Cassandra: An open source Monte Carlo package for molecular simulation.

Cassandra is an open source atomistic Monte Carlo software package that is effective in simulating the thermodynamic properties of fluids and solids. The different features and algorithms used in Cassandra are described, along with implementation details and theoretical underpinnings to various methods used. Benchmark and example calculations are shown, and information on how users can obtain the package and contribute to it are provided. © 2017 Wiley Periodicals, Inc.

Beyond histograms: efficiently estimating radial distribution functions via spectral Monte Carlo.

Despite more than 40 years of research in condensed-matter physics, state-of-the-art approaches for simulating the radial distribution function (RDF) g(r) still rely on binning pair-separations into a histogram. Such methods suffer from undesirable properties, including subjectivity, high uncertainty, and slow rates of convergence. Moreover, such problems go undetected by the metrics often used to assess RDFs. To address these issues, we propose (I) a spectral Monte Carlo (SMC) quadrature method that yields g(r) as an analytical series expansion; and (II) a Sobolev norm that assesses the quality of RDFs by quantifying their fluctuations. Using the latter, we show that, relative to histogram-based approaches, SMC reduces by orders of magnitude both the noise in g(r) and the number of pair separations needed for acceptable convergence. Moreover, SMC reduces subjectivity and yields simple, differentiable formulas for the RDF, which are useful for tasks such as coarse-grained force-field calibration via iterative Boltzmann inversion.

Bayesian calibration of coarse-grained forces: Efficiently addressing transferability.

Generating and calibrating forces that are transferable across a range of state-points remains a challenging task in coarse-grained (CG) molecular dynamics. In this work, we present a coarse-graining workflow, inspired by ideas from uncertainty quantification and numerical analysis, to address this problem. The key idea behind our approach is to introduce a Bayesian correction algorithm that uses functional derivatives of CG simulations to rapidly and inexpensively recalibrate initial estimates f0 of forces anchored by standard methods such as force-matching. Taking density-temperature relationships as a running example, we demonstrate that this algorithm, in concert with various interpolation schemes, can be used to efficiently compute physically reasonable force curves on a fine grid of state-points. Importantly, we show that our workflow is robust to several choices available to the modeler, including the interpolation schemes and tools used to construct f0. In a related vein, we also demonstrate that our approach can speed up coarse-graining by reducing the number of atomistic simulations needed as inputs to standard methods for generating CG forces.

Exploring the ability of a multiscale coarse-grained potential to describe the stress-strain response of glassy polystyrene.

A new particle-based bottom-up method to develop coarse-grained models of polymers is presented and applied to polystyrene. The multiscale coarse-graining (MS-CG) technique of Izvekov et al. [J. Chem. Phys. 120, 10896 (2004)] is applied to a polymer system to calculate nonbonded interactions. The inverse Boltzmann inversion method was used to parametrize the bonded and bond-angle bending interactions. Molecular dynamics simulations were performed, and the CG model exhibited a significantly lower modulus compared to the atomistic model at low temperature and high strain rate. In an attempt to improve the CG model performance, several other parametrization schemes were used to build other models from this base model. The first of these models included standard frictional forces through use of the constant-temperature dissipative particle dynamics method that improved the modulus, yet was not transferrable to higher temperatures and lower strain rates. Other models were built by increasing the attraction between CG beads through direct manipulation of the nonbonded potential, where an improvement of the stress response was found. For these models, two parametrization protocols that shifted the force to more attractive values were explored. The first protocol involved a uniform shift, while the other protocol shifted the force in a more localized region. The uniformly shifted potential greatly affected the structure of the equilibrium model as compared to the locally shifted potential, yet was more transferrable to different temperatures and strain rates. Further improvements in the coarse-graining protocol to generate models that more satisfactorily capture mechanical properties are suggested.

Reaction Ensemble Monte Carlo Simulation of Complex Molecular Systems.

