Combining ab initio quantum mechanics with a dipole-field model to describe acid dissociation reactions in water: First-principles free energy and entropy calculations

Journal of Chemical Physics

Volumn 132, Issue 7, 2010, Pages

  Maurer, Patrick ^a   Iftimie, Radu ^a  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

A-DENSITY; AB INITIO; AB INITIO MOLECULAR DYNAMICS SIMULATION; ACID DISSOCIATION; CHEMICAL RESIDUES; DISSOCIATION ENERGIES; EFFECTIVE POTENTIALS; ENTROPY EFFECTS; ENTROPY VALUE; EXCHANGE-CORRELATION FUNCTIONALS; EXPERIMENTAL OBSERVATION; EXPERIMENTAL VALUES; EXTERNAL POTENTIAL; FIELD MODEL; FIRST-PRINCIPLES; FREE-ENERGY PERTURBATION METHODS; GAS-PHASE GEOMETRY; NUMBER OF ELECTRONS; PROTON DISSOCIATION; QUANTUM MECHANICS; STRONG ACIDS; TRIFLUOROACETIC ACIDS; TRIFLUOROMETHYL; WATER BINDING; WEAK ACIDS;

ACIDS; BINDING ENERGY; DISSOCIATION; ENTROPY; FREE ENERGY; MECHANICS; MOLECULAR DYNAMICS; PERTURBATION TECHNIQUES; QUANTUM THEORY; REACTION KINETICS;

DENSITY FUNCTIONAL THEORY;

ACID; PROTON; SOLVENT; WATER;

ARTICLE; CHEMICAL MODEL; CHEMISTRY; ELECTRON; ENTROPY; KINETICS; MOLECULAR DYNAMICS; QUANTUM THEORY;

ACIDS; ELECTRONS; ENTROPY; KINETICS; MODELS, CHEMICAL; MOLECULAR DYNAMICS SIMULATION; PROTONS; QUANTUM THEORY; SOLVENTS; WATER;

EID: 77149144482     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3317398     Document Type: Article

References (129)

