  In this work, we propose a multi-scale protocol for routine theoretical
studies of chemical reaction mechanisms. The initial reaction paths of our
investigated systems are sampled using the Nudged-Elastic Band (NEB) method
driven by a cheap electronic structure method. Forces recalculated at the more
accurate electronic structure theory for a set of points on the path are fitted
with a machine-learning technique (in our case symmetric gradient domain
machine learning or sGDML) to produce a semi-local reactive Potential Energy
Surface (PES), embracing reactants, products and transition state (TS) regions.
This approach has been successfully applied to a unimolecular (Bergman
cyclization of enediyne) and a bimolecular (S$_\text{N}$2 substitution)
reaction. In particular, we demonstrate that with only 50 to 150 energy-force
evaluations with the accurate reference methods (here CASSCF and CCSD) it is
possible to construct a semi-local PES giving qualitative agreement for
stationary-point geometries, intrinsic reaction-coordinates and barriers.
Furthermore, we find a qualitative agreement in vibrational frequencies and
reaction rate coefficients. The key aspect of the method's performance is its
multi-scale nature, which not only saves computational effort but also allows
extracting meaningful information along the reaction path, characterized by
zero gradients in all but one direction. Agnostic to the nature of the TS and
computationally economic, the protocol can be readily automated and routinely
used for mechanistic reaction studies.
