Search

7-Hydroxycoumarin is a privileged structure for anti-inflammatory drug development. In this study, several new 3-acetyl-7-hydroxycoumarin derivatives were designed, synthesized and tested as anti-inflammatory agents. Interestingly, Mannich bases and Betti bases were separately obtained under acidic or neutral conditions. The regioselectivity of aminomethylation was studied based on the atomic electron density distribution by analysing the Voronoi deformation density (VDD) atomic charges, which reasonably explained the experimental outcome. Detection of nitric oxide (NO) and tumour necrosis factor alpha (TNF-α) release revealed that Mannich bases displayed stronger anti-inflammatory activity than the corresponding Betti bases.

Nitric oxide is involved in a series of biological processes. Ruthenium tetraammine complexes are model structures to control the NO availability. The influence of ligands is critical to determine the Ru–NO bond stability. Herein, the ligands of different natures and charges, namely, σ-donors (NH3 and H−), (ii) π-donors (H2O and NH2−), and (iii) σ-donors/π-acceptors (CO and CN−) were evaluated relative to the effect promoted by same ligands not only in the cis position to the NO group, but also in the trans position to NO. The energy decomposition analysis shows linear Ru–NO+ and bent Ru–NO0 bonds in ruthenium tetraammine complexes independent of ligands in cis or trans positions with regard to the NO group. Overall, the substitution of one σ-donor ligand with one π-donor ligand in the cis position to the NO group not stabilized the Ru–NO bond. These substitutions involving ligands in the trans position to NO stabilized the Ru–NO bond. Complexes with σ-donor/π-acceptor ligands compared to compounds with π-donor ligands in the cis or trans position to the NO group destabilized the Ru–NO bond. Charge distribution investigation realized from the Voronoi deformation density (VDD) method presents the Ru–NO bond more stabilized by negatively charged σ-donor, π-donor and σ-donor/π-acceptor ligands, in the cis or trans position to NO. These findings provide crucial information to the rational design of new NO storage–release systems with potential to deliver NO to desired targets in a controlled manner.

Nitric oxide (NO) is an important endogenously produced molecule. Ruthenium–NO tetraamine complexes appear as model structures to investigate the control of nitric oxide bioavailability. NO release typically occurs through the trans-[RuII(NH3)4Ltrans(NO+)]3+/2+ + e− → trans-[RuII(NH3)4Ltrans(NO0)]2+/+ reduction reaction, followed by the trans-[RuII(NH3)4Ltrans(NO0)]2+/+ + H2O → trans-[RuII(NH3)4Ltrans(H2O)]2+/+ + NO0 hydrolysis reaction. The choice of the NO trans ligand, Ltrans, is fundamental to control the Ru–NO bond stability. Here, the nature and charge influences of Ltrans were evaluated considering the following ligands Ltrans = σ-donors (NH3 and H−), π-donors (H2O and NH2−), and π-donors and π-acceptors (CO and CN−) through the ZORA-BP86/TZ2P computational model. Energy Decomposition Analysis in conjunction with the Natural Orbitals for Chemical Valence methodology (EDA-NOCV) showed that molecules with Ltrans = H2O and NH2− promoted larger Ru–NO stabilization than complexes with Ltrans = NH3 and H−, respectively, mainly due to the interaction orbital energy (ΔEoi). The opposite trend was observed in compounds with Ltrans = CO and CN− compared to structures with Ltrans = H2O and NH2−. The study of the charge distribution, performed using the Voronoi Deformation Density (VDD) method, and the topological analysis of the electron density, realized using the Quantum Theory of Atoms in Molecules (QTAIM), on the investigated complexes indicated that Ltrans with negative charge promoted, in general, predominantly a decrease of the electron flux in the Ltrans(σ) → Ru(dσ*) ← NO(σ) process.

This article studies two kinds of information extracted from statistical correlations between methods for assigning net atomic charges (NACs) in molecules. First, relative charge transfer magnitudes are quantified by performing instant least squares fitting (ILSF) on the NACs reported by Cho et al. (ChemPhysChem, 2020, 21, 688–696) across 26 methods applied to ∼2000 molecules. The Hirshfeld and Voronoi deformation density (VDD) methods had the smallest charge transfer magnitudes, while the quantum theory of atoms in molecules (QTAIM) method had the largest charge transfer magnitude. Methods optimized to reproduce the molecular dipole moment (e.g., ACP, ADCH, CM5) have smaller charge transfer magnitudes than methods optimized to reproduce the molecular electrostatic potential (e.g., CHELPG, HLY, MK, RESP). Several methods had charge transfer magnitudes even larger than the electrostatic potential fitting group. Second, confluence between different charge assignment methods is quantified to identify which charge assignment method produces the best NAC values for predicting via linear correlations the results of 20 charge assignment methods having a complete basis set limit across the dataset of ∼2000 molecules. The DDEC6 NACs were the best such predictor of the entire dataset. Seven confluence principles are introduced explaining why confluent quantitative descriptors offer predictive advantages for modeling a broad range of physical properties and target applications. These confluence principles can be applied in various fields of scientific inquiry. A theory is derived showing confluence is better revealed by standardized statistical analysis (e.g., principal components analysis of the correlation matrix and standardized reversible linear regression) than by unstandardized statistical analysis. These confluence principles were used together with other key principles and the scientific method to make assigning atom-in-material properties non-arbitrary. The N@C60 system provides an unambiguous and non-arbitrary falsifiable test of atomic population analysis methods. The HLY, ISA, MK, and RESP methods failed for this material.

