Pair Radial Distribution Functions Research Articles

Splay-induced order in systems of hard tapers.

The main objective of this work is to clarify the role that taper-shaped elongated molecules, i.e., molecules with one end wider than the other, can play in stabilizing orientational order. The focus is exclusively on entropy-driven self-organization induced by purely excluded volume interactions. Drawing an analogy to RM734 (4-[(4-nitrophenoxy)carbonyl]phenyl-2,4-dimethoxybenzoate), which is known to stabilize ferroelectric nematic (N_{F}) and nematic splay (N_{S}) phases, and assuming that molecular biaxiality is of secondary importance, we consider monodisperse systems composed of hard molecules. Each molecule is modeled using six collinear tangent spheres with linearly decreasing diameters. Through hard-particle, constant-pressure Monte Carlo simulations, we study the emergent phases as functions of the ratio between the smallest and largest diameters of the spheres (denoted as d) and the packing fraction (η). To analyze global and local molecular orderings, we examine molecular configurations in terms of nematic, smectic, and hexatic order parameters. Additionally, we investigate the radial pair distribution function, polarization correlation function, and the histogram of angles between molecular axes. The last characteristic is utilized to quantify local splay. The findings reveal that splay-induced deformations drive unusual long-range orientational order at relatively high packing fractions (η>0.5), corresponding to crystalline phases. When η<0.5, only short-range order is affected, and in addition to the isotropic liquid, only the standard nematic and smectic-A liquid crystalline phases are stabilized. However, for η>0.5, apart from the ordinary nonpolar hexagonal crystal, three additional frustrated crystalline polar blue phases with long-range splay modulation are observed: antiferroelectric splay crystal (Cr_{S}P_{A}), antiferroelectric double-splay crystal (Cr_{DS}P_{A}), and ferroelectric double-splay crystal (Cr_{DS}P_{F}). Finally, we employ Onsager-Parsons-Lee local density functional theory to investigate whether any sterically induced (anti)ferroelectric nematic or smectic-A type of ordering is possible for our system, at least in a metastable regime.

Accurate SCC-DFTB Parametrization of Liquid Water with Improved Atomic Charges and Iterative Boltzmann Inversion.

This work presents improvements of the description of liquid water within the self-consistent-charge density-functional based tight-binding scheme combining the use of Weighted Mulliken (WMull) charges and optimized O-H repulsive potential through the iterative Boltzmann inversion (IBI) process. The quality of the newly developed models is validated considering pair radial distribution functions (RDFs), as well as other structural, energetic, thermodynamic, and dynamic properties. The use of WMull charges certainly improves the agreement with experimental data, however leading to over-structured RDFs at short distance, that can be further improved by considering an optimized O-H repulsive potential obtained by the IBI process. Three different schemes were used to optimize this potential: (i) optimization including short O-H distances. This led to accurate RDFs as well as improved self-diffusion coefficient and heat of vaporization, while the proton transfer energy barrier is severely deteriorated; (ii) optimization starting at long distance. The proton transfer energy barrier is recovered while the heat of vaporization is deteriorated and the O-H RDF is less accurate at short distance; (iii) optimization within the path-integral molecular dynamics scheme which allows us to exclude nuclear quantum effects from the repulsive potential. The latter potential, in conjunction with the WMull improved atomic charges, provides similar results as (i) for structural, dynamic, and thermodynamic properties while recovering a large part of the proton transfer energy barrier. It therefore offers a good compromise to study both dynamic properties and chemistry within liquid water at a quantum chemical level.

A Molecular Dynamic Study of the Effects of Surface Partitioning on the OH Radical Interactions with Solutes in Multicomponent Aqueous Aerosols

