Benchmarking Hierarchical Double-Ended Transition-State Search Methods for Metal-Catalyzed Reactions

Efficient and reliable identification of transition states (TS) is critical for reaction modeling. Among the available approaches, the combination of double-ended TS search with eigenvector-following, referred to as hierarchical TS search, is an effective tool for locating TSs starting from reactant and product geometries. However, systematic benchmarking of these methods on transition metal-catalyzed reactions remains limited. Here, we benchmark eight pipelined hierarchical methods using out-of-the-box settings on a diverse set of 30 single-step, closed-shell metal-catalyzed reactions, evaluating their success rate and computational efficiency. Most workflows achieve high success rates across the data set, indicating that modern double-ended methods are generally robust for locating TSs in elementary organometallic reactions, and the main differences between methods lie in their computational efficiency. The benchmark also reveals several key trends: (i) the final eigenvector-following step requires an accurate Hessian matrix or explicitly calculated min-mode for a high success rate, (ii) TS searches from interpolation-only paths (e.g., image-dependent pair potential, IDPP) and bracket methods (e.g., Dewar-Healy-Stewart, DHS) are often more efficient than popular methods, such as climbing image nudged elastic band (CI-NEB), (iii) different hierarchical workflows can converge to different TSs even when starting from the same two minima, (iv) larger structural changes between reactants and products are associated with lower success rates and higher computational costs. We also show that further parameter tuning can reduce computational expense without reducing the success rate on our data set. These conclusions are further supported by two case studies involving industrially relevant organometallic reactions.