1. S. C. L. Kamerlin, M. Haranczyk, and A. Warshel, J. Phys. Chem. B JPCBFK 1089-5647 113, 1253 (2009). 10.1021/jp8071712
2. G. A. Voth, Acc. Chem. Res. ACHRE4 0001-4842 39, 143 (2006). 10.1021/ar0402098
3. D. Marx, ChemPhysChem CPCHFT 1439-4235 7, 1848 (2006). 10.1002/cphc.200600128
4. S. Braun-Sand, M. Strajbl, and A. Warshel, Biophys. J. BIOJAU 0006-3495 87, 2221 (2004). 10.1529/biophysj.104.043257 (Pubitemid 41071325)
5. T. E. Decoursey, Physiol. Rev. PHREA7 0031-9333 83, 475 (2003).
6. S. Cukierman, Biochim. Biophys., Acta-Bioenerg. 1757, 876 (2006). 10.1016/j.bbabio.2005.12.001 (Pubitemid 44462696)
7. C. A. Wraight, Biochim. Biophys., Acta-Bioenerg. 1757, 886 (2006). 10.1016/j.bbabio.2006.06.017 (Pubitemid 44462697)
8. J. M. J. Swanson, C. M. Maupin, H. N. Chen, M. K. Petersen, J. C. Xu, Y. J. Wu, and G. A. Voth, J. Phys. Chem. B JPCBFK 1089-5647 111, 4300 (2007). 10.1021/jp070104x (Pubitemid 46787622)
9. E. J. King, Acid-Base Equilibria (MacMillan, New York, 1965).
10. D. R. Lide, CRC Handbook of Chemistry and Physics (Taylor & Francis, New York, 2008).
11. R. L. Thurlkill, G. R. Grimsley, J. M. Scholtz, and C. N. Pace, Protein Sci. PRCIEI 0961-8368 15, 1214 (2006). 10.1110/ps.051840806
12. C. A. Fitch, D. A. Karp, K. K. Lee, W. E. Stites, E. E. Lattman, and E. B. Garcia-Moreno, Biophys. J. BIOJAU 0006-3495 82, 3289 (2002). 10.1016/S0006-3495(02)75670-1
13. C. Reichardt, Solvents and Solvent Effects in Organic Chemistry, 3rd ed. (Wiley-VCH, New York, 2003).
14. W. P. Jencks, Catalysis in Chemistry and Enzimology (Dover, New York, 1987).
15. A. Warshel, Annu. Rev. Biophys. Biomol. Struct. ABBSE4 1056-8700 32, 425 (2003). 10.1146/annurev.biophys.32.110601.141807 (Pubitemid 37056236)
16. N. C. Ha, M. S. Kim, W. Lee, K. Y. Choi, and B. H. Oh, J. Biol. Chem. JBCHA3 0021-9258 275, 41100 (2000). 10.1074/jbc.M007561200 (Pubitemid 32054939)
17. A. Warshel, P. K. Sharma, M. Kato, Y. Xiang, H. B. Liu, and M. H. M. Olsson, Chem. Rev. (Washington, D.C.) CHREAY 0009-2665 106, 3210 (2006). 10.1021/cr0503106 (Pubitemid 44376933)
18. D. G. Isom, B. R. Cannon, C. A. Castaneda, A. Robinson, and E. B. Garcia-Moreno, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 105, 17784 (2008). 10.1073/pnas.0805113105
19. H. Hu and W. Yang, Annu. Rev. Phys. Chem. ARPLAP 0066-426X 59, 573 (2008). 10.1146/annurev.physchem.59.032607.093618 (Pubitemid 351703398)
20. R. Friesner and B. Dunietz, Acc. Chem. Res. ACHRE4 0001-4842 34, 351 (2001). 10.1021/ar980111r
21. H. Lin and D. G. Truhlar, Theor. Chem. Acc. TCACFW 1432-881X 117, 185 (2007). 10.1007/s00214-006-0143-z
22. M. S. Gordon, L. Slipchenko, H. Li, J. H. Jensen, D. C. Spellmeyer, and R. Wheeler, Annu. Rep. Comp. Chem. ZZZZZZ 1574-1400 3, 177 (2007). 10.1016/S1574-1400(07)03010-1
23. N. Ghosh and Q. Cui, J. Phys. Chem. B JPCBFK 1089-5647 112, 8387 (2008). 10.1021/jp800168z
24. M. Kato and A. Warshel, J. Phys. Chem. B JPCBFK 1089-5647 110, 11566 (2006). 10.1021/jp061190o (Pubitemid 43999526)
25. D. Marx and J. Hutter, Ab Initio Molecular Dynamics (Cambridge University Press, New York, 2009). 10.1017/CBO9780511609633
26. M. Sprik, Chem. Phys. CMPHC2 0301-0104 258, 139 (2000). 10.1016/S0301-0104(00)00129-4
