Thermally Averaged Magnetic Anisotropy Tensors via Machine Learning Based on Gaussian Moments

Learning QM/MM potential using equivariant multiscale model

The machine learning (ML) method emerges as an efficient and precise surrogate model for high-level electronic structure theory. Its application has been limited to closed chemical systems without considering external potentials from the surrounding environment. To address this limitation and incorporate the influence of external potentials, polarization effects, and long-range interactions between a chemical system and its environment, the first two terms of the Taylor expansion of an electrostatic operator have been used as extra input to the existing ML model to represent the electrostatic environments. However, high-order electrostatic interaction is often essential to account for external potentials from the environment. The existing models based only on invariant features cannot capture significant distribution patterns of the external potentials. Here, we propose a novel ML model that includes high-order terms of the Taylor expansion of an electrostatic operator and uses an equivariant model, which can generate a high-order tensor covariant with rotations as a base model. Therefore, we can use the multipole-expansion equation to derive a useful representation by accounting for polarization and intermolecular interaction. Moreover, to deal with long-range interactions, we follow the same strategy adopted to derive long-range interactions between a target system and its environment media. Our model achieves higher prediction accuracy and transferability among various environment media with these modifications.

Rapid and Accurate Prediction of the Axial Magnetic Anisotropy in Cobalt(II) Complexes Using a Machine-Learning Approach

Estimating the magnetic anisotropy for single-ion magnets is complex due to its multireference nature. This study demonstrates that deep neural networks (DNNs) can provide accurate axial magnetic anisotropy (D) values, closely matching the complete-active-space self-consistent-field (CASSCF) quality using density functional theory (DFT) data. We curated an 86-parameter database (UFF1) with electronic data from over 33000 cobalt(II) compounds. The DNN achieved an R2 of 0.906 and a mean absolute error of 18.1 cm-1 in comparison to reference CASSCF D values. Remarkably, it is 11 times more accurate than DFT methods and 7700 times faster. This approach hints at DNNs predicting the anisotropy in larger molecules, even when trained on smaller ligands.

MDSuite: comprehensive post-processing tool for particle simulations

Particle-Based (PB) simulations, including Molecular Dynamics (MD), provide access to system observables that are not easily available experimentally. However, in most cases, PB data needs to be processed after a simulation to extract these observables. One of the main challenges in post-processing PB simulations is managing the large amounts of data typically generated without incurring memory or computational capacity limitations. In this work, we introduce the post-processing tool: MDSuite. This software, developed in Python, combines state-of-the-art computing technologies such as TensorFlow, with modern data management tools such as HDF5 and SQL for a fast, scalable, and accurate PB data processing engine. This package, built around the principles of FAIR data, provides a memory safe, parallelized, and GPU accelerated environment for the analysis of particle simulations. The software currently offers 17 calculators for the computation of properties including diffusion coefficients, thermal conductivity, viscosity, radial distribution functions, coordination numbers, and more. Further, the object-oriented framework allows for the rapid implementation of new calculators or file-readers for different simulation software. The Python front-end provides a familiar interface for many users in the scientific community and a mild learning curve for the inexperienced. Future developments will include the introduction of more analysis associated with ab-initio methods, colloidal/macroscopic particle methods, and extension to experimental data.

Computational design of magnetic molecules and their environment using quantum chemistry, machine learning and multiscale simulations

Having served as a playground for fundamental studies on the physics of d and f electrons for almost a century, magnetic molecules are now becoming increasingly important for technological applications, such as magnetic resonance, data storage, spintronics and quantum information. All of these applications require the preservation and control of spins in time, an ability hampered by the interaction with the environment, namely with other spins, conduction electrons, molecular vibrations and electromagnetic fields. Thus, the design of a novel magnetic molecule with tailored properties is a formidable task, which does not only concern its electronic structures but also calls for a deep understanding of the interaction among all the degrees of freedom at play. This Review describes how state-of-the-art ab initio computational methods, combined with data-driven approaches to materials modelling, can be integrated into a fully multiscale strategy capable of defining design rules for magnetic molecules.

Ab initio machine learning of phase space averages

Equilibrium structures determine material properties and biochemical functions. We here propose to machine learn phase space averages, conventionally obtained by ab initio or force-field-based molecular dynamics (MD) or Monte Carlo (MC) simulations. In analogy to ab initio MD, our ab initio machine learning (AIML) model does not require bond topologies and, therefore, enables a general machine learning pathway to obtain ensemble properties throughout the chemical compound space. We demonstrate AIML for predicting Boltzmann averaged structures after training on hundreds of MD trajectories. The AIML output is subsequently used to train machine learning models of free energies of solvation using experimental data and to reach competitive prediction errors (mean absolute error ∼ 0.8 kcal/mol) for out-of-sample molecules-within milliseconds. As such, AIML effectively bypasses the need for MD or MC-based phase space sampling, enabling exploration campaigns of Boltzmann averages throughout the chemical compound space at a much accelerated pace. We contextualize our findings by comparison to state-of-the-art methods resulting in a Pareto plot for the free energy of solvation predictions in terms of accuracy and time.

Thermally Averaged Magnetic Anisotropy Tensors via Machine Learning Based on Gaussian Moments

We propose a machine learning method to model molecular tensorial quantities, namely, the magnetic anisotropy tensor, based on the Gaussian moment neural network approach. We demonstrate that the proposed methodology can achieve an accuracy of 0.3-0.4 cm^-1 and has excellent generalization capability for out-of-sample configurations. Moreover, in combination with machine-learned interatomic potential energies based on Gaussian moments, our approach can be applied to study the dynamic behavior of magnetic anisotropy tensors and provide a unique insight into spin-phonon relaxation.