Hoover Thermostat Research Articles

The structural and electronic configuration of an amorphous silica surface, from its liquid to glassy state

Through classical molecular dynamics computational simulations, the surface of amorphous silica (vitreous silica) was generated for a system comprising 64 SiO2 molecules (192 atoms) via the classical three-body glass potential. Starting from the liquid state of silica at 3400 K, it was cooled in three different ways at intervals of 200, 400, and 2000 K, with a cooling rate of 4.4 K/ps and establishing relaxation at intermediate temperatures, yielding three groups of surfaces from 3400 to 1400 K. Subsequently, these systems underwent sudden cooling from 1400 to 300 K via the Andersen and Nosé‒Hoover thermostats, followed by relaxation at 300 K via a microcanonical ensemble (NVE constant). Each surface that underwent relaxation was analyzed through ab initio molecular dynamics for the following three physical properties, which are temperature dependent. The average electric charges of oxygen and silicon. Microstructures on the outermost part of the surface were observed and comprised nonbridging oxygen atoms, undercoordinated silicon, and N-membered rings (3 ≤ N ≤ 5). The radial distribution functions were analyzed for all surfaces. Below 2000 K, a type of freezing is observed in all the structures because of the glass transition. All analyses were performed at zero pressure.

Simulation of the Diffusion of Copper Atom on Graphene by Molecular Dynamics

The results of studying the effect of geometric and thermodynamic parameters of thermal evaporation and copper deposition on graphene lying on the Cu(111) surface on the adsorption of copper atoms, as well as their surface diffusion, are presented. The simulation was carried out by classical molecular dynamics using chains of Nose–Hoover thermostats. Interatomic interactions were determined by the Tersoff–Brenner, Rosato–Gillop–Legrand, and modified Morse potentials. A simple criterion for the thermalization of adatoms on graphene lying on a Cu(111) surface was formulated and tested. The average length and mean time of free path of a copper atom before and after thermalization at low (7 K) and room temperatures were studied for two evaporation temperatures. The probability of adsorption of a copper atom was found. The distributions along the directions of motion of adatoms during equilibrium diffusion were constructed. The distributions of the free path length and time were shown to have an exponential form. The influence of the Cu(111) substrate on the diffusion of the Cu atom on graphene was studied. The results obtained can be used to simulate the growth of copper nanoclusters on graphene by the kinetic Monte Carlo method.

On the Actual Difference between the Nosé and the Nosé–Hoover Thermostats: A Critical Review of Canonical Temperature Control by Molecular Dynamics

This article has to be intended both as a review and as an historical tribute to the ideas developed almost 40 years ago by S. Nosé, establishing the theoretical foundations of the implementation and use of thermostats in molecular dynamics (MDs). The original motivation of this work is enriched by an observation related to the connection between the Nosé seminal expression of temperature control and the extension proposed in 1985 by W. G. Hoover, known as the Nosé–Hoover thermostat. By carefully rederiving the equations of motion in both formalisms, it appears that all features of Nosé–Hoover framework (replacement of the Nosé variables by a single friction coefficient in the equations of motion) are already built in the Nosé approach. Therefore, one is able to work directly within the Nosé formalism with the addition of a single variable only, by greatly extending its general impact and simplicity and somewhat making redundant the Nosé–Hoover extension. Having been implicitly (and somewhat inadvertently) put to good use by a multitude of users over the past 40 years (in the context of classical and first‐principles MDs), this finding does not need any specific application to be assessed.

Multiscale Methods Framework with the 3D-RISM-KH Molecular Solvation Theory for Supramolecular Structures, Nanomaterials, and Biomolecules: Where Are We Going?

