  Artificial neural networks are used to fit a potential energy surface. We
demonstrate the benefits of using not only energies, but also their first and
second derivatives as training data for the neural network. This ensures smooth
and accurate Hessian surfaces, which are required for rate constant
calculations using instanton theory. Our aim was a local, accurate fit rather
than a global PES, because instanton theory requires information on the
potential only in the close vicinity of the main tunneling path. Elongations
along vibrational normal modes at the transition state are used as coordinates
for the neural network. The method is applied to the hydrogen abstraction
reaction from methanol, calculated on a coupled-cluster level of theory. The
reaction is essential in astrochemistry to explain the deuteration of methanol
in the interstellar medium.