For a series of organonitrile [RCN (R = Me, CF3, Ph, CH3Ph, CF3Ph)] ligands, the nature of the N–Pt bond in the related cis-/trans-(RCN)2PtCl2 complexes has been computationally investigated by Density Functional Theory. A fragment based bond analysis has been performed in the canonical Kohn–Sham molecular orbitals framework, and it has been ultimately assessed that this bond is characterized both by N→Pt σ and by N←Pt π contributions. Voronoi Deformation Density charges further confirms the occurrence of N←Pt π interactions. Moreover, the Energy Decomposition Analysis-Natural Orbital for Chemical Valence (EDA-NOCV) method shows that the strength of the N←Pt π interaction is not negligible by contributing to about 30–40% of the total orbital interaction. Finally, the well-known νCN blue-shift occurring upon coordination to PtII, has been thoroughly investigated by exploiting the EDA-NOCV and by evaluating νCN and force constants. The origin of the νCN blue-shift in these systems has been discussed on the basis of the CN bond polarization. N←Pt π backbonding causes only a systematic decrease of the observed νCN blue-shift when compared to the one calculated for RCN–X (X = H+, alkaline, Lewis acids) herein reported (X = purely σ acceptors).

We have quantum chemically studied the structure and nature of alkali‐ and coinage‐metal bonds (M‐bonds) versus that of hydrogen bonds between A−M and B− in archetypal [A−M⋅⋅⋅B]− model systems (A, B=F, Cl and M=H, Li, Na, Cu, Ag, Au), using relativistic density functional theory at ZORA‐BP86‐D3/TZ2P. We find that coinage‐metal bonds are stronger than alkali‐metal bonds which are stronger than the corresponding hydrogen bonds. Our main purpose is to understand how and why the structure, stability and nature of such bonds are affected if the monovalent central atom H of hydrogen bonds is replaced by an isoelectronic alkali‐ or coinage‐metal atom. To this end, we have analyzed the bonds between A−M and B− using the activation strain model, quantitative Kohn‐Sham molecular orbital (MO) theory, energy decomposition analysis (EDA), and Voronoi deformation density (VDD) analysis of the charge distribution., The same and not the same. Coinage‐metal bonds and, to a lesser extent, alkali‐metal bonds in [A−M⋅⋅⋅B]− model complexes are stronger than the corresponding hydrogen bonds in [A−H⋅⋅⋅B]−. Kohn‐Sham MO analyses reveal the origin of the responsible stronger electrostatic and orbital interactions.

We have analyzed the structure and stability of archetypal pnictogen-bonded model complexes D3Pn⋯A− (Pn = N, P, As, Sb; D, A = F, Cl, Br) using state-of-the-art relativistic density functional calculations at the ZORA-M06/QZ4P level. We have accomplished two tasks: (i) to compute accurate trends in pnictogen-bond strength based on a set of consistent data; and (ii) to rationalize these trends in terms of detailed analyses of the bonding mechanism based on quantitative Kohn–Sham molecular orbital (KS-MO) theory in combination with a canonical energy decomposition analysis (EDA) and Voronoi deformation density (VDD) analyses of the charge distribution. We have found that pnictogen bonds have a significant covalent character stemming from strong HOMO–LUMO interactions between the lone pair of A− and σ* of D3Pn. As such, the underlying mechanism of the pnictogen bond is similar to that of hydrogen, halogen, and chalcogen bonds., Our quantitative molecular orbital analyses show that pnictogen bonds are not solely electrostatic phenomena, but also have a strongly stabilizing covalent component, just like chalcogen-, halogen-, and hydrogen bonds.

The structural and electronic properties of edge-functionalized graphene sheets are systematically investigated utilizing Density Functional Theory (DFT). The functionalization includes alkyl, alkene, and seven different polyacetylene side chains as an alternative for a hydrogen atom in eight different kinds of graphene sheets. CH3 and longer side chains functionalization have high stability and remains unaffected by increasing the size of the graphene sheet. The weak binding energy and large formation energy are observed for CH2, C3H4 and C5H6 functionalization in all eight different kinds of the graphene sheet. The high charge transfer from graphene to side chain having high σ bonds is interpreted by Voronoi deformation density (VDD) method. The delocalization of the graphene ring decreases in side chain functionalization and gets decreased further when the size of the graphene sheet is increased. The high alteration in aromaticity is illustrated by decrease in Para Delocalization Index (PDI) value with an increase in aromatic Fluctuation Index (FLU) value in weakly binded side chains. The decrease in Highest Occupied Molecular Orbital (HOMO) along with a decrease in band gap on the substitution of nine different side chains in both pristine and defected sheet is observed. Moreover, the decrease in electron accepting ability is observed for CH3, C3H5 and C5H7 functionalization in all kinds of graphene sheets, which is inferred from the decrease in Lowest Unoccupied Molecular Orbital (LUMO).

