Fig. 1. Network architecture and learned representations. (a) Scheme of the network blocks for generating the field-dependent representation. Starting from an initial representation of atom types and zero vectors for the dipole features, the conventional SchNet features x_i are augmented by a set of local dipole features μ_i. Interactions between the dipole features and the dipole features with the external field are used to update the representation x^T_i in each layer. (b) The energies are predicted from the final set of features based on a sum of atomic contributions. By applying the appropriate derivative operations to the energy, different response properties can be computed, such as molecular forces F, dipole moments μ, polarizabilities α and shielding tensors σ_i. (c) Schematic comparison of charge and dipole based interactions in the water molecule shown for the whole molecule (top) and the oxygen atom (bottom). The introduction of dipoles allows for a more fine grained spatial resolution of the environment which is particularly clear to see in the case of the atomic oxygen contributions where charge like features only capture radial dependencies. (d) Representations for a hydrogen probe at position R projected onto a ∑_i|R_i − R|² isosurface, shown for the ethanol molecule. From top to bottom: FieldSchNet descriptor without an external field, FieldSchNet descriptor in the presence of an external field applied to the z-plane of the molecule and response of the descriptor with respect to the z-component of an external field.