The surface-bulk partitioning of small saccharide and amide molecules in aqueous droplets was investigated using molecular dynamics. The air-particle interface was modeled using a 80 Å cubic water box containing a series of organic molecules and surrounded by gaseous OH radicals. The properties of the organic solutes within the interface and the water bulk were examined at a molecular level using density profiles and radial pair distribution functions. Molecules containing only polar functional groups such as urea and glucose are found predominantly in the water bulk, forming an exclusion layer near the water surface. Substitution of a single polar group by an alkyl group in sugars and amides leads to the migration of the molecule toward the interface. Within the first 2 nm from the water surface, surface-active solutes lose their rotational freedom and adopt a preferred orientation with the alkyl group pointing toward the surface. The different packing within the interface leads to different solvation shell structures and enhanced interaction between the organic molecules and absorbed OH radicals. The simulations provide quantitative information about the dimension, composition, and organization of the air-water interface as well as about the nonreactive interaction of the OH radicals with the organic solutes. It suggests that increased concentrations, preferred orientations, and decreased solvation near the air-water surface may lead to differences in reactivities between surface-active and surface-inactive molecules. The results are important to explain how heterogeneous oxidation mechanisms and kinetics within interfaces may differ from those of the bulk.

Halide-sodalites: thermal behavior at low temperatures and local deviations from the average structure

Abstract Sodalites of the general type |Na8X2|[T1T2O4]6 with X = Cl−, Br−, I− have been synthesized for Al–Si, Ga–Si, Al–Ge and Ga–Ge as T1–T2 frameworks. The structures were examined using in-house and synchrotron X-ray diffraction, Raman spectroscopy, force-field structure optimizations and DFT based ab-initio molecular dynamics (MD) computations. Calculated phonon density of states (PDOS) of the 12 compounds show only minor differences within a framework composition with a lowering of certain phonon energies with increasing anion size. Earlier published Debye and Einstein temperatures obtained with a Debye-Einstein-anharmonicity (DEA) model approach are confirmed using the determined low-temperature lattice parameters (18 K–293 K) and show no correlation with the respective PDOS. Small-box refinements against radial pair distribution functions (PDF) allowed the determination of anisotropic displacement ellipsoids (ADP) for Na+ and O2−, indicating a strong dependency of the ADP of Na+ on the chemical composition. Significantly lower thermal displacements from MD calculations suggested an influence of structural displacements. For compounds with an aspherical ADP for sodium, structural models could be refined in which the sodium is located on two 8e or one 24i site (both partially occupied), and also temperature-dependent (100 K–300 K) for the compounds with Ga–Ge framework. 3D-plots of the bond-valence sums of Na+ further validate the structural differences. These results imply that the local structure of halide-sodalites in many cases is not best described by the known average structure and may even not be cubic.

Ion Solvation Free Energy Calculation Based on Ab Initio Molecular Dynamics Using a Hybrid Solvent Model.

Free energy calculation of small molecules or ion species in aqueous solvent is one of the most important problems in electrochemistry study. Although there are many previous approaches to calculate such free energies, they are based on ab initio methods and suffer from various limitations and approximations. In the current work, we developed a hybrid approach based on ab initio molecular dynamics (AIMD) simulations to calculate the ion solvation energy. In this approach, a small water cluster surrounding the central ion is used, and implicit solvent model is applied outside the water cluster. A dynamic potential well is used during AIMD to keep the water cluster together. Quasi-harmonic approximation is used to calculate the entropy contribution, while the total energy average is used to calculate the enthalpy term. The obtained solvation voltages of the bulk metal agree with experiments within 0.3 eV, and the simulation results for the solvation energies of gaseous ions are close to the experimental observations. Besides the free energies, radial pair distribution functions and coordination numbers of hydrated cations are also obtained. The remaining challenges of this method are also discussed.

The investigation of dynamic heterogeneity in lead silicate liquid via molecular dynamic simulation

The structure and dynamics of liquid lead silicate with a wide range of PbO ratio are done by molecular dynamics methods. The simulated result shows that the pair radial distribution functions (PRDFs) are in good agreement with the results of previous studies. Our calculated data indicates that the system exists regions of fast and slow atoms determined via the mean square displacement (MSD) in the same interval. The exhibition of dynamical heterogeneity (DH) is also found in this paper.

Structural properties of silica under the temperature

The structure of the SiO2 system consisting of 12800 atoms is performed via molecular dynamics simulation with the Tersoff potential. Our simulation shows that the onset of the melting temperature is at 3450 K. This value is much higher than the previous result of Ringdalen and co-workers [26]. The structural evolution of the system is analyzed through the pair radial distribution function, the distribution of the bond length and the distribution of the bond angle. Structural parameters are compared with the previous experimental and simulated results. The mean square displacement is also discussed in this paper.

