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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 applications in this contribution, the proposed equivariant framework for deep learning on point clouds is promising also beyond, say, in computer vision or graphics.
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We introduce the SE(3)-Transformer, a variant of the self-attention module for 3D point clouds and graphs, which is equivariant under continuous 3D roto-translations. Equivariance is important to ensure stable and predictable performance in the presence of nuisance transformations of the data input. A positive corollary of equivariance is increased weight-tying within the model. The SE(3)-Transformer leverages the benefits of self-attention to operate on large point clouds and graphs with varying number of points, while guaranteeing SE(3)-equivariance for robustness. We evaluate our model on a toy N-body particle simulation dataset, showcasing the robustness of the predictions under rotations of the input. We further achieve competitive performance on two real-world datasets, ScanObjectNN and QM9. In all cases, our model outperforms a strong, non-equivariant attention baseline and an equivariant model without attention.
Hyperconjugation is a basic conception of chemistry. Its straightforward effect is exhibited by the spatial delocalization characteristics of the electron density distributions or wavefunctions. Such effects on the electron wavefunctions of the highest-occupied molecular orbitals (HOMO) of two ethanol conformers are demonstrated with electron momentum spectroscopy together with natural bond orbital analyses, exhibiting the distinctly different symmetries of the HOMO wavefunctions in momentum space.
This work presents Neural Equivariant Interatomic Potentials (NequIP), a SE(3)-equivariant neural network approach for learning interatomic potentials from ab-initio calculations for molecular dynamics simulations. While most contemporary symmetry-aware models use invariant convolutions and only act on scalars, NequIP employs SE(3)-equivariant convolutions for interactions of geometric tensors, resulting in a more information-rich and faithful representation of atomic environments. The method achieves state-of-the-art accuracy on a challenging set of diverse molecules and materials while exhibiting remarkable data efficiency. NequIP outperforms existing models with up to three orders of magnitude fewer training data, challenging the widely held belief that deep neural networks require massive training sets. The high data efficiency of the method allows for the construction of accurate potentials using high-order quantum chemical level of theory as reference and enables high-fidelity molecular dynamics simulations over long time scales.
When manipulating three-dimensional data, it is possible to ensure that rotational and translational symmetries are respected by applying so-called SE(3)-equivariant models. Protein structure prediction is a prominent example of a task which displays these symmetries. Recent work in this area has successfully made use of an SE(3)-equivariant model, applying an iterative SE(3)-equivariant attention mechanism. Motivated by this application, we implement an iterative version of the SE(3)-Transformer, an SE(3)-equivariant attention-based model for graph data. We address the additional complications which arise when applying the SE(3)-Transformer in an iterative fashion, compare the iterative and single-pa
The ability to reliably predict the structures and stabilities of a molecular crystal and its polymorphs without any prior experimental information would be an invaluable tool for a number of fields, with specific and immediate applications in the design and formulation of pharmaceuticals. In this case, detailed knowledge of the polymorphic energy landscape for an active pharmaceutical ingredient yields profound insight regarding the existence and likelihood of late-appearing polymorphs. However, the computational prediction of the structures and stabilities of molecular crystal polymorphs is particularly challenging due to the high dimensionality of conformational and crystallographic space accompanied by the need for relative (free) energies to within $approx$ 1 kJ/mol per molecule. In this work, we combine the most successful crystal structure sampling strategy with the most accurate energy ranking strategy of the latest blind test of organic crystal structure prediction (CSP), organized by the Cambridge Crystallographic Data Centre (CCDC). Our final energy ranking is based on first-principles density functional theory (DFT) calculations that include three key physical contributions: (i) a sophisticated treatment of Pauli exchange-repulsion and electron correlation effects with hybrid functionals, (ii) inclusion of many-body van der Waals dispersion interactions, and (iii) account of vibrational free energies. In doing so, this combined approach has an optimal success rate in producing the crystal structures corresponding to the five blind-test molecules. With this practical approach, we demonstrate the feasibility of obtaining reliable structures and stabilities for molecular crystals of pharmaceutical importance, paving the way towards an enhanced fundamental understanding of polymorphic energy landscapes and routine industrial application of molecular CSP methods.
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