A time-independent free energy estimator for metadynamics.

Metadynamics is a powerful and well-established enhanced sampling method for exploring and quantifying free energy surfaces of complex systems as a function of appropriately chosen variables. In the limit of long simulation time, metadynamics converges to the exact free energy surface plus a time-dependent constant. In this article, we analyze in detail this time-dependent constant. We show an easy way to calculate it, and by explicitly calculating the time dependence of this constant, we are able to derive a time-independent and locally convergent free energy estimator for metadynamics. We also derive an alternate procedure for obtaining the full unbiased distributions of generic operators from biased metadynamics simulations and explicitly test its usefulness.

[1]  Michele Parrinello,et al.  Well-tempered metadynamics converges asymptotically. , 2014, Physical review letters.

[2]  Michele Parrinello,et al.  Assessing the Reliability of the Dynamics Reconstructed from Metadynamics. , 2014, Journal of chemical theory and computation.

[3]  M. Parrinello,et al.  From metadynamics to dynamics. , 2013, Physical review letters.

[4]  Axel van de Walle,et al.  Accelerated molecular dynamics through stochastic iterations and collective variable based basin identification , 2013 .

[5]  M. Parrinello,et al.  Metadynamics with Adaptive Gaussians. , 2012, Journal of chemical theory and computation.

[6]  P. Bolhuis,et al.  Multiple state transition interface sampling of alanine dipeptide in explicit solvent. , 2011, The Journal of chemical physics.

[7]  Axel van de Walle,et al.  Hybrid deterministic and stochastic approach for efficient atomistic simulations at long time scales , 2011 .

[8]  Andreas Heuer,et al.  Calculation of free energy landscapes: A histogram reweighted metadynamics approach , 2010, J. Comput. Chem..

[9]  Alessandro Laio,et al.  Metadynamics convergence law in a multidimensional system. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Massimiliano Bonomi,et al.  Reconstructing the equilibrium Boltzmann distribution from well‐tempered metadynamics , 2009, J. Comput. Chem..

[11]  Massimiliano Bonomi,et al.  PLUMED: A portable plugin for free-energy calculations with molecular dynamics , 2009, Comput. Phys. Commun..

[12]  M. Parrinello,et al.  Well-tempered metadynamics: a smoothly converging and tunable free-energy method. , 2008, Physical review letters.

[13]  Guido Tiana,et al.  Estimation of microscopic averages from metadynamics , 2007, 0711.2984.

[14]  A. Laio,et al.  Equilibrium free energies from nonequilibrium metadynamics. , 2006, Physical Review Letters.

[15]  Holger Gohlke,et al.  The Amber biomolecular simulation programs , 2005, J. Comput. Chem..

[16]  A. Laio,et al.  Escaping free-energy minima , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[17]  A. Voter,et al.  Extending the Time Scale in Atomistic Simulation of Materials Annual Re-views in Materials Research , 2002 .

[18]  David Chandler,et al.  Transition path sampling: throwing ropes over rough mountain passes, in the dark. , 2002, Annual review of physical chemistry.

[19]  Berk Hess,et al.  GROMACS 3.0: a package for molecular simulation and trajectory analysis , 2001 .

[20]  C. Dellago,et al.  Reaction coordinates of biomolecular isomerization. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[21]  John W. Wilkins,et al.  Simple bias potential for boosting molecular dynamics with the hyperdynamics scheme , 1998 .

[22]  Berk Hess,et al.  LINCS: A linear constraint solver for molecular simulations , 1997, J. Comput. Chem..

[23]  A. Voter.  A method for accelerating the molecular dynamics simulation of infrequent events , 1997 .

[24]  Grubmüller,et al.  Predicting slow structural transitions in macromolecular systems: Conformational flooding. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[25]  Andrew E. Torda,et al.  Local elevation: A method for improving the searching properties of molecular dynamics simulation , 1994, J. Comput. Aided Mol. Des..

[26]  T. Darden,et al.  Particle mesh Ewald: An N⋅log(N) method for Ewald sums in large systems , 1993 .