Hyperdynamics Method Research Articles

Hyperdynamics simulations with ab initio forces.

By applying the locally optimal rotation method to deal with the lowest eigenvalue of a Hessian matrix, we have efficiently incorporated the hyperdynamics method into the ab initio scheme. In the present method, we only need to calculate the first derivative of the potential and several more force calls in each molecular dynamics (MD) step, which makes hyperdynamics simulation applicable in ab initio MD simulations. With this implementation, we are able to simulate defect diffusion in silicon with boost factors up to 105. We utilized both direct MD and the hyperdynamics method to investigate diffusion of lithium atoms and silicon vacancies in silicon. We identified the complex diffusion process. The obtained diffusion coefficients of Li atoms and Si vacancies are in good agreement with the direct MD results.

Molecular dynamics simulations for initial formation process of polycyclic aromatic hydrocarbons in n-hexane and cyclohexane combustion

Molecular dynamics simulations are conducted to study the initial formation mechanism of polycyclic aromatic hydrocarbon (PAH) in n-hexane and cyclohexane combustion using the ReaxFF reactive force field method and adaptive hyperdynamics method (accelerated molecular dynamics method). The results of the simulations on the fuel-rich conditions indicate that the first 5- or 6-membered ring is formed via entanglement of chain molecules which are formed during the pyrolysis and combustion process. And larger PAHs are generated by repeating attachment and entanglement of these chain molecules.

Hyperdynamics Simulation of the Diffusion of a Vacancy in a Crystal

The diffusion of a vacancy in a deformed aluminum crystal is simulated by the methods of hyperdynamics and classical molecular dynamics. The method used to construct the bias potential for the hyperdynamic method was previously developed for the example of two-dimensional systems using pair potentials. The results indicate the possibility of applying the considered bias potential for the simulation of realistic three-dimensional systems through the use of many-body potentials. The dependences of acceleration of the simulation by the hyperdynamics method in comparison with molecular dynamics on temperature and the bias value of the potential are studied.

Molecular Hyperdynamics Coupled with the Nonorthogonal Tight-Binding Approach: Implementation and Validation.

We present the molecular hyperdynamics algorithm and its implementation to the nonorthogonal tight-binding model NTBM and the corresponding software. Due to its multiscale structure, the proposed approach provides the long time scale simulations (more than 1 s), unavailable for conventional molecular dynamics. No preliminary information about the system's potential landscape is needed for the use of this technique. The optimal interatomic potential modification is automatically derived from the previous simulation steps. The average time between adjusted potential energy fluctuations provides an accurate evaluation of physical time during the hyperdynamics simulation. The main application of the presented hyperdynamics method is the study of thermal-induced defects arising in the middle-sized or relatively large atomic systems at low temperatures. To validate the presented method, we apply it to the C60 cage and its derivative C60NH2. Hyperdynamics leads to the same results as a conventional molecular dynamics, but the former possesses much higher performance and accuracy due to the wider temperature region. The coefficient of acceleration achieves 107 and more.

Accelerated molecular dynamics simulation of large systems with parallel collective variable-driven hyperdynamics

The limitation in time and length scale is a major issue of molecular dynamics (MD) simulation. Although several methods have been developed to extend the MD time scale, their performance usually deteriorates with increasing system size. Therefore, an acceleration method which is applicable to large systems is required to bridge the gap between the MD simulations and target phenomena. In this study, an accelerated MD method for large system is developed based on the collective variable-driven hyperdynamics (CVHD) method [K.M. Bal and E.C. Neyts, 2015]. The key idea is to run CVHD in parallel with rate control and accelerate multiple possible events simultaneously. Using this novel method, carbon diffusion in bcc-iron bicrystal with grain boundary is examined as an application for practical materials. Carbon atoms reaching at the grain boundary are trapped whereas carbon atoms in the bulk region diffuse randomly, and both dynamic regimes can be simultaneously accelerated with the parallel CVHD technique.