The rapidly solidified Al-Co alloy is studied in a favored composition range of 25–75 at.% of aluminum (Al) by performing a set of classical molecular dynamics simulations (MD) based on the Embedded Atom Method (EAM). We have examined particularly the structure using several analyzing techniques such as: the radial distribution function (RDF), the Voronoi tessellation analysis and the structure factor. We observed a splitting in the second peak of both the RDF and the structure factor, indicating metallic glass formation. The Voronoi analysis shows that it is difficult to define a dominant type of coordination polyhedra for all compositions, manifesting two different Voronoi polyhedral (VP): 0,3,6,4 > and 0,2,8,4 > , and this distribution varies with increasing Al content. The structure factor is further examined via illustrating two of their important parameters: the full width at half maximum (FWHM) and the positon of the first sharp peak (FSP) as a function of the composition and the atomic volume, respectively. The first parameter showed a maximum for the A l 50 C o 50 alloy according to the dominance of unlike pairs, while the second one revealed a power law that allowed to compute the fractal dimension which is almost comparable to that found out from the analysis of the cumulative coordination number (CN).

The internal structure of a sheared assembly of monodisperse ellipsoids is investigated using three-dimensional Voronoi analysis. The discrete element method is employed to simulate isotropic and triaxial compression tests of ellipsoidal particles. A recently developed Voronoi tessellation technique, i.e., Set Voronoi tessellation, is applied to constructing Voronoi cells of assemblies at a series of shearing states. Several quantities are provided to quantify the properties of Voronoi cells, including local porosity, reduced surface area, sphericity, and a modified Minkowski tensor. We show that average local porosity, average reduced surface area, and average sphericity are functions of global porosity and mean coordination number during shearing, suggesting a relationship between void and particle networks. Moreover, local porosity and reduced surface area statistically comply with a modified lognormal distribution regardless of particle shape for a similar global porosity. However, the shape of a Voronoi cell is significantly dependent on the particle it encloses. Shear-induced inhomogeneity and anisotropy measured by Voronoi-based quantities are also examined. Increasing shear-induced entropy is observed, which means a more disordered void network during shearing. Furthermore, anisotropy of Voronoi cell orientations shows a comparable trend with anisotropy of contact normals. These findings are useful for developing a better understanding of void networks and their relationship with particle networks for non-spherical assemblies.

The local atomic structure in aluminium monatomic metallic glass is studied using molecular dynamics simulations combined with the embedded atom method (EAM). We have used a variety of analytical methods to characterise the atomic configurations of our system: the Pair Distribution Function (PDF), the Common Neighbour Analysis (CNA) and the Voronoi Tessellation Analysis. CNA was used to investigate the order change from liquid to amorphous phases, recognising that the amount of icosahedral clusters increases with the decrease of temperature. The Voronoi analysis revealed that the icosahedral-like polyhedral are the predominant ones. It has been observed that the PDF function shows a splitting in the second peak, which cannot be attributed to the only ideal icosahedral polyhedron 〈0, 0, 12, 0〉, but also to the formation of other Voronoi polyhedra 〈0, 1, 10, 2〉 . Further, the PDFs were then integrated giving the cumulative coordination number in order to compute the fractal dimension (df).

In this paper, we propose a novel domain decomposition method for large-scale simulations in continuum mechanics by merging the concepts of Centroidal Voronoi Tessellation (CVT) and Voronoi Particle dynamics (VP). The CVT is introduced to achieve a high-level compactness of the partitioning subdomains by the Lloyd algorithm which monotonically decreases the CVT energy. The number of computational elements between neighboring partitioning subdomains, which scales the communication effort for parallel simulations, is optimized implicitly as the generated partitioning subdomains are convex and simply connected with small aspect-ratios. Moreover, Voronoi Particle dynamics employing physical analogy with a tailored equation of state is developed, which relaxes the particle system towards the target partition with good load balance. Since the equilibrium is computed by an iterative approach, the partitioning subdomains exhibit locality and the incremental property. Numerical experiments reveal that the proposed Centroidal Voronoi Particle (CVP) based algorithm produces high-quality partitioning with high efficiency, independently of computational-element types. Thus it can be used for a wide range of applications in computational science and engineering.

Chemical reactivity properties such as regioselectivity, electrophilicity and nucleophilicity are important chemical concepts, yet their understanding and quantification are still far from being accomplished. Applying density functional theory (DFT) to appreciate these properties is one route to pursue in the literature. In this work, we present a comparative study to benchmark two approaches in DFT to predict regioselectivity, electrophilicity and nucleophilicity: one with the Hirshfeld charge and the other with the Fukui function. We also examine the impact of 15 different ways to compute atomic charges on the performance of their predictions about these chemical reactivity properties. Our results show that the Hirshfeld charge is able to reliably determine regioselectivity and simultaneously accurately quantify both electrophilicity and nucleophilicity. The Fukui function behaves reasonably well for the prediction of electrophilicity but performs poorly for nucleophilicity. Among all other atomic charges examined in this study, it is only the Voronoi deformation density charge that yields the similar result as the Hirshfeld charge. As the first systematic benchmark study in the literature to compare the two available approaches in DFT about reactivity predictions, this work should fill in the needed knowledge gap and provide an impetus for the future development of chemical reactivity theory using DFT language.

We present a structural analysis of the packings of identical non-spherical particles based on Voronoi cells. The packings are generated by discrete element method (DEM) simulations. The particles include axisymmetric ellipsoidal particles from oblates to prolates and cylindrical particles from disks to rods. The Voronoi cells are constructed by virtue of space discretization and surface reconstruction, which is shown to be universal for different shapes. The effects of particle aspect ratio and sliding friction coefficient on the properties of Voronoi cells, including the reduced volume, reduced surface area and sphericity, are quantified. The reduced volume and surface area are found to observe log-normal distributions, while their mean values and standard deviations have different dependencies on particle shape and friction. By analyzing the correlations and using inherent relationships between different Voronoi cell properties, we establish a group of universal equations to predict these distributions according to particle sphericity and overall packing fraction. Such findings can not only improve our understanding on the packings of non-spherical particles but also provide a basis for evaluating the transport properties and advancing the statistical mechanics theory for granular matter composed of non-spherical particles.

