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Register a new userEffective Sampling in the Configurational Space by the Multicanonical-Multioverlap Algorithm
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We propose a new generalized-ensemble algorithm, which we refer to as the multicanonical-multioverlap algorithm. By utilizing a non-Boltzmann weight factor, this method realizes a random walk in the multi-dimensional, energy-overlap space and explores widely in the configurational space including specific configurations, where the overlap of a configuration with respect to a reference state is a measure for structural similarity. We apply the multicanonical-multioverlap molecular dynamics method to a penta peptide, Met-enkephalin, in vacuum as a test system. We also apply the multicanonical and multioverlap molecular dynamics methods to this system for the purpose of comparisons. We see that the multicanonical-multioverlap molecular dynamics method realizes effective sampling in the configurational space including specific configurations more than the other two methods. From the results of the multicanonical-multioverlap molecular dynamics simulation, furthermore, we obtain a new local-minimum state of the Met-enkephalin system.
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We present a novel Ensemble Monte Carlo Growth method to sample the equilibrium thermodynamic properties of random chains. The method is based on the multicanonical technique of computing the density of states in the energy space. Such a quantity is temperature independent, and therefore microcanonical and canonical thermodynamic quantities, including the free energy, entropy, and thermal averages, can be obtained by re-weighting with a Boltzmann factor. The algorithm we present combines two approaches: the first is the Monte Carlo ensemble growth method, where a population of samples in the state space is considered, as opposed to traditional sampling by long random walks, or iterative single-chain growth. The second is the flat-histogram Monte Carlo, similar to the popular Wang-Landau sampling, or to multicanonical chain-growth sampling. We discuss the performance and relative simplicity of the proposed algorithm, and we apply it to known test cases.
We propose two efficient algorithms for configurational sampling of systems with rough energy landscape. The first one is a new method for the determination of the multicanonical weight factor. In this method a short replica-exchange simulation is performed and the multicanonical weight factor is obtained by the multiple-histogram reweighting techniques. The second one is a further extension of the first in which a replica-exchange multicanonical simulation is performed with a small number of replicas. These new algorithms are particularly useful for studying the protein folding problem.
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.
A polymer chain pinned in space exerts a fluctuating force on the pin point in thermal equilibrium. The average of such fluctuating force is well understood from statistical mechanics as an entropic force, but little is known about the underlying force distribution. Here, we introduce two phase space sampling methods that can produce the equilibrium distribution of instantaneous forces exerted by a terminally pinned polymer. In these methods, both the positions and momenta of mass points representing a freely jointed chain are perturbed in accordance with the spatial constraints and the Boltzmann distribution of total energy. The constraint force for each conformation and momentum is calculated using Lagrangian dynamics. Using terminally pinned chains in space and on a surface, we show that the force distribution is highly asymmetric with both tensile and compressive forces. Most importantly, the mean of the distribution, which is equal to the entropic force, is not the most probable force even for long chains. Our work provides insights into the mechanistic origin of entropic forces, and an efficient computational tool for unbiased sampling of the phase space of a constrained system.
Configurational states that are to be associated, according to Goldstein, with the basins in the potential energy landscape cannot be characterized by any particular basin identifier such as the basin minima, the lowest barrier, the most probable energy barrier, etc. since the basin free energy turns out to be independent of the energies of these identifiers. Thus, our analysis utilizes basin free energies to characterize configurational states. When the basin identifier energies are monotonic, we can express the equilibrium basin free energy as a function of an equilibrium basin identifier energy, as we explain, but it is not necessarily unique.
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