Riemannian Denoising Score Matching for Molecular Structure Optimization with Chemical Accuracy

We introduce a novel framework for molecular structure optimization using Riemannian denoising score matching (R-DSM), a method grounded in a physics-informed Riemannian manifold. Unlike conventional approaches operating in Euclidean space, our method leverages a Riemannian metric that better aligns with molecular energy change, enabling more robust modeling of potential energy surfaces. By incorporating internal coordinates reflective of energetic properties, R-DSM achieves state-of-the-art performance, attaining chemical accuracy with a mean energy error below 1 kcal/mol. Comparative evaluations on QM9 and GEOM datasets demonstrate significant improvements in both structural and energetic accuracy, surpassing conventional Euclidean-based methods. This approach highlights the transformative potential of physics-informed coordinates for tackling complex molecular optimization problems, with broad implications for computational chemistry and materials science.