Ionic Dynamics and Vibrational Spectral Diffusion of a Protic Alkylammonium Ionic Salt through Intrinsic Cationic N-H Vibrational Probe from FPMD Simulations.

We employed density functional theory (DFT)-based molecular dynamics simulations to explore the structure, dynamics, and spectral properties of the protic ionic entity trimethylammonium chloride (TMACl). Structural investigations include calculating the site-site radial distribution functions (RDFs), the distribution of constituent cations and anions in three-dimensional space, and combined distribution functions of the hydrogen-bonded pair RDF versus angle, revealing the structural characteristics of the ionic solvation and the intermolecular interactions within ions. Further, we determined the instantaneous vibrational stretching frequencies of the intrinsic N-H stretch probe modes by applying the time-series wavelet method. The associated ionic dynamics within the protic ionic compound were investigated by calculating the time-evolution of the fluctuating frequencies and the frequency-time correlation functions (FFCFs). The time scale related to the local structural relaxation process and the average hydrogen bond lifetime, ion cage dynamics, and mean squared displacement were investigated. The faster decay component of the FFCFs, depicting the intermolecular motion of intact hydrogen bonds in TMACl, is 0.07 ps for the Perdew-Burke-Ernzerhof (PBE)-based simulation and 0.06 ps for the PBE-D2 representation. The slower time scale of the longer picosecond decay time component of PBE and PBE-D2 representations are 3.13 and 2.87 ps, respectively. These picosecond time scales represent more significant fluctuations of the hydrogen-bonding partners in the ionic entity and hydrogen-bond jump events accompanied by large angular jumps. The longest picosecond time scales represent structural relaxation, including large angular jumps and ion-pair dynamics. Also, ion cage lifetimes correlate with the slowest time scale of the associated dynamics of vibrational spectral diffusion despite the type of DFT functional. This study benchmarks DFT treatments of the exchange-correlation functional with and without the van der Waals (vdW) dispersion correction scheme. The inclusion of vdW interactions to the PBE functional represents a less structured state of the ionic entity and faster dynamics of the molecular motions relative to the one predicted by the PBE system. All the results illustrate the necessity of accurately describing the Coulomb interactions, vdW dispersive interactive forces, and localized hydrogen bonds required to sustain the energetic balance in this ionic salt.

Heteroatom-containing phosphoramides as carbon steel corrosion inhibitors: Density functional theory and molecular dynamics simulations

In an attempt to introduce a new class of carbon steel corrosion inhibitors, the anti-corrosion properties of two heteroatom-containing phosphoramides; N-(5-methylisoxazol-3-yl)-P,P-diphenylphosphinic amide (MAPP) and diphenyl (5-methylisoxazol-3-yl)phosphoramidate (PMAP) were theoretically investigated. Density functional theory (DFT) calculations were performed using B3LYP functional and 6–31+G(d,p) basis set to evaluate the inhibition efficacy of MAPP and PMAP in the presence of HCl molecule. Based on the frontier molecular orbitals energy gap (Eg), dipole moment, global hardness, electrophilicity, and nucleophilicity values, we concluded that PMAP acts as a strong anti-corrosion. With the aim of identifying the most stable configuration of inhibitor-HCl, the HCl molecule was approached to all probable reactive sites of inhibitors determined by molecular electrostatic potential plots. It was revealed that molecule PMAP forms a stronger hydrogen bond with the HCl molecule and has a higher ΔH (-4.33 kcal.mol−1) than MAPP (ΔH = -3.50 kcal.mol−1). Adsorption behavior of MAPP and PMAP on a Fe (1 1 0) superlattice was studied using molecular dynamics (MD) simulations at T = 298, 308, and 318 K and in the presence of n = 1–4 molecules of MAPP and PMAP. Radial pair distribution function analysis revealed that molecules MAPP and PMAP have the ability to form a chemical bond with metal, and thus protect it from corrosion. The best anti-corrosion performance occurs at T = 298 K and higher concentrations of inhibitors. The adsorption energy of the PMAP molecule on the steel surface (-258.8 kcal.mol−1 at 298 K and for n = 4) is more negative than that of MAPP (-239.5 kcal.mol−1) at the same conditions, indicating that PMAP can be used as an effective corrosion inhibitor for carbon steel in acidic media.

