Often, the dynamics of complex condensed materials is characterized by the presence of a wide range of different time scales, complicating the study of such processes with computer simulations. Consider, for instance, dynamical processes occurring in liquid water. Here, the fastest molecular processes are intramolecular vibrations with periods in the 10-20 fs range. The translational and rotational motions of water molecules occur on a significantly longer time scale. Typically, the direction of translational motion of a molecule persist for about 500 fs, corresponding to 50 vibrational periods. Hydrogen bonds, responsible for many of the unique properties of liquid water, have an average lifetime of about 1 ps and the rotational motion of water molecules stays correlated for about 10 ps. Much longer time scales are typically involved if covalent bonds are broken and formed. For instance, the average lifetime of a water molecule in liquid water before it dissociates and forms hydroxide and hydronium ions is on the order of 10 hours. This enormous range of time scales, spanning nearly 20 orders of magnitude, is a challenge for the computer simulator who wants to study such processes.

We have successfully applied the transition path sampling method to the deterministic dynamics of a many-body system with long-ranged interactions. The process we investigate, dissociation of a model Na+Cl- ion pair in water, involves a wide range of transition pathways in which collective solvent motions play an important role. Transition states along these pathways encompass a broad distribution of ionic separations. Ion pairs in contact remain associated for ∼20 ps on average, a time scale considerably longer than the ∼3ps predicted by transition state theory with ionic separation as the order parameter. In contrast to theories of barrier crossing based upon frictional effects (with or without memory), we find that the discrepancy between these time scales arises from neglected solvent free energy barriers rather than stochastic buffeting of the ion pair.

The empirical valence bond (EVB) methodology was developed by Warshel and collaborators [1,2], extending earlier ideas of Coulson and Danielsson [3].[1] A. Warshel and R. M. Weiss, J. Am. Chem. Soc. 102, 6218 (1980).

Over the past years high-dimensional neural network potentials (HDNNPs), fitted to accurately reproduce ab initio potential energy surfaces, have become a powerful tool in chemistry, physics and materials science. Here, we focus on the training of the neural networks that lies at the heart of the HDNNP method. We present an efficient approach for optimizing the weight parameters of the neural network via multistream Kalman filtering, using potential energies and forces as reference data. In this procedure, the choice of the free parameters of the Kalman filter can have a significant impact on the fit quality. Carrying out a large parameter study, we determine optimal settings and demonstrate how to optimize training results of HDNNPs. Moreover, we illustrate our HDNNP training approach by revisiting previously presented fits for water and developing a new potential for copper sulfide. This material, accessible in computer simulations so far only via first-principles methods, forms a particularly complex solid structure at low temperatures and undergoes a phase transition to a superionic state upon heating. Analyzing MD simulations carried out with the Cu2S HDNNP, we confirm that the underlying ab initio reference method indeed reproduces this behavior.

Computer simulations of molecular processes such as nucleation in first order phase transitions or the folding of a protein are often complicated by widely disparate time scales related to important but rare events. Here, we will review several recently developed computational methods designed to address the rare-events-problem. In doing so, we will focus on the transition path sampling methodology.

No abstract

Molecular self-organization driven by concerted many-body interactions produces the ordered structures that define both inanimate and living matter. Here we present an autonomous path sampling algorithm that integrates deep learning and transition path theory to discover the mechanism of molecular self-organization phenomena. The algorithm uses the outcome of newly initiated trajectories to construct, validate and—if needed—update quantitative mechanistic models. Closing the learning cycle, the models guide the sampling to enhance the sampling of rare assembly events. Symbolic regression condenses the learned mechanism into a human-interpretable form in terms of relevant physical observables. Applied to ion association in solution, gas-hydrate crystal formation, polymer folding and membrane-protein assembly, we capture the many-body solvent motions governing the assembly process, identify the variables of classical nucleation theory, uncover the folding mechanism at different levels of resolution and reveal competing assembly pathways. The mechanistic descriptions are transferable across thermodynamic states and chemical space.

When gold nanorods are exposed to low-energy laser pulses, they can undergo shape transitions at temperatures below melting. In the present study such transitions are reproduced in molecular dynamics simulations of gold nanorods consisting of 10 3 -10 4 atoms. We find that the shape change is accompanied by a structural change. On the basis of the simulation results, a mechanism is suggested that explains the intermediate products and the internal defects of gold nanorods observed in laser heating experiments.