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Register a new userWell-Tempered Metadynamics: A Smoothly Converging and Tunable Free-Energy Method
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We present a method for determining the free energy dependence on a selected number of collective variables using an adaptive bias. The formalism provides a unified description which has metadynamics and canonical sampling as limiting cases. Convergence and errors can be rigorously and easily controlled. The parameters of the simulation can be tuned so as to focus the computational effort only on the physically relevant regions of the order parameter space. The algorithm is tested on the reconstruction of alanine dipeptide free energy landscape.
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In this paper we propose a new formalism to map history-dependent metadynamics in a Markovian process. We apply this formalism to a model Langevin dynamics and determine the equilibrium distribution of a collection of simulations. We demonstrate that the reconstructed free energy is an unbiased estimate of the underlying free energy and analytically derive an expression for the error. The present results can be applied to other history-dependent stochastic processes such as Wang-Landau sampling.
Sampling complex potential energies is one of the most pressing challenges of contemporary computational science. Inspired by recent efforts that use quantum effects and discretized Feynmans path integrals to overcome large barriers we propose a replica exchange method. In each replica two copies of the same system with halved potential strengths interact via inelastic springs. The strength of the spring is varied in the different replicas so as to bridge the gap between the infinitely strong spring, that corresponds to the Boltzmann replica and the less tight ones. We enhance the spring length fluctuations using Metadynamics. We test the method on simple yet challenging problems.
We propose a general method (based on the Wang-Landau algorithm) to compute numerically free energies that are obtained from the logarithm of the ratio of suitable partition functions. As an application, we determine with high accuracy the order-order interface tension of the four-state Potts model in three dimensions on cubic lattices of linear extension up to L=56. The infinite volume interface tension is then extracted at each beta from a fit of the finite volume interface tension to a known universal behavior. A comparison of the order-order and order-disorder interface tension at the critical value of beta provides a clear numerical evidence of perfect wetting.
We estimated the residual entropy of ice Ih by the recently developed simulation protocol, namely, the combination of Replica-Exchange Wang-Landau algorithm and Multicanonical Replica-Exchange Method. We employed a model with the nearest neighbor interactions on the three-dimensional hexagonal lattice, which satisfied the ice rules in the ground state. The results showed that our estimate of the residual entropy is found to be within 0.038 % of series expansion estimate by Nagle and within 0.000077 % of PEPS algorithm by Vanderstraeten. In this article, we not only give our latest estimate of the residual entropy of ice Ih but also discuss the importance of the uniformity of a random number generator in MC simulations.
In the molecular dynamics calculations for the free energy of ions and ionic molecules, we often encounter wet charged molecular systems where electrical neutrality condition is broken. This causes a problem in the evaluation of electrostatic interaction under periodic boundary condition. A standard remedy for the problem is to consider a hypothetical homogeneous background charge density to neutralize the total system. Here, we present a new expression for the evaluation of electrostatic interactions for the system including the background charge by fast multipole method (FMM). Further, an efficient scheme to evaluate solute-solvent interaction energy by FMM has been developed to reduce the computation of far-field part. We have calculated hydration free energy of ions, Mg$^{2+}$, Na$^{+}$, and Cl$^{-}$ dissolved in neutral solvent using the new expression. The calculated free energy showed a good agreement with the result using well-established particle mesh Ewald method, demonstrating the validity of the present expression in the framework of FMM. An advantage of the present scheme is in an efficient free energy calculation of a large-scale charged systems (particularly over million particles) based on highly parallel computations.
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