Physical properties of N-Cbz-protected amino acids in methanol as predicted through molecular dynamics calculations at different temperatures and constant pressure

Molecular dynamic simulation (MD) is an important and useful tool for the calculation of properties of solutions. In this study, MD simulation was performed for N-Cbz-L-phenylalanine (N-Cbz-L-pheala), N-Cbz-L-valine (N-Cbz-L-val), N-Cbz-L-alanine (N-Cbz-L-ala), and N-Cbz-L-glycine (N-Cbz-L-gly), solvated in methanol (MeOH) at different temperatures (T = 298.15 K, 308.15 K, and 318.15 K) and constant pressure (1 bar). During simulations, the temperatures and pressure were controlled with the certain thermostats. For each studied system, at first, we drew and optimized Cbz-aa molecule and then put certain number of solvent molecules (methanol) around it. After that, each system was located in a box with certain dimension (x, y, z) and MD simulation were performed for these boxes (systems). For these systems, some important structural properties such as the radial pair distribution function, g(r), hydrogen bonds, HB, and conformation, along their diagrams, were extracted from the respective MD simulations using VMD (Visual Molecular Dynamics) at the range of temperatures and constant pressure. Each of these structural properties and its diagrams were carefully analyzed. This data leads us to a better understanding of the interactions between solvent and solute molecules as well as structure of the solute molecules in solutions. For system (Cbz- pheala + MeOH), we varied the number the solvent molecules and studied the effect of variation of the number of solvent molecules on the number of hydrogen bonds. For others systems, we kept constant the number of solvent molecules at different temperatures. Conformation data showed that there are three types of dihedral angles, regarding their values, in our studied Cbz-aa’s. Also, for our studied systems, hydrogen bonds as well as conformation data showed some good orders about the number of hydrogen bonds and height of peak of g(r) for atoms, respectively.

The performance of a C2N membrane for heavy metal ions removal from water under external electric field

Using molecular dynamic simulations, the performance of carbon nitride (C2N) was studied for the separation of Cu2+ and Hg2+ as heavy metal ions from water. The high porosity of the single layer C2N nanosheet in comparison with other similar carbon-based membranes and the existence of nitrogen atoms at the edge of the pores increase the efficiency of C2N for water purification. The separation of heavy metal ions through the nanosheet is performed by applying an external voltage across the membrane. Investigation of the ions permeation through the membrane demonstrates that the permeability of the Cu2+ ions through the C2N is about 2.5 times higher than that of Hg2+. The results of radial pair distribution function analysis illustrate that the energy barrier for ions passage is due to the hydration shell of the cations. Also, the density of the cations and water molecules, and the hydrogen bonds between water molecules in the whole system are analysed for the study of the performance of C2N nanosheet for ion separation and these results demonstrate that this membrane has the selectivity performance for heavy metal removal and higher permeability of the cations than that of other carbon-based membrane because of high porosity.

Nonideal self-gravity and cosmology: Importance of correlations in the dynamics of the large-scale structures of the Universe

Aims. Inspired by the statistical mechanics of an ensemble of interacting particles (BBGKY hierarchy), we propose to account for small-scale inhomogeneities in self-gravitating astrophysical fluids by deriving a nonideal virial theorem and nonideal Navier-Stokes equations. These equations involve the pair radial distribution function (similar to the two-point correlation function used to characterize the large-scale structures of the Universe), similarly to the interaction energy and equation of state in liquids. Within this framework, small-scale correlations lead to a nonideal amplification of the gravitational interaction energy, whose omission leads to a missing mass problem, for instance, in galaxies and galaxy clusters. Methods. We propose to use a decomposition of the gravitational potential into a near- and far-field component in order to account for the gravitational force and correlations in the thermodynamics properties of the fluid. Based on the nonideal virial theorem, we also propose an extension of the Friedmann equations in the nonideal regime and use numerical simulations to constrain the contribution of these correlations to the expansion and acceleration of the Universe. Results. We estimate that the nonideal amplification factor of the gravitational interaction energy of the baryons lies between 5 and 20, potentially explaining the observed value of the Hubble parameter (since the uncorrelated energy accounts for ∼5%). Within this framework, the acceleration of the expansion emerges naturally because the number of substructures induced by gravitational collapse increases, which in turn increases their contribution to the total gravitational energy. A simple estimate predicts a nonideal deceleration parameter qni ≃ −1; this is potentially the first determination of the observed value based on an intuitively physical argument. We also suggest that small-scale gravitational interactions in bound structures (spiral arms or local clustering) could yield a transition to a viscous regime that can lead to flat rotation curves. This transition could also explain the dichotomy between (Keplerian) low surface brightness elliptical galaxy and (nonkeplerian) spiral galaxy rotation profiles. Overall, our results demonstrate that nonideal effects induced by inhomogeneities must be taken into account, potentially with our formalism, in order to properly determine the gravitational dynamics of galaxies and the large-scale Universe.

