Specialized methods for improving ergodic sampling using molecular dynamics and Monte Carlo simulations

Springer Series in Chemical Physics

Volumn 86, Issue , 2007, Pages 277-322

  Andricioaei, Ioan ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 62849089908     PISSN: 01726218     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-38448-9_8     Document Type: Review

References (158)

1. Eckmann, J.P.; Ruelle, D., Ergodic theory of chaos and strange attractors, Rev. Mod. Phys. 1985, 57, 617-656
2. Berne, B.J.; Straub, J.E., Novel methods of sampling phase space in the simulation of biological systems, Curr. Opin. Struct. Biol. 1997, 7, 181-189
3. Hodel, A.; Simonson, T.; Fox, R.O.; Brunger, A.T., Conformational substates and uncertainty in macromolecular free-energy calculations, J. Phys. Chem. 1993, 97, 3409-3417
4. Mountain, R.D.; Thirumalai, D., Measures of effective ergodic convergence in liquids, J. Phys. Chem. 1989, 93, 6975-6979
5. Mountain, R.D.; Thirumalai, D., Quantitative measure of efficiency of Monte-Carlo simulations, Physica A 1994, 210, 453-460
6. Straub, J.E.; Thirumalai, D., Exploring the energy landscape in proteins, Proc. Natl Acad. Sci. USA 1993, 90, 809-813
7. Straub, J.E.; Rashkin, A.; Thirumalai, D., Dynamics in rugged energy landscapes with applications to the S-peptide and Ribonuclease A, J. Am. Chem. Soc. 1994, 116, 2049
8. Siepmann, J.I.; Sprik, M., Folding of model heteropolymers by configurational-bias Monte Carlo, Chem. Phy. Lett. 1992, 199, 220
9. Rossky, P.J.; Doll, J.D.; Friedman, H.L., Brownian dynamics as smart Monte Carlo simulation, J. Chem. Phys. 1978, 69, 4628
10. Cao, J.; Berne, B.J., Monte Carlo methods for accelerating barrier crossing: anti-force-bias and variable step algorithms, J. Chem. Phys. 1990, 92, 1980
11. Frantz, D.D.; Freeman, D.L.; Doll, J.D., Reducing quasi-ergodic behavior in Monte Carlo simulation by J-walking: Applications to atomic clusters, J. Chem. Phys. 1990, 93, 2769
12. 8 clusters, J. Chem. Phys. 1993, 99, 6957
13. Marinari, E.; Parisi, G., Simulated tempering - a new Monte-Carlo scheme, Europhys. Lett. 1992, 19, 451-458
14. Geyer, C.J.; Thompson, E.A., Annealing Markov-chain Monte-Carlo with applications to ancestral inference, J. Am. Stat. Assoc. 1995, 90, 909-920
15. Hukushima, K.; Nemoto, K., Exchange Monte Carlo method and application to spin glass simulations, J. Phys. Soc. Jpn. 1996, 65, 1604-1608
16. Berg, B.A.; Neuhaus, T., Multicanonical algorithms for 1st order phase-transitions, Phys. Lett. B 1991, 267, 249-253
17. Berg, B.A.; Neuhaus, T., Multicanonical ensemble - a new approach to simulate 1st-order phase-transitions, Phys. Rev. Lett. 1992, 68, 9-12
18. Swendsen, R.H.; Wang, J.S., Nonuniversal critical-dynamics in Monte-Carlo simulations, Phys. Rev. Lett. 1987, 58, 86-88
19. Hansmann, U.H.E.; Okamoto, Y.; Eisenmenger, F., Molecular dynamics, Langevin and hybrid Monte Carlo simulations in a multicanonical ensemble, Chem. Phys. Lett. 1996, 259, 321-330
20. Torrie, G.M.; Valleau, J.P., Non-physical sampling distributions in Monte-Carlo free-energy estimation - umbrella sampling, J. Comput. Phys. 1977, 23, 187-199
21. Carter, E.A.; Ciccotti, G.; Haynes, J.T.; Kapral, R., Constrained reaction coordinate dynamics for the simulation of rare events, Chem. Phys. Lett. 1989, 156, 472-477
22. Darve, E.; Pohorille, A., Calculating free energies using average force, J. Chem. Phys. 2001, 115, 9169-9183
23. Torrie, G.M.; Valleau, J.P., Monte Carlo free energy estimates using non-Boltzmann sampling: Application to the subcritical Lennard-Jones fluid, Chem. Phys. Lett. 1974, 28, 578-581