3D-RISM-KH molecular solvation theory based on statistical mechanics has been an engine of the multiscale methods framework, which also includes molecular simulation techniques. Its applications range from the solvation energy of small molecules to the phase behavior of polymers and biomolecules. Molecular solvation theory predicts and explains the molecular mechanisms and functioning of a variety of chemical and biomolecular systems. This includes the self-assembly and conformational stability of synthetic organic rosette nanotubes (RNTs), the aggregation of peptides and proteins related to neurodegeneration, the binding of ligands to proteins, and the solvation properties of biomolecules related to their functions. The replica RISM-KH-VM molecular solvation theory predicts and explains the structure, thermodynamics, and electrochemistry of electrolyte solutions sorbed in nanoporous carbon supercapacitor electrodes, and is part of recent research and development efforts. A new quasidynamics protocol couples multiple time step molecular dynamics (MTS-MD) stabilized with an optimized isokinetic Nosé–Hoover (OIN) thermostat driven by 3D-RISM-KH mean solvation forces at gigantic outer time steps of picoseconds, which are extrapolated forward at short inner time steps of femtoseconds with generalized solvation force extrapolation (GSFE). The OIN/3D-RISM-KH/GSFE quasidynamics is implemented in the Amber Molecular Dynamics package. It is validated on miniprotein 1L2Y and protein G in ambient aqueous solution, and shows the rate of sampling 150 times faster than in standard MD simulations on these biomolecules in explicit water. The self-consistent field version of Kohn–Sham DFT in 3D-RISM-KH mean solvation forces is implemented in the Amsterdam Density Functional (ADF) package. Its applications range from solvation thermochemistry, conformational equilibria, and photochemistry to activation barriers of different nanosystems in solutions and ionic liquids.

Further cautionary tales on thermostatting in molecular dynamics: Energy equipartitioning and non-equilibrium processes in gas-phase simulations.

Molecular dynamics (MD) simulations of gas-phase chemical reactions are typically carried out on a small number of molecules near thermal equilibrium by means of various thermostatting algorithms. Correct equipartitioning of kinetic energy among translations, rotations, and vibrations of the simulated reactants is critical for many processes occurring in the gas phase. As thermalizing collisions are infrequent in gas-phase simulations, the thermostat has to efficiently reach equipartitioning in the system during equilibration and maintain it throughout the actual simulation. Furthermore, in non-equilibrium simulations where heat is released locally, the action of the thermostat should not lead to unphysical changes in the overall dynamics of the system. Here, we explore issues related to both obtaining and maintaining thermal equilibrium in MD simulations of an exemplary ion-molecule dimerization reaction. We first compare the efficiency of global (Nosé-Hoover and Canonical Sampling through Velocity Rescaling) and local (Langevin) thermostats for equilibrating a system of flexible compounds and find that of these three only the Langevin thermostat achieves equipartition in a reasonable simulation time. We then study the effect of the unphysical removal of latent heat released during simulations involving multiple dimerization events. As the Langevin thermostat does not produce the correct dynamics in the free molecular regime, we only consider the commonly used Nosé-Hoover thermostat, which is shown to effectively cool down the reactants, leading to an overestimation of the dimerization rate. Our findings underscore the importance of thermostatting for the proper thermal initialization of gas-phase systems and the consequences of global thermostatting in non-equilibrium simulations.

Topological and quantum stability of low-dimensional crystalline lattices with multiple nonequivalent sublattices* *Dedicated to the memory of our close friend, fellow colleague, former student (PA) and teacher (AK) Prof. A A Kuzubov (1974–2016).