On the orientational correlations in the supercooled chloride lithium aqueous solution using the hybrid reverse Monte Carlo simulation

Employing the Hybrid Reverse Monte Carlo (HRMC) simulation, we compute, using the obtained three-dimensional configurations, the orientational correlations of water molecules in the supercooled 9.26 molal LiCl aqueous solution. This study aims to add relevant structural properties to those obtained in our latest studies and further support our findings. The Li/Cl pair ions hydration shells and the water molecules distribution studied using the Radial Pair Distribution Functions (RPDF), ([Formula: see text]) and ([Formula: see text]) are further described using the Orientational Pair Correlation Functions (OPCF), [Formula: see text] which describes the probability of a water molecule oriented by the Euler angles [Formula: see text], being located at the position [Formula: see text], with respect to another water molecule oriented [Formula: see text] placed at the origin. The high dimensionality of the orientational correlation functions has not presented a calculation disability, as known with several simulations, in the face of the efficiency of the HRMC and the water–water orientational correlation functions showed the dominant impact of ions on the water molecular dipole orientations within the hydration shells and in the hydrogen bonded molecules network.

Study of Effect of Size on Iron Nanoparticle by Molecular Dynamics Simulation

We use the molecular dynamics simulation to study iron nanoparticles (NPs) consisting of 4000, 5000, 6000 atoms at temperatures of 300 and 900 K. The crystallization and microstructure were analyzed through the pair radial distribution function (PRDF), the potential energy per atom, the distribution of atom types and dynamical local structure parameters &lt;fx&gt;, where x is the bcc, ico or 14. The simulation indicated that amorphous NP contains a large number of ico-type atoms that play a role in preventing the crystallization. Amorphous NP is crystallized through transformations of f14 &gt; 0 and fbcc = 0 type to bcc-type atoms when it is annealed at 900 K upon 40 ns. The growth of crystal clusters happens parallel with changing its microstructure. The behavior of the crystal cluster resembles the nucleation process described by classical nucleation theory. Furthermore, we found that the amorphous NP has two parts: the core has the structure similar to the one of amorphous bulk, in while the surface structure is more porous amorphous. Unlike amorphous NP, the crystalline NP also has three parts: the core is the bcc, the next part the distorted bcc and the surface is amorphous. Amorphous and crystalline NPs have part core which has the structure not depend on size. Doi: 10.28991/HIJ-2021-02-03-01 Full Text: PDF

Validity of the compressibility equation and Kirkwood-Buff theory for crystalline matter.

Volume integrals over the radial pair-distribution function, so-called Kirkwood-Buff integrals (KBIs), play a central role in the theory of solutions by linking structural with thermodynamic information. The simplest example is the compressibility equation, a fundamental relation in statistical mechanics of fluids. Until now, KBI theory could not be applied to crystals because the integrals strongly diverge when computed in the standard way. We solve the divergence problem and generalize KBI theory to crystalline matter by using the recently proposed finite-volume theory. For crystals with harmonic interaction, we derive an analytic expression for the peak shape of the pair-distribution function at finite temperature. From this we demonstrate that the compressibility equation holds exactly in harmonic crystals.