27. I. Ivanov, B. Chen, S. Raugei, and M. L. Klein, J. Phys. Chem. B JPCBFK 1089-5647 110, 6365 (2006). 10.1021/jp056750i
28. M. Sulpizi and M. Sprik, Phys. Chem. Chem. Phys. PPCPFQ 1463-9076 10, 5238 (2008). 10.1039/b802376j
29. J. J. Christensen, R. M. Izatt, and L. D. Hansen, J. Am. Chem. Soc. JACSAT 0002-7863 89, 213 (1967). 10.1021/ja00978a005
30. J. L. Kurz and J. M. Farrar, J. Am. Chem. Soc. JACSAT 0002-7863 91, 6057 (1969). 10.1021/ja01050a021
31. R. I. Gelb, L. M. Schwartz, and D. A. Laufer, J. Am. Chem. Soc. JACSAT 0002-7863 103, 5664 (1981). 10.1021/ja00409a006
32. M. Shirts, D. L. Mobley, and J. D. Chodera In, Annu. Rep. Comp. Chem. ZZZZZZ 1574-1400 3, 41 (2007). 10.1016/S1574-1400(07)03004-6
33. J. P. Perdew, R. G. Parr, M. Levy, and J. L. Balduz, Phys. Rev. Lett. PRLTAO 0031-9007 49, 1691 (1982). 10.1103/PhysRevLett.49.1691
34. Y. Zhang and W. Yang, Theor. Chem. Acc. TCACFW 1432-881X 103, 346 (2000). 10.1007/s002149900021
35. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Clarendon, Oxford, 1987), p 50.
36. A. Warshel, F. Sussman, and G. King, Biochemistry BICHAW 0006-2960 25, 8368 (1986). 10.1021/bi00374a006
37. V. Luzhkov and A. Warshel, J. Comput. Chem. JCCHDD 0192-8651 13, 199 (1992). 10.1002/jcc.540130212
38. X. Zeng, H. Hu, X. Hu, A. J. Cohen, and W. Yang, J. Chem. Phys. JCPSA6 0021-9606 128, 124510 (2008). 10.1063/1.2832946
39. K. A. Sharp and B. Honig, Annu. Rev. Biophys. Chem. 19, 301 (1990). 10.1146/annurev.bb.19.060190.001505 0021-9606
40. B. Honig and A. Nicholls, Science SCIEAS 0036-8075 268, 1144 (1995). 10.1126/science.7761829
41. M. Gunner and E. Alexov, Biochim. Biophys. Acta BBACAQ 0006-3002 1485, 63 (2000).
42. C. N. Schutz and A. Warshel, Proteins 18PLAF 0887-3585 44, 400 (2001). 10.1002/prot.1106 (Pubitemid 32768578)
43. C. P. Kelly, C. J. Cramer, and D. G. Truhlar, J. Phys. Chem. A JPCAFH 1089-5639 110, 2493 (2006). 10.1021/jp055336f
44. J. Kästner and W. Thiel, J. Chem. Phys. JCPSA6 0021-9606 123, 144104 (2005). 10.1063/1.2052648 (Pubitemid 41476700)
45. J. Hermans, J. Phys. Chem. JPCHAX 0022-3654 95, 9029 (1991). 10.1021/j100176a002
46. C. Jarzynski, Phys. Rev. Lett. PRLTAO 0031-9007 78, 2690 (1997). 10.1103/PhysRevLett.78.2690
47. G. Li, X. Zhang, and Q. Cui, J. Phys. Chem. B JPCBFK 1089-5647 107, 8643 (2003). 10.1021/jp034286g
48. A. Warshel, Computer Modeling of Chemical Reactions in Enzymes and Solutions (Wiley, Toronto, 1991).
49. C. Maupin, K. F. Wong, A. V. Soudakov, S. Kim, and G. A. Voth, J. Phys. Chem. A JPCAFH 1089-5639 110, 631 (2006). 10.1021/jp053596r (Pubitemid 43164653)
50. R. Vuilleumier and M. Sprik, Chem. Phys. Lett. CHPLBC 0009-2614 365, 305 (2002). 10.1016/S0009-2614(02)01435-5
51. R. Car and M. Parrinello, Phys. Rev. Lett. PRLTAO 0031-9007 55, 2471 (1985). 10.1103/PhysRevLett.55.2471
52. N. Lu, J. K. Singh, and D. A. Kofke, J. Chem. Phys. JCPSA6 0021-9606 118, 2977 (2003). 10.1063/1.1537241
53. M. R. Shirts, E. Bair, G. Hooker, and V. S. Pande, Phys. Rev. Lett. PRLTAO 0031-9007 91, 140601 (2003). 10.1103/PhysRevLett.91.140601
54. C. Chipot and A. Pohorille, Free Energy Calculations: Theory and Applications in Chemistry and Biology (Springer, New York, 2007).
