Molecular crystals are a highly polymorphic class of materials, with a single molecule commonly crystallizing via multiple packing patterns, making structure and property prediction very challenging. Crystal structure prediction typically comprises the production of sets of promising candidate structures, each considered in isolation rather than as samples in a thermodynamic distribution. Likewise, modern generative approaches to this problem, despite naturally sampling distributions of crystals, lack a concrete formulation of the distributions being sampled. Two components are required to impart meaning to the distributions of crystals generated under such models: a canonical parameterization, and a loss function which equilibrates the generated samples to some target distribution. We develop such a parameterization, and train energy-based generative flow networks (GFlowNets) to approximate the Boltzmann distribution over crystal structures for target molecules and space groups. Combined, these components comprise our MXtalGFlow framework for molecular crystal modeling. Going beyond sampling disconnected sets of low-energy structures, MXtalGFlow yields a thermodynamic distribution over crystal structures. We sample and analyze distributions of crystals for two molecules, each under two energy functions, a Lennard-Jones potential and the Universal Model for Atoms. We characterize the local structural basins about the known polymorphs, and identify additional as-yet un-reported packing modes with competitive probabilities to the known experimental structures. With MXtalGFlow, we illustrate how to define and train a model to sample a thermodynamically meaningful distribution of molecular crystals, and analyze such a distribution to glean useful information.
Michael Kilgour, A. Dong, M. Tuckerman et al.· 0 citations
Accurate solvation free energies from molecular dynamics simulations require efficient sampling of coupled slow variables, including solvent coordinates, solute conformational modes, and the alchemical coordinate $\lambda$. Here, we develop a $\lambda$-dynamics framework that combines mass scaling, on-the-fly probability enhanced sampling (OPES), and driven adiabatic free energy dynamics (d-AFED) to address these sampling challenges within a unified protocol. For rigid organic solutes, Hamiltonian replica exchange with mass scaling is first used to quantify the effect of octanol solvent relaxation. Reducing all octanol atomic masses by a factor of ten accelerates convergence by more than fivefold while preserving equilibrium solvation free energies. These calculations then provide reference benchmarks for $\lambda$-OPES, a dual-bias $\lambda$-dynamics strategy that combines the"standard"and"explore"variants of OPES to promote transitions along the alchemical coordinate. This approach reaches convergence on timescales comparable to replica exchange, but without predefined $\lambda$ windows or multiple parallel simulations. For flexible $N$-acetyl amino-acid amide solutes, $\lambda$-OPES is coupled with d-AFED on selected backbone and side-chain dihedrals to enable simultaneous alchemical and conformational enhanced sampling. This combined strategy improves agreement with experimental octanol-water partition coefficients and reduces the mean absolute error from 0.75 log units with $\lambda$-OPES alone to 0.30 log units with $\lambda$-OPES-d-AFED. Overall, this work establishes an integrated enhanced sampling protocol for solvation free energy calculations across rigid organic solutes and flexible peptide-like solutes, and provides a foundation for the application of alchemical free energy methods to larger and more conformationally complex systems.
Gabriela B. Correa, C. Abreu, Nishanth N Nair et al.· 0 citations