24. Lee, J., New Monte-Carlo algorithm - entropic sampling, Phys. Rev. Lett. 1993, 71, 211-214
25. Nakajima, N.; Nakamura, H.; Kidera, A., Multicanonical ensemble generated by molecular dynamics simulation for enhanced conformational sampling of peptides, J. Phys. Chem. B 1997, 101, 817-824
26. Lyubartsev, A.P.; Martsinovski, A.A.; Shevkunov, S.V.; Vorontsovvelyaminov, P.N., New approach to Monte-Carlo calculation of the free-energy - method of expanded ensembles, J. Chem. Phys. 1992, 96, 1776-1783
27. Hesselbo, B.; Stinchcombe, R.B., Monte-Carlo simulation and global optimization without parameters, Phys. Rev. Lett. 1995, 74, 2151-2155
28. Bartels, C.; Karplus, M., Multidimensional adaptive umbrella sampling: applications to main chain and side chain peptide conformations, J. Comput. Chem. 1997, 18, 1450-1462
29. Darve, E.; Wilson, M.A.; Pohorille, A., Calculating free energies using a scaled-force molecular dynamics algorithm, Mol. Simul. 2002, 28, 113-144
30. Kumar, S.; Bouzida, D.; Swendsen, R.H.; Kollman, P.A.; Rosenberg, J.M., The weighted histogram analysis method for free-energy calculations on biomolecules. I. The method, J. Comput. Chem. 1992, 13, 1011-1021
31. Tsallis, C., Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys. 1988, 52, 479-487
32. Curado, E.M.F.; Tsallis, C., Generalized statistical mechanics: Connection with thermodynamics, J. Phys. A: Math. Gen. 1991, 24, L69
33. Andricioaei, I.; Straub, J.E., Generalized simulated annealing algorithms using Tsallis statistics: application to conformational optimization of a tetrapeptide, Phys. Rev. E 1996, 53, R3055-R3058
34. Andricioaei, I.; Straub, J.E.; Karplus, M., Simulation of quantum systems using path integrals in a generalized ensemble, Chem. Phys. Lett. 2001, 346, 274-282
35. Andricioaei, I.; Straub, J.E., On Monte Carlo and molecular dynamics methods inspired by Tsallis statistics: methodology, optimization, and application to atomic clusters, J. Chem. Phys. 1997, 107, 9117-9124
36. Bhattacharya, K.K.; Sethna, J.P., Multicanonical methods, molecular dynamics, and Monte Carlo methods: comparison for Lennard-Jones glasses, Phys. Rev. E 1998, 57, 2553-2562
37. Swendsen, R.H.; Wang, J.S., Replica Monte-Carlo simulation of spin-glasses, Phys. Rev. Lett. 1986, 57, 2607-2609
38. Manousiouthakis, V.I.; Deem, M.W., Strict detailed balance is unnecessary in Monte Carlo simulation, J. Chem. Phys. 1999, 110, 2753-2756
39. Kofke, D.A., On the acceptance probability of replica-exchange Monte Carlo trials, J. Chem. Phys. 2002, 117, 6911-6914
40. Predescu, C.; Predescu, M.; Ciobanu, C.V., On the efficiency of exchange in parallel tempering Monte Carlo simulations, J. Phys. Chem. B 2005, 109, 4189-4196
41. Schug, A.; Herges, T.; Wenzel, W., All-atom folding of the three-helix HIV accessory protein with an adaptive parallel tempering method, Proteins-Struct. Funct. Bioinform. 2004, 57, 792-798
42. Rathore, N.; Chopra, M.; de Pablo, J.J., Optimal allocation of replicas in parallel tempering simulations, J. Chem. Phys. 2005, 122
43. Sugita, Y.; Okamoto, Y., Replica-exchange molecular dynamics method for protein folding, Chem. Phys. Lett. 1999, 314, 141-151
44. Calvo, F., All-exchanges parallel tempering, J. Chem. Phys. 2005, 123
45. Calvo, F.; Neirotti, J.P.; Freeman, D.L.; Doll, J.D., Phase changes in 38-atom Lennard-Jones clusters. II. A parallel tempering study of equilibrium and dynamic properties in the molecular dynamics and microcanonical ensembles, J. Chem. Phys. 2000, 112, 10350-10357
