  Simulation of surface processes is a key part of computational chemistry that
offers atomic-scale insights into mechanisms of heterogeneous catalysis,
diffusion dynamics, as well as quantum tunneling phenomena. The most common
theoretical approaches involve optimization of reaction pathways, including
semiclassical tunneling pathways (called instantons). However, the
computational effort can be demanding, especially for instanton optimizations
with ab initio electronic structure. Recently, machine learning has been
applied to accelerate reaction-pathway optimization, showing great potential
for a wide range of applications. However, previous methods suffer from
practical issues such as unfavorable scaling with respect to the size of the
descriptor, and were mostly designed for reactions in the gas phase. We propose
an improved framework based on Gaussian process regression for general
transformed coordinates, which can alleviate the size problem. The descriptor
combines internal and Cartesian coordinates, which improves the performance for
modeling surface processes. We demonstrate with eleven instanton optimizations
in three example systems that the new approach makes ab initio instanton
optimization significantly cheaper, such that it becomes not much more
expensive than a classical transition-state theory calculation.
