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Register a new userRethinking Metadynamics: from bias potentials to probability distributions
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Metadynamics is an enhanced sampling method of great popularity, based on the on-the-fly construction of a bias potential that is function of a selected number of collective variables. We propose here a change in perspective that shifts the focus from the bias to the probability distribution reconstruction, while keeping some of the key characteristics of metadynamics, such as the flexible on-the-fly adjustments to the free energy estimate. The result is an enhanced sampling method that presents a drastic improvement in convergence speed, especially when dealing with suboptimal and/or multidimensional sets of collective variables. The method is especially robust and easy to use, in fact it requires only few simple parameters to be set, and it has a straightforward reweighting scheme to recover the statistics of the unbiased ensemble. Furthermore it gives more control on the desired exploration of the phase space, since the deposited bias is not allowed to grow indefinitely and it does not push the simulation to uninteresting high free energy regions. We demonstrate the performance of the method in a number of representative examples.
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The universal mathematical form of machine-learning potentials (MLPs) shifts the core of development of interatomic potentials to collecting proper training data. Ideally, the training set should encompass diverse local atomic environments but the conventional approach is prone to sampling similar configurations repeatedly, mainly due to the Boltzmann statistics. As such, practitioners handpick a large pool of distinct configurations manually, stretching the development period significantly. Herein, we suggest a novel sampling method optimized for gathering diverse yet relevant configurations semi-automatically. This is achieved by applying the metadynamics with the descriptor for the local atomic environment as a collective variable. As a result, the simulation is automatically steered toward unvisited local environment space such that each atom experiences diverse chemical environments without redundancy. We apply the proposed metadynamics sampling to H:Pt(111), GeTe, and Si systems. Throughout the examples, a small number of metadynamics trajectories can provide reference structures necessary for training high-fidelity MLPs. By proposing a semi-automatic sampling method tuned for MLPs, the present work paves the way to wider applications of MLPs to many challenging applications.
We present a method to sample reactive pathways via biased molecular dynamics simulations in trajectory space. We show that the use of enhanced sampling techniques enables unconstrained exploration of multiple reaction routes. Time correlation functions are conveniently computed via reweighted averages along a single trajectory and kinetic rates are accessed at no additional cost. These abilities are illustrated analyzing a model potential and the umbrella inversion of NH$_3$ in water. The algorithm allows a parallel implementation and promises to be a powerful tool for the study of rare events.
We show how standard Metadynamics coupled with classical Molecular Dynamics can be successfully ap- plied to sample the configurational and free energy space of metallic and bimetallic nanopclusters via the implementation of collective variables related to the pair distance distribution function of the nanoparticle itself. As paradigmatic examples we show an application of our methodology to Ag147, Pt147 and their alloy AgshellPtcore at 1:1 and 2:1 chemical compositions. The proposed scheme is not only able to reproduce known structural transformation pathways, as the five and the six square-diamond mechanisms both in pure and core-shell nanoparticles but also to predict a new route connecting icosahedron to anti-cuboctahedron.
The functional method to derive the fractional Fokker-Planck equation for probability distribution from the Langevin equation with Levy stable noise is proposed. For the Cauchy stable noise we obtain the exact stationary probability density function of Levy flights in different smooth potential profiles. We find confinement of the particle in the superdiffusion motion with a bimodal stationary distribution for all the anharmonic symmetric monostable potentials investigated. The stationary probability density functions show power-law tails, which ensure finiteness of the variance. By reviewing recent results on these statistical characteristics, the peculiarities of Levy flights in comparison with ordinary Brownian motion are discussed.
In this paper we introduce and analyse Langevin samplers that consist of perturbations of the standard underdamped Langevin dynamics. The perturbed dynamics is such that its invariant measure is the same as that of the unperturbed dynamics. We show that appropriate choices of the perturbations can lead to samplers that have improved properties, at least in terms of reducing the asymptotic variance. We present a detailed analysis of the new Langevin sampler for Gaussian target distributions. Our theoretical results are supported by numerical experiments with non-Gaussian target measures.
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