55. S. Goedecker, M. Teter, and J. Hutter, Phys. Rev. B PRBMDO 0163-1829 54, 1703 (1996). 10.1103/PhysRevB.54.1703
56. P. Amara and M. J. Field, Theor. Chem. Acc. TCACFW 1432-881X 109, 43 (2003). 10.1007/s00214-002-0413-3 (Pubitemid 36299366)
57. W. Koch and M. C. Holthausen, A Chemist's Guide to Density Functional Theory (VCH, New York, 2000).
58. R. M. Martin, Electronic Structure: Basic Theory and Practical Methods (Cambridge University Press, New York, 2008).
59. D. Frenkel and B. Smit, Understanding Molecular Simulation: From Algorithms to Applications, 2nd ed. (Academic, New York, 2001).
60. G. J. Martyna and M. E. Tuckerman, J. Chem. Phys. JCPSA6 0021-9606 110, 2810 (1999). 10.1063/1.477923
61. L. P. Hammett, Physical Organic Chemistry, 2nd ed. (McGraw-Hill, New York, 1970).
62. E. V. Anslyn and D. A. Dougherty, Modern Physical Organic Chemistry, 3rd ed. (University Science Books, Sausalito, 2006).
63. G. A. DiLabio, M. M. Hurley, and P. A. Christiansen, J. Chem. Phys. JCPSA6 0021-9606 116, 9578 (2002). 10.1063/1.1477182 (Pubitemid 34690607)
64. S. Komin and D. Sebastiani, J. Chem. Theory Comput. JCTCCE 1549-9618 5, 1490 (2009). 10.1021/ct800525u
65. P. Slavíček and T. J. Martinez, J. Chem. Phys. JCPSA6 0021-9606 124, 084107 (2006). 10.1063/1.2173992 (Pubitemid 43313490)
66. R. Ponec and S. Van Damme, J. Phys. Org. Chem. JPOCEE 0894-3230 20, 662 (2007). 10.1002/poc.1228 (Pubitemid 47508029)
67. K. B. Wiberg, J. Org. Chem. JOCEAH 0022-3263 67, 1613 (2002). 10.1021/jo011051x (Pubitemid 34211608)
68. C. H. Bennett, J. Comput. Phys. JCTPAH 0021-9991 22, 245 (1976). 10.1016/0021-9991(76)90078-4
69. M. R. Shirts and V. S. Pande, J. Chem. Phys. JCPSA6 0021-9606 122, 144107 (2005). 10.1063/1.1873592 (Pubitemid 40858302)
70. F. M. Ytreberg, R. H. Swendsen, and D. M. Zuckerman, J. Chem. Phys. JCPSA6 0021-9606 125, 184114 (2006). 10.1063/1.2378907 (Pubitemid 44749470)
71. N. Lu, D. A. Kofke, and T. B. Woolf, J. Phys. Chem. B JPCBFK 1089-5647 107, 5598 (2003). 10.1021/jp027627j
72. C. Peter, C. Oostenbrink, A. Van Dorp, and W. F. Van Gunsteren, J. Chem. Phys. JCPSA6 0021-9606 120, 2652 (2004). 10.1063/1.1636153
73. S. Z. Wan, R. H. Stote, and M. Karplus, J. Chem. Phys. JCPSA6 0021-9606 121, 9539 (2004). 10.1063/1.1789935 (Pubitemid 40001718)
74. A. Ghoufi and P. Malfreyt, Mol. Phys. MOPHAM 0026-8976 104, 2929 (2006). 10.1080/00268970600893060 (Pubitemid 44439161)
75. J. Carlsson and J. Aqvist, J. Phys. Chem. B JPCBFK 1089-5647 113, 10255 (2009). 10.1021/jp900818z
76. J. Carlsson and J. Aqvist, J. Phys. Chem. B JPCBFK 1089-5647 109, 6448 (2005). 10.1021/jp046022f (Pubitemid 40496862)
77. J. Florián and A. Warshel, J. Phys. Chem. B JPCBFK 1089-5647 103, 10282 (1999). 10.1021/jp992041r
78. J. Hermans and L. Wang, J. Am. Chem. Soc. JACSAT 0002-7863 119, 2707 (1997). 10.1021/ja963568+ (Pubitemid 27189565)
79. M. Strajbl, Y. Y. Sham, J. Villa, Z. T. Chu, and A. Warshel, J. Phys. Chem. B JPCBFK 1089-5647 104, 4578 (2000). 10.1021/jp0003095
80. N. Singh and A. Warshel, J. Phys. Chem. B JPCBFK 1089-5647 113, 7372 (2009). 10.1021/jp811063v
81. C. L. Brooks, J. Phys. Chem. JPCHAX 0022-3654 90, 6680 (1986). 10.1021/j100283a017
