  A trivial flaw in the utilization of artificial neural networks in
interpolating chemical potential energy surfaces (PES) whose descriptors are
Cartesian coordinates is their dependence on simple translations and rotations
of the molecule under consideration. A different set of descriptors can be
chosen to circumvent this problem, internuclear distances, inverse internuclear
distances or z-matrix coordinates are three such descriptors. The objective is
to use an interpolated PES in instanton rate constant calculations, hence
information on the energy, gradient and Hessian is required at coordinates in
the vicinity of the tunneling path. Instanton theory relies on smoothly fitted
Hessians, therefore we use energy, gradients and Hessians in the training
procedure. A major challenge is presented in the proper back-transformation of
the output gradients and Hessians from internal coordinates to Cartesian
coordinates. We perform comparisons between our method, a previous approach and
on-the-fly rate constant calcuations on the hydrogen abstraction from methanol
and on the hydrogen addition to isocyanic acid.
