  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 achieves speedups of
over three orders of magnitude compared to ab initio methods and reduces
prediction errors by up to two orders of magnitude compared to the previous
state-of-the-art. This accuracy 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. Additionally, the
predicted wavefunctions can serve as initial guess in conventional ab initio
methods, decreasing the number of iterations required to arrive at a converged
solution, thus leading to significant speedups without any loss of accuracy or
robustness.
