Nudged Elastic Membranes for Constructing Reduced Two-Dimensional Potential Energy Surfaces

TL;DR

The paper introduces the nudged elastic membrane method for constructing reduced two-dimensional potential energy surfaces using energies and forces, capturing complex features beyond traditional path methods.

Contribution

It presents a novel membrane-based framework that efficiently constructs 2D PES regions without requiring Hessian calculations, applicable to chemical systems.

Findings

Successfully applied to a 3D model and formaldehyde system

Captured both reaction paths and 2D structures including a new saddle point

Provides structures for further PES refinement

Abstract

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.