46. Yan, Q.L.; de Pablo, J.J., Hyper-parallel tempering Monte Carlo: Application to the Lennard-Jones fluid and the restricted primitive model, J. Chem. Phys. 1999, 111, 9509-9516
47. Andricioaei, I.; Straub, J.E., On Monte Carlo and molecular dynamics methods inspired by Tsallis statistics: methodology, optimization, and application to atomic clusters, J. Chem. Phys. 1997, 107, 9117-9124
48. Whitfield, T.W.; Bu, L.; Straub, J.E., Generalized parallel sampling, Physica A - Stat. Mech. Appl. 2002, 305, 157-171
49. Jang, S.M.; Shin, S.; Pak, Y., Replica-exchange method using the generalized effective potential, Phys. Rev. Lett. 2003, 91
50. Liu, H.B.; Jordan, K.D., On the convergence of parallel tempering Monte Carlo simulations of LJ(38), J. Phys. Chem. A 2005, 109, 5203-5207
51. Sugita, Y.; Kitao, A.; Okamoto, Y., Multidimensional replica-exchange method for free-energy calculations, J. Chem. Phys. 2000, 113, 6042-6051
52. Fukunishi, H.; Watanabe, O.; Takada, S., On the Hamiltonian replica exchange method for efficient sampling of biomolecular systems: application to protein structure prediction, J. Chem. Phys. 2002, 116, 9058-9067
53. Sugita, Y.; Okamoto, Y., Replica-exchange multicanonical algorithm and multicanonical replica-exchange method for simulating systems with rough energy landscape, Chem. Phys. Lett. 2000, 329, 261-270
54. Faller, R.; Yan, Q.L.; de Pablo, J.J., Multicanonical parallel tempering, J. Chem. Phys. 2002, 116, 5419-5423
55. Hansmann, U.H.E., Parallel tempering algorithm for conformational studies of biological molecules, Chem. Phys. Lett. 1997, 281, 140-150
56. Garcia, A.E.; Onuchic, J.N., Folding a protein in a computer: An atomic description of the folding/unfolding of protein A, Proc. Natl Acad. Sci. USA 2003, 100, 13898-13903
57. Falcioni, M.; Deem, M.W., A biased Monte Carlo scheme for zeolite structure solution, J. Chem. Phys. 1999, 110, 1754-1766
58. Haliloglu, T.; Kolinski, A.; Skolnick, J., Use of residual dipolar couplings as restraints in ab initio protein structure prediction, Biopolymers 2003, 70, 548-562
59. Earl, D.J.; Deem, M.W., Parallel tempering: theory, applications, and new perspectives, Phys. Chem. Chem. Phys. 2005, 7, 3910-3916
60. Frantz, D.D.; Freeman, D.L.; Doll, J.D., Reducing quasi-ergodic behavior in Monte-Carlo simulations by J-walking - applications to atomic clusters, J. Chem. Phys. 1990, 93, 2769-2784
61. Neirotti, J.P.; Calvo, F.; Freeman, D.L.; Doll, J.D., Phase changes in 38-atom Lennard-Jones clusters. I. A parallel tempering study in the canonical ensemble, J. Chem. Phys. 2000, 112, 10340-10349
62. Stolovitzky, G.; Berne, B.J., Catalytic tempering: A method for sampling rough energy landscapes by Monte Carlo, Proc. Natl Acad. Sci. USA 2000, 97, 11164-11169
63. Purisima, E.O.; Scheraga, H.A., An approach to the multiple-minima problem by relaxing dimensionality, Proc. Natl Acad. Sci. USA 1986, 83, 2782-2786
64. Faken, D.B.; Voter, A.F.; Freeman, D.L.; Doll, J.D., Dimensional strategies and the minimization problem: barrier-avoiding algorithms, J. Phys. Chem. A 1999, 103, 9521-9526
65. Stillinger, F.H.; Weber, T.A., Hidden structure in liquids, Phys. Rev. A 1982, 25, 978-989
66. Stillinger, F.H.; Weber, T.A., Packing structures and transitions in liquids and solids, Science 1984, 225, 983-989
67. Zhou, R.; Berne, B.J., Smart walking: A new method for Boltzmann sampling of protein conformations, J. Chem. Phys. 1997, 107, 9185
68. Li, Z.Q.; Scheraga, H.A., Monte-Carlo-minimization approach to the multiple-minima problem in protein folding, Proc. Natl Acad. Sci. USA 1987, 84, 6611-6615
