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