Efficiently exploring a system’s potential energy surface (PES) is essential to match simulated properties to experimental ones. Often, a material is not simply the single most stable structure on the PES, but consists of an ensemble of structures, each representing a metastable minimum on the PES. Improvements in the analytical and predictive power of atomistic simulations necessitate a rigorous sampling of energetically accessible minima. Furthermore, sampling transitions between minima enables simulation of material dynamics, which is key to understanding materials under realistic conditions.

Significant work has gone into developing effective software for global optimization,[1–3] molecular dynamics and metadynamics-based methods,[4–6] and further advanced sampling techniques,[7,8] often prioritizing HPC parallelization. Advances in algorithmic performance have also enhanced sampling efficiency and applicability.[9,10] 

The advent of fast and accurate[11] machine-learned interatomic potentials (MLIPs) has dramatically reduced the computational cost of sampling.[12] Significantly larger numbers of structures can now be explored, compared to ab initio or semi-empirical methods. Furthermore, active learning for MLIPs could be considered PES exploration.[13,14]

This increased speed has resulted in new challenges for PES exploration. Notably, approaches to dealing with large amounts of data. Now, a major computational bottleneck during PES sampling is enforcing diversity via structural comparison over huge datasets.[1,9,15] This requires advances in efficient alternative representations of structures. There have been recent innovations in whole-structure embedding,[1,16,17] and improvements to clustering algorithms.[9,17]

Computational PES exploration has enabled deeper insight into realistic battery and catalyst materials,[6,18–23] as well as exhaustive exploration of crystal structures,[24] and other functional materials.[5,25] PES sampling can also enhance analysis of experimental spectra. Spectra from the sampled atomic environments can be simulated and compared to experiments to identify material structures or dynamics under realistic conditions.[26,27]

System dynamics are also of paramount interest; i.e. exploring how metastable states of a PES are connected. MD-based enhanced sampling can identify such system dynamics.[5,6,28] This approach enables natural sampling of transitions on the PES, including both temperature and anharmonic effects. Thus, they provide accurate dynamics, and can readily explore the convolution between different contributions.[6] However, these approaches are expensive, and can only reach limited timescales.

Alternatively, transition state search (TSS) methods[29–32] explicitly identify saddle points between PES minima. Automation of these TSSs can enable us to efficiently sample even complex barriers for material restructuring.[33,34] This information can be used for kinetic Monte Carlo simulations which can reach longer time-scales,[35] bridging the gap between computational simulation and experimental observations.

Example applications of these techniques include exploring catalytic reaction mechanisms on surfaces,[6,36] identifying structural dynamics of catalytic interfaces under reaction conditions,[33,34,37–40] and exploring material phase transformations. [5,25] Many of these approaches utilize MLIP-accelerated PES sampling.

Recent advances in methodology, both in PES sampling algorithms and high-accuracy MLIP surrogate models allow us to address the complexity of materials like never before. From exploring active catalyst interfaces to batteries and other functional materials under operating conditions, this workshop will marry methodological advances with applications to complex systems, pushing the frontier of realistic modelling of materials.