The terms of topological and quantum stabilities of low-dimensional crystalline carbon lattices with multiple non-equivalent sublattices are coined using theoretical analysis, multilevel simulations, and available experimental structural data. It is demonstrated that complex low-dimensional lattices are prone to periodicity breakdown caused by structural deformations generated by linear periodic boundary conditions (PBC). To impose PBC mandatory limitations for complex low-dimensional lattices, the topology conservation theorem (TCT) is introduced, formulated and proved. It is shown that the lack of perfect filling of planar 2D crystalline space by structural units may cause the formation of (i) structure waves of either variable or constant wavelength; (ii) nanotubes or rolls; (iii) saddle structures; (iv) aperiodic ensembles of irregular asymmetric atomic clusters. In some cases the lattice can be stabilized by aromatic resonance, correlation effects, or van-der-Waals interactions. The effect of quantum instability and periodicity breakdown of infinite structural waves is studied using quasiparticle approach. It is found that both perfect finite-sized, or stabilized structural waves can exist and can be synthesized. It is shown that for low-dimensional lattices prone to breakdown of translation invariance (TI), complete active space of normal coordinates cannot be reduced to a subspace of TI normal coordinates. As a result, constrained TI subspace structural minimization may artificially return a regular point at the potential energy surface as either a global/local minimum/maximum. It is proved that for such lattices, phonon dispersion cannot be used as solid and final proof of either stability or metastability. It is shown that ab initio molecular dynamics (MD) PBC Nosé–Hoover thermostat algorithm constrains the linear dimensions of the periodic slabs in MD box preventing their thermostated equilibration. Based on rigorous TCT analysis, a flowchart algorithm for structural analysis of low-dimensional crystals is proposed and proved to be a powerful tool for theoretical design of advanced complex nanomaterials.

Atomistic Investigation Using Molecular Dynamics Simulation of τ<sub>4</sub>-Al<sub>3</sub>FeSi<sub>2</sub> and τ<sub>12</sub>-Al<sub>3</sub>Fe<sub>2</sub>Si Phases under Tensile Deformation

Aluminum-Iron-Silicon (Al-Fe-Si) alloys are extremely applied in many specific industries, such as aerospace and automobiles. Their atomic concentration influences the mechanical behavior of the investigated τ4-Al3Fe2Si and τ12-Al3FeSi2 phases. The uniaxial-tensile deformation is used to compare their structural evolution under the same conditions.Atomic displacement and mechanical behavior have an interest in the elastic and plastic areas. Stress-Strain responses and Radial Distribution Function (RDF) are required. Further, atomic simulations using molecular dynamics demonstrate the change occurs. Its process is carried out at a strain rate of 21×1010 s-1 using the NPT (isothermal-isobaric) with roughly 20 700 atoms at a pressure of 105 Pa. Furthermore, using a Nosée Hoover thermostat at the temperature of 300 k is decisive.The Modified Embedded Atoms Method (MEAM) is the applied potential between Al, Fe, and Si atoms. The elastic modulus and single pair atomic correlation before and after straining are increased by this method. The atomic correlations are shown in short- and long-range order and the τ12-Al3Fe2Si phase illustrates stronger properties compared to τ4-Al3Fe2Si phase. Our results underscore an important variation associated with the change of iron and silicon concentration. More specifics are covered in the selection paper.

Addressing Dynamics at Catalytic Heterogeneous Interfaces with DFT-MD: Anomalous Temperature Distributions from Commonly Used Thermostats.

Density functional theory-based molecular dynamics (DFT-MD) has been widely used for studying the chemistry of heterogeneous interfacial systems under operational conditions. We report frequently overlooked errors in thermostated or constant-temperature DFT-MD simulations applied to study (electro)catalytic chemistry. Our results demonstrate that commonly used thermostats such as Nosé–Hoover, Berendsen, and simple velocity-rescaling methods fail to provide a reliable temperature description for systems considered. Instead, nonconstant temperatures and large temperature gradients within the different parts of the system are observed. The errors are not a “feature” of any particular code but are present in several ab initio molecular dynamics implementations. This uneven temperature distribution, due to inadequate thermostatting, is well-known in the classical MD community, where it is ascribed to the failure in kinetic energy equipartition among different degrees of freedom in heterogeneous systems (Harvey et al. J. Comput. Chem.1998, 726−740) and termed the flying ice cube effect. We provide tantamount evidence that interfacial systems are susceptible to substantial flying ice cube effects and demonstrate that the traditional Nosé–Hoover and Berendsen thermostats should be applied with care when simulating, for example, catalytic properties or structures of solvated interfaces and supported clusters. We conclude that the flying ice cube effect in these systems can be conveniently avoided using Langevin dynamics.