69. Rahman, J.A.; Tully, J.C., Puddle-jumping: A flexible sampling algorithm for rare event systems, Chem. Phys. 2002, 285, 277-287
70. Bogdan, T.V.; Wales, D.J.; Calvo, F., Equilibrium thermodynamics from basin-sampling, J. Chem. Phys. 2006, 124
71. Nigra, P.; Freeman, D.L.; Doll, J.D., Combining smart darting with parallel tempering using Eckart space: Application to Lennard-Jones clusters, J. Chem. Phys. 2005, 122
72. Amadei, A.; Linssen, A.B.M.; Berendsen, H.J.C., Essential dynamics of proteins, Proteins 1993, 17, 412-425
73. Balsera, M.A.; Wriggers, W.; Oono, Y.; Schulten, K., Principal component analysis and long time protein dynamics, J. Phys. Chem. 1996, 100, 2567-2572
74. Duane, S.; Kennedy, A.D.; Pendleton, B.J.; Roweth, D., Hybrid Monte Carlo, Phys. Lett. B 1987, 195, 216-222
75. Mehlig, B.; Heermann, D.W.; Forrest, B.M., Hybrid Monte Carlo method for condensed-matter systems, Phys. Rev. B 1992, 45, 679-685
76. Metropolis, N.; Rosenbluth, A.W.; Rosenbluth, N.N.; Teller, A.H.; Teller, E., Equation of state calculations by fast computing machines, J. Chem. Phys. 1953, 21, 1087-1092
77. Miller, M.A.; Amon, L.M.; Reinhardt, W.P., Should one adjust the maximum step size in a Metropolis Monte Carlo simulation? Chem. Phys. Lett. 2000, 331, 278-284
78. Bouzida, D.; Kumar, S.; Swendsen, R.H., Efficient Monte Carlo methods for the computer simulation of biological systems, Phys. Rev. A 1992, 45, 8894-8901
79. Ryckaert, J.P.; Ciccotti, G.; Berendsen, H.J.C., Numerical integration of the Cartesian equations of motion of a system with constraints: Molecular dynamics of n-alkanes, J. Comput. Phys. 1977, 23, 327-341
80. Chun, H.M.; Padilla, C.E.; Chin, D.N.; Watanabe, M.; Karlov, V.I.; Alper, H.E.; Soosaar, K.; Blair, K.B.; Becker, O.M.; Caves, L.S.D.; Nagle, R.; Haney, D.N.; Farmer, B.L., MBO(N)D: A multibody method for long-time molecular dynamics simulations, J. Comput. Chem. 2000, 21, 159-184
81. Tuckerman, M.E.; Martyna, G.J.; Berne, B.J., Molecular-dynamics algorithm for condensed systems with multiple time scales, J. Chem. Phys. 1990, 93, 1287-1291
82. Elber, R.; Meller, J.; Olender, R., Stochastic path approach to compute atomically detailed trajectories: application to the folding of C peptide, J. Phys. Chem. B 1999, 103, 899-911
83. Elber, R.; Ghosh, A.; Cardenas, A., Long time dynamics of complex systems, Acc. Chem. Res. 2002, 35, 396-403
84. Nadler, W.; Schulten, K., Generalized moment expansion for Brownian relaxation processes, J. Chem. Phys. 1985, 82, 151-160
85. Kostov, K.S.; Freed, K.F., Mode coupling theory for calculating the memory functions of flexible chain molecules: influence on the long time dynamics of oligoglycines, J. Chem. Phys. 1997, 106, 771-783
86. Space, B.; Rabitz, H.; Askar, A., Long time scale molecular dynamics subspace integration method applied to anharmonic crystals and glasses, J. Chem. Phys. 1993, 99, 9070-9079
87. Dauber-Osguthorpe, P.; Maunder, C.M.; Osguthorpe, D.J., Molecular dynamics: Deciphering the data, J. Comput. Aided Mol. Des. 1996, 10, 177-185
88. Phillips, S.C.; Essex, J.W.; Edge, C.M., Digitally filtered molecular dynamics: the frequency specific control of molecular dynamics simulations, J. Chem. Phys. 2000, 112, 2586-2597
89. Elber, R.; Karplus, M., Enhanced sampling in molecular-dynamics - use of the time-dependent Hartree approximation for a simulation of carbon-monoxide diffusion through myoglobin, J. Am. Chem. Soc. 1990, 112, 9161-9175
90. Ulitsky, A.; Elber, R., Application of the locally enhanced sampling (LES) and a mean-field with a binary collision correction (CLES) to the simulation of Ar diffusion and NO recombination in myoglobin, J. Phys. Chem. 1994, 98, 1034-1043
