  We introduce a novel class of localized atomic environment representations,
based upon the Coulomb matrix. By combining these functions with the Gaussian
approximation potential approach, we present LC-GAP, a new system for
generating atomic potentials through machine learning (ML). Tests on the QM7,
QM7b and GDB9 biomolecular datasets demonstrate that potentials created with
LC-GAP can successfully predict atomization energies for molecules larger than
those used for training to chemical accuracy, and can (in the case of QM7b)
also be used to predict a range of other atomic properties with accuracy in
line with the recent literature. As the best-performing representation has only
linear dimensionality in the number of atoms in a local atomic environment,
this represents an improvement both in prediction accuracy and computational
cost when considered against similar Coulomb matrix-based methods.
