Monte Carlo free energy estimates using non-Boltzmann sampling: Application to the sub-critical Lennard-Jones fluid
TL;DR: In this paper, the free energy of a Lennard-Jones fluid in the liquid-vapour coexistence region was estimated by relating it to that of the inverse-twelve (soft sphere) fluid, which itself shows no condensation.
About: This article is published in Chemical Physics Letters.The article was published on 1974-10-15. It has received 1179 citations till now. The article focuses on the topics: Direct simulation Monte Carlo & Monte Carlo molecular modeling.
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TL;DR: An overview of the CHARMM program as it exists today is provided with an emphasis on developments since the publication of the original CHARMM article in 1983.
Abstract: CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecu- lar simulation program. It has been developed over the last three decades with a primary focus on molecules of bio- logical interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estima- tors, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numer- ous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.
7,035 citations
TL;DR: The Weighted Histogram Analysis Method (WHAM) as mentioned in this paper is an extension of Ferrenberg and Swendsen's multiple histogram technique for complex biomolecular Hamiltonians.
Abstract: The Weighted Histogram Analysis Method (WHAM), an extension of Ferrenberg and Swendsen's Multiple Histogram Technique, has been applied for the first time on complex biomolecular Hamiltonians. The method is presented here as an extension of the Umbrella Sampling method for free-energy and Potential of Mean Force calculations. This algorithm possesses the following advantages over methods that are currently employed: (1) It provides a built-in estimate of sampling errors thereby yielding objective estimates of the optimal location and length of additional simulations needed to achieve a desired level of precision; (2) it yields the “best” value of free energies by taking into account all the simulations so as to minimize the statistical errors; (3) in addition to optimizing the links between simulations, it also allows multiple overlaps of probability distributions for obtaining better estimates of the free-energy differences. By recasting the Ferrenberg–Swendsen Multiple Histogram equations in a form suitable for molecular mechanics type Hamiltonians, we have demonstrated the feasibility and robustness of this method by applying it to a test problem of the generation of the Potential of Mean Force profile of the pseudorotation phase angle of the sugar ring in deoxyadenosine. © 1992 by John Wiley & Sons, Inc.
5,784 citations
TL;DR: In this paper, the authors describe the use of arbitrary sampling distributions chosen to facilitate the estimate of the free energy difference between a model system and some reference system, but the conventional Monte Carlo methods of obtaining such averages are inadequate for the free-energy case.
5,058 citations
IBM1
TL;DR: Near-optimal strategies are developed for estimating the free energy difference between two canonical ensembles, given a Metropolis-type Monte Carlo program for sampling each one, and their efficiency is never less or greater than that obtained by sampling only one ensemble.
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TL;DR: In this paper, the pressure and entropy for soft-sphere particles interacting with an inverse twelfth-power potential were determined using the Monte Carlo method, and the results were compared with the predictions of the virial series, lattice dynamics, perturbation theories, and cell models.
Abstract: The pressure and entropy for soft‐sphere particles interacting with an inverse twelfth‐power potential are determined using the Monte Carlo method. The solid‐phase entropy is calculated in two ways: by integrating the single‐occupancy equation of state from the low density limit to solid densities, and by using solid‐phase Monte Carlo pressures to evaluate the anharmonic corrections to the lattice‐dynamics high‐density limit. The two methods agree, and the entropy is used to locate the melting transition. The computed results are compared with the predictions of the virial series, lattice dynamics, perturbation theories, and cell models. For the fluid phase, perturbation theory is very accurate up to two‐thirds of the freezing density. For the solid phase, a correlated cell model predicts pressures very close to the Monte Carlo results.
287 citations
TL;DR: In this article, a method for estimating the free energy and entropy of an assembly of particles is described, which is done by using Metropolis Monte Carlo techniques to generate energy distributions from which we may calculate the absolute volume of configuration space corresponding to a given energy, and thus the configuration integral.
Abstract: A method is described for estimating the free energy and entropy of an assembly of particles. This is done by using Metropolis Monte Carlo techniques to generate energy distributions from which we may calculate the absolute volume of configuration space corresponding to a given energy, and thus the configuration integral. One incidentally obtains the thermodynamic quantities over a wide range of reduced temperature. It is particularly easy to apply the method to particles having hard cores, and calculations are reported for hard spheres with Coulombic forces.
238 citations
TL;DR: In this article, Monte Carlo free energy results for a fluid of point dipoles embedded in hard spheres are reported for a multistage sampling method compared with thermodynamic integration techniques, and the resulting free energies are compared with recent theoretical results obtained from the mean spherical model approximation and from a perturbation theory approach.
118 citations
TL;DR: In this paper, a Monte Carlo method for the evaluation of equilibrium thermodynamic properties of a system of interacting particles is described, where the classical configurational partition function at a given density is calculated from the estimated value of the weight function γ(Φ), up to a factor that is independent of temperature.
Abstract: A Monte Carlo method for the evaluation of equilibrium thermodynamic properties of a system of interacting particles is described. The classical configurational partition function at a given density is calculated from the estimated value of the weight function γ(Φ), up to a factor that is independent of temperature; γ(Φ)dΦ is the fraction of all accessible configurations of N particles confined to a fixed volume for which the total potential energy has a value between Φ and Φ+dΦ. The weight function is found to vary approximately as (Φ—Φ0)n, where Φ0 and n are constants; n increases roughly linearly with density. The method is applied to the calculation of thermodynamic properties of gaseous argon at four densities in the temperature range between −100° and 150°C. A Lennard‐Jones potential function is used and though the agreement with experiment is good there is evidence of inadequacy in the Leonnard‐Jones model. All calculations are made for N=32.
93 citations
TL;DR: In this article, it was shown that the Lennard-Jones 12-6 potential with the parameters proposed by Michels et al. leads to internal energies and pressures which are in fair agreement with the experimental values.
Abstract: Monte Carlo calculations of thermodynamic properties of argon are reported for the temperature range between the triple point and the critical temperature at pressures up to 700 atm. It is shown that the Lennard‐Jones 12–6 potential with the parameters proposed by Michels et al., viz., e / k = 119.8°K and σ = 3.405 A, leads to internal energies and pressures which are in fair agreement with the experimental values. The over‐all agreement with experiment may be substantially improved by reducing the depth of the potential well to e / k = 117.2°K. The use of other potentials, the importance of nonadditivity corrections, and the agreement between the Monte Carlo results and those obtained by the method of molecular dynamics are briefly discussed.
82 citations