SE(3)-equivariant prediction of molecular wavefunctions and electronic densities

Abstract

Machine learning has enabled the prediction of quantum chemical properties with high accuracy and efficiency, allowing to bypass computationally costly ab initio calculations. Instead of training on a fixed set of properties, more recent approaches attempt to learn the electronic wavefunction (or density) as a central quantity of atomistic systems, from which all other observables can be derived. This is complicated by the fact that wavefunctions transform non-trivially under molecular rotations, which makes them a challenging prediction target. To solve this issue, we introduce general SE(3)-equivariant operations and building blocks for constructing deep learning architectures for geometric point cloud data and apply them to reconstruct wavefunctions of atomistic systems with unprecedented accuracy. Our model reduces prediction errors by up to two orders of magnitude compared to the previous state-of-the-art and makes it possible to derive properties such as energies and forces directly from the wavefunction in an end-to-end manner. We demonstrate the potential of our approach in a transfer learning application, where a model trained on low accuracy reference wavefunctions implicitly learns to correct for electronic many-body interactions from observables computed at a higher level of theory. Such machine-learned wavefunction surrogates pave the way towards novel semi-empirical methods, offering resolution at an electronic level while drastically decreasing computational cost. While we focus on physics * These authors contributed equally.

Δ-Quantum machine-learning for medicinal chemistry

“…Recent advances in geometric deep learning, such as the development of E(3)-equivariant neural networks, have led to improved prediction accuracy of energies, [26][27][28] forces for molecular dynamics simulations, [29][30][31] and wave functions in the form of local bases of atomic orbitals. 32,33 In parallel to these developments, D-QML (delta-QML) approaches, which aim to learn corrections between computationally inexpensive QM methods and more accurate, albeit more expensive ones, have been shown to deliver promising results. 35 Machine-learned corrections of this kind have been reported for both coupled cluster theory 36,37 via DFT, and for DFT via the semiempirical family of methods GFN-xTB, 38,39 as well as for other combinations.…”

Orbital Mixer: Using Atomic Orbital Features for Basis Dependent Prediction of Molecular Wavefunctions

“…Follow-up work from Gastegger et al (Gastegger et al, 2020) reports improved accuracy on select molecules by applying SchNOrb trained on a minimal basis set representation of molecular wavefunctions. More recently, Unke et al (Unke et al, 2021a) propose PhiSNet, which draws upon insights of SE(3)-equivariant models to maintain that Hamiltonian predictions remain explicitly covariant with respect to rigid rotations or translations while also reporting significantly improved prediction accuracies. Notably, Nigam et al (Nigam et al, 2021) devise similarly equivariant Hamiltonian representations for uses in other applications such as kernel machines.…”

“…Using ML, we can rather directly predict the molecular electronic structure which then provides access to a plethora of these derived properties without needing to train specialized models for each property of interest. Previous works of Schütt et al (Schütt et al, 2019) (SchNOrb) and most recently Unke et al (Unke et al, 2021a) (PhiSNet) present deep learning architectures for predicting molecular wavefunctions and electronic densities by purposing only information of the atomic coordinates and molecular composition. Though inputs to these models rely only on the raw features of the molecule, they are trained on molecular wavefunctions from real quantum chemistry calculations, which necessarily associates the model's predictions with a prescribed basis.…”

Geometric Deep Learning on Molecular Representations

“…Prediction of quantum chemical energies [43][44][45], forces [45][46][47] and wave-functions [48] 3D convolutional neural networks 3D grid Structure-based drug design and property prediction [49][50][51] Mesh convolutional neural networks Surface encoded as a mesh (represented as 2D grid or 3D graph)…”

“…energies [43,44,46,47,[101][102][103], interatomic potentials for molecular dynamics simulations [45,46,104], and wave-functions [48]. SE(3) equivariant neural networks possess reflection-equivariance, and thereby enable the model to distinguish between chiral molecules [99].…”