Assessing the Accuracy of Metadynamics
Abstract
Metadynamics is a powerful technique that has been successfully exploited to explore the multidimensional free energy surface of complex polyatomic systems and predict transition mechanisms in very different fields, ranging from chemistry and solid-state physics to biophysics. We here derive an explicit expression for the accuracy of the methodology and provide a way to choose the parameters of the method in order to optimize its performance.
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In metadynamics, the volume of a free energy minimum grows exponentially with the dimensionality d of collective variable space, and so does the time to accumulate sufficient bias to escape the free-energy basin.
“Take for instance the case of metadynamics, in which a repulsive bias is accumulated in locations that have already been visited during the trajectory, forcing the system out of free energy minima 93,94 . The volume of one of these minima grows exponentially with the dimensionality d of collective variable space, and so does the time to accumulate sufficient bias to escape the freeenergy basin.”
From Unsupervised machine learning in atomistic simulations, between predictions and understanding (2019) · cites this paper as [93]
Cites
A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules
Cornell, W. D., Cieplak, P., Bayly, C. I., Gould, I. R., Merz, K. M., Ferguson, D. M., Spellmeyer, D. C., Fox, T., Caldwell, J. W., & Kollman, P. A. (1995) · Journal of the American Chemical Society · doi:10.1021/ja00124a002 · Cited by 13,111 · see citing works
Unified Approach for Molecular Dynamics and Density-Functional Theory
Car, R., & Parrinello, M. (1985) · Physical Review Letters · doi:10.1103/physrevlett.55.2471 · Cited by 10,737 · see citing works
Self-citationA molecular dynamics method for simulations in the canonical ensemble
Nosé, S. (1984) · Molecular Physics · doi:10.1080/00268978400101201 · Cited by 10,049 · see citing works
Laio, A., & Parrinello, M. (2002) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.202427399 · Cited by 5,626 · see citing works
Self-citationNonequilibrium Equality for Free Energy Differences
Jarzynski, C. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.2690 · Cited by 5,400 · see citing works
Crystal Structure and Pair Potentials: A Molecular-Dynamics Study
Parrinello, M., & Rahman, A. (1980) · Physical Review Letters · doi:10.1103/physrevlett.45.1196 · Cited by 3,782 · see citing works
Self-citationHandbook of Stochastic Methods
Gardiner, C. W. (2004) · Springer series in synergetics · doi:10.1007/978-3-662-05389-8 · Cited by 3,376 · see citing works
Efficient, Multiple-Range Random Walk Algorithm to Calculate the Density of States
Wang, F., & Landau, D. P. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.2050 · Cited by 2,913 · see citing works
New Monte Carlo technique for studying phase transitions
Ferrenberg, A. M., & Swendsen, R. H. (1988) · Physical Review Letters · doi:10.1103/physrevlett.61.2635 · Cited by 2,681 · see citing works
The calculation of the potential of mean force using computer simulations
Roux, B. (1995) · Computer Physics Communications · doi:10.1016/0010-4655(95)00053-i · Cited by 1,812 · see citing works
Constrained reaction coordinate dynamics for the simulation of rare events
Carter, E. A., Ciccotti, G., Hynes, J. T., & Kapral, R. (1989) · Chemical Physics Letters · doi:10.1016/s0009-2614(89)87314-2 · Cited by 1,023 · see citing works
Calculating free energies using average force
Darve, E. F., & Pohorille, A. (2001) · The Journal of Chemical Physics · doi:10.1063/1.1410978 · Cited by 998 · see citing works
Free energy from constrained molecular dynamics
Sprik, M., & Ciccotti, G. (1998) · The Journal of Chemical Physics · doi:10.1063/1.477419 · Cited by 944 · see citing works
Predicting Crystal Structures: The Parrinello-Rahman Method Revisited
Martoňák, R., Laio, A., & Parrinello, M. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.075503 · Cited by 894 · see citing works
Self-citationMultidimensional free‐energy calculations using the weighted histogram analysis method
Kumar, S., Rosenberg, J. M., Bouzida, D., Swendsen, R. H., & Kollman, P. A. (1995) · Journal of Computational Chemistry · doi:10.1002/jcc.540161104 · Cited by 868 · see citing works
Efficient Exploration of Reactive Potential Energy Surfaces Using Car-Parrinello Molecular Dynamics
Iannuzzi, M., Laio, A., & Parrinello, M. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.238302 · Cited by 817 · see citing works
Self-citationLecture notes in computational science and engineering
Viola, I. M., Ponzini, R., Rocchi, D., et al. (2010) · Cited by 808 · see citing works
