Scalar fields, such as electron densities and potential energies, are fundamental for determining material properties. The structure and dynamics of materials are governed by the complex shapes of potential energy landscapes experienced by individual atoms [1]. In particular, the configurations of particles within a solid are determined by the shapes and presence of energetic basins, while the self-diffusion of mobile particles is defined by the connectivity of these basins. Understanding atomistic diffusion is crucial for applications such as ion-conduction in solid-state batteries and solar cells, as well as for separation processes like carbon capture and water purification. The analysis of bonds based on the shape of scalar fields derived from electron densities enables an assessment of a material’s stability.
In a collaboration led by Senja Barthel (mathematics department at VU Amsterdam) and Amber Mace (Angstrom laboratory at Uppsala University), a computational multi-scale method is being developed to automatically generate geometric and topological descriptors from scalar fields [2,3]. This includes decomposing sub-level sets into basins and transition states, detecting transition rates, and identifying diffusion paths. The method has been successfully applied to study gas diffusion in crystalline nanoporous materials [2], Li-ion transport in solid-state batteries [3], and has provided a tool for the quantitative comparison of bond formation in materials under varying pressures [4]. Furthermore, the derived geometric and topological descriptors can be utilized for machine learning studies [5]. These studies demonstrate that exploring mass-transport through a geometrical lens holds promise for improving modeling methodologies and enhancing our understanding of structure-dynamic property relationships.
Despite recent progress [6], many challenges remain in achieving relevant length and time scales necessary for studying complex materials. In the future, the project will focus on methodological improvements for flexible and compound materials.
[1] F. Schwarz, S. Barthel, A. Mace, Understanding Mobile Particles in Solid-Sate Materials: From the Perspective of Potential Energy Surfaces, Chemistry of Materials 36 (23), 11359-11376 (2024)
[2] A. Mace, S. Barthel, B. Smit, Automated multiscale approach to predict self-diffusion from a potential energy field, Journal of Chemical Theory and Computation 15 (4), 2127-2141 (2019)
[3] H. Gustafsson, M. Kozdra, B. Smit, S. Barthel, A. Mace, Predicting Ion Diffusion from the Shape of Potential Energy Landscapes, Journal of Chemical Theory and Computation 20 (1), 18-29 (2023)
[4] B. Meyer, S. Barthel, A. Mace, L. Vanity, B. Guillot, B. Smit, C. Corminboef, DORI Reveals the Influence of Noncovalent Interactions on Covalent Bonding Patterns in Molecular Crystals Under Pressure, Journal of physical chemistry letters 10 (7), 1482-1488 (2019)
[5] E. Ren, F.-X. Coudert, Prediction of the Diffusion Coefficient through Machine Learning Based on Transition-State Theory Descriptors, Journal of Physical Chemistry C 128 (16), 6917-6926 (2024)
[6] H. Gustafsson, F. Schwarz, T. Smolders, S. Barthel, A. Mace, Computationally efficient DFT-based sampling of ion diffusion in crystalline solids, ChemRxiv (2024)