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In the past two and a half decades machine learning potentials have evolved from a special purpose solution to a broadly applicable tool for large-scale atomistic simulations. By combining the efficiency of empirical potentials and force fields with an accuracy close to first-principles calculations they now enable computer simulations of a wide range of molecules and materials. In this perspective, we summarize the present status of these new types of models for extended systems, which are increasingly used for materials modelling. There are several approaches, but they all have in common that they exploit the locality of atomic properties in some form. Long-range interactions, most prominently electrostatic interactions, can also be included even for systems in which non-local charge transfer leads to an electronic structure that depends globally on all atomic positions. Remaining challenges and limitations of current approaches are discussed. Graphic Abstract

Collective variable-based enhanced sampling methods have been widely used to study thermodynamic properties of complex systems. Efficiency and accuracy of these enhanced sampling methods are affected by two factors: constructing appropriate collective variables for enhanced sampling and generating accurate free energy surfaces. Recently, many machine learning techniques have been developed to improve the quality of collective variables and the accuracy of free energy surfaces. Although machine learning has achieved great successes in improving enhanced sampling methods, there are still many challenges and open questions. In this perspective, we shall review recent developments on integrating machine learning techniques and collective variable-based enhanced sampling approaches. We also discuss challenges and future research directions including generating kinetic information, exploring high-dimensional free energy surfaces, and efficiently sampling all-atom configurations. Graphic abstract

Imaginary-time path-integral or ‘ring-polymer’ methods have been used to simulate quantum (Boltzmann) statistical properties since the 1980s. This article reviews the more recent extension of such methods to simulate quantum dynamics, summarising the chain of approximations that links practical path-integral methods, such as centroid molecular dynamics (CMD) and ring-polymer molecular dynamics (RPMD), to the exact quantum Kubo time-correlation function. We focus on single-surface Born–Oppenheimer dynamics, using the infrared spectrum of water as an illustrative example, but also survey other recent applications and practical techniques, as well as the limitations of current methods and their scope for future development. Graphic abstract

The exact factorization of the time-dependent electron–nuclear wavefunction has been employed successfully in the field of quantum molecular dynamics simulations for interpreting and simulating light-induced ultrafast processes. In this work, we summarize the major developments leading to the formulation of a trajectory-based approach, derived from the exact factorization equations, capable of dealing with nonadiabatic electronic processes, and including spin-orbit coupling and the non-perturbative effect of an external time-dependent field. This trajectory-based quantum-classical approach has been dubbed coupled-trajectory mixed quantum-classical (CT-MQC) algorithm, whose performance is tested here to study the photo-dissociation dynamics of IBr. Graphic abstract

Molecular dynamics simulations often adopt coarse-grained (CG) models to investigate length- and time-scales that cannot be effectively addressed with atomically detailed models. However, the effective potentials that govern CG models are configuration-dependent free energies with significant entropic contributions that have important consequences for the transferability and thermodynamic properties of CG models. This review summarizes recent work investigating the fundamental origin and practical ramifications of these entropic contributions, as well as their sensitivity to the CG mapping. We first analyze the energetic and entropic components of the many-body potential of mean force. By adopting a simple model for protein fluctuations, we examine how these components vary with the CG representation. We then introduce a “dual potential” approach for addressing these entropic considerations in more complex systems, such as ortho-terphenyl (OTP). We demonstrate that this dual approach not only accurately describes the structure and energetic properties of the underlying atomic model, but also accurately predicts the temperature-dependence of the CG potentials. Furthermore, by considering two different CG representations of OTP, we elucidate how these contributions vary with resolution. In sum, we hope this work will prove useful for improving the transferability and thermodynamic properties of CG models for soft materials.

In molecular simulations, the identification of suitable reaction coordinates is central to both the analysis and sampling of transitions between metastable states in complex systems. If sufficient simulation data are available, a number of methods have been developed to reduce the vast amount of high-dimensional data to a small number of essential degrees of freedom representing the reaction coordinate. Likewise, if the reaction coordinate is known, a variety of approaches have been proposed to enhance the sampling along the important degrees of freedom. Often, however, neither one nor the other is available. One of the key questions is therefore, how to construct reaction coordinates and evaluate their validity. Another challenges arises from the physical interpretation of reaction coordinates, which is often addressed by correlating physically meaningful parameters with conceptually well-defined but abstract reaction coordinates. Furthermore, machine learning based methods are becoming more and more applicable also to the reaction coordinate problem. This perspective highlights central aspects in the identification and evaluation of reaction coordinates and discusses recent ideas regarding automated computational frameworks to combine the optimization of reaction coordinates and enhanced sampling. Graphic abstract

In this work, we elaborate on two recently discovered invariance principles, according to which transport coefficients are, to a large extent, independent of the microscopic definition of the densities and currents of the conserved quantities being transported (energy, momentum, mass, charge). The first such principle, gauge invariance , allows one to define a quantum adiabatic energy current from density-functional theory, from which the heat conductivity can be uniquely defined and computed using equilibrium ab initio molecular dynamics. When combined with a novel topological definition of atomic oxidation states , gauge invariance also sheds new light onto the mechanisms of charge transport in ionic conductors. The second principle, convective invariance , allows one to extend the analysis to multi-component systems. These invariance principles can be combined with new spectral analysis methods for the current time series to be fed into the Green–Kubo formula to obtain accurate estimates of transport coefficients from relatively short molecular dynamics simulations. Graphic abstract

We review the materials science applications of the nested sampling (NS) method, which was originally conceived for calculating the evidence in Bayesian inference. We describe how NS can be adapted to sample the potential energy surface (PES) of atomistic systems, providing a straightforward approximation for the partition function and allowing the evaluation of thermodynamic variables at arbitrary temperatures. After an overview of the basic method, we describe a number of extensions, including using variable cells for constant pressure sampling, the semi-grand-canonical approach for multicomponent systems, parallelizing the algorithm, and visualizing the results. We cover the range of materials applications of NS from the past decade, from exploring the PES of Lennard–Jones clusters to that of multicomponent condensed phase systems. We highlight examples how the information gained via NS promotes the understanding of materials properties through a novel way of visualizing the PES, identifying thermodynamically relevant basins, and calculating the entire pressure–temperature(–composition) phase diagram. Graphic abstract

In this article, we review some recent theoretical results about intrusion and extrusion of non-wetting liquids in and out of cavities of nanotextured surfaces and nanoporous materials. Nanoscale confinement allows these processes to happen at conditions which significantly differ from bulk phase coexistence. In particular, the pressure at which a liquid penetrates in and exits from cavities is of interest for many technological applications such as energy storage, dissipation, and conversion, materials with negative compressibility, ion channels, liquid chromatography, and more. Notwithstanding its technological interest, intrusion/extrusion processes are difficult to understand and control solely via experiments: the missing step is often a simple theory capable of providing a microscopic interpretation of the results, e.g., of liquid porosimetry or other techniques used in the field, especially in the case of complex nanoporous media. In this context, simulations can help shedding light on the relation between the morphology of pores, the chemical composition of the solids and liquids, and the thermodynamics and kinetics of intrusion and extrusion. Indeed, the intrusion/extrusion kinetics is determined by the presence of free energy barriers and special approaches, the so-called rare event techniques, must be used to study these processes. Usually, rare event techniques are employed to investigate processes occurring in relatively simple molecular systems, while intrusion/extrusion concerns the collective dynamics of hundreds to thousands of degrees of freedom, the molecules of a liquid entering in or exiting from a cavity, which, from the methodological point of view, is itself a challenge.