Well-tempered metadynamics converges asymptotically

Physical Review Letters

Volumn 112, Issue 24, 2014, Pages

  Dama, James F ^a   Parrinello, Michele ^b   Voth, Gregory A ^a  

^a UNIVERSITY OF CHICAGO   (United States)

^b UNIVERSITY OF LUGANO   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMIC PHYSICS;

BIOMOLECULAR SYSTEM; BOUNDARY CORRECTION; COLLECTIVE VARIABLES; COMPUTATIONAL STUDIES; CONVERGENCE ANALYSIS; ENHANCED SAMPLINGS; METADYNAMICS; UMBRELLA SAMPLING;

PHYSICS;

ALGORITHM; ARTICLE; MOLECULAR DYNAMICS; STATISTICAL MODEL;

ALGORITHMS; MODELS, STATISTICAL; MOLECULAR DYNAMICS SIMULATION;

EID: 84902817448     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.112.240602     Document Type: Article

References (51)

1. A. Laio and M. Parrinello, Proc. Natl. Acad. Sci. U.S.A. 99, 12562 (2002). PNASA6 0027-8424 10.1073/pnas.202427399
2. A. Barducci, G. Bussi, and M. Parrinello, Phys. Rev. Lett. 100, 020603 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.100.020603
3. A. Barducci, M. Bonomi, and M. Parrinello, Wiley Interdiscip. Rev.: Comput. Mol. Sci. 1, 826 (2011). 10.1002/wcms.31
4. L. Sutto, S. Marsili, and F.L. Gervasio, Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2, 771 (2012). 10.1002/wcms.1103
5. M. Karplus and J.A. McCammon, Nat. Struct. Biol. 9, 646 (2002). NSBIEW 1072-8368 10.1038/nsb0902-646
6. R. Martoňák, A. Laio, and M. Parrinello, Phys. Rev. Lett. 90, 075503 (2003). PRLTAO 0031-9007 10.1103/PhysRevLett.90.075503
7. A.R. Oganov, R. Martoňák, A. Laio, P. Raiteri, and M. Parrinello, Nature (London) 438, 1142 (2005). NATUAS 0028-0836 10.1038/nature04439
8. J. Sun, D.D. Klug, R. Martoňák, J.A. Montoya, M.-S. Lee, S. Scandolo, and E. Tosatti, Proc. Natl. Acad. Sci. U.S.A. 106, 6077 (2009). PNASA6 0027-8424 10.1073/pnas.0812624106
9. J.P.M. Jämbeck and A.P. Lyubartsev, J. Phys. Chem. Lett. 4, 1781 (2013). JPCLCD 1948-7185 10.1021/jz4007993
10. F.L. Gervasio, A. Laio, and M. Parrinello, J. Am. Chem. Soc. 127, 2600 (2005). JACSAT 0002-7863 10.1021/ja0445950
11. J. Pfaendtner, D. Branduardi, M. Parrinello, T.D. Pollard, and G.A. Voth, Proc. Natl. Acad. Sci. U.S.A. 106, 12723 (2009). PNASA6 0027-8424 10.1073/pnas.0902092106
12. V. Limongelli, M. Bonomi, L. Marinelli, F.L. Gervasio, A. Cavalli, E. Novellino, and M. Parrinello, Proc. Natl. Acad. Sci. U.S.A. 107, 5411 (2010). PNASA6 0027-8424 10.1073/pnas.0913377107
13. M. Mezei, J. Comput. Phys. 68, 237 (1987). JCTPAH 0021-9991 10.1016/0021-9991(87)90054-4
14. F. Glover, Computers & Operations Research 13, 533 (1986).
15. T. Huber, A.E. Torda, and W.F. van Gunsteren, J. Comput.-Aided Mol. Des. 8, 695 (1994). JCADEQ 0920-654X 10.1007/BF00124016
16. B.A. Berg and T. Neuhaus, Phys. Rev. Lett. 68, 9 (1992). PRLTAO 0031-9007 10.1103/PhysRevLett.68.9
17. C. Bartels and M. Karplus, J. Comput. Chem. 18, 1450 (1997). JCCHDD 0192-8651 10.1002/(SICI)1096-987X(199709)18:12<1450::AID-JCC3>3.0.CO;2-I
18. E. Darve and A. Pohorille, J. Chem. Phys. 115, 9169 (2001). JCPSA6 0021-9606 10.1063/1.1410978
19. S. Marsili, A. Barducci, R. Chelli, P. Procacci, and V. Schettino, J. Phys. Chem. B 110, 14011 (2006). JPCBFK 1520-6106 10.1021/jp062755j
20. E. Darve, D. Rodríguez-Gómez, and A. Pohorille, J. Chem. Phys. 128, 144120 (2008). JCPSA6 0021-9606 10.1063/1.2829861
21. L. Zheng, M. Chen, and W. Yang, Proc. Natl. Acad. Sci. U.S.A. 105, 20227 (2008). PNASA6 0027-8424 10.1073/pnas.0810631106
22. B.M. Dickson, F. Legoll, T. Lelièvre, G. Stoltz, and P. Fleurat-Lessard, J. Phys. Chem. B 114, 5823 (2010). JPCBFK 1520-6106 10.1021/jp100926h
23. S. Singh, C.-c. Chiu, and J.J. Pablo, J. Stat. Phys. 145, 932 (2011). JSTPBS 0022-4715 10.1007/s10955-011-0301-0
