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The paper introduces a nudged elastic membrane method to construct two-dimensional reduced potential energy surfaces (PES) using energy and force data, avoiding the need for computationally expensive Hessian calculations. This method captures both one-dimensional reaction paths and two-dimensional features of PES, such as higher-order saddle points. The method is validated on a 3D prototype and the triplet formaldehyde system, revealing a previously unreported second-order saddle point.
Discovering hidden features of potential energy surfaces just got easier: this new method finds 2D structures without needing costly Hessian calculations.
Path optimization methods have been widely used and highly successful for the analysis of chemical reactions. Yet, they can fail to capture intrinsically multidimensional features of potential energy surfaces (PES). We introduce the nudged elastic membrane method, a framework for constructing two-dimensional reduced potential-energy surfaces in chemically relevant regions of a PES using only energies and forces without requiring more costly Hessian information. The method is demonstrated for a three-dimensional prototype model and for the triplet formaldehyde molecular system. In both cases, the resulting membrane captures one-dimensional reaction-path features as well as genuinely two-dimensional structures such as a yet unreported reported second-order saddle point in the PES of triplet formaldehyde. The method further provides direct access to structures that can serve as starting points for subsequent refinement. Our results show that the method offers a practical route to exploring multidimensional PES topography beyond the single-path picture.