In this paper, we present methods that directly model the random structure of porous media using Voronoi tessellations. Three basic structures were generated and they correspond to porous medium geometries with intersecting fractures (granular), interconnected tubes (tubular), and fibers (fibrous). Fluid flow through these models was solved by a massively parallelized lattice Boltzmann code. We established the porosity-permeability relations for these basic geometry models. It is found that, for granular and tubular geometries, the specific surface area is a critical structural parameter that can bring their porosity-permeability relations together under a unified Kozeny-Carman equation. A connected fracture network, superimposed on the basic Voronoi structure, increases the dimensionless permeability relative to the Kozeny-Carman equation; isolated large pores (vugs), on the other hand, decreases the dimensionless permeability relative to the Kozeny-Carman equation. The Kozeny-Carman equation, however, cannot distinguish a heterogeneous structure with an embedded partially penetrating fracture. The porosity-permeability relation for fibrous geometries in general agrees with those established for simple-cubic, body-centered cubic, and face-centered cubic models. In the dilute limit, however, the dependence on the solid fraction is weaker in Voronoi geometries, indicating weaker hydrodynamic interactions among randomly interconnected fibers than those in the idealized models.

Structural changes occurring in C60 fullerenes after ball-milling processing were studied. The quantitative characteristics of the local atomic configurations were reconstructed by the reverse Monte Carlo method in the structure of pristine and ball-milled fullerenes C60, respectively. It is shown that 3-fold atomic rings, indicating complete amorphization of crystalline fullerenes, are dominant in the structure of material after 14 h treatment. The behavior of the distribution of the sphericity coefficient of Voronoi polyhedra validates a gradual structural disordering of molecular crystal of C60 and, respectively, the formation of amorphous carbon with randomly arranged close-packed structure after continuous ball-milling treatment.

In this paper, we introduce a new approach for irregular porous structure modeling based on centroidal Voronoi tessellation (CVT) and B-Spline. Given an arbitrary domain, a CVT is first constructed on it, decomposing the domain into a set of Voronoi cells. A scaled Voronoi cell is then generated within each Voronoi cell of the CVT with respect to a unique scale factor. Finally, a pore is generated in each Voronoi cell by using B-Spline with the vertices of each scaled Voronoi cell being the control points. Compared to existing approaches, the proposed method is much more flexible to control the pore size and distribution both globally and locally. In addition, our method can effectively prevent overly large or small angles within Voronoi cells, which are the source of simulation errors and computational burdens in finite element analysis (FEA).

The self-assembly of nanoscopic building blocks into higher order macroscopic patterns is one possible approach for the bottom-up fabrication of complex functional systems. Macroscopic pattern formation, in general, is determined by the reaction and diffusion of ions and molecules. In some cases macroscopic patterns emerge from diffusion and interactions existing between nanoscopic or microscopic building blocks. In systems where the distribution of the interaction-determining species is influenced by the presence of a diffusion barrier, the evolving macroscopic patterns will be determined by the spatiotemporal evolution of the building blocks. Here we show that a macroscopic pattern can be generated by the spatiotemporally controlled aggregation of like-charged carboxyl-terminated gold nanoparticles in a hydrogel, where clustering is induced by the screening effect of the sodium ions that diffuse in a hydrogel. Diffusion fronts of the sodium ions and the induced nanoparticle aggregation generate Voronoi diagrams, where the Voronoi cells consist of aggregated nanoparticles and their edges are aggregation-free and nanoparticle-free zones. We also developed a simple aggregation-diffusion model to adequately describe the evolution of the experimentally observed Voronoi patterns.

NMRspectroscopy is one of the most useful methods for detection andcharacterization of hydrogen bond (H-bond) interactions in biological systems.For H-bonds X-H⋯Y, where X and Y are O or N, it is generally believed that adecrease of 1H-shielding constants relates to a shortening of H-bondsdonor-acceptor distance. Here, we investigated computationally the trend of1H-shielding constants for hydrogen-bonded protons in a series of GuanineC8-substituted GC pair model compounds as a function of the molecularstructure. Furthermore, the electron density distribution around the hydrogenatom was analyzed with the Voronoi deformation density (VDD) method. Ourfindings demonstrate that 1H-shielding values of the hydrogen bond aredetermined by the depletion of charge around the hydrogen atom which stems fromthe fact that electrons obey the Pauli exclusion principle. Fil: Zarycz, Maria Natalia Cristina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Investigaciones en Físico-química de Córdoba. Universidad Nacional de Córdoba. Facultad de Ciencias Químicas. Instituto de Investigaciones en Físico-química de Córdoba; Argentina Fil: Fonseca Guerra, Célia. Vrije Unviversiteit; Países Bajos. Leiden University; Países Bajos

Numerous numerical models of mimicking cellular structures have been proposed, but, in many cases, those models were not able to describe the random cell geometry which is common for most cellular products. The concept of Voronoi tessellation has recently applied to construct the random characteristics of cell structures, but the structure generated by classical Voronoi tessellation method is too ideal by comparing with the actual cell structures. Moreover, the verification of physical and mechanical behaviors of random cell structures is scarcely researched due to the complexity of fabricating the cell structures which are numerically generated. In this study, Central Voronoi Tessellation (CVT) theory which considers the center of mass of each cell for further iteration of cell structure modification is adopted to generate realistic shape of cell structures. Some key parameters such as relative density, anisotropy, and number of iteration are considered. Mechanical behaviors of samples with numerically generated cell structures are investigated using elasto-plastic finite element analysis considering instability conditions. In addition, test samples in some cases considered in FEA are fabricated by aluminum alloy using 3-D printer based on the selective laser melting (SLM) technique, and the test results are compared with the numerical simulation results.