91. Huber, T.; van Gunsteren, W.F., SWARM-MD: searching conformational space by cooperative molecular dynamics, J. Phys. Chem. A 1998, 102, 5937-5943
92. Simmerling, C.; Fox, T.; Kollman, P.A., Use of locally enhanced sampling in free energy calculations: Testing and application to the alpha → beta anomerization of glucose, J. Am. Chem. Soc. 1998, 120, 5771-5782
93. Piela, L.; Kostrowicki, J.; Scheraga, H.A., The multiple-minima problem in the conformational-analysis of molecules - deformation of the potential-energy hypersurface by the diffusion equation method, J. Phys. Chem. 1989, 93, 3339-3346
94. Liu, Z.H.; Berne, B.J., Method for accelerating chain folding and mixing, J. Chem. Phys. 1993, 99, 6071-6077
95. Whitfield, T.W.; Bu, L.; Straub, J.E., Generalized parallel sampling, Physica A 2002, 305, 157-171
96. Krivov, S.V.; Chekmarev, S.F.; Karplus, M., Potential energy surfaces and conformational transitions in biomolecules: A successive confinement approach applied to a solvated tetrapeptide, Phys. Rev. Lett. 2002, 88, 038101
97. Andricioaei, I.; Straub, J.E., On Monte Carlo and molecular dynamics methods inspired by Tsallis statistics: methodology, optimization, and application to atomic clusters, J. Chem. Phys. 1997, 107, 9117-9124
98. Hansmann, U.H.E.; Okamoto, Y., Generalized-ensemble Monte Carlo method for systems with rough energy landscapes, Phys. Rev. E 1997, 56, 2228-2233
99. Frantz, D.D.; Freeman, D.L.; Doll, J.D., Reducing quasi-ergodic behavior in Monte Carlo simulations by J-walking: applications to atomic clusters, J. Chem. Phys. 1990, 93, 2769-2784
100. Marinari, E.; Parisi, G., Simulated tempering - A new Monte Carlo scheme, Europhys. Lett. 1992, 19, 451-458
101. Hansmann, U.H.E., Parallel tempering algorithm for conformational studies of biological molecules, Chem. Phys. Lett. 1997, 281, 140-150
102. Hess, B., Similarities between principal components of protein dynamics and random diffusion, Phys. Rev. E 2000, 62, 8438-8448
103. Tuckerman, M.; Berne, B.J.; Martyna, G.J., Reversible multiple time scale molecular dynamics, J. Chem. Phys. 1992, 97, 1990-2001
104. Jarzynski, C., Nonequilibrium equality for free energy differences, Phys. Rev. Lett. 1997, 78, 2690-2693
105. Jorgensen, W.L.; Ravimohan, C., Monte Carlo simulation of differences in free energies of hydration, J. Chem. Phys. 1985, 83, 3050-3054
106. Hummer, G.; Szabo, A., Free energy reconstruction from nonequilibrium single-molecule pulling experiments, Proc. Natl Acad. Sci. USA 2001, 98, 3659-3661
107. Dellago, C.; Bolhuis, P.G.; Csajka, F.S.; Chandler, D., Transition path sampling and the calculation of rate constants, J. Chem. Phys. 1998, 108, 1964-1977
108. Dellago, C.; Bolhuis, P.G.; Chandler, D., On the calculation of reaction rate constants in the transition path ensemble, J. Chem. Phys. 1999, 110, 6617-6625
109. Oberhofer, H.; Dellago, C.; Geissler, P.L., Biased sampling of nonequilibrium trajectories: can fast switching simulations outperform conventional free energy calculation methods?, J. Phys. Chem. B 2005, 109, 6902-6915
110. Corcelli, S.A.; Rahman, J.A.; Tully, J.C., Efficient thermal rate constant calculation for rare event systems, J. Chem. Phys. 2003, 118, 1085-1088
111. Voter, A.F., Hyperdynamics: Accelerated molecular dynamics of infrequent events, Phys. Rev. Lett. 1997, 78, 3908-3911
112. Voter, A.F., A method for accelerating the molecular dynamics simulation of infrequent events, J. Chem. Phys. 1997, 106, 4665-4677
