The efficacy of machine learning methods critically depends on developing an appropriate
kernel, or equivalently, on identifying relevant features in the input space that are used to com-
pare data items. In the context of materials modelling, the input space of all possible molecules
and solids is vast. We can drastically reduce the learning task by focussing on local atomic
environments instead, and using a kernel between local environments as a building block.
We use the Smooth Overlap of Atomic Positions (SOAP) kernel, which is the overlap in-
tegral of the neighbour density within a finite cutoff rc, smoothed by a Gaussian with a length
scale governed by the interatomic spacing, and finally integrated over all 3D rotations and nor-
malised. This kernel is equivalent to the scalar product of the spherical power spectra of the
neighbour density (15), which therefore constitutes a chemical descriptor of the neighbour en-
vironment. Both the kernel and the descriptor respect all physical symmetries (rotations, trans-
lations, permutations), are smooth functions of atomic coordinates and can be refined at will to
provide a complete description of each environment.