(310k) Navigating the Unknown: Efficiently Locating the Transition State of the Diels-Alder Reaction through Adaptively Sampled Point Clouds

Locating transition states of chemical reactions is crucial for understanding reaction mechanisms and kinetics. Traditional methods such as metadynamics [1] and adaptive biasing force [2] require a priori knowledge of collective variables and exhaustive exploration to understand the potential energy surface; other methods, like the Nudged Elastic Band [3], require knowledge of good collective variables as well as of the minima to be connected. Here, we present an alternative approach, that does not require a priori knowledge of the collective variables, “Staying the Course,” to locate the transition state of the Diels-Alder reaction in a data-driven fashion.

Our method builds upon previous work [5, 6, 7] in locating saddle points of stochastic dynamical systems without a priori knowledge of the manifold or collective variables. Instead, point clouds (positions of the atoms in the system) are adaptively & iteratively sampled along a 1D curve (here, an isocline) that drives the system from an initial conformation (typically a stable equilibrium) to a saddle point. When collective variables are unknown, we couple the algorithm with manifold learning techniques (diffusion maps) and Gaussian process regression to obtain the sought after path through local adaptive parameterizations of the effective free energy surface.

By integrating our algorithm with available atomistic and molecular simulation packages, we efficiently navigate the high-dimensional potential energy surface of an example problem (here, the Diels-Alder reaction). This approach allows for the automatic and adaptive identification of relevant reduced coordinates and the transition state without exhaustive sampling of the entire free energy landscape. Our results highlight the versatility of combining “Staying the Course” with molecular simulation codes for studying complex chemical reactions, showcasing its potential for applications in more complex reaction environments. We compare this to the metadynamics approach taken in [8].

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