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Deep neural networks (DNNs) have been used to successfully predict molecularproperties calculated based on the Kohn--Sham density functional theory(KS-DFT). Although this prediction is fast and accurate, we believe that a DNNmodel for KS-DFT must not only predict the properties but also provide theelectron density of a molecule. This letter presents the quantum deep field(QDF), which provides the electron density with an unsupervised but end-to-endphysics-informed modeling by learning the atomization energy on a large-scaledataset. QDF performed well at atomization energy prediction, generated validelectron density, and demonstrated extrapolation. Our QDF implementation isavailable at https://github.com/masashitsubaki/QuantumDeepField_molecule.

physical review letters

Quantum deep field: data-driven wave function, electron density  generation, and atomization energy prediction and extrapolation with machine  learning