113. Hamelberg, D.; Mongan, J.; McCammon, J.A., Accelerated molecular dynamics: a promising and efficient simulation method for biomolecules, J. Chem. Phys. 2004, 120, 11919-11929
114. Laio, A.; Parrinello, M., Escaping free-energy minima, Proc. Natl Acad. Sci. USA 2002, 99, 12562-12566
115. Huber, G.A.; Kim, S., Weighted-ensemble Brownian dynamics simulations for protein association reactions, Biophys. J. 1996, 70, 97-110
116. Grubmuller, H., Predicting slow structural transitions in macromolecular systems - conformational flooding, Phys. Rev. E 1995, 52, 2893-2906
117. MacFadyen, J.; Andricioaei, I., A skewed-momenta method to efficiently generate conformational-transition trajectories, J. Chem. Phys. 2005, 123, 074107
118. Brooks, B.R.; Janezic, D.; Karplus, M., Harmonic-analysis of large systems. 1. Methodology, J. Comput. Chem. 1995, 16, 1522-1542
119. Andricioaei, I.; Dinner, A.R.; Karplus, M., Self-guided enhanced sampling methods for thermodynamic averages, J. Chem. Phys. 2003, 118, 1074-1084
120. Go, N.; Noguti, T.; Nishikawa, T., Dynamics of a small globular protein in terms of low-frequency vibrational-modes, Proc. Natl Acad. Sci. USA - Biol. Sci. 1983, 80, 3696-3700
121. Levitt, M.; Sander, C.; Stern, P.S., Protein normal-mode dynamics - trypsin-inhibitor, crambin, ribonuclease and lysozyme, J. Mol. Biol. 1985, 181, 423-447
122. Brooks, B.; Karplus, M., Normal-modes for specific motions of macromolecules - application to the hinge-bending mode of lysozyme, Proc. Natl Acad. Sci. USA 1985, 82, 4995-4999
123. Ma, J.P.; Karplus, M., Ligand-induced conformational changes in ras p21: a normal mode and energy minimization analysis, J. Mol. Biol. 1997, 274, 114-131
124. Cui, Q.; Li, G.H.; Ma, J.P.; Karplus, M., A normal mode analysis of structural plasticity in the biomolecular motor F-1-ATPase, J. Mol. Biol. 2004, 340, 345-372
125. Tama, F.; Sanejouand, Y.H., Conformational change of proteins arising from normal mode calculations, Protein Eng. 2001, 14, 1-6
126. Krebs, W.G.; Alexandrov, V.; Wilson, C.A.; Echols, N.; Yu, H.Y.; Gerstein, M., Normal mode analysis of macromolecular motions in a database framework: developing mode concentration as a useful classifying statistic, Proteins-Struct. Funct. Gene. 2002, 48, 682-695
127. Delarue, M.; Sanejouand, Y.H., Simplified normal mode analysis of conformational transitions in DNA-dependent polymerases: the elastic network model, J. Mol. Biol. 2002, 320, 1011-1024
128. Tama, F.; Valle, M.; Frank, J.; Brooks, C.L., Dynamic reorganization of the functionally active ribosome explored by normal mode analysis and cryo-electron microscopy, Proc. Natl Acad. Sci. USA 2003, 100, 9319-9323
129. Braun, O.; Hanke, A.; Seifert, U., Probing molecular free energy landscapes by periodic loading, Phys. Rev. Lett. 2004, 93
130. Sun, S.X., Equilibrium free energies from path sampling of nonequilibrium trajectories, J. Chem. Phys. 2003, 118, 5769-5775
131. Ytreberg, F.M.; Zuckerman, D.M., Single-ensemble nonequilibrium path-sampling estimates of free energy differences, J. Chem. Phys. 2004, 120, 10876-10879
132. Mukamel, S., Quantum extension of the Jarzynski relation: analogy with stochastic dephasing, Phys. Rev. Lett. 2003, 90
133. Lua, R.C.; Grosberg, A.Y., Practical applicability of the Jarzynski relation in statistical mechanics: a pedagogical example, J. Phys. Chem. B 2005, 109, 6805-6811
134. Palmer, A.G., NMR characterization of the dynamics of biomacromolecules, Chem. Rev. 2004, 104, 3623-3640
135. Kleinert, H., Path Integrals in Quantum Mechanics, Statistics, Polymer Physics and Financial Markets, (3rd edition), World Scientific, Singapore
