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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

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

We provide an overview of the Adaptive Resolution Simulation method (AdResS) based on discussing its basic principles and presenting its current numerical and theoretical developments. Examples of applications to systems of interest to soft matter, chemical physics, and condensed matter illustrate the method’s advantages and limitations in its practical use and thus settle the challenge for further future numerical and theoretical developments. Graphic abstract

The maximum caliber approach implements the maximum entropy principle for trajectories by maximizing a path entropy under external constraints. The maximum caliber approach can be applied to a diverse set of equilibrium and non-equilibrium problems concerning the properties of trajectories connecting different states of a system. In this review, we recapitulate the basic concepts of the maximum entropy principle and of its maximum caliber implementation for path ensembles, and review recent applications of this approach. In particular, we describe how we recently used this approach to introduce a framework, called here the continuum path ensemble maximum caliber (CoPE-MaxCal) method, to impose kinetic constraints in molecular simulations, for instance to include experimental information about transition rates. Such incorporation of dynamical information can ameliorate inaccuracies of empirical force fields, and lead to improved mechanistic insights. We conclude by offering an outlook for future research. Graphic Abstract

A dynamical approach to nonequilibrium molecular dynamics (D-NEMD), proposed in the 1970s by Ciccotti et al., is undergoing a renaissance and is having increasing impact in the study of biological macromolecules. This D-NEMD approach, combining MD simulations in stationary (in particular, equilibrium) and nonequilibrium conditions, allows for the determination of the time-dependent structural response of a system using the Kubo–Onsager relation. Besides providing a detailed picture of the system’s dynamic structural response to an external perturbation, this approach also has the advantage that the statistical significance of the response can be assessed. The D-NEMD approach has been used recently to identify a general mechanism of inter-domain signal propagation in nicotinic acetylcholine receptors, and allosteric effects in β -lactamase enzymes, for example. It complements equilibrium MD and is a very promising approach to identifying and analysing allosteric effects. Here, we review the D-NEMD approach and its application to biomolecular systems, including transporters, receptors, and enzymes. 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.

We present a review of extended Lagrangian Born–Oppenheimer molecular dynamics and its most recent development. The molecular dynamics framework is first derived for general Hohenberg–Kohn density functional theory and it is then presented in explicit forms for thermal Hartree–Fock theory using a density matrix formalism, for self-consistent charge density functional tight-binding theory, and for general non-linear charge relaxation models that can be designed and optimized using modern machine learning methods. Our intention is to give a self-contained but brief and hopefully pedagogical presentation. Graphic abstract

The methodology to simulate transport phenomena in bulk systems is well-established. In contrast, there is no clear consensus about the choice of techniques to model cross-transport phenomena and phoretic transport, mainly because some of the hydrodynamic descriptions are incomplete from a thermodynamic point of view. In the present paper, we use a unified framework to describe diffusio-osmosis(phoresis), and we report non-equilibrium molecular dynamics (NEMD) on such systems. We explore different simulation methods to highlight some of the technical problems that arise in the calculations. For diffusiophoresis, we use two NEMD methods: boundary-driven and field-driven. Although the two methods should be equivalent in the limit of very weak gradients, we find that finite Peclet-number effects are much stronger in boundary-driven flows than in the case where we apply fictitious color forces. Graphic abstract