On the construction of a bias potential for atomic system simulation by the hyperdynamics method

Hyperdynamics is the method of accelerated molecular dynamics simulation based on lowering energy barriers while performing the dynamic simulation of a nano/atomic system. A system with reduced energy barriers between different states is obtained by changing the potential of interaction, namely, by constructing the so-called bias potential. An approach allowing a bias potential to be obtained is considered. To demonstrate this method, the hyperdynamics simulation of the diffusion of an atom, adsorbed on a 2D crystal surface, and a vacancy, located in its bulk, is carried out. The results are compared with relevant results obtained by molecular dynamics. It is shown that the hyperdynamics approach makes it possible to obtain statistical results, similar to those provided by molecular dynamics. This allows the accelerated simulation of atomic systems to be conducted with minor losses in the accuracy of results.

Assessing Generic Collective Variables for Determining Reaction Rates in Metadynamics Simulations

A persistent challenge in using the metadynamics method is deciding which degrees of freedom, or collective variables, should be biased because these selections are not obvious and require intuition about the system being studied. There are, however, collective variables, which can be constructed with only basic knowledge about the system studied, that provide an opportunity to alleviate this issue. We simulated two different reacting systems where two types of such collective variables (SPRINT coordinates and the collective variable-driven hyperdynamics method) were biased following the infrequent metadynamics method in order to recover the rates of reactions. We demonstrate that both generic collective variables are capable of reproducing the reaction rates of both systems and can enhance the efficiency of the simulation when compared to typical collective variables.

Accelerated molecular dynamics simulations for characterizing plastic deformation in crystalline materials with cracks

Molecular Dynamics (MD) simulations are often used for comprehending evolving deformation mechanisms in materials at the atomic scale and also for assessing continuum-scale material properties. A major limitation of conventional MD simulations is that very small MD time-scale (∼fs), restrict the achievable strain-rates to be much higher (∼107 or higher) than experimentally observed rates, needed for continuum scale modeling, e.g. using crystal plasticity finite element methods. A strain-boost hyperdynamics method based accelerated MD tool is adopted and developed to overcome these limitations. This method biases the atomic system to make it evolve at much faster time-scales and achieve strain-rates that are at least three order of magnitude smaller than the lowest strain-rate achievable in MD. The hyperdynamics algorithm is implemented in a parallel version of LAMMPS, and validated with conventional MD. It is then used to predict evolution of plastic state variables at lower strain-rates for a Nickel single crystal with an embedded atomistic crack. It is shown that at lower strain-rates, not only the evolution of plastic variables are different, but for some configurations there is a shift in the plastic deformation mechanism from twin dominated to dislocation dominated.

Merging metadynamics into hyperdynamics: accelerated molecular simulations reaching time scales from microseconds to seconds.

The hyperdynamics method is a powerful tool to simulate slow processes at the atomic level. However, the construction of an optimal hyperdynamics potential is a task that is far from trivial. Here, we propose a generally applicable implementation of the hyperdynamics algorithm, borrowing two concepts from metadynamics. First, the use of a collective variable (CV) to represent the accelerated dynamics gives the method a very large flexibility and simplicity. Second, a metadynamics procedure can be used to construct a suitable history-dependent bias potential on-the-fly, effectively turning the algorithm into a self-learning accelerated molecular dynamics method. This collective variable-driven hyperdynamics (CVHD) method has a modular design: both the local system properties on which the bias is based, as well as the characteristics of the biasing method itself, can be chosen to match the needs of the considered system. As a result, system-specific details are abstracted from the biasing algorithm itself, making it extremely versatile and transparent. The method is tested on three model systems: diffusion on the Cu(001) surface and nickel-catalyzed methane decomposition, as examples of “reactive” processes with a bond-length-based CV, and the folding of a long polymer-like chain, using a set of dihedral angles as a CV. Boost factors up to 109, corresponding to a time scale of seconds, could be obtained while still accurately reproducing correct dynamics.

Time Recovery for a Complex Process Using Accelerated Dynamics.

