  Identifying transition states -- saddle points on the potential energy
surface connecting reactant and product minima -- is central to predicting
kinetic barriers and understanding chemical reaction mechanisms. In this work,
we train an equivariant neural network potential, NewtonNet, on an ab initio
dataset of thousands of organic reactions from which we derive the analytical
Hessians from the fully differentiable machine learning (ML) model. By reducing
the computational cost by several orders of magnitude relative to the Density
Functional Theory (DFT) ab initio source, we can afford to use the learned
Hessians at every step for the saddle point optimizations. We have implemented
our ML Hessian algorithm in Sella, an open source software package designed to
optimize atomic systems to find saddle point structures, in order to compare
transition state optimization against quasi-Newton Hessian updates using DFT or
the ML model. We show that the full ML Hessian robustly finds the transition
states of 240 unseen organic reactions, even when the quality of the initial
guess structures are degraded, while reducing the number of optimization steps
to convergence by 2--3$\times$ compared to the quasi-Newton DFT and ML methods.
All data generation, NewtonNet model, and ML transition state finding methods
are available in an automated workflow.
