Nudged elastic membranes for constructing reduced two-dimensional potential energy surfaces

Minimum-energy paths and intrinsic reaction coordinates are central tools for analyzing chemical reactions. As one-dimensional objects, however, individual paths do not provide a continuous representation of the surrounding potential energy surface (PES), including the arrangement of adjacent valleys, ridges, and higher-order saddle regions. We introduce the nudged elastic membrane method, which constructs a two-dimensional reduced PES in a selected region of configuration space using energies and forces, without requiring Hessian evaluations. The method is demonstrated for a three-dimensional analytical model and for triplet formaldehyde. In both cases, the membrane recovers known reaction-path and stationary-point regions. For formaldehyde, it also reveals a previously unreported second-order saddle point on the fitted PES. Structures extracted from the membrane provide starting points for subsequent stationary-point refinement.