Using multiscale preconditioning to accelerate the convergence of iterative molecular calculations

Iterative procedures for optimizing properties of molecular models often converge slowly owing to the computational cost of accurately representing features of interest. Here, we introduce a preconditioning scheme that allows one to use a less expensive model to guide exploration of the energy landscape of a more expensive model and thus speed the discovery of locally stable states of the latter. We illustrate our approach in the contexts of energy minimization and the string method for finding transition pathways. The relation of the method to other multilevel simulation techniques and possible extensions are discussed.