136. Onsager, L.; Machlup, S., Fluctuations and irreversible processes, Phys. Rev. 1953, 91, 1505-1512
137. Elber, R.; Meller, J.; Olender, R., Stochastic path approach to compute atomically detailed trajectories: application to the folding of C peptide, J. Phys. Chem. B 1999, 103, 899-911
138. Zuckerman, D.M.; Woolf, T.B., Efficient dynamic importance sampling of rare events in one dimension, Phys. Rev. E 2001, 6302, 016702
139. Chandler, D.; Wolynes, P.G., Exploiting the isomorphism between quantum theory and classical statistical mechanics of polyatomic fluids, J. Chem. Phys. 1981, 74, 4078-4095
140. Berne, B.J.; Thirumalai, D., On the simulation of quantum systems: path integral methods, Annu. Rev. Phys. Chem. 1986, 37, 401-424
141. Feynman, R.P.; Hibbs, A.R., Quantum Mechanics and Path Integrals, McGraw-Hill: New York, 1965
142. Barker, J.A., A quantum-statistical Monte Carlo method: Path integrals with boundary conditions, J. Chem. Phys. 1979, 70, 2914-2918
143. Parrinello, M.; Rahman, A., Study of an F center in molten KCl, J. Chem. Phys. 1980, 80, 860-867
144. Kuharski, R.A.; Rossky, P.J., Quantum mechanical contributions to the structure of liquid water, Chem. Phys. Lett. 1984, 103, 357-362
145. Thirumalai, D.; Wallqvist, A.; Berne, B.J., Path-integral Monte Carlo simulations of electron localization in water clusters, J. Stat. Phys. 1986, 43, 973-984
146. Hinsen, K.; Roux, B., Potential of mean force and reaction rates for proton transfer in acetylacetone, J. Chem. Phys. 1997, 106, 3567-3577
147. Ceperley, D.M., Path-integrals in the theory of condensed helium, Rev. Mod. Phys. 1995, 67, 279-355
148. Schweizer, K.S.; Stratt, R.M.; Chandler, D.; Wolynes, P.G., Convenient and accurate discretized path integral methods for equilibrium quantum mechanical calculations, J. Chem. Phys. 1981, 75, 1347-1364
149. Pollock, E.L.; Ceperley, D.M., Simulation of quantum many-body systems by path-integral methods, Phys. Rev. B 1984, 30, 2555-2568
150. Raedt, H.De; Raedt, B.De, Applications of the generalized Trotter formula, Phys. Rev. A 1983, 28, 3575-3580
151. Sprik, M.; Klein, M.L.; Chandler, D., Staging: A sampling technique for the Monte Carlo evaluation of path integrals, Phys. Rev. B 1985, 31, 4234-4244
152. Herman, M.F.; Bruskin, E.J.; Berne, B.J., On path integral Monte Carlo simulations, J. Chem. Phys. 1982, 76, 5150-5155
153. Friesner, R.A.; Levy, R.M., An optimized harmonic reference system for the evaluation of discretized path integrals, J. Chem. Phys. 1984, 80, 4488-4495
154. Straub, J.E.; Andricioaei, I., Computational methods inspired by Tsallis statistics: Monte Carlo and molecular dynamics algorithms for the simulation of classical and quantum systems, Braz. J. Phys. 1999, 29, 179-186
155. Andricioaei, I.; Straub, J.E., Computational methods for the simulation of classical and quantum many body systems sprung from the nonextensive thermostatistics. In Nonextensive Statistical Mechanics and Its Application, Abe, S.; Okamoto, Y., Eds., Lecture Notes in Physics. Springer: Berlin, Heidelberg, New York, 2001, ch. IV, pp. 195-235
156. Tsallis, C., Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys. 1988, 52, 479-487
157. Chandler, D. Quantum processes in liquids. In Liquids, Freezing and Glass Transition, Levesque, D.; Hansen, J.; Zinn-Justin, J., Eds. Elsevier: New York, 1990, pp. 195-285
158. Cao, J.; Voth, G.A., The formulation of quantum statistical mechanics based on Feynman path centroid density, J. Chem. Phys. 1994, 100, 5093-5105