Flat-histogram extrapolation as a useful tool in the age of big data

Monte Carlo molecular simulations with FEASST version 0.25.1

FEASST is an open-source Monte Carlo software package for particle-based simulations. This software, which was released in 2017, has been used to study phase equilibrium, self-assembly, aggregation or gelation in biological materials, colloids, polymers, ionic liquids, and adsorption in porous networks. We highlight some of the unique features available in FEASST, such as flat-histogram grand canonical ensemble, Gibbs ensemble, and Mayer-sampling simulations with support for anisotropic models and parallelization with flat-histogram and prefetching. We also discuss how the challenges of supporting a variety of Monte Carlo algorithms were overcome by an object-oriented design. This also allows others to extend classes, which improves software interoperability, as inspired by LAMMPS classes and user packages. This article describes version 0.25.1 with benchmarks, compilation instructions, and introductory tutorials for running, restarting, and testing simulations, user guidelines, software design strategies, alternative interfaces, and the test-driven development strategy.

Temperature Extrapolation of Henry's Law Constants and the Isosteric Heat of Adsorption

Computational screening of adsorbent materials often uses the Henry's law constant (K_H) (at a particular temperature) as a first discriminator metric due to its relative ease of calculation. The isosteric heat of adsorption in the limit of zero pressure (q_st^∞) is often calculated along with the Henry's law constant, and both properties are informative metrics of adsorbent material performance at low-pressure conditions. In this article, we introduce a method for extrapolating K_H as a function of temperature, using series-expansion coefficients that are easily computed at the same time as K_H itself; the extrapolation function also yields q_st^∞. The extrapolation is highly accurate over a wide range of temperatures when the basis temperature is sufficiently high, for a wide range of adsorbent materials and adsorbate gases. Various results suggest that the extrapolation is accurate when the extrapolation range in inverse-temperature space is limited to |β - β₀ | < 0.5 mol/kJ. Application of the extrapolation to a large set of materials is shown to be successful provided that K_H is not extremely large and/or the extrapolation coefficients converge satisfactorily. The extrapolation is also able to predict q_st^∞ for a system that shows an unusually large temperature dependence. The work provides a robust method for predicting K_H and q_st^∞ over a wide range of industrially relevant temperatures with minimal effort beyond that necessary to compute those properties at a single temperature, which facilitates the addition of practical operating (or processing) conditions to computational screening exercises.

Direct free energy evaluation of classical and quantum many-body systems via field-theoretic simulation

The accurate evaluation of free energies within molecular simulations is important to many scientific fields, including fluid and solid phase equilibria, biomolecular condensates, and quantum phase transitions, among others. Unfortunately, free energy estimation is tedious and computationally expensive for molecular models whose degrees of freedom are expressed in particle coordinates. We show that alternative representations of a model as a classical or quantum field theory provide access to a chemical potential operator that can be averaged to yield a direct and low-cost estimate of the Gibbs free energy. The averaging is performed using a “field-theoretic” computer simulation that employs fluctuating fields rather than particles.

Free energy evaluation in molecular simulations of both classical and quantum systems is computationally intensive and requires sophisticated algorithms. This is because free energy depends on the volume of accessible phase space, a quantity that is inextricably linked to the integration measure in a coordinate representation of a many-body problem. In contrast, the same problem expressed as a field theory (auxiliary field or coherent states) isolates the particle number as a simple parameter in the Hamiltonian or action functional and enables the identification of a chemical potential field operator. We show that this feature leads a “direct” method of free energy evaluation, in which a particle model is converted to a field theory and appropriate field operators are averaged using a field-theoretic simulation conducted with complex Langevin sampling. These averages provide an immediate estimate of the Helmholtz free energy in the canonical ensemble and the entropy in the microcanonical ensemble. The method is illustrated for a classical polymer solution, a block copolymer melt exhibiting liquid crystalline and solid mesophases, and a quantum fluid of interacting bosons.

On the calculation of free energies over Hamiltonian and order parameters via perturbation and thermodynamic integration

In this work, complementary formulas are presented to compute free-energy differences via perturbation (FEP) methods and thermodynamic integration (TI). These formulas are derived by selecting only the most statistically significant data from the information extractable from the simulated points involved. On the one hand, commonly used FEP techniques based on overlap sampling leverage the full information contained in the overlapping macrostate probability distributions. On the other hand, conventional TI methods only use information on the first moments of those distributions, as embodied by the first derivatives of the free energy. Since the accuracy of simulation data degrades considerably for high-order moments (for FEP) or free-energy derivatives (for TI), it is proposed to consider, consistently for both methods, data up to second-order moments/derivatives. This provides a compromise between the limiting strategies embodied by common FEP and TI and leads to simple, optimized expressions to evaluate free-energy differences. The proposed formulas are validated with an analytically solvable harmonic Hamiltonian (for assessing systematic errors), an atomistic system (for computing the potential of mean force with coordinate-dependent order parameters), and a binary-component coarse-grained model (for tracing a solid-liquid phase diagram in an ensemble sampled through alchemical transformations). It is shown that the proposed FEP and TI formulas are straightforward to implement, perform similarly well, and allow robust estimation of free-energy differences even when the spacing of successive points does not guarantee them to have proper overlapping in phase space.