Velocity Autocorrelation Function Research Articles

Comparative studies of role of different structure factors in various physical properties of some simple liquid metals

In the current work, the comparison of the structure factors and pair correlation functions produced by using eight different theoretical models based on the Perckus-Yevick Hard Sphere (PYHS), Hard Sphere Yukawa (HSY), Mean Spherical Approximation (MSA), Generalized Mean Spherical Approximation (GMSA), Soft Sphere (SS), One-Component Plasma (OCP), Optimized Random Phase Approximation (ORPA) and Charged Hard Sphere (CHS) models for liquid metals viz. Li, Na, K, Rb, Cs, Mg, Zn, Ca, Al, Ga, In, Pb, Sn, Bi and Sb are carried out. Our own model potential is used with the Taylor (TY) screening function in the present computation. With this, certain physical properties such as electrical transport (electrical resistivity), vibrational property (phonon dispersion), dynamical property (velocity autocorrelation function (VACF)) and static (long wavelength of structure factor) properties has also been calculated. When the several theoretical models of the structure factors of the researched simple liquid metals are compared, it is discovered that the experimental data is consistent and in good agreement with the theoretical models.

On the molecular mechanisms of / uptake in confined ionic liquids: A computational study

Classical molecular dynamics and hybrid grand canonical Monte Carlo/molecular dynamics simulations were combined to analyse the gas uptake mechanism of hydrogen and nitrogen molecules inside carbon nanotubes filled with an ionic liquid. Several nanotube diameters (from 6 Å to 12.24 Å) and two different ionic liquids (ethylammonium nitrate and 1-ethyl-3-methylimidazolium tetrafluoroborate) were considered to study their effect on the gas capture capacity and on the location of gas molecules within the nanotubes. The simulations showed that nitrogen absorption ability is, in general, greater than that of hydrogen, with the aprotic ionic liquid being more efficient for gas confinement. In addition, gas capture was observed to increase from a scarce 0.4% in bulk ionic liquids up to 8%-25% inside small nanotubes, and the maximum gas uptake was observed for those nanotubes that allow for a greater degree of conformational freedom of the ionic liquid. However, our calculations show that, whereas hydrogen storage is mainly governed by the amount of accessible free volume, for understanding that of nitrogen solvation energetics must be also considered. In all cases, gas molecules are absorbed in the ionic liquid-rich-region, but the interactions with the other components of the system favour their accommodation closer to the carbon wall than to the nanotube center. Finally, single-particle dynamics of gas molecules was analyzed by means of the velocity autocorrelation functions and the vibrational density of states, which show a blue-shifting when increasing the radius of the nanotube.

Molecular simulations of hydrogen diffusion in underground porous media: Implications for storage under varying pressure, confinement, and surface chemistry conditions

Assessing the feasibility of porous formations for hydrogen geo-storage demands a comprehensive understanding of hydrogen (H2) transport behavior in porous media at subsurface conditions. In this study, we employ molecular dynamics simulations to evaluate the effects of pressure (20–500 atm), pore size (2–20 nm), and surface composition on H2 diffusion and interactions within organic and inorganic slit pores. Our analysis of H2 density profiles and interaction energies reveals a distinct preference for H2 molecules to adsorb more readily onto graphene surfaces than kaolinite surfaces. However, self-diffusion results demonstrate that H2 molecules interact relatively weakly with both substrate types. Further insights are provided by velocity autocorrelation functions, emphasizing the occurrence of wall-mediated collisions as H2 molecules diffuse along the pore surfaces, particularly within kaolinite. This highlights the significance of surface roughness in mitigating H2 loss via diffusion in subsurface nanopores, given the small molecular size of H2 and its limited interactions with both organic and inorganic materials. Furthermore, the results demonstrate that self-diffusion coefficients in both pore types increase with pore size and decrease with pressure. Notably, surface composition plays a critical role in low-pressure environments, with self-diffusion coefficients beginning to converge beyond a pressure of 100 atm. Self-diffusion coefficients also become less sensitive to slit aperture beyond a pressure of 50 atm. In high-pressure environments, hydrogen transport is governed by thermal collisions between gas molecules, leading to negligible property variations between pore types. These findings hold significance in the investigation of efficient H2 storage within porous media and caprock formations.

Alkali hydroxide (LiOH, NaOH, KOH) in water: Structural and vibrational properties, including neutron scattering results.