Impact of thermostat on interfacial thermal conductance prediction from non-equilibrium molecular dynamics simulations

The knowledge of interfacial thermal conductance (ITC) is key to understand thermal transport in nanostructures. The non-equilibrium molecular dynamics (NEMD) simulation is a useful tool to calculate the ITC. In this study, we investigate the impact of thermostat on the prediction of the ITC. The Langevin thermostat is found to result in larger ITC than the Nose–Hoover thermostat. In addition, the results from NEMD simulations with the Nose–Hoover thermostat exhibit strong size effect of thermal reservoirs. Detailed spectral heat flux decomposition and modal temperature calculation reveal that the acoustic phonons in hot and cold thermal reservoirs are of smaller temperature difference than optical phonons when using the Nose–Hoover thermostat, while phonons in the Langevin thermostat are of identical temperatures. Such a non-equilibrium state of phonons in the case of the Nose–Hoover thermostat reduces the heat flux of low-to-middle-frequency phonons. We also discuss how enlarging the reservoirs or adding an epitaxial rough wall to the reservoirs affects the predicted ITC, and find that these attempts could help to thermalize the phonons, but still underestimate the heat flux from low-frequency phonons.

Anionic Tuning of Zeolite Crystallization

Zeolites are of great industrial relevance as catalysts, adsorbents, and ion-exchangers and typically synthesized under hydrothermal conditions. Rational regulation of their crystallization process...

Molecular dynamics modeling of the influence forming process parameters on the structure and morphology of a superconducting spin valve.

This work is a study of the formation processes and the effect of related process parameters of multilayer nanosystems and devices for spintronics. The model system is a superconducting spin valve, which is a multilayer structure consisting of ferromagnetic cobalt nanolayers separated by niobium superconductor nanolayers. The aim was to study the influence of the main technological parameters including temperature, concentration and spatial distribution of deposited atoms over the nanosystem surface on the atomic structure and morphology of the nanosystem. The studies were carried out using the molecular dynamics method using the many-particle potential of the modified embedded-atom method. In the calculation process the temperature was controlled using the Nose–Hoover thermostat. The simulation of the atomic nanolayer formation was performed by alternating the directional deposition of different composition layers under high vacuum and stationary temperature conditions. The structure and thickness of the formed nanolayers and the distribution of elements at their interfaces were studied. The alternating layers of the formed nanosystem and their interfaces are shown to have significantly different atomic structures depending on the main parameters of the deposition process.

Polarizable molecular dynamics simulations of ionic liquids: Influence of temperature control.

Ionic liquids are an interesting class of soft matter with viscosities of one or two orders of magnitude higher than that of water. Unfortunately, classical, non-polarizable molecular dynamics (MD) simulations of ionic liquids result in too slow dynamics and demonstrate the need for explicit inclusion of polarizability. The inclusion of polarizability, here via the Drude oscillator model, requires amendments to the employed thermostat, where we consider a dual Nosé-Hoover thermostat, as well as a dual Langevin thermostat. We investigate the effects of the choice of a thermostat and the underlying parameters such as the masses and force constants of the Drude particles on static and dynamic properties of ionic liquids. Here, we show that Langevin thermostats are not suitable for investigating the dynamics of ionic liquids. Since polarizable MD simulations are associated with high computational costs, we employed a self-developed graphics processing unit enhanced code within the MD program CHARMM to keep the overall computational effort reasonable.

Horseshoes for Singly Thermostated Hamiltonians

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 27 January 2020Accepted: 16 June 2020Published online: 13 October 2020Keywordsthermostats, Nosé--Hoover thermostat, Hamiltonian mechanics, transverse homoclinic points, horseshoesAMS Subject Headings37J30, 37A60, 37J46, 82B03Publication DataISSN (online): 1536-0040Publisher: Society for Industrial and Applied MathematicsCODEN: sjaday

Influence of thermostatting on nonequilibrium molecular dynamics simulations of heat conduction in solids.

