Normal-Mode-Based Nudged Band (NM-NEB) Method: Retrieving Potential Energy Surface Information from Local Hessians to Improve Transition State Search

Traditional nudged elastic band (NEB) methods often yield unphysical initial paths due to the lack of curvature information from the potential energy surface (PES). To overcome this limitation, we propose a Normal-Mode-based NEB (NM-NEB) method that only leverages Hessian matrices of reactant and product minima. Key PES information is extracted from the local Hessian matrices of reactants and products via frequency calculations, and dominant reaction modes are identified using a Franck–Condon factor-based vibrational mode matching strategy. By displacing reactants and products along these modes, we obtain two improved end points near the true transition state, from which a physically reasonable initial path is constructed. Validation on 20 diverse benchmark reactions at the B3LYP-D3/6–31G* level shows that NM-NEB achieves stable convergence where Cartesian- and internal coordinate-NEB fail, with geometric and energy errors within 0.1 Å and 1.0 kcal/mol, respectively. The mode-guided path also reduces optimization iterations and avoids unphysical artifacts inherent in traditional interpolation. By leveraging only local Hessian information at the end point minima, this strategy achieves robust and efficient transition state search and provides a promising approach for medium-to-large systems, with its reliability fully validated on 20 diverse small-molecule benchmark reactions.