Structural and vibrational properties of aqueous solutions of alkali hydroxides (LiOH, NaOH, and KOH) are computed using quantum molecular dynamics simulations for solute concentrations ranging between 1 and 10M. Element-resolved partial radial distribution functions, neutron and x-ray structure factors, and angular distribution functions are computed for the three hydroxide solutions as a function of concentration. The vibrational spectra and frequency-dependent conductivity are computed from the Fourier transforms of velocity autocorrelation and current autocorrelation functions. Our results for the structure are validated with the available neutron data for 17M concentration of NaOH in water [Semrouni et al., Phys. Chem. Chem. Phys. 21, 6828 (2019)]. We found that the larger ionic radius [rLi+<rNa+<rK+] and higher concentration disturb the hydrogen-bond network of water, resulting in more disordered cationic hydration shell. Our abinitio simulation data for solute concentrations ranging between 1 and 10M can be used to guide future elastic and inelastic neutron-scattering experiments.

Exploring Challenging Properties of Liquid Metallic Systems through Machine Learning: Liquid La and Li4Pb Systems.

In this machine learning (ML) study, we delved into the unique properties of liquid lanthanum and the Li4Pb alloy, revealing some unexpected features and also firmly establishing some of the debated characteristics. Leveraging interatomic potentials derived from ab initio calculations, our investigation achieved a level of precision comparable to first-principles methods while at the same time entering the hydrodynamic regime. We compared the structure factors and pair distribution functions to experimental data and unearthed distinctive collective excitations with intriguing features. Liquid lanthanum unveiled two transverse collective excitation branches, each closely tied to specific peaks in the velocity autocorrelation function spectrum. Furthermore, the analysis of the generalized specific heat ratio in the hydrodynamic regime investigated with the ML molecular dynamics simulations uncovered a peculiar behavior, impossible to discern with only ab initio simulations. Liquid Li4Pb, on the other hand, challenged existing claims by showcasing a rich array of branches in its longitudinal dispersion relation, including a high-frequency LiLi mode with a nonhydrodynamic optical character that maintains a finite value as q → 0. Additionally, we conducted an in-depth analysis of various transport coefficients, expanding our understanding of these liquid metallic systems. In summary, our ML approach yielded precise results, offering new and captivating insights into the structural and dynamic aspects of these materials.

Chemically Specific Systematic Coarse-Grained Polymer Model with Both Consistently Structural and Dynamical Properties.

The coarse-grained (CG) model serves as a powerful tool for the simulation of polymer systems; its reliability depends on the accurate representation of both structural and dynamical properties. However, strong correlations between structural and dynamical properties on different scales and also a strong memory effect, enforced by chain connectivity between monomers in polymer systems, render developing a chemically specific systematic CG model a formidable task. In this study, we report a systematic CG approach that combines the iterative Boltzmann inversion (IBI) method and the generalized Langevin equation (GLE) dynamics. Structural properties are ensured by using conservative CG potentials derived from the IBI method. To retrieve the correct dynamical properties in the system, we demonstrate that using a combination of a Rouse-type delta function and a time-dependent short-time kernel in the GLE simulation is practically efficient. The former can be used to adjust the long-time diffusion dynamics, and the latter can be reconstructed from an iterative procedure according to the velocity autocorrelation function (ACF) from all-atomistic (AA) simulations. Taking the polystyrene as an example, we show that not only structural properties of radial distribution function, intramolecular bond, and angle distributions can be reproduced but also dynamical properties of mean-square displacement, velocity ACF, and force ACF resulted from our CG model have quantitative agreement with the reference AA model. In addition, reasonable agreements are observed in other collective properties between our GLE-CG model and the AA simulations as well.

Theoretical investigation of atomic dynamics of molten metals at melting points

In molten metals, the atomic dynamics have been studied in the present study with the help of equations of motion in terms of the velocity autocorrelation function (VACF), power spectrum G ( ω ) , and mean square displacement r 2 ( t ) . The pair correlation function g ( r ) is used to produce VACF for molten metals in the current study with the help of three different types of structure factor methods i.e. hard sphere Yukawa (HSY) method, optimised random phase approximation (ORPA) method and charged hard sphere (CHS) method. The presently obtained results for molten metals of different groups like Na (Z = 1), Mg (Z = 2), Al (Z = 3), Sn (Z = 4), and Sb (Z = 5) are compared with the molecular dynamic (MD) study and also with the other theoretical data available in the literature. For the present study, our own developed pseudopotential has been used for the calculations of the above-mentioned properties. The screening effect is also been observed over and beyond the bare ion potential with Hartree (H) and the effects of exchanges and correlation were computed using procedures given by Taylor (T) and Nagy (N).