Structural and mechanical properties of Al2O3.2SiO2 glass: Insights from molecular dynamics simulations

The Al2O3.2SiO2 glass sample was constructed by using the molecular dynamics method. The structural characteristics were analyzed by the pair radial distribution function, bond angle distribution, coordination number, simplex analysis and local configuration entropy responsible for their mechanical behavior. The AS2 glass exhibits brittle behavior, at which most SiO4 units are maintained and the breakages of Al-O bonds cause the transition of AlOy units from higher- to lower-fold Al coordination. The big simplexes, with the radii ≥ 2.6 Å, tend to gather to form the clusters, where the large pores locate. Big simplexes are formed under the tensile deformation. Most atoms belonging to these big simplexes have the highest configurational entropy, which are considered as liquid-like atoms. These atoms play important roles in the evolution and coalescence of the big simplexes causing the crack propagation. Most of them are O atoms, which belong to the big simplexes.

Structural and dynamic properties of lithium silicate liquid: A view from molecular dynamics simulation

In this work, we have investigated the liquid lithium silicate by the method of molecular dynamics simulation (MD) using the Born-Mayer pairwise potentials under compression. The simulations have been carried out by systems including various pressure values from 5 to 30 GPa. The microstructure of lithium silicate was clarified through the thorough analysis of short-range order (SRO) and intermediate range order (IRO). The short-range order was investigated through factors such as pair radial distribution functions (PRDFs), coordination distributions, angular distributions. The results show that the structure of the system has a transformation from low-coordination to high-coordination under the influence of compression. Besides, the analysis of intermediate range order shows that the structure network in model consists of SiOx and LiOx units connected to others via an Oxygen atom. In the case for the intermediate range order, the fraction of OTy bond calculated under compression shows that their bonding angle and bond length are very little dependent on the pressure changes. Furthermore, the dynamics of liquid lithium silicates calculated through the diffusion coefficients of the atoms shows that there is a dependence of atomic mobility on pressure. The obtained results of simulations are in good agreement with previous experimental and simulated data.

BoltzmaNN: Predicting effective pair potentials and equations of state using neural networks.

Neural networks (NNs) are employed to predict equations of state from a given isotropic pair potential using the virial expansion of the pressure. The NNs are trained with data from molecular dynamics simulations of monoatomic gases and liquids, sampled in the NVT ensemble at various densities. We find that the NNs provide much more accurate results compared to the analytic low-density limit estimate of the second virial coefficient and the Carnahan-Starling equation of state for hard sphere liquids. Furthermore, we design and train NNs for computing (effective) pair potentials from radial pair distribution functions, g(r), a task that is often performed for inverse design and coarse-graining. Providing the NNs with additional information on the forces greatly improves the accuracy of the predictions since more correlations are taken into account; the predicted potentials become smoother, are significantly closer to the target potentials, and are more transferable as a result.

Correlation between microstructure and density of Germania melts: insight from molecular dynamics simulation

Molecular dynamics simulation of Germania (GeO2) melt at different densities has been carried out to investigate the microstructural transformation, polyamorphism and structural heterogeneity. The structure of GeO2 is studied by GeOx basic units and their cluster. The simulation results show that the structure of GeO2 is formed by GeOx structural units linking to each other via with corner-sharing, edge-sharing, face-sharing bond. The polyamorphism and structural heterogeneity in GeO2 depend on fraction of GeOx units and distribution of GeOx cluster. The relationship between structure and density is analyzed via the change of pair radial distribution function (PRDF). The edge- and face-sharing bonds are responsible for the first peak splitting of Ge–Ge PRDF. The location of the two first sub-peaks of Ge–Ge PRDF corresponds to the length of edge- and corner-sharing bonds.

The microstructure of liquid Lead Silicate under PbO content

The structural characteristics of liquid lead silicate xPbO(1-x)SiO2 are performed by means of molecular dynamics simulation at ambient pressure using the Born-Mayer pairwise potentials. The simulations have been performed on the systems which include different samples with a large range of PbO content ( 0.05 ⩽ x ⩽0.75). The short and intermediate range order in liquid xPbO(1-x)SiO2 have been analysed via pair radial distribution function (PRDFs), coordination distribution, angular distribution and bond length distribution. Calculations show that most of the basic structural units in liquid lead silicate network are SiO4, PbO2 and PbO3 at low ratio of PbO and SiO4, PbO3 and PbO4 at high ratio of PbO. The distribution of O-T-O bond angle and T-O bond length (T is Si or Pb) in SiO4, PbO4 and PbO5 basic structural units are slightly changed when PbO content increase. In intermediate range order, the topology structure of OTy linkages (y=2,3,4) is also investigated in detail.