24. F. Wang and D.P. Landau, Phys. Rev. Lett. 86, 2050 (2001). PRLTAO 0031-9007 10.1103/PhysRevLett.86.2050
25. K.M. Aberg, A.P. Lyubartsev, S.P. Jacobsson, and A. Laaksonen, J. Chem. Phys. 120, 3770 (2004). JCPSA6 0021-9606 10.1063/1.1642601
26. S. Trebst, D.A. Huse, and M. Troyer, Phys. Rev. E 70, 046701 (2004). PLEEE8 1539-3755 10.1103/PhysRevE.70.046701
27. R.E. Belardinelli and V.D. Pereyra, Phys. Rev. E 75, 046701 (2007). PLEEE8 1539-3755 10.1103/PhysRevE.75.046701
28. F.A. Escobedo and F.J. Martinez-Veracoechea, J. Chem. Phys. 129, 154107 (2008). JCPSA6 0021-9606 10.1063/1.2994717
29. F. Liang, C. Liu, and R.J. Carroll, J. Am. Stat. Assoc. 102, 305 (2007). JSTNAL 0162-1459 10.1198/016214506000001202
30. Y.F. Atchadé and J.S. Liu, Statistica Sinica 20, 209 (2010). STSNEO
31. N. Chopin, T. Lelièvre, and G. Stoltz, Stat. Comput. 22, 897 (2012). STACE3 0960-3174 10.1007/s11222-011-9257-9
32. I. Bilionis and P. Koutsourelakis, J. Comput. Phys. 231, 3849 (2012). JCTPAH 0021-9991 10.1016/j.jcp.2012.01.033
33. A. Laio, A. Rodriguez-Fortea, F.L. Gervasio, M. Ceccarelli, and M. Parrinello, J. Phys. Chem. B 109, 6714 (2005). JPCBFK 1520-6106 10.1021/jp045424k
34. G. Bussi, A. Laio, and M. Parrinello, Phys. Rev. Lett. 96, 090601 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.96.090601
35. D. Min, Y. Liu, I. Carbone, and W. Yang, J. Chem. Phys. 126, 194104 (2007). JCPSA6 0021-9606 10.1063/1.2731769
36. T. Lelièvre, M. Rousset, and G. Stoltz, Nonlinearity 21, 1155 (2008). NONLE5 0951-7715 10.1088/0951-7715/21/6/001
37. Y. Crespo, F. Marinelli, F. Pietrucci, and A. Laio, Phys. Rev. E 81, 055701 (2010). PLEEE8 1539-3755 10.1103/PhysRevE.81.055701
38. G.A. Tribello, M. Ceriotti, and M. Parrinello, Proc. Natl. Acad. Sci. U.S.A. 107, 17509 (2010). PNASA6 0027-8424 10.1073/pnas.1011511107
39. B.M. Dickson, Phys. Rev. E 84, 037701 (2011). PLEEE8 1539-3755 10.1103/PhysRevE.84.037701
40. M. McGovern and J. de Pablo, J. Chem. Phys. 139, 084102 (2013). JCPSA6 0021-9606 10.1063/1.4818153
41. R.E. Belardinelli and V.D. Pereyra, J. Chem. Phys. 127, 184105 (2007). JCPSA6 0021-9606 10.1063/1.2803061
42. R.E. Belardinelli, S. Manzi, and V.D. Pereyra, Phys. Rev. E 78, 067701 (2008). PLEEE8 1539-3755 10.1103/PhysRevE.78.067701
43. G. Fort, B. Jourdain, E. Kuhn, T. Lelièvre, and G. Stoltz, arXiv:1207.6880.
44. M. Bonomi, D. Branduardi, G. Bussi, C. Camilloni, D. Provasi, P. Raiteri, D. Donadio, F. Marinelli, F. Pietrucci, R.A. Broglia, and M. Parrinello, Comput. Phys. Commun. 180, 1961 (2009). CPHCBZ 0010-4655 10.1016/j.cpc.2009.05. 011
45. G. Fiorin, M.L. Klein, and J. Hénin, Mol. Phys. 111, 3345 (2013). MOPHAM 0026-8976 10.1080/00268976.2013.813594
46. G.A. Tribello, M. Bonomi, D. Branduardi, C. Camilloni, and G. Bussi, Comput. Phys. Commun. 185, 604 (2014). CPHCBZ 0010-4655 10.1016/j.cpc.2013.09. 018
47. H.J. Kushner and G.G. Yin, Stochastic Approximation and Recursive Algorithms and Applications (Springer, New York, 1997), 2nd ed.
48. G.A. Tribello, M. Ceriotti, and M. Parrinello, Proc. Natl. Acad. Sci. U.S.A. 109, 5196 (2012). PNASA6 0027-8424 10.1073/pnas.1201152109
49. D. Branduardi, G. Bussi, and M. Parrinello, J. Chem. Theory Comput. 8, 2247 (2012). JCTCCE 1549-9618 10.1021/ct3002464
50. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevLett.112.240602 for detailed discussion of the Lyapunov function Eq. (11), especially algebraic manipulations used to derive Eq. (12) and its analog in the case (Equation presented) is not unique.
51. F. Baftizadeh, X. Biarnes, F. Pietrucci, F. Affinito, and A. Laio, J. Am. Chem. Soc. 134, 3886 (2012). JACSAT 0002-7863 10.1021/ja210826a