Comparison of effective and stable Langevin dynamics integrators

Langevin and Brownian simulations play a prominent role in computational research, and state of the art integration algorithms provide trajectories with different stability ranges and accuracy in reproducing statistical averages. The practical usability of integrators is an important aspect to allow choosing large time steps while ensuring numerical stability and overall computational efficiency. In this work, different use cases and practical features are selected in order to perform a cumulative comparison of integrators with a focus on evaluating the derived velocity and position autocorrelation functions, a comparison that is often disregarded in the literature. A standard industrial open-source software methodology is suggested to compare systematically the different algorithms.

Understanding melting of Ti crystals with spherical voids from molecular dynamics simulations

Titanium (Ti) is one of the most important metals used in several industrial applications, and the presence of spherical defect reduces its strength and stability. We simulate the melting of Ti crystals with a spherical void of radii 0.6, 0.8, 1.0, and 1.5 nm and also of the crystal without it. Ti is modeled using embedded atom method ,and all crystals are heated at 1 atm from 300 to 2200 K till it melts completely. All molecular dynamics trajectories are analyzed using radial distribution functions, bond-orientational order parameters, Voronoi tessellation, and velocity auto-correlation functions. The results show that 0.6, 0.8, 1.0, and 1.5 nm voids fill before the crystals melt and they fill immediately within few picoseconds; thereafter, atoms rearrange/order to crystal like arrangements, wherein overall crystallinity remains hcp for crystals with 0.6 and 0.8 nm void and changes to bcc for the crystals with 1.0 and 1.5 nm voids. For all crystals with and without void, melting takes place with the loss of both long- and short-range orders and not from liquid like nuclei as proposed by classical nucleation theory.

A Novel Fractional Brownian Dynamics Method for Simulating the Dynamics of Confined Bottle-Brush Polymers in Viscoelastic Solution.

In crowded fluids, polymer segments can exhibit anomalous subdiffusion due to the viscoelasticity of the surrounding environment. Previous single-particle tracking experiments revealed that such anomalous diffusion in complex fluids (e.g., in bacterial cytoplasm) can be described by fractional Brownian motion (fBm). To investigate how the viscoelastic media affects the diffusive behaviors of polymer segments without resolving single crowders, we developed a novel fractional Brownian dynamics method to simulate the dynamics of polymers under confinement. In this work, instead of using Gaussian random numbers ("white Gaussian noise") to model the Brownian force as in the standard Brownian dynamics simulations, we introduce fractional Gaussian noise (fGn) in our homemade fractional Brownian dynamics simulation code to investigate the anomalous diffusion of polymer segments by using a simple "bottle-brush"-type polymer model. The experimental results of the velocity autocorrelation function and the exponent that characterizes the subdiffusion of the confined polymer segments can be reproduced by this simple polymer model in combination with fractional Gaussian noise (fGn), which mimics the viscoelastic media.

Investigating thermal conductivity and mechanical properties of a hybrid material based on cellulose nanofibers and boron nitride nanotubes using molecular dynamics simulations

Cellulose nanofibers (NFCs) have emerged as a preferred choice for fabricating nanomaterials with exceptional mechanical properties. At the same time, boron nitride nanotubes (BNNTs) have long been favored in thermal management devices due to their superior thermal conductivity (k). This study uses reverse non-equilibrium molecular dynamics (MD) simulations to investigate k for a hybrid material based on NFCs and BNNTs. The result is then compared with pure NFC and BNNT-based structures with equivalent total weight content to elucidate how incorporating BNNT fillers enhances k for the hybrid system. Furthermore, the fundamental phonon vibration modes responsible for driving thermal transport in NFC-based materials upon incorporating BNNTS are identified by computing the vibrational density of states from the Fourier transform analysis of the averaged mass-weighted velocity autocorrelation function. Additionally, MD simulations demonstrate how both NFCs and BNNTs synergistically improve the constituting hybrid structure’s mechanical properties (e.g. tensile strength and stiffness). The overarching aim is to contribute towards the engineered design of novel functional materials based on nanocellulose that simultaneously improve crucial physical properties pertaining to thermal transport and mechanics.

Subdiffusive dynamics and hydrodynamic fluctuations: how the latter affect the former.