Nonequilibrium molecular dynamics (NEMD) has been extensively used to study thermal transport at various length scales in many materials. In this method, two local thermostats at different temperatures are used to generate a nonequilibrium steady state with a constant heat flux. Conventionally, the thermal conductivity of a finite system is calculated as the ratio between the heat flux and the temperature gradient extracted from the linear part of the temperature profile away from the local thermostats. Here, we show that, with a proper choice of the thermostat, the nonlinear part of the temperature profile should actually not be excluded in thermal transport calculations. We compare NEMD results against those from the atomistic Green's function method in the ballistic regime and those from the homogeneous nonequilibrium molecular dynamics method in the ballistic-to-diffusive regime. These comparisons suggest that in all the transport regimes, one should directly calculate the thermal conductance from the temperature difference between the heat source and sink and, if needed, convert it into the thermal conductivity by multiplying it with the system length. Furthermore, we find that the Langevin thermostat outperforms the Nosé-Hoover (chain) thermostat in NEMD simulations because of its stochastic and local nature. We show that this is particularly important for studying asymmetric carbon-based nanostructures, for which the Nosé-Hoover thermostat can produce artifacts leading to unphysical thermal rectification.

Novel Gear-like predictor–corrector integration methods for molecular dynamics

A new class of predictor–corrector integration methods intended for molecular dynamics simulation is presented. The methods are derived from the original Gear methods by analysing the numerical solution of the harmonic oscillator. The corrector coefficients are chosen to improve the time-reversibility while keeping maximum stability. Tests performed on systems with forces not dependent on velocities (classical two-body problem and three simple atomistic systems) show good energy conservation and reduced deviations of measured quantities in comparison with the Verlet method. As regards the systems with velocity-dependent right-hand sides, a moderate improvement is found for the Nosé–Hoover thermostat but no improvement for fixed bonds constrained by the general constraint dynamics based on Lagrange multipliers.

Simulation of deformation and fracture processes in nanocomposites

The paper studies the processes of deformation and fracture in nanocomposites. The study was curry out by the method of mathematical modeling. The behavior of the nanosystem was described by the molecular dynamics apparatus. A modified immersed atom method was used as a potential. Demonstrated theoretical approaches to the study of the mechanical properties of nanocosposites and the processes of their destruction. Formulas for calculating the stress, strain tensors and displacement veare given. To maintain a constant temperature in the nanosystem, a Nose – Hoover thermostat was used. The destruction of nanocomposites was considered in the process of tension and shear deformation. Pure aluminum, a composite with an aluminum matrix and a filler in the form of spherical iron particles, and a composite with an aluminum matrix and a filler in the form of a cylindrical iron fiber were used as samples. After the filler was introduced into the nanocomposite, the sample was relaxed to ensure its more stable state. The simulation allowed us to establish the basic laws of changes in the atomic structure of the matrix and nanocomposite fillers during deformation and fracture. It is shown that the processes of deformation and destruction of nanocomposites substantially depend both on the structure and types of loading of the material. The results of the research can be used to study the processes of deformation of nanocomposite materials with promising functional properties.

Reactive Molecular Dynamics Study of the Thermal Decomposition of Phenolic Resins

The thermal decomposition of polyphenolic resins was studied by reactive molecular dynamics (RMD) simulation at elevated temperatures. Atomistic models of the polyphenolic resins to be used in the RMD were constructed using an automatic method which calls routines from the software package Materials Studio. In order to validate the models, simulated densities and heat capacities were compared with experimental values. The most suitable combination of force field and thermostat for this system was the Forcite force field with the Nosé–Hoover thermostat, which gave values of heat capacity closest to those of the experimental values. Simulated densities approached a final density of 1.05–1.08 g/cm3 which compared favorably with the experimental values of 1.16–1.21 g/cm3 for phenol-formaldehyde resins. The RMD calculations were run using LAMMPS software at temperatures of 1250 K and 3000 K using the ReaxFF force field and employing an in-house routine for removal of products of condensation. The species produced during RMD correlated with those found experimentally for polyphenolic systems and rearrangements to form cyclopropane moieties were observed. At the end of the RMD simulations a glassy carbon char resulted.

