LongTime Convergence of an Adaptive Biasing Force

Authors: T Lelièvre K Minoukadeh

Publish Date: 2011/05/05

Volume: 202, Issue: 1, Pages: 1-34

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Abstract

We present convergence results for an adaptive algorithm to compute free energies namely the adaptive biasing force ABF method Darve and Pohorille in J Chem Phys 115209169–9183 2001 Hénin and Chipot in J Chem Phys 1212904 2004 The free energy is the effective potential associated to a socalled reaction coordinate ξq where q = q1 … q3N is the position vector of an Nparticle system Computing free energy differences remains an important challenge in molecular dynamics due to the presence of metastable regions in the potential energy surface The ABF method uses an onthefly estimate of the free energy to bias dynamics and overcome metastability Using entropy arguments and logarithmic Sobolev inequalities previous results have shown that the rate of convergence of the ABF method is limited by the metastable features of the canonical measures conditioned to being at fixed values of ξ Lelièvre et al in Nonlinearity 2161155–1181 2008 In this paper we present an improvement on the existing results in the presence of such metastabilities which is a generic case encountered in practice More precisely we study the socalled bichannel case where two channels along the reaction coordinate direction exist between an initial and final state the channels being separated from each other by a region of very low probability With hypotheses made on ‘channeldependent’ conditional measures we show on a bichannel model which we introduce that the convergence of the ABF method is in fact not limited by metastabilities in directions orthogonal to ξ under two crucial assumptions i exchange between the two channels is possible for some values of ξ and ii the free energy is a good bias in each channel This theoretical result supports recent numerical experiments Minoukadeh et al in J Chem Theory Comput 61008–1017 2010 where the efficiency of the ABF approach is demonstrated for such a multiplechannel situation

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