The evolution of many systems is dominated by rare activated events that occur on timescale ranging from nanoseconds to the hour or more. For such systems, simulations must leave aside the full thermal description to focus specifically on mechanisms that generate a configurational change. We present here the activation relaxation technique (ART), an open-ended saddle point search algorithm, and a series of recent improvements to ART nouveau and kinetic ART, an ART-based on-the-fly off-lattice self-learning kinetic Monte Carlo method. 1. Introduction There has been considerable interest, in the last two decades, in the development of accelerated numerical methods for sampling the energy landscape of complex materials. The goal is to understand the long-time kinetics of chemical reactions, self-assembly, defect diffusion, and so forth associated with high-dimensional systems counting many tens to many thousands of atoms. Some of these methods are extension of molecular dynamics (MD), such as Voter’s hyperdynamics [1, 2], which provides an accelerated scheme that incorporates directly thermal effects, Laio and Parrinello’s metadynamics [3], an ill-named but successful algorithm that focuses on computing free-energy barriers for specific mechanisms, and basin-hopping by Wales and Doye [4] and Goedecker [5]. Most approaches, however, select to follow transition state theory and treat the thermal contributions in a quasi-harmonic fashion, focusing therefore on the search for transition states and the computation of energy barriers. A number of these methods require the knowledge of both the initial and final states. This is the case, for example, for the nudged-elastic band method [6] and the growing-string method [7]. In complex systems, such approaches are of very limited application to explore the energy landscapes, as by definition few states are known. In these situations, open-ended methods, which more or less follow the prescription first proposed by Cerjan and Miller [8] and Simons et al. [9, 10] for low-dimensional systems, are preferred. Examples are the activation-relaxation technique (ART nouveau) [11–13], which is presented here, but also the eigenvector-following method [14], a hybrid version [15], and the similar dimer method [16]. Once a method is available for finding saddle points and adjacent minima, we must decide what to do with this information. A simple approach is to sample these minima and saddle points and classify the type of events that can take place, providing basic information on the possible evolution of these systems. This
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