The characteristics of subdiffusion are influenced by hydrodynamic fluctuations, not the scaling of the mean square displacement (MSD) at the long time limit, but rather the transition of this property from ballistic behaviour at early times to its final scaling at large times. Additionally, since a significant portion of the normalised velocity autocorrelation function (NVAF), a widely used motion descriptor, no longer adequately describes the antipersistent character that is typical of a subdiffusive motion, it is also impacted by these fluctuations. The combined findings can lead to misleading conclusions if hydrodynamic fluctuations are not taken into account. Diffusing and vorticity time scales are crucial for the way the motion turns into the final subdiffusion dynamics, whose exponent is determined by the scaling of the friction.

A comparative study of deep eutectic solvents based on fatty acids and the effect of water on their intermolecular interactions

In this work, intermolecular interactions among the species of fatty acids-based DESs with different hydrogen bond acceptors (HBA) in the adjacent water have been investigated using molecular dynamics (MD) simulation. The results of this work provide deep insights into understanding the water stability of the DESs based on thymol and the eutectic mixtures of choline chloride and fatty acids at a temperature of 353.15 K and atmospheric pressure. Stability, hydrogen bond occupancy analysis, and the distribution of the HBA and HBD around each other were attributed to the alkyl chain length of FAs and the type of HBA. Assessed structural properties include the combined distribution functions (CDFs), the radial distribution functions (RDFs), the angular distribution functions (ADFs), and the Hydrogen bonding network between species and Spatial distribution functions (SDF). The reported results show the remarkable role of the strength of the hydrogen bond between THY molecules and fatty acids on the stability of DES in water. The transport properties of molecules in water–eutectic mixtures were analyzed by using the mean square displacement (MSD) of the centers of mass of the species, self-diffusion coefficients, vector reorientation dynamics (VRD) of bonds and the velocity autocorrelation function (VACF) for the center of the mass of species.

Pure and Sc-doped diopside (CaMgSi2O6) vibrational spectra: modelling and experiments.

We investigated the structure of pure and Sc-doped synthetic diopside (a monoclinic single-chain silicate nominally CaMgSi2O6); in Sc-doped diopside, Sc3+ substitutes Mg2+ in the structure and, to achieve charge balance, vacancies form at the expense of Ca2+. We compared the structure obtained from ab initio modelling techniques at the density functional theory (DFT) level with the structure solved by employing single crystal X-ray diffraction. Furthermore, we compared IR and Raman spectroscopy experiments with vibrational density of states (VDOS) calculated from the Fourier transform of the velocity autocorrelation function obtained using ab initio (DFT) molecular dynamics simulations. In this framework, we developed a computational tool to assign the vibrational mode associated with a specific frequency. This method consists of projecting velocities along a specific set of internal coordinates such as stretching or bending, in cases involving defects or vacancies, to calculate a partial VDOS (pVDOS) that takes into account only the vibrations associated with selected internal modes, aiding the interpretation of the total VDOS and the experimental spectra in a relevant way. The computed data were validated with the experiments and we observed that doping the diopside structure with Sc produces peak broadening and the occurrence of new peaks in the Raman spectra and that site vacancies are associated with the nearby Sc site. The present work constitutes an interesting starting point to exploit the calculated VDOS/pVDOS to characterize experimental vibrational spectra of complex systems containing local vacancies, substitutions or defects as the Sc-doped diopside.

On hydrogen bonding in two carboxyl-functionalised imidazolium based ionic liquids

Dynamics in ionic liquids (ILs) are mainly governed by Coulombic interactions and strong, long-lived hydrogen bonds (HBs). This molecular dynamics (MD) study focuses on carboxyl-functionalised imidazolium based ILs at a temperature of 400 K, using an explicit atom force field. HB dynamics play a crucial role in determining the arrangement of ions and the structure in the bulk phase of ILs. We investigated the abundance of the defined HBs formed between the constituent ions and their lifetimes in the bulk phase of these ILs. These HBs can form between ions bearing opposite charges or pairs of like-charged ions. HBs between pairs of cations, though less in number, are longer lived than other HBs. The HB lifetimes were observed to correspond to timescales ranging from a few picoseconds to hundreds of picoseconds. Each component is associated with a different physical process leading to their breaking and reformation. Abbreviations: IL: ionic liquid; HB: hydrogen bond; IR: infrared; VDoS: vibrational density of states; VACF: velocity autocorrelation function; MD: molecular dynamics; RDF: radial distribution function

