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Solving the low dimensional Smoluchowski equation with a singular value basis set
Author(s) -
Scott Gregory,
Gruebele Martin
Publication year - 2010
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.21535
Subject(s) - singular value decomposition , basis (linear algebra) , relaxation (psychology) , smoluchowski coagulation equation , scaling , jump , matrix (chemical analysis) , statistical physics , set (abstract data type) , energy (signal processing) , basis set , density matrix , mathematics , temperature jump , physics , thermodynamics , chemistry , computer science , algorithm , computational chemistry , quantum mechanics , density functional theory , geometry , psychology , social psychology , chromatography , quantum , programming language
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