Vapor-Liquid Phase Equilibria Using Monte Carlo Wang-Landau Simulations

The experimental determination of the critical point of metals is inherently connected with difficulties of measuring large temperatures and pressures. On the other hand, that of straight alkane chains larger than ten carbon atoms and branched chains larger than eight atoms is burdensome due to decomposition of the molecules while in the vapor phase. Therefore molecular simulations stand as an appropriate alternative for determining the critical point and phase coexistence properties of these fluids. Most simulation methods that are apt for this task rely on particles insertion and deletion moves that can significantly complicate the simulation, since high density in the liquid phases restrains this type of move. In our simulation this issue is avoided by combining the Wang-Landau (WL) sampling method in the NPT ensemble with efficient techniques for simulating dense liquid regions, such as configurational bias Monte Carlo (CBMC) and hybrid Monte Carlo (HMC). We simulate the liquid-vapor equilibria curves of copper and branched alkanes, isobutane and isopentane, by combining the HMC technique with the WL sampling. The standard boiling points of n-alkanes such as eicosane, tetracosane and triacontane are simulated by implementing the CBMC technique in the WL method in order to sample efficiently the various conformations of the long chain molecules. For copper we obtain a critical temperature Tc=5695 ± 50 K, critical pressure Pc=1141 ± 100 bar and critical density Ρc=1.80 ± 0.03 g/cm3. All of these values lie within the range of experimental data. The vapor-liquid equilibria curves and critical points of the branched alkanes are in excellent agreement with experimental data as well as simulation results using the Gibbs ensemble Monte Carlo method. The boiling points of the above listed n-alkanes also show good match with experimental data, with deviations in the range of 2 to 3 %. The WL simulations in the NPT ensemble is a simple and robust method for establishing vapor-liquid phase diagrams, as a single simulation run is necessary to evaluate the properties at a given temperature and for a large variety of substances. Its reliability is proven by the good agreement between experimental and simulation results

Advanced Monte Carlo simulation techniques to study polymers under equilibrium conditions

The advances in materials and biological sciences have necessitated the use of molecular simulations to study polymers. The Markov chain Monte Carlo simulations enable the sampling of relevant microstates of polymeric systems by traversing paths that are impractical in molecular dynamics simulations. Several advances in applying Monte Carlo simulations to polymeric systems have been reported in recent decades. The proposed methods address sampling challenges encountered in studying different aspects of polymeric systems. Tracking the above advances has become increasingly challenging due to the extensive literature generated in the field. Moreover, the incorporation of new methods in the existing Monte Carlo simulation packages is cumbersome due to their complexity. Identifying the foundational algorithms that are common to different methods can significantly ease their implementation and make them accessible to the broader simulation community. The present chapter classifies the Monte Carlo methods for polymeric systems based on their objectives and standard features of their algorithms. We begin the article by providing an overview of advanced Monte Carlo techniques used for polymeric systems and their specific applications. We then classify the above techniques into two broad categories: 1) Monte Carlo moves and 2) Advanced sampling schemes. The former category is further divided to distinguish the Monte Carlo moves in the canonical and other ensembles. The advanced sampling schemes attempt to improve Monte Carlo sampling via approaches other than Monte Carlo moves. We use the above classification to identify common features of the methods and derive general expressions that explain their implementation. Such a strategy can help readers select the methods that are suitable for their study and develop computer programs that can be easily modified to implement new methods.Comment: 22 pages, 4 figures, 2 table

Ensemble of expanded ensembles: A generalized ensemble approach with enhanced flexibility and parallelizability

Over the past decade, alchemical free energy methods like Hamiltonian replica exchange (HREX) and expanded ensemble (EXE) have gained popularity for the computation of solvation free energies and binding free energies. These methods connect the end states of interest via nonphysical pathways defined by states with different modified Hamiltonians. However, there exist systems where traversing all alchemical intermediate states is challenging, even if alchemical biases (e.g., in EXE) or coordinate exchanges (e.g., in HREX) are applied. This issue is exacerbated when the state space is multidimensional, which can require extensive communications between hundreds of cores that current parallelization schemes do not fully support. To address this challenge, we present the method of ensemble of expanded ensembles (EEXE), which integrates the principles of EXE and HREX. Specifically, the EEXE method periodically exchanges coordinates of EXE replicas sampling different ranges of states and allows combining weights across replicas. With the solvation free energy calculation of anthracene, we show that the EEXE method achieves accuracy akin to the EXE and HREX methods in free energy calculations, while offering higher flexibility in parameter specification. Additionally, its parallelizability opens the door to wider applications, such as estimating free energy profiles of serial mutations. Importantly, extensions to the EEXE approach can be done asynchronously, allowing looser communications between larger numbers of loosely coupled processors, such as when using cloud computing, than methods such as replica exchange. They also allow adaptive changes to the parameters of ensembles in response to data collected. All algorithms for the EEXE method are available in the Python package ensemble_md, which offers an interface for EEXE simulation management without modifying the source code in GROMACS

A Tutorial on Advanced Dynamic Monte Carlo Methods for Systems with Discrete State Spaces

Advanced algorithms are necessary to obtain faster-than-real-time dynamic simulations in a number of different physical problems that are characterized by widely disparate time scales. Recent advanced dynamic Monte Carlo algorithms that preserve the dynamics of the model are described. These include the $n$-fold way algorithm, the Monte Carlo with Absorbing Markov Chains (MCAMC) algorithm, and the Projective Dynamics (PD) algorithm. To demonstrate the use of these algorithms, they are applied to some simplified models of dynamic physical systems. The models studied include a model for ion motion through a pore such as a biological ion channel and the metastable decay of the ferromagnetic Ising model. Non-trivial parallelization issues for these dynamic algorithms, which are in the class of parallel discrete event simulations, are discussed. Efforts are made to keep the article at an elementary level by concentrating on a simple model in each case that illustrates the use of the advanced dynamic Monte Carlo algorithm.Comment: 53 pages, 17 figure