Locating Ab Initio Transition States via Approximate Geodesics on Machine Learned Potential Energy Surfaces

TL;DR

Locating transition states efficiently remains a bottleneck in computational chemistry. This work constructs geodesic paths between reactants and products on a machine-learned PES to generate high-quality TS guesses without any ab initio calculations, then refines the TS on the ab initio PES. Across two benchmark datasets, ML geodesics typically reduce the required P-RFO iterations by about 30% and often outperform FSM-based guesses, enabling faster TS optimization and potential discovery of multistep pathways. While promising, the approach relies on reliable ML PES behavior and is complemented by future work on Hessian guidance, automatic pathway discovery, and extension to periodic systems.

Abstract

Efficient and reliable identification and optimization of transition state structures is a longstanding challenge in computational chemistry. Popular chain-of-states methods require hundreds if not thousands of ab initio calculations to generate initial guesses for local quasi-Newton optimizers, with persistent risk of collapse to an alternative stationary point on the potential energy surface (PES). Here, we show that high-quality guess structures for transition state optimization can be obtained by constructing the geodesic path between reactant and product structures on the PES generated by machine learning potentials (MLPs). We present an algorithm for optimization of such geodesic paths, as well as the associated codebase. We demonstrate effectiveness of this approach using the recent eSEN-sm-cons MLP. On average, the highest-energy point along these MLP geodesics requires 30% fewer quasi-Newton optimization steps to converge to the transition state compared to guesses from the fully ab initio frozen string method. Our approach therefore completely eliminates the need for ab initio calculations for generation of transition state guesses and considerably speeds up subsequent structural optimization. Geodesic construction on ML PES thus promises to be a useful approach for efficient computational elucidation of complex chemical reaction networks.

Figures (5)

• Figure 1: The model Müller-Brownmuller1979location PES with stationary points and connecting MEPs highlighted (left) and the PES cross-section along the first elementary step connecting minimum energy points 1 and 2 via saddle 1 (right). Energy differences between the transition state and the minimum energy points $\Delta E^\ddagger$ for both the forward and backward processes are also shown for the right panel.
• Figure 2: Scheme for transition state optimization with the protocol described in this work (with the steps most pertinent to this work bounded in blue). A Morse-geodesic path is initially interpolated between reactant and product structures that have been optimized on the ab initio PES. This initial guess path is then optimized to a geodesic on the MLP. The highest-energy node geometry is subsequently optimized to a stationary TS geometry with P-RFO on the ab initio PES, enabling the estimation of TST rates and other transition state properties.
• Figure 3: Comparison of the number of P-RFO iterations required for converging the FSM and MLP geodesic starting guesses to the transition state structure for 76 reactions in the dataset from Ref. asgeirsson2021nudged. Each point corresponds to a separate reaction.
• Figure 4: Histograms of the number of P-RFO iterations required for converging the FSM and MLP geodesic starting guesses to the transition state structure for 76 reactions in the dataset from Ref. asgeirsson2021nudged (left) and the ratio of the iterations needed from MLP geodesic generated guesses to FSM generated guesses (right). A ratio less than 1 indicates a more efficient MLP geodesic guess. The corresponding kernel density estimates (KDE) of the associated probability distribution is also shown.
• Figure 5: Two reactions in the dataset from Ref. asgeirsson2021nudged for which MLP geodesic construction identifies a lower energy two-step pathway (blue solid line) over a higher energy elementary process (red dotted line): Rearrangement of perfluoropropylene oxide to perfluoroacetone (left panel) and addition of ethene to butadiene to form 1,3-hexadiene (right). The corresponding transition state structures (bordered by the line-style corresponding to the reaction mechanism) and the intermediate for the two-step path are also shown, as are energies of all stationary points (in kcal/mol, relative to the reactant). Energies are not to scale.