Fast Nosé-Hoover thermostat: molecular dynamics in quasi-thermodynamic equilibrium.

An extension of the Nosé-Hoover thermostat equation for molecular dynamics (MD) simulation is introduced, which perturbs fast degrees of freedom out of canonical equilibrium, while preserving the average temperature of the system. Based on the generalised Liouville equation, it is shown that the newly introduced fast Nosé-Hoover (FNH) equations give rise to a dynamical system with a well-defined non-equilibrium probability distribution. Corresponding thermostat parameters are identified, which in principle allow to sample arbitrarily close to canonical equilibrium. Results show that the dynamic system properties (e.g. self-diffusion, shear viscosity, dielectric permittivity and rotational relaxation times) are only moderately perturbed for typical FNH setups. However, the non-equilibrium FNH equations modify the occurrence of rare events substantially and thus offer a novel approach for enhanced sampling in MD. In particular, it is shown that the FNH thermostat increased significantly the frequency of the folding and unfolding process of short β-peptides. The efficiency of the phase-space exploration solely depends on the additionally imposed quasi-equilibrium conditions, i.e. it does not rely on any modification of the potential-energy surface.

Optimal determination of force field parameters for reduced molecular dynamics model

Using a gradient-based optimization method, the time-consuming atomistic model of substrate is replaced by computationally efficient Lennard-Jones (L-J) potential walls whose parameters are determined to appropriately represent the interactions between the nanoparticles and the substrate. To obtain the required design sensitivity with respect to design variables for the constant temperature molecular dynamics (MD) simulations that use the Nosé–Hoover thermostat, the finite difference method is impractical due to the huge amount of computational costs. Thus, we developed an adjoint design sensitivity analysis (DSA) method that is efficient for the system of many design variables. In numerical examples, we replace the complicated and time-consuming silicate structure to a multiple layer model of L-J potential wall, through the design optimization that includes the design variables of ϵ, σ, and the positions of each layer. The objective is to minimize the squared difference of time averaged performance between the full and the reduced models during the whole time span. The proposed method could lead to a significant reduction of computational costs, together with comparable outcomes from MD simulations.

Thermalizing and Damping in Structural Dynamics

Structural damping, that is the presence of a velocity dependent dissipative term in the equation of motion, is rationalized as a thermalization process between a structure (here a beam) and an outside bath (understood in a broad sense as a system property). This is achieved via the introduction of the kinetic temperature of structures and formalized by means of an extended Lagrangian formulation of a structure in contact with an outside bath at a given temperature. Using the Nosé–Hoover thermostat, the heat exchange rate between structure and bath is identified as a mass damping coefficient, which evolves in time in function of the kinetic energy/temperature history exhibited by the structure. By way of application to a simple beam structure subjected to eigen-vibrations and dynamic buckling, commonality and differences of the Nosé–Hoover beam theory with constant mass damping models are shown, which permit a handshake between classical damping models and statistical mechanics–based thermalization models. The solid foundation of these thermalization models in statistical physics provides new insights into stability and instability for engineering structures. Specifically, since two systems are considered in (thermodynamic) equilibrium when they have the same temperature, we show in the case of dynamic buckling that a persistent steady-state difference in kinetic temperature between structure and bath is but indicative of the instability of the system. This shows that the kinetic temperature can serve as a structural order parameter to identify and comprehend failure of structures, possibly well beyond the elastic stability considered here.