Local Voronoi decompositions are applied to extraction of crack surfaces.Cracks propagate in mono-dispersed particulate media simulated by the DEM.The geometry of crack surfaces is accurately defined by faces of the decomposition.Generation of local decompositions rather than global meshes reduces execution time.The sufficiently high speed-up of distributed visualization software is achieved. The paper presents a novel visualization technique for cracks propagating in mono-dispersed particulate material. The proposed technique is based on local space decompositions generated in fractured areas. The contact surfaces of the neighboring particles are defined by the local Voronoi decomposition generated according to the lattice topology employed in computations of the discrete element method. The visual model validation helps to indicate the regions of a highly deformed lattice, where the defects detected between the pairs of the neighboring particles on the lattice connections cannot be directly mapped onto the relevant edges of the Voronoi diagram. The parallel implementation of the visualization technique is based on the domain decomposition and two layers of ghost vertices and connections. The technique is implemented in the distributed visualization software VisPartDEM. Datasets of the elastic solid problem exhibiting non-uniform distribution of fracture force values are considered to validate the performance of the proposed technique. The parallel speed-up of the visualization software is investigated. The superior performance of the applied local technique is compared to the performance observed by using the standard global Voronoi algorithm.

Summary A generalised Voronoi tessellation is proposed to create three-dimensional microstructural finite element model, which can effectively reproduce the grain size distribution and grain aspect ratio obtained from experiments. This new approach consists of two steps. The first step generates the desired lognormal grain size distribution with a given average grain volume and standard deviation. The second step requires grouping meshed elements to create a specific grain aspect ratio, using the Voronoi generators from the first step. A new concept is introduced to describe the transition from the Poisson–Voronoi tessellation to the centroidal Voronoi tessellation. More importantly, instead of using the conventional way where the Voronoi cells are first generated and then meshed into finite elements, this new approach discretises the pre-meshed specimen with the Voronoi generators. This new technique prevents the presence of high density mesh at the vertices of Voronoi cells, and can tessellate irregular geometry much more easily. Examples of microstructures with different size distributions, non-equiaxed grains and complicated specimen geometries further demonstrate that the proposed approach can offer great flexibility to model various specimen geometries while keeping the process simple and efficient. Copyright © 2015 John Wiley & Sons, Ltd.

Molecular cavities, which include voids and channels, are critical for molecular function. We present a webserver, BetaCavityWeb, which computes these cavities for a given molecular structure and a given spherical probe, and reports their geometrical properties: volume, boundary area, buried area, etc. The server's algorithms are based on the Voronoi diagram of atoms and its derivative construct: the beta-complex. The correctness of the computed result and computational efficiency are both mathematically guaranteed. BetaCavityWeb is freely accessible at the Voronoi Diagram Research Center (VDRC) (http://voronoi.hanyang.ac.kr/ betacavityweb).

When the discrete element method (DEM) is used to simulate confined compression of granular materials, the need arises to estimate the void space surrounding each particle with Voronoi polyhedra. This entails recurring Voronoi tessellation with small changes in the geometry, resulting in a considerable computational overhead. To overcome this limitation, we propose a method with the following features: • A local determination of the polyhedron volume is used, which considerably simplifies implementation of the method. • A linear approximation of the polyhedron volume is utilised, with intermittent exact volume calculations when needed. • The method allows highly accurate volume estimates to be obtained at a considerably reduced computational cost.

An analytical method is presented that provides quantitative insight into light‐driven electron density rearrangement using the output of standard time‐dependent density functional theory (TD‐DFT) computations on molecular compounds. Using final and initial electron densities for photochemical processes, the subtraction of summed electron density in each atom‐centered Voronoi polyhedron yields the electronic charge difference, Q VECD. This subtractive method can also be used with Bader, Mulliken and Hirshfeld charges. A validation study shows Q VECD to have the most consistent performance across basis sets and good conservation of charge between electronic states. Besides vertical transitions, relaxation processes can be investigated as well. Significant electron transfer is computed for isomerization on the excited state energy surface of azobenzene. A number of linear anilinepyridinium donor‐bridge‐acceptor chromophores was examined using Q VECD to unravel the influence of its pi‐conjugated bridge on charge separation. Finally, the usefulness of the presented method as a tool in optimizing charge transfer is shown for a homologous series of organometallic pigments. The presented work allows facile calculation of a novel, relevant quantity describing charge transfer processes at the atomic level. © 2017 The Authors Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

