Solving the low dimensional Smoluchowski equation with a singular value basis set

Reaction kinetics on free energy surfaces with small activation barriers can be computed directly with the Smoluchowski equation. The procedure is computationally expensive even in a few dimensions. We present a propagation method that considerably reduces computational time for a particular class of problems: when the free energy surface suddenly switches by a small amount, and the probability distribution relaxes to a new equilibrium value. This case describes relaxation experiments. To achieve efficient solution, we expand the density matrix in a basis set obtained by singular value decomposition of equilibrium density matrices. Grid size during propagation is reduced from (100–1000) N to (2–4) N in N dimensions. Although the scaling with N is not improved, the smaller basis set nonetheless yields a significant speed up for low‐dimensional calculations. To demonstrate the practicality of our method, we couple Smoluchowsi dynamics with a genetic algorithm to search for free energy surfaces compatible with the multiprobe thermodynamics and temperature jump experiment reported for the protein α 3 D. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010