Об анизотропии диффузии углеродных нанотрубок в жидкости

This article discusses the methodology and results of molecular dynamics simulation of the diffusion of carbon nanotubes in water. The main goals of this work were to study diffusion longitudinal to an axis of the nanotube and transverse to this axis and determine the velocity autocorrelation functions and diffusion coefficients in these directions. The interaction of water molecules with each other was described by the Lennard-Jones potential, and that of carbon nanotube molecules by the AIREBO potential. The diameters of the nanotubes were 1.15 and 1.44 nanometers, their length varied from 5 to 15 nanometers. The number of water molecules in the simulation cell reached one hundred thousand. It is shown that the nanotube center of mass velocity autocorrelation function in the longitudinal direction decays much more slowly than in the transverse direction. The corresponding values of the diffusion coefficients differ by a factor of 2–4; this diffe¬rence increases with increasing ratio of the nanotube length to its diameter. The directionally averaged diffusion coefficients of flexible nanotubes decrease with increasing nanotube length. Its values exceed the corresponding values for their solid analogues. A nonmonotonic decay of the nanotubes center of mass velocity autocorrelation function was discovered. The characteristic time between the maxima of this function coincides with the period of bending vibrations of the nanotube.

Analysis of Velocity Autocorrelation Functions from Molecular Dynamics Simulations of a Small Peptide by the Generalized Langevin Equation with a Power-Law Kernel.

Internal motions play an essential role in the biological functions of proteins and have been the subject of numerous theoretical and spectroscopic studies. Such complex environments are associated with anomalous diffusion where, in contrast to the classical Brownian motion, the relevant correlation functions have power law decays with time. In this work, we investigate the presence of long memory stochastic processes through the analysis of atomic velocity autocorrelation functions. Analytical expressions of the velocity autocorrelation function spectrum obtained through a Mori-Zwanzig projection approach were shown to be compatible with molecular dynamics simulations of a small helical peptide (8-polyalanine).

Static and Dynamic Properties of SPC/E Water Model

In this work, we have studied static and dynamic properties of bulk water using SPC/E water model. We have considered 1500 water molecules confined to a three dimensional box. LAMMPS software has been used to perform molecular dynamic simulation under canonical ensemble. The partial radial distribution functions, diffusion coefficients, velocity autocorrelation functions, and mean square displacements have been calculated at 300K for different densities ranging from 900 kg/m3 to 1000 kg/m3. The principle peak heights of the partial radial distribution functions are found to decrease with increase in high density regime showing abnormal behaviour in this density regime.

Molecular Dynamics Simulation of Diffusion Behavior in Liquid Sn and Pb

This study aimed to clarify the effect of a unique structure with a “shoulder,” which represents a hump on the high wave vector side of the first peak of static structure factor, in liquid Sn (liq-Sn) on the self-diffusion behavior through molecular dynamics (MD) simulation. The MD simulations of liq-Sn at 573 K and liquid Pb (liq-Pb) at 773 K were performed for comparison. The former and latter were selected as element with and without shoulder structure and reliable self-diffusion coefficients in liquid have been measured in both elements. The calculated self-diffusion coefficients of liq-Sn and liq-Pb were reproduced as the same order of magnitude with the referred reliable data of diffusion coefficients, which were obtained by experiments on the ground. The microscopic diffusion behavior of liq-Sn is unlike that of the hard-sphere model because the atoms become sluggish in the range that corresponds to the shoulder appearing in the pair distribution function of liq-Sn as well as in the structure factor of liq-Sn based on the local atomic configurations and time-series analyses of individual atoms. Therefore, the velocity autocorrelation function (VACF) converges to zero more rapidly than that of liq-Pb, and it is reproduced by the hard-sphere model. However, the macroscopic diffusion behavior of liq-Sn expressed by the self-diffusion coefficient is the same as that of the hard-sphere model with the non-correlation of the VACF in the long time.

Construction of Coarse-Grained Molecular Dynamics with Many-Body Non-Markovian Memory.

We introduce a machine-learning-based coarse-grained molecular dynamics model that faithfully retains the many-body nature of the intermolecular dissipative interactions. Unlike the common empirical coarse-grained models, the present model is constructed based on the Mori-Zwanzig formalism and naturally inherits the heterogeneous state-dependent memory term rather than matching the mean-field metrics such as the velocity autocorrelation function. Numerical results show that preserving the many-body nature of the memory term is crucial for predicting the collective transport and diffusion processes, where empirical forms generally show limitations.