Preface to the special issue on ‘Monte Carlo Codes, Tools and Algorithms’

Monte Carlo molecular simulation is a popular method for studying the properties of a wide variety of molecular systems at equilibrium. Typically, it is possible to carry out simulations of many thousands of molecules on a standard desktop PC, or larger systems with parallel software and machines. However, while the molecular dynamics community has been served by several robust, highly polished and well-known software packages for many years, the corresponding Monte Carlo molecular simulation software is perhaps less well known. This is probably understandable given the differences in approach, but nevertheless the situation with Monte Carlo molecular simulation software has developed to a point in recent years that deserves to be highlighted, with several general-purpose commercial and non-commercial codes currently available. The aim of this special issue on ‘Monte Carlo Codes, Tools and Algorithms’, then, is to provide a resource for the molecular simulation community covering the latest advances in available software and advanced algorithms in this area.

Monte Carlo simulations of equilibrium molecular systems are possible because the underlying probability distribution of microstates is known, and given by the Boltzmann (or Gibbs) distribution. The main issue with this approach is production of a good sample of microstates in order to make accurate and efficient estimates of ensemble averages and free energies. The key idea in this research field, described in the seminal 1953 paper by Metropolis et al. [1], concerns the use of importance sampling to generate the sequence of microstates, i.e. ‘instead of choosing configurations randomly, then weighting them with exp(-E/kT), we choose configurations with a probability exp(-E/kT) and weight them evenly’.[1]

This is vastly more efficient than random selection of microstates for most states of interest. In general, Markov chains and detailed balance are used together to achieve importance sampling according to the Boltzmann/Gibbs distribution. However, the resulting sequence of microstates is now correlated, since only small steps between them can be made. So, one of the main challenges in Metropolis Monte Carlo molecular simulation is to design Monte Carlo moves that traverse phase space in the most efficient manner. This requires insight into the behaviour of a given system, and is likely the reason for the tendency of the research community to develop bespoke codes as needed, as opposed to general-purpose codes.

Several articles in this special issue concern developments of this kind in advanced Monte Carlo moves, including those of Moučka et al. [2], in which multiple particles moves are investigated for efficient sampling of aqueous systems involving polarisable water models, and Cortés Morales et al. [3] who investigated the efficiency of Gibbs simulations with different step sizes.

The key advantage of Metropolis Monte Carlo can also be its Achilles heel, if one desires to access different macrostates (to calculate the difference in free energy between them, for example), since the likelihood of traversing between different macrostates can be very small. In this case, biased sampling can often overcome these problems, and the article by Kumar and Errington [4] uses a scheme of this type involving expanded ensemble simulations to obtain the wetting properties of a model water system. Several other articles in this special issue also include details of biased sampling methods, notably configuration bias and hybrid Monte Carlo.

Although molecular dynamics is still the more popular route to molecular simulations, especially biomolecular simulations, available Monte Carlo software for molecular simulations has become very capable in recent years and the general method has some clear advantages for certain problems, such as phase coexistence, free energy calculations, equilibria in open ensembles and reaction equilibria. In addition, for certain systems with many correlated degrees of freedom, e.g. for polymers or clusters of molecules, an insightful choice of advanced Monte Carlo move can traverse phase space quite efficiently, while for systems involving intermolecular potentials with discrete steps or hard cores, Monte Carlo simulation, which does not require calculation of forces, is an obvious choice.

The remaining articles, except one, in this special issue feature several of these publicly available codes, and their associated tools. Two articles describe the capability of commercial Monte Carlo molecular simulation codes, namely components and tools within the Materials Studio suite of software developed by Accelrys,[5] and the MedeA®-GIBBS [6] software developed by Materials Design. Three more articles describe freely available software developed by members of the Monte Carlo simulation research community, along with the issues that arise in the development and support of such software. These are: (i) MCCCS Towhee,[7] developed by the Siepmann research group (including Marcus Martin) at the University of Minnesota, (ii) Music, [8] developed by the Snurr research group at Northwestern University and beyond and (iii) Faunus, [9] a recently released software developed at Lund university with a particularly interesting and flexible architecture. Another article describes the recent DL_Monte code, [10] developed by the Science and Technology Facilities Council, UK, at their Daresbury Laboratory (particularly by John Purton) for the molecular simulation community. Each code described here incorporates a somewhat different selection of advanced Monte Carlo moves, biasing techniques and force fields, and so is suited to specific problems. Most of these codes have been designed to operate in tandem with molecular dynamics codes, i.e. they can share standard output files or can use the same force fields, so that simulations can be carried out with molecular dynamics or Monte Carlo methods according to the demands of a particular problem. Moreover, some recent Monte Carlo codes (DL_Monte and MedeA®-GIBBS in particular) are parallelised using OpenMP and/or MPI methods.

The final article in this special issue, a review by Dubbeldam et al. [11], provides an excellent introduction to Monte Carlo molecular simulation for the novice as well as an insightful refresher for the more experienced. It covers many of the issues outlined in this preface, such as advanced Monte Carlo moves and biased sampling techniques, as well advice for those developing their own Monte Carlo molecular simulation software. I recommend reading this article first.