration of complementary predictors

Protein motion is often the link between structure and function and a substantial fraction of proteins move through a domain hinge bending mechanism. Predicting the location of the hinge from a single structure is thus a logical first step towards predicting motion. Here, we describe ways to predict the hinge location by grouping residues with correlated normal-mode motions. We benchmarked our normal-mode based predictor against a gold standard set of carefully annotated hinge locations taken from the Database of Macromolecular Motions. We then compared it with three existing structure-based hinge predictors (TLSMD, StoneHinge, and FlexOracle), plus HingeSeq, a sequence-based hinge predictor. Each of these methods predicts hinges using very different sources of information-normal modes, experimental thermal factors, bond constraint networks, energetics, and sequence, respectively. Thus it is logical that using these algorithms together would improve predictions. We integrated all the methods into a combined predictor using a weighted voting scheme. Finally, we encapsulated all our results in a web tool which can be used to run all the predictors on submitted proteins and visualize the results.

Fragment Molecular Orbital method‐based Molecular Dynamics (FMO‐MD) as a simulator for chemical reactions in explicit solvation

Fragment Molecular Orbital based-Molecular Dynamics (FMO-MD, Komeiji et al., Chem Phys Lett 2003, 372, 342) is an ab initio MD method suitable for large molecular systems. Here, FMO-MD was implemented to conduct full quantum simulations of chemical reactions in explicit solvation. Several FMO-MD simulations were performed for a sphere of water to find a suitable simulation protocol. It was found that annealing of the initial configuration by a classical MD brought the subsequent FMO-MD trajectory to faster stabilization, and also that use of bond constraint in the FMO-MD heating stage effectively reduced the computation time. Then, the blue moon ensemble method (Sprik and Ciccotti, J Chem Phys 1998, 109, 7737) was implemented and was tested by calculating free energy profiles of the Menschutkin reaction (H3N + CH3Cl --> +H3NCH3 + Cl-) in the presence and absence of the solvent water via FMO-MD. The obtained free energy profiles were consistent with the Hammond postulate in that stabilization of the product by the solvent, namely hydration of Cl-, shifted the transition state to the reactant-side. Based on these FMO-MD results, plans for further improvement of the method are discussed.

Bond constraint theory studies of chalcogenide phase change memories

Studies of amorphous (a-) semiconductors have been driven by technological advances as well as fundamental theories. Observation of electrical switching, for example, fueled early interest in a-chalcogenides. More recently a-chalcogenide switching has been applied successfully to programmable memory devices as well as DVD technology where the quest for the discovery of better-suited materials continues. Thus, switching grants researchers today with an active arena of technological as well as fundamental study. Bond constraint theory (BCT) and rigidity theory provide a powerful framework for understanding the structure and properties of a-materials. Application of these theories to switching in a-chalcogenides holds the promise of finding the best composition suited for switching applications. Extended X-ray absorption fine structure (EXAFS) spectroscopy is an ideally suited technique to investigate the switching properties of these materials. Films of amorphous Ge2Sb2Te4, Ge2Sb2Te5, and Ge2Sb2Te7 exhibit differing bonding structures and bond statistics, which result in different electronic and optical properties. Results of new EXAFS experiments on these three critical compositions in the Ge–Sb–Te system are presented in light of BCT and rigidity theory.

Defect scaling in non-crystalline floppy/under-constrained and rigid/over-constrained thin films: Applications to a-Se, a-Si, and a-Si(H)

Bond constraint theory provides insights into glass and intermediate phase formation in covalently-bonded non-crystalline networks. Metrics are the average number of bonds/atom, Nav, and average number of bending and stretching constraints per atom, Cav. Cav is a linear function of Nav:Cav=2.5Nav−3, with ideal, low defect density glasses and thin films having values of Nav and Cav equal to 2.4, and 3.0, respectively. In over-constrained films, it has been argued and demonstrated experimentally, that the density of intrinsic defects is proportional to Nav−2.4. In this paper we demonstrate that this scaling relationship, with the same empirical constants applies to floppy or under-constrained films with the example being a-Se where Nav has been determined from EXAFS studies and is ∼2.2. In addition we demonstrate that the density of defects in as deposited a-Si with a 6% density deficit, and broken bonding constraints, can be treated in the same way as spacing–filling over-constrained networks.

Bond constraint theory and the quest for the glass computer

Electronic switching in amorphous chalcogenide semiconductors has been observed and studied for nearly forty years. Technological exploitation of this phenomenon has most recently emerged in DVD’s where GST, a compound of germanium, antimony, and tellurium, is used to store information. We explain how GST behaves as a switch and how X-ray absorption fine structure can be used to unlock the specifics of the switching process. The tool that leads to this deeper understanding is the bond constraint theory. We explain how this theory leads to an explanation of switching and of the behavior and properties of amorphous materials in general. Finally, the prospects for developing GST-related materials into non-volatile memory media that could be the basis for glass computers are discussed.

Intermediate phases in binary and ternary alloys: a new perspective on semi-empirical bondconstraint theory

This paper extends the scope of semi-empirical bond constraint theory, (SEBCT) and usesthis extension to provide quantitative insights into the atomic scale bonding interactionsfor the two transitions that bracket intermediate phases (IPs) in binary and ternary alloys.Reversibility windows have usually been defined in terms of the average bonding coordination,rc (also, Nav, ), and show considerable scatter between different alloys when displayed in this way. Thispaper analyzes and plots these transitions in terms of the average number of bondingconstraints/atom,nc (also Cav), and thereby provides important insights into the extent to which SEBCT must bemodified by either extending, or contracting the force field with respect to the2-body bond-stretching and 3-bond-bending valence forces of the original SEBCTformulation. These modifications include (i) broken bond-bending constraints that reducenc below the level determined from stretching and bending constraints of the SEBCT,and (ii) additional forces due to repulsions between non-bonding lone-pair orbitalson two-fold coordinated Se, three-fold coordinated As, and terminal or one-foldcoordinated I atoms that add additional constraints to the SEBCT counting. Thesemodifications identify the bonding interactions that give rise to the scatter in therc-based plots, and then use the IP plots based onrc to provide a way of determining whether broken or additional constraints move the windowthreshold, respectively above or below the SEBCT value of 2.4.