  With the recent advances in machine learning for quantum chemistry, it is now
possible to predict the chemical properties of compounds and to generate novel
molecules. Existing generative models mostly use a string- or graph-based
representation, but the precise three-dimensional coordinates of the atoms are
usually not encoded. First attempts in this direction have been proposed, where
autoregressive or GAN-based models generate atom coordinates. Those either lack
a latent space in the autoregressive setting, such that a smooth exploration of
the compound space is not possible, or cannot generalize to varying chemical
compositions. We propose a new approach to efficiently generate molecular
structures that are not restricted to a fixed size or composition. Our model is
based on the variational autoencoder which learns a translation-, rotation-,
and permutation-invariant low-dimensional representation of molecules. Our
experiments yield a mean reconstruction error below 0.05 Angstrom,
outperforming the current state-of-the-art methods by a factor of four, and
which is even lower than the spatial quantization error of most chemical
descriptors. The compositional and structural validity of newly generated
molecules has been confirmed by quantum chemical methods in a set of
experiments.