While high-throughput density functional theory (DFT) has become a prevalent tool for materials discovery, it is limited by the relatively large computational cost. In this paper, we explore using DFT data from high-throughput calculations to create faster, surrogate models with machine learning (ML) that can be used to guide new searches. Our method works by using decision tree models to map DFT-calculated formation enthalpies to a set of attributes consisting of two distinct types: (i) composition-dependent attributes of elemental properties (as have been used in previous ML models of DFT formation energies), combined with (ii) attributes derived from the Voronoi tessellation of the compound's crystal structure. The ML models created using this method have half the cross-validation error and similar training and evaluation speeds to models created with the Coulomb matrix and partial radial distribution function methods. For a dataset of 435 000 formation energies taken from the Open Quantum Materials Database (OQMD), our model achieves a mean absolute error of 80 meV/atom in cross validation, which is lower than the approximate error between DFT-computed and experimentally measured formation enthalpies and below 15% of the mean absolute deviation of the training set. We also demonstrate that our method can accurately estimate the formation energy of materials outside of the training set and be used to identify materials with especially large formation enthalpies. We propose that our models can be used to accelerate the discovery of new materials by identifying the most promising materials to study with DFT at little additional computational cost.

A big problem in triangular remeshing is to generate meshes when the triangle size approaches the feature size in the mesh. The main obstacle for Centroidal Voronoi Tessellation (CVT)-based remeshing is to compute a suitable Voronoi diagram. In this paper, we introduce the localized restricted Voronoi diagram (LRVD) on mesh surfaces. The LRVD is an extension of the restricted Voronoi diagram (RVD), but it addresses the problem that the RVD can contain Voronoi regions that consist of multiple disjoint surface patches. Our definition ensures that each Voronoi cell in the LRVD is a single connected region. We show that the LRVD is a useful extension to improve several existing mesh-processing techniques, most importantly surface remeshing with a low number of vertices. While the LRVD and RVD are identical in most simple configurations, the LRVD is essential when sampling a mesh with a small number of points and for sampling surface areas that are in close proximity to other surface areas, e.g., nearby sheets. To compute the LRVD, we combine local discrete clustering with a global exact computation.

This study comprehensively quantifies the effects of regularity on the geometrical properties of a random three-dimensional Voronoi tessellation (VT), where regularity was defined as the ratio of the minimum seed distance to the seed distance of the correlated body-centred cubic lattice. A scheme to generate Voronoi tessellations with controlled regularity is proposed, which was used to simulate 106 cells for a series of regularities. The results were used to derive probability distributions for the properties of the tessellation, including faces and edges per cell, vertex and dihedral cell angles, cell areas and volumes, etc. An understanding of the relation between a simple, measurable parameter characterizing the degree of regularity of a Voronoi tessellation and its geometrical properties is essential in generating virtual microstructures that are statistically representative of reality; the statistical results are also relevant to all other applications involving random Voronoi tessellations. Finally, an application is presented of the proposed Voronoi tessellation generation scheme applied to micromechanical modelling of grain structures with defined regularities for crystal plasticity finite element analysis.

For the characterization of the equiaxed polycrystalline structure the Dirichlet tessellation is often used. The results of this space decomposition Voronoi polyhedrons are convex but not necessarily bounded. Size, volume and other characteristics of these bodies are the random variables. Parameters of theAveraged Voronoi Polyhedronare used in the presented paper for the modeling of the diffusion controlled peritectic transformation. Proposed model takes into account decreasing of the transformation interface surface in the remote regions of the diffusion field due to the probabilistic grains impingements. The results of the modeling are compared with the microstructure of the Pb-32 wt.% Bi alloy and thermal analysis results.

Molecular external structure is important for molecular function, with voids on the surface and interior being one of the most important features. Hence, recognition of molecular voids and accurate computation of their geometrical properties, such as volume, area and topology, are crucial, yet most popular algorithms are based on the crude use of sampling points and thus are approximations even with a significant amount of computation. In this article, we propose an analytic approach to the problem using the Voronoi diagram of atoms and the beta-complex. The correctness and efficiency of the proposed algorithm is mathematically proved and experimentally verified. The benchmark test clearly shows the superiority of BetaVoid to two popular programs: VOIDOO and CASTp. The proposed algorithm is implemented in the BetaVoid program which is freely available at the Voronoi Diagram Research Center (http://voronoi.hanyang.ac.kr).

The Voronoi diagram of balls, corresponding to atoms of van der Waals radii, is particularly well-suited for the analysis of three-dimensional structures of biological macromolecules. However, due to the shortage of practical algorithms and the corresponding software, simpler approaches are often used instead. Here, we present a simple and robust algorithm for computing the vertices of the Voronoi diagram of balls. The vertices of Voronoi cells correspond to the centers of the empty tangent spheres defined by quadruples of balls. The algorithm is implemented as an open-source software tool, Voronota. Large-scale tests show that Voronota is a fast and reliable tool for processing both experimentally determined and computationally modeled macromolecular structures. Voronota can be easily deployed and may be used for the development of various other structure analysis tools that utilize the Voronoi diagram of balls. Voronota is available at: http://www.ibt.lt/bioinformatics/voronota.

The quantitative characteristics of a short- and a medium-range order in amorphous carbon synthesized by electric discharge treatment of hydrocarbons are determined by a combined application of X-ray diffraction analysis, Reverse Monte Carlo modeling and Voronoi diagram method. The obtained characteristics exhibit a graphite- or a mixed graphite–diamond-like type of short-range order and, at the same time, a large portion of carbon atoms within chemical bond lengths is combined into 3-fold rings of the tetrahedral structures. Statistical analysis of Voronoi polyhedra has revealed a wide distribution of their topological and metric characteristics that are inherited by disordered materials with predominated 5-fold faces which are typical for amorphous structures. The regular configuration polyhedra (clusters) are virtually absent in the synthesized carbon nanomaterials.