Assessing the efficiency of free energy calculation methods
Rodriguez-Gomez, D., Darve, E., & Pohorille, A. (2004) · The Journal of Chemical Physics · doi:10.1063/1.1642607 · Cited by 211 · see citing works
Reconstructing the Density of States by History-Dependent Metadynamics
Micheletti, C., Laio, A., & Parrinello, M. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.170601 · Cited by 161 · see citing works
Self-citationGeneral projection operator formalism for the dynamics and thermodynamics of complex fluids
Öttinger, H. C. (1998) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.57.1416 · Cited by 142 · see citing works
Microscopic Mechanism of Antibiotics Translocation through a Porin
Ceccarelli, M., Danelon, C., Laio, A., & Parrinello, M. (2004) · Biophysical Journal · doi:10.1529/biophysj.103.037283 · Cited by 93 · see citing works
Self-citationProton Transfer in Heterocycle Crystals
Iannuzzi, M., & Parrinello, M. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.025901 · Cited by 83 · see citing works
Self-citationAb Initio Study of Dehydroxylation−Carbonation Reaction on Brucite Surface
Churakov, S. V., Iannuzzi, M., & Parrinello, M. (2004) · The Journal of Physical Chemistry B · doi:10.1021/jp037935x · Cited by 80 · see citing works
Self-citationStirling, A., Iannuzzi, M., Laio, A., et al. (2004) · ChemPhysChem · doi:10.1002/cphc.200400063 · Cited by 80 · see citing works
Self-citationA Minimum Free Energy Reaction Path for the E2 Reaction between Fluoro Ethane and a Fluoride Ion
Ensing, B., Laio, A., Gervasio, F. L., Parrinello, M., & Klein, M. L. (2004) · Journal of the American Chemical Society · doi:10.1021/ja048285t · Cited by 77 · see citing works
Self-citationShear viscosity and dielectric constant of liquid acetonitrile
Mountain, R. D. (1997) · The Journal of Chemical Physics · doi:10.1063/1.474767 · Cited by 34 · see citing works
Zipoli, F., Bernasconi, M., & Martoňák, R. (2004) · The European Physical Journal B · doi:10.1140/epjb/e2004-00168-y · Cited by 32 · see citing works
(1976) · The Journal of Dermatologic Surgery and Oncology · doi:10.1111/j.1524-4725.1976.tb00196.x · Cited by 24 · see citing works
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Barducci, A., Bussi, G., & Parrinello, M. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.020603 · Cited by 3,184 · see citing works
Self-citationLaio, A., & Gervasio, F. L. (2008) · Reports on Progress in Physics · doi:10.1088/0034-4885/71/12/126601 · Cited by 1,619 · see citing works
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Rohrdanz, M. A., Zheng, W., & Clementi, C. (2013) · Annual Review of Physical Chemistry · doi:10.1146/annurev-physchem-040412-110006 · Cited by 242 · see citing works
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Bonomi, M., Branduardi, D., Gervasio, F. L., & Parrinello, M. (2008) · Journal of the American Chemical Society · doi:10.1021/ja803652f · Cited by 97 · see citing works
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Spiwok, V., & Králová, B. (2011) · The Journal of Chemical Physics · doi:10.1063/1.3660208 · Cited by 70 · see citing works
Piana, S., Laio, A., Marinelli, F., Van Troys, M., Bourry, D., Ampe, C., & Martins, J. C. (2008) · Journal of Molecular Biology · doi:10.1016/j.jmb.2007.10.020 · Cited by 48 · see citing works
Self-citation
- Authors
- Laio, A., Rodriguez-Fortea, A., Gervasio, F. L., Ceccarelli, M., & Parrinello, M.
- Affiliations
- ETH Zurich (CH)
- Computational Science, Department of Chemistry and Applied Biosciences, ETH Zurich, c/o USI Campus, Via Buffi 13, CH-6900 Lugano, Switzerland
- Venue
- The Journal of Physical Chemistry B
- Publisher
- American Chemical Society (ACS)
- Published
- 2005-02-15
- Volume
- 109
- Issue
- 14
- Pages
- 6714-6721
- ISSN
- 1520-5207 (ISSN-L)
- 1520-6106
- OpenAlex
- W2091283009
- Cited by
- 517
- References
- 28
- Citations by year
- 2026: 9 · 2025: 18 · 2024: 10 · 2023: 41 · 2022: 19 · 2021: 33 · 2020: 26 · 2019: 19 · 2018: 25 · 2017: 35 · 2016: 25 · 2015: 27 · 2014: 30 · 2013: 21 · 2012: 26
- FWCI
- 15.78
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- The Journal of Physical Chemistry B (publishedVersion)
- PubMed (publishedVersion)
- UCL Discovery (University College London) (submittedVersion)
- SDL (submittedVersion)
- UNICA IRIS Institutional Research Information System (University of Cagliari) (submittedVersion)
- Topics
- Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
- Keywords
- metadynamics, free energy landscape, accuracy analysis, transition mechanism, polyatomic systems, free energy calculation
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