The hyperdynamics method (HD) developed by Voter (J. Chem. Phys. 1996, 106, 4665) sets the theoretical basis to construct an accelerated simulation scheme that holds the time scale information. Since HD is based on transition state theory, pseudoequilibrium conditions (PEC) must be satisfied before any system in a trapped state may be accelerated. As the system evolves, many trapped states may appear, and the PEC must be assumed in each one to accelerate the escape. However, since the system evolution is a priori unknown, the PEC cannot be permanently assumed to be true. Furthermore, the different parameters of the bias function used may need drastic recalibration during this evolution. To overcome these problems, we present a general scheme to switch between HD and conventional molecular dynamics (MD) in an automatic fashion during the simulation. To decide when HD should start and finish, criteria based on the energetic properties of the system are introduced. On the other hand, a very simple bias function is proposed, leading to a straightforward on-the-fly set up of the required parameters. A way to measure the quality of the simulation is suggested. The efficiency of the present hybrid HD-MD method is tested for a two-dimensional model potential and for the coalescence process of two nanoparticles. In spite of the important complexity of the latter system (165 degrees of freedoms), some relevant mechanistic properties were recovered within the present method.

Practical hyperdynamics method for systems with large changes in potential energy.

A practical hyperdynamics method is proposed to accelerate systems with highly endothermic and exothermic reactions such as hydrocarbon pyrolysis and oxidation reactions. In this method, referred to as the "adaptive hyperdynamics (AHD) method," the bias potential parameters are adaptively updated according to the change in potential energy. The approach is intensively examined for JP-10 (exo-tetrahydrodicyclopentadiene) pyrolysis simulations using the ReaxFF reactive force field. Valid boost parameter ranges are clarified as a result. It is shown that AHD can be used to model pyrolysis at temperatures as low as 1000 K while achieving a boost factor of around 10(5).

Polymer escape from a confining potential

The rate of escape of polymers from a two-dimensionally confining potential well has been evaluated using self-avoiding as well as ideal chain representations of varying length, up to 80 beads. Long timescale Langevin trajectories were calculated using the path integral hyperdynamics method to evaluate the escape rate. A minimum is found in the rate for self-avoiding polymers of intermediate length while the escape rate decreases monotonically with polymer length for ideal polymers. The increase in the rate for long, self-avoiding polymers is ascribed to crowding in the potential well which reduces the free energy escape barrier. An effective potential curve obtained using the centroid as an independent variable was evaluated by thermodynamic averaging and Kramers rate theory then applied to estimate the escape rate. While the qualitative features are well reproduced by this approach, it significantly overestimates the rate, especially for the longer polymers. The reason for this is illustrated by constructing a two-dimensional effective energy surface using the radius of gyration as well as the centroid as controlled variables. This shows that the description of a transition state dividing surface using only the centroid fails to confine the system to the region corresponding to the free energy barrier and this problem becomes more pronounced the longer the polymer is. A proper definition of a transition state for polymer escape needs to take into account the shape as well as the location of the polymer.

Local hyperdynamics

We present a new formulation of the hyperdynamics method in which the biasing effect is local, making it suitable for large systems. In standard hyperdynamics, the requirement that the bias potential be zero everywhere on the dividing surface bounding the state has the consequence that as the system size increases the boost factor decays to unity, regardless of the form of the bias potential. In the new method, the bias force on each atom is obtained by differentiating a local bias energy that depends only on the coordinates of atoms within a finite range of this atom. This bias force is thus independent of the bias force in distant parts of the system, providing a method that gives a constant boost factor, independent of the system size. We demonstrate for some realistic atomistic systems that the method gives escape rates in excellent agreement with direct molecular dynamics simulations.

Hyper-QC: An accelerated finite-temperature quasicontinuum method using hyperdynamics

The quasicontinuum (QC) method is a spatial multiscale method that extends the length scales accessible to fully atomistic simulations (like molecular dynamics (MD)) by several orders of magnitude. While the recent development of the so-called “hot-QC method” enables dynamic simulations at finite temperature, the times accessible to these simulations remain limited to the sub-microsecond time scale due to the small time step required for stability of the numerical integration. To address this limitation, we develop a novel finite-temperature QC method that can treat much longer time scales by coupling the hot-QC method with hyperdynamics—a method for accelerating time in MD simulations. We refer to the new approach as “hyper-QC”. As in the original hyperdynamics method, hyper-QC is targeted at dynamical systems that exhibit a separation of time scales between short atomic vibration periods and long waiting times in metastable states. Acceleration is achieved by modifying the hot-QC potential energy to reduce the energy barriers between metastable states in a manner that ensures that the characteristic dynamics of the system are preserved. First, the high accuracy of hot-QC in reproducing rare event kinetics is demonstrated. Then, the hyper-QC methodology is validated by comparing hyper-QC results with those of hot-QC and full MD for a one-dimensional chain of atoms interacting via a Lennard–Jones potential.

