Exploring equivariant models for electronic properties

In recent years, equivariant machine learning models have emerged as the preferred approach for accurately predicting the electronic properties of materials and molecules. This talk will provide an overview of various equivariant models used for different quantum chemical tasks and discuss how their architectures are adapted based on the specific requirements of each task. We will first examine PhiSNet, a neural network model designed to predict electron densities and wavefunctions. We will highlight the crucial role of equivariant coupling of higher-degree spherical harmonics in achieving accurate predictions of electronic structure and explore how the network architecture can be modified to further enhance accuracy. We will demonstrate how these accurate electronic structure approximations can be leveraged to derive other electronic properties on demand, enabling their application across a broad spectrum of quantum chemical applications. On the other hand, if we are interested in electronic properties that have a simpler structure, such as energies and forces, the coupling of higher-degree spherical harmonics may be unnecessary. For such cases, we introduce SO3krates, a lightweight model that employs only a fraction of the operations commonly found in equivariant networks while maintaining high accuracy and stability, resulting in substantial computational speedup. SO3krates can thus be used to perform long and accurate molecular dynamics simulations with a unique combination of accuracy, stability, and speed, allowing for in-depth analysis of quantum properties of matter over extended time and system size scales.