82. S. H. Fleischman and C. L. Brooks, J. Chem. Phys. JCPSA6 0021-9606 87, 3029 (1987). 10.1063/1.453039
83. A. D. Becke, Phys. Rev. A PLRAAN 1050-2947 38, 3098 (1988). 10.1103/PhysRevA.38.3098
84. C. T. Lee, W. T. Yang, and R. G. Parr, Phys. Rev. B PRBMDO 0163-1829 37, 785 (1988). 10.1103/PhysRevB.37.785
85. N. Troullier and J. L. Martins, Phys. Rev. B PRBMDO 0163-1829 43, 1993 (1991). 10.1103/PhysRevB.43.1993
86. CPMD, Version 3, 11, Copyright IBM Corp 1990-2006, Copyright MPI für Festkörperforschung Stuttgart 1997-2001. For more details see www.cpmd.org.
87. M. E. Tuckerman, D. A. Yarne, S. O. Samuelson, A. L. Hughes, and G. J. Martyna, Comput. Phys. Commun. CPHCBZ 0010-4655 128, 333 (2000). 10.1016/S0010-4655(00)00077-1 (Pubitemid 30879018)
88. G. J. Martyna, M. L. Klein, and M. Tuckerman, J. Chem. Phys. JCPSA6 0021-9606 97, 2635 (1992). 10.1063/1.463940
89. See supplementary material at http://dx.doi.org/10.1063/1.3317398 E-JCPSA6-132-036007 for a complete set of geometry optimization parameters.
90. O. A. von Lilienfeld, I. Tavernelli, U. Rothlisberger and D. Sebastiani, J. Chem. Phys. JCPSA6 0021-9606 122, 014113 (2005). 10.1063/1.1829051 (Pubitemid 41047756)
91. H. Lin and D. G. Truhlar, J. Phys. Chem. A JPCAFH 1089-5639 109, 3991 (2005). 10.1021/jp0446332
92. P. H. Konig, M. Hoffmann, Th. Frauenheim, and Q. Cui, J. Phys. Chem. B JPCBFK 1089-5647 109, 9082 (2005). 10.1021/jp0442347 (Pubitemid 40750945)
93. B. A. Berg, Markov Chain Monte Carlo Simulations and their Statistical Analysis (World Scientific, New York, 2004).
94. I. F. W. Kuo, C. J. Mundy, M. J. Mcgrath, J. I. Siepmann, J. VandeVondele, M. Sprik, J. Hutter, B. Chen, M. L. Klein, F. Mohamed, M. Krack, and M. Parrinello, J. Phys. Chem. B JPCBFK 1089-5647 108, 12990 (2004). 10.1021/jp047788i
95. M. V. Fernández-Serra and E. Artacho, J. Chem. Phys. JCPSA6 0021-9606 121, 11136 (2004). 10.1063/1.1813431 (Pubitemid 40020652)
96. M. V. Fernández-Serra, G. Ferlat, and E. Artacho, Mol. Simul. MOSIEA 0892-7022 31, 361 (2005). 10.1080/08927020500066726 (Pubitemid 40844349)
97. V. Thomas and R. Iftimie, J. Phys. Chem. B JPCBFK 1089-5647 113, 4152 (2009). 10.1021/jp807378x
98. P. H. L. Sit and N. Marzari, J. Chem. Phys. JCPSA6 0021-9606 122, 204510 (2005). 10.1063/1.1908913 (Pubitemid 40858511)
99. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. PRLTAO 0031-9007 77, 3865 (1996). 10.1103/PhysRevLett.77.3865
100. A. Fortunelli, J. Mol. Struct.: THEOCHEM THEODJ 0166-1280 357, 117 (1995). 10.1016/0166-1280(95)04264-7
101. A. K. Covington, J. G. Freeman, and T. H. Lilley, J. Phys. Chem. JPCHAX 0022-3654 74, 3773 (1970). 10.1021/j100715a011
102. Iupac Project No. 2000-003-1-500. www.iupac.org/web/ins/2000-003-1-500.
103. I. C. Lin, A. P. Seitsonen, M. D. Coutinho-Neto, I. Tavernelli, and U. Rothlisberger, J. Phys. Chem. B JPCBFK 1089-5647 113, 1127 (2009). 10.1021/jp806376e
104. G. S. Fanourgakis, G. K. Schenter, and S. S. Xantheas, J. Chem. Phys. JCPSA6 0021-9606 125, 141102 (2006). 10.1063/1.2358137 (Pubitemid 44570765)
105. H. S. Lee and M. E. Tuckerman, J. Chem. Phys. JCPSA6 0021-9606 125, 154507 (2006). 10.1063/1.2354158 (Pubitemid 44601814)