Adaptive strain-boost hyperdynamics simulations of stress-driven atomic processes

The deformation and failure phenomena of materials are the results of stress-driven, thermally activated processes at the atomic scale. Molecular-dynamics (MD) simulations can only span a very limited time range which hinders one from gaining full view of the deformation physics. Inspired by the Eshelby transformation formalism, we present here a transformation ``strain-boost'' method for accelerating atomistic simulations, which is often more efficient and robust than the bond-boost hyperdynamics method [R. A. Miron and K. A. Fichthorn, J. Chem. Phys. 119, 6210 (2003)] for exploring collective stress-driven processes such as dislocation nucleation, that have characteristic activation volumes larger than one atomic volume. By introducing an adaptive algorithm that safely maximizes the boost factor, we directly access the finite-temperature dynamical process of dislocation nucleation in compressed Cu nanopillar over time scale comparable to laboratory experiments. Our method provides stress- and temperature-dependent activation enthalpy, activation entropy and activation volume for surface-dislocation nucleation with no human guidance about crystallography or deformation physics. Remarkably, the accelerated MD results indicate that harmonic transition-state theory and the empirical Meyer-Neldel compensation rule give reasonable approximations of the dislocation nucleation rate.

Polymer escape from a metastable Kramers potential: Path integral hyperdynamics study

We study the dynamics of flexible, semiflexible, and self-avoiding polymer chains moving under a Kramers metastable potential. Due to thermal noise, the polymers, initially placed in the metastable well, can cross the potential barrier, but these events are extremely rare if the barrier is much larger than thermal energy. To speed up the slow rate processes in computer simulations, we extend the recently proposed path integral hyperdynamics method to the cases of polymers. We consider the cases where the polymers' radii of gyration are comparable to the distance between the well bottom and the barrier top. We find that, for a flexible polymers, the crossing rate (R) monotonically decreases with chain contour length (L), but with the magnitude much larger than the Kramers rate in the globular limit. For a semiflexible polymer, the crossing rate decreases with L but becomes nearly constant for large L. For a fixed L, the crossing rate becomes maximum at an intermediate bending stiffness. For the self-avoiding chain, the rate is a nonmonotonic function of L, first decreasing with L, and then, above a certain length, increasing with L. These findings can be instrumental for efficient separation of biopolymers.

Accelerated molecular dynamics simulation of low-velocity frictional sliding

Accelerated molecular dynamics (MD) simulations are implemented to model the sliding process of atomic force microscope (AFM) experiments and to lower the sliding speeds below those in a conventional MD simulation. In this study the hyperdynamics method, originally devised to extend MD time scales for non-driven systems, is applied to the frictional sliding system. This technique is combined with a parallel algorithm that simultaneously simulates the system over a range of slider positions so that the overall acceleration rate is approximately the number of processors multiplied by the boost factor from the hyperdynamics method. The new methodologies are tested using two-dimensional and three-dimensional Lennard-Jones AFM models. Direct comparison with the results from conventional MD shows close agreement validating the methods. The acceleration rate achieved in this study is four orders of magnitude in 2D and three orders of magnitude in 3D.

Hyperdynamics for entropic systems: Time-space compression and pair correlation function approximation

We develop a generalized hyperdynamics method that is able to simulate slow dynamics in atomistic general (both energy- and entropy-dominated) systems. We show that a few functionals of the pair correlation function, involving two-body entropy, form a low-dimensional collective space, which is a good approximation that is able to distinguish stable and transitional conformations. A bias potential, which raises the energy in stable regions, is constructed on the fly. We examine the slow nucleation processes of a Lennard-Jones gas and show that our method can generate correct long-time dynamics without prior knowledge.