Acceptance rules for reaction ensemble Monte Carlo (RxMC) simulations containing classically modeled atomistic degrees of freedom are derived for complex molecular systems where insertions and deletions are achieved gradually by utilizing the continuous fractional component (CFC) method. A self-consistent manner in which to utilize statistical mechanical data contained in ideal gas free energy parameters during RxMC moves is presented. The method is tested by applying it to two previously studied systems containing intramolecular degrees of freedom: the propene metathesis reaction and methyl-tert-butyl-ether (MTBE) synthesis. Quantitative agreement is found between the current results and those of Keil et al. (J. Chem. Phys. 2005, 122, 164705) for the propene metathesis reaction. Differences are observed between the equilibrium concentrations of the present study and those of Lísal et al. (AIChE J. 2000, 46, 866-875) for the MTBE reaction. It is shown that most of this difference can be attributed to an incorrect formulation of the Monte Carlo acceptance rule. Efficiency gains using CFC MC as opposed to single stage molecule insertions are presented.

Fluid phase behavior of a model colloid-polymer mixture: Influence of polymer size and interaction strength.

We examine how the fluid-fluid phase behavior of a model colloid-polymer mixture evolves with variation of polymer size and/or interaction strength. Polymer-polymer interactions are approximated through Gaussian-core potentials while colloid-colloid and colloid-polymer interactions are assumed purely hard. Grand canonical transition matrix Monte Carlo simulation is used to construct binary liquid-liquid phase diagrams for a wide range of polymer sizes and interaction strengths. Overall, our results indicate that independently decreasing the polymer size or increasing the strength of repulsion between polymers have similar effects; these variations lead to an increase in the critical colloid concentration and decrease in the critical polymer concentration. An examination of the phase diagrams collected in this study reduced by their critical reservoir polymer concentration and critical colloid concentration reveals a single common phase envelope that is quantitatively similar to that for common models used to describe simple fluids. Finally, evaluation of the osmotic second virial coefficient in the vicinity of the critical point suggests that this quantity cannot be used as a reliable predictor for the conditions under which colloid-polymer mixtures phase separate.

Phase behavior of model confined fluids. Influence of substrate-fluid interaction strength.

We examine the relationship between the macroscopic phase behavior of nanoconfined fluids and the nature of microscopic interactions between a confining substrate and fluid. Two model slit-pore systems are explored using grand canonical transition-matrix Monte Carlo simulation. One system consists of a square-well fluid interacting with a square-well substrate, and the other contains an embedded point charge model of lysozyme interacting with a mica surface. Fluid phase diagrams are constructed for a broad range of substrate conditions. Our results indicate that one observes a maximum in the critical temperature of the fluid phase envelope upon variation of substrate strength for a given slit width. Both systems studied exhibit such maxima at intermediate wall strength. The physical rationale for this observation suggests that this behavior should be generally expected. We introduce two metrics that enable one to predict conditions that produce maxima in critical temperature. The first is related to the contact angle a fluid develops at a single confining substrate. The second is based upon virial coefficient information and requires knowledge of the substrate-fluid and fluid-fluid interaction potentials only.

Investigation of the phase behavior of an embedded charge protein model through molecular simulation.

The phase behavior of an embedded-charge model for lysozyme developed by Carlsson and co-workers (J. Phys. Chem. B 2001, 105, 9040) is investigated using grand canonical transition matrix Monte Carlo simulation. Within this model, protein-protein interactions are approximated through a combination of hard-sphere repulsion, isotropic hydrophobic attraction, and screened electrostatic interactions through a series of embedded point charges located at the positions of charged amino acid groups within lysozyme. Liquid-liquid phase diagrams are constructed for a wide range of solution conditions and compared with experimental data. Our results indicate that the model is generally capable of describing qualitative trends in the evolution of protein phase behavior with variation of pH and ionic strength. From a quantitative perspective, model estimates for both the change in critical temperature with variation of the solution conditions and the critical concentration do not agree with experimental results. We find the width of model coexistence curves to be independent of solution conditions and narrow relative to experimentally obtained phase envelopes. Connections between the value of the second virial coefficient evaluated at the critical temperature and the location of the liquid-liquid phase envelope are also examined.