Several approaches to quantitative local structure characterization for particulate assemblies, such as structural glasses or jammed packings, use the partition of space provided by the Voronoi diagram. The conventional construction for spherical mono-disperse particles, by which the Voronoi cell of a particle is that of its centre point, cannot be applied to configurations of aspherical or polydisperse particles. Here, we discuss the construction of a Set Voronoi diagram for configurations of aspherical particles in three-dimensional space. The Set Voronoi cell of a given particle is composed of all points in space that are closer to the surface (as opposed to the centre) of the given particle than to the surface of any other; this definition reduces to the conventional Voronoi diagram for the case of mono-disperse spheres. An algorithm for the computation of the Set Voronoi diagram for convex particles is described, as a special case of a Voronoi-based medial axis algorithm, based on a triangula...

A modified Voronoi model is established based on the Richards method to generate 2D non-equiaxed initial microstructure for Monte Carlo simulation. Microstructures produced by the ordinary Voronoi model are isotropic and cannot reflect the effects of the deformed grain shape on the annealing process. The modified Voronoi model based on ellipse set can be used to construct the deformed microstructure. The initial microstructure reflects the mean strain and the grain size distribution follows lognormal distribution.

Geometric models of molecular structures are often described as a set of balls, where balls represent individual atoms. The ability to describe and explore the empty space among these balls is important, e.g., in the analysis of the interaction of enzymes with substrates, ligands and solvent molecules. Voronoi diagrams from the field of computational geometry are often used here, because they provide a mathematical description of how the whole space can be divided into regions assigned to individual atoms. This paper introduces a combination of two different types of Voronoi diagrams into a new hybrid Voronoi diagram - one part of this diagram belongs to the additively weighted (aw-Voronoi) diagram and the other to the power diagram. The boundary between them is controlled by a user-defined constant (the probe radius). Both parts are computed by different algorithms, which are already known. The reduced aw-Voronoi diagram is then obtained by removing the power diagram part from the hybrid diagram. Reduced aw-Voronoi diagrams are perfectly tailored for the analysis of dynamic molecular structures, their computation is faster and storage requirements are lower than in the case of complete aw-Voronoi diagrams. Here, we showed their application to key proteins in cancer research such as p53 and ARID proteins as case study. We identified a biologically relevant cavity in p53 structural ensembles generated by molecular dynamics simulations and analyzed its accessibility, attesting the potential of our approach. This method is relevant for cancer research since it permits to depict a dynamical view of cavities and pockets in proteins that could be affected by mutations in the disease. Our approach opens novel prospects for the study of cancer-related proteins by molecular simulations and the identification of novel targets for drug design.

To study the influence of intra- and intermolecular interactions on properties of the nitro group in para-substituted nitrobenzene derivatives, two sources of data were used: (i) Cambridge Structural Database and (ii) quantum chemistry modeling. In the latter case, “pure” intramolecular interactions were simulated by gradual rotation of the nitro group in para-nitroaniline, whereas H-bond formation at the amino group allowed the intermolecular interactions to be accounted for. BLYP functional with dispersion correction and TZ2P basis set (ADF program) were used to perform all calculations. It was found that properties of the nitro group dramatically depend on both its orientation with respect to the benzene ring as well as on the substituent in the para-position. The nitro group lies in the plane of the benzene ring for only a small number of molecules, whereas the mean value of the twist angle is 7.3 deg, mostly due to intermolecular interactions in the crystals. This distortion from planarity and the nature of para-substituent influence the aromaticity of the ring (described by HOMA index) and properties of the nitro group due to electronic effects. The results obtained by QM calculations fully coincide with observations found for the data set of crystal structures.

Metallic foams have a very particular structure due to their high specific stiffness. Density plays an important role on their structural response and is also determinant to the foam’s weight. The main goal of this paper is to find an ideal density distribution to open-cell metallic foams in order to achieve optimized structural performance. A density distribution optimization using an irregular description of the foam by a Voronoi tessellation and a genetic algorithm for the numerical optimization is presented in this work. The structural analysis is performed with linear elastic beam finite elements and the foam structure is modeled as a Voronoi tessellation. The density is related to the number of Voronoi seeds, which may configure lighter or denser foams and vary throughout the model. The minimization and maximization of stiffness were analyzed for different structural applications in order to demonstrate the capability of the developed methodology.

We present a new algorithm for automatic parallel load balancing in classical molecular dynamics. It assumes a spatial domain decomposition of particles into Voronoi cells. It is a gradient method which attempts to minimize a cost function by displacing Voronoi sites associated with each processor/sub-domain along steepest descent directions. Excellent load balance has been obtained for quasi-2D and 3D practical applications, with up to 440 ⋅ 10 6 particles on 65,536 MPI tasks.

Molecular simulation of clathrate hydrate has provided significant advancements in our understanding of hydrate properties and formation. In this work, we report the application of Voronoi tessellation to characterize the structuring of water and guest molecules forming hydrates. Tessellation of perfect sI and sII hydrate reveals positions of Voronoi vertices similar to the oxygen atoms of enclathrating water molecules. Applying tessellation to a simulation trajectory of hydrate formation, and using a further selection criteria based on polyhedra volume and coordination number, we identify numbers and types of cagelike polyhedra. Voronoi analysis of this type results in similar numbers of identified cages but with differing topologies. However, once nearest neighbor methanes are also enclathrated, the topologies of the Voronoi polyhedra approach that of the actual water cages. Since only methane coordinates are required, Voronoi tessellation is a fast and simple tool that can be used as an order parameter...

