Restricted-Variance Constrained, Reaction Path, and Transition State Molecular Optimizations Using Gradient-Enhanced Kriging

Gaussian process
regression has recently been explored as an alternative
to standard surrogate models in molecular equilibrium geometry optimization.
In particular, the gradient-enhanced Kriging approach in association
with internal coordinates, restricted-variance optimization, and an
efficient and fast estimate of hyperparameters has demonstrated performance
on par or better than standard methods. In this report, we extend
the approach to constrained optimizations and transition states and
benchmark it for a set of reactions. We compare the performance of
the newly developed method with the standard techniques in the location
of transition states and in constrained optimizations, both isolated
and in the context of reaction path computation. The results show
that the method outperforms the current standard in efficiency as
well as in robustness.