106. B. Santra, A. Michaelides, and M. Scheffler, J. Chem. Phys. JCPSA6 0021-9606 127, 184104 (2007). 10.1063/1.2790009 (Pubitemid 350115909)
107. J. S. Arey, P. C. Aeberhard, I. C. Lin, and U. Rothlisberger, J. Phys. Chem. B JPCBFK 1089-5647 113, 4726 (2009). 10.1021/jp810323m
108. M. D. Liptak and G. C. Shields, Int. J. Quantum Chem. IJQCB2 0020-7608 105, 580 (2005). 10.1002/qua.20686 (Pubitemid 43082095)
109. F. C. Pickard Iv, D. R. Griffith, S. J. Ferrara, M. D. Liptak, K. N. Kirschner, and G. C. Shields, Int. J. Quantum Chem. IJQCB2 0020-7608 106, 3122 (2006). 10.1002/qua.21105 (Pubitemid 44726692)
110. O. A. von Lilienfeld, I. Tavernelli, U. Rothlisberger, and D. Sebastiani, Phys. Rev. Lett. PRLTAO 0031-9007 93, 153004 (2004). 10.1103/PhysRevLett.93. 153004
111. G. Caldwell, R. Renneboog, and P. Kebarle, Can. J. Chem. CJCHAG 0008-4042 67, 611 (1989). 10.1139/v89-092
112. M. Sheves, A. Albeck, N. Friedman, and M. Ottolenghi, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 83, 3262 (1986). 10.1073/pnas.83.10.3262
113. A. Warshel and M. Levitt, J. Mol. Biol. JMOBAK 0022-2836 103, 227 (1976). 10.1016/0022-2836(76)90311-9
114. A. Warshel and M. Karplus, J. Am. Chem. Soc. JACSAT 0002-7863 94, 5612 (1972). 10.1021/ja00771a014
115. C. J. Cramer and D. G. Truhlar, Chem. Rev. (Washington, D.C.) CHREAY 0009-2665 99, 2161 (1999). 10.1021/cr960149m
116. J. D. Chodera, W. C. Swope, J. W. Pitera, C. Seok, and K. A. Dill, J. Chem. Theory Comput. JCTCCE 1549-9618 3, 26 (2007). 10.1021/ct0502864
117. M. Kendall, A. Stuart, and J. Keith Ord, Design and Analysis, and Time-Series, 3rd ed. (Charles Griffin, London, 1983), Vol. 3, p. 444.
118. M. Kendall, A. Stuart, and J. Keith Ord, Design and Analysis, and Time-Series, 3rd ed. (Charles Griffin, London, 1983), Vol. 3, p. 550-552.
119. I. P. Castro In, An Introduction to the Digital Analysis of Stationary Signals: A Computer Illustrated Text (Taylor & Francis, New York, 1989), pp. 94-95.
120. R. Jimenez, G. R. Fleming, P. V. Kumar, and M. Maroncelli, Nature (London) NATUAS 0028-0836 369, 471 (1994). 10.1038/369471a0 (Pubitemid 24212119)
121. D. B. Spry and M. D. Fayer, J. Chem. Phys. JCPSA6 0021-9606 128, 084508 (2008). 10.1063/1.2825297 (Pubitemid 351328709)
122. J. Carlsson and J. Aqvist, Phys. Chem. Chem. Phys. PPCPFQ 1463-9076 8, 5385 (2006). 10.1039/b608486a
123. M. M. Kubo, E. Gallicchio, and R. M. Levy, J. Phys. Chem. B JPCBFK 1089-5647 101, 10527 (1997). 10.1021/jp972598b
124. W. L. Jorgensen, D. S. Maxwell, and J. Tirado-Rives, J. Am. Chem. Soc. JACSAT 0002-7863 118, 11225 (1996). 10.1021/ja9621760 (Pubitemid 26399746)
125. W. L. Jorgensen and J. Gao, J. Phys. Chem. JPCHAX 0022-3654 90, 2174 (1986). 10.1021/j100401a037
126. W. L. Jorgensen, J. Chandrasekhar, J. F. Madura, R. W. Impey, and M. L. Klein, J. Chem. Phys. JCPSA6 0021-9606 79, 926 (1983). 10.1063/1.445869
127. B. Hess, C. Kutzner, D. Van Der Spoel, and E. Lindahl, J. Chem. Theory Comput. JCTCCE 1549-9618 4, 435 (2008). 10.1021/ct700301q
128. G. Bussi, D. Donadio, and M. Parrinello, J. Chem. Phys. JCPSA6 0021-9606 126, 014101 (2007). 10.1063/1.2408420 (Pubitemid 46068390)
129. E. L. Lehmann and G. Casella, Theory of Point Estimation (Springer, New York, 1998).