We present an algorithm that computes a 3 dimensional Voronoi diagram for a protein molecule in this paper. The molecule is represented as a set of spheres with van der Waals radii. The Voronoi diagram is constructed in the 3D space by finding the voxels containing it. For the feasibility of the computation, we represent the molecule as a BVH (bounding volume hierarchy), and our system is accelerated by modern graphics hardware with CUDA programming support. Compared to single-core CPU implementations, experimental results show 323 times faster performance in the computation time, when the space is partitioned into voxels.

We have carried out extensive computational analyses of the structure and bonding mechanism in trihalides DX⋅⋅⋅A(-) and the analogous hydrogen-bonded complexes DH⋅⋅⋅A(-) (D, X, A=F, Cl, Br, I) using relativistic density functional theory (DFT) at zeroth-order regular approximation ZORA-BP86/TZ2P. One purpose was to obtain a set of consistent data from which reliable trends in structure and stability can be inferred over a large range of systems. The main objective was to achieve a detailed understanding of the nature of halogen bonds, how they resemble, and also how they differ from, the better understood hydrogen bonds. Thus, we present an accurate physical model of the halogen bond based on quantitative Kohn-Sham molecular orbital (MO) theory, energy decomposition analyses (EDA) and Voronoi deformation density (VDD) analyses of the charge distribution. It appears that the halogen bond in DX⋅⋅⋅A(-) arises not only from classical electrostatic attraction but also receives substantial stabilization from HOMO-LUMO interactions between the lone pair of A(-) and the σ* orbital of D-X.

The Voronoi tessellation technique is one of the most useful tools to analyze atomic structures such as the short-range order of icosahedra in metallic glasses. In the ordinary Voronoi tessellation technique, the polyhedral plane is placed halfway between two atoms of different size. However, this essentially creates analytical errors. An alternative approach, called the radical plane method, takes the atomic size difference into consideration. Here, the method is applied to metallic glasses with different compositions and compared to the ordinary Voronoi tessellation technique. The results show that properties such as the Voronoi index and the spatial distribution of icosahedra analyzed by the ordinary Voronoi tessellation technique may be entirely incorrect.

Constrained density functional theory (cDFT) is a powerful tool to investigate the dynamics of the electrons accompanying various physical-chemical processes. In this article we present our recent progresses in the implementation of the method in the parallelized version of the DFT program deMon2k. We take advantage of the possibility to express atomic densities in terms of linear combination of Hermite Gaussian functions to improve the computation of the cDFT integration weights within the Hirshfeld and Voronoi deformation density electronic population approaches. The efficiency of the method is illustrated on the computation of the average electronic coupling for an electron transfer (ET) through a glycine polypeptide of increasing length. The sampling is based on cDFT and hybrid cDFT/molecular mechanics molecular dynamics simulations. We also report the first estimations of quantum decoherence times from cDFT-based simulations for an ET reaction.

A modified Voronoi tessellation (MVT) is proposed for the computer simulation of realistic microstructures. Compared with standard tessellations, the present algorithm provides the desired grain size distribution in a one-step, non-evolutionary procedure. This is obtained by relaxing the constraints of Voronoi tessellation on position and orientation of the grain boundaries, with the only side effect being the formation of a limited amount of eliminable voids. As an example, it is shown how to directly obtain a distribution of grains of given variance and with a shape statistically close to the lognormal one.

Damage and mass transport behavior of particulate materials depend on the spatial distribution and orientation of the phase fractions and the properties of their interfaces. Discretization of this three-dimensional setting is the first critical step in the modeling of such behavior. In this paper, a general procedure is developed for discretizing particulate materials, such as particles embedded within a cementing matrix, in which the particle inclusions are assumed to be randomly generated polyhedra. Polyhedron discretization is based on the Voronoi tessellation of a set of points, which is obtained through a multistep process that relies on the concept of point saturation. The matrix–particle and/or particle–particle interfaces are explicitly constructed. To demonstrate the utility of the approach, uniaxial tensile tests (of a single particle, embedded in a matrix) are simulated using a lattice model. It is seen that interface debonding is strongly affected by inclusion shape and orientation with respect to the tension field. A procedure is developed for the discretization and analysis of multi-particle systems.

Charge transfer at the Bovine pancreatic trypsin inhibitor (BPTI) protein–water interface was analyzed by means of ab initio Born–Oppenheimer molecular dynamics simulation of the entire protein running on graphical processing units (GPUs). The efficiency of the GPU-based quantum chemistry algorithms implemented in our TeraChem program enables us to perform these calculations on a desktop computer. Mulliken and Voronoi deformation density (VDD) population analysis reveals that between 2.0 and 3.5 electrons are transferred from surrounding water molecules to the protein over the course of the 8.8 ps simulation. Solving for the electronic structure of BPTI in the absence of surrounding water molecules (i.e., in the gas phase) leads to large intraprotein charge transfer, where approximately one electron in total is transferred from neutral to polar residues. Solvation relieves this polarization stress, leading to a neutralization of the excess positive charge of the neutral residues.