A global view of reactive coordinate manifolds from nonlinear dimensionality reduction

This work explores methods for generating low-dimensional representations of the internal molecular motion using nonlinear dimensionality reduction. The internal degrees of freedom are described as a Riemannian manifold by imposing a set of holonomic constraints. Manifold points are generated by Markov chain Monte Carlo with average-distance and Jacobian-norm weighted sampling. We investigate intrinsic dimension estimates and the reconstruction errors of low-dimensional nonlinear embeddings using Isomap and locally linear embedding methods. Using the Nyström method, the embedding of the coordinate manifold can be applied to project arbitrary molecular structures into the reduced-dimensional representation. We illustrate this approach by generating a two-dimension visualization of the critical points of the CH 2 O potential energy surface.