Recent developments in QM/MM methods towards open-boundary multi-scale simulations

Molecular Simulation

Volumn 41, Issue 1-3, 2015, Pages 168-189

  Pezeshki, Soroosh ^a   Lin, Hai ^a  

^a UNIVERSITY OF COLORADO   (United States)

Author keywords

adaptive partition; conservation of energy and momentum; electronegativity equalisation; on the fly reclassification; partial charge transfer

Indexed keywords

CHARGE TRANSFER; CHEMICAL BONDS; ELECTRONEGATIVITY; MOLECULAR MODELING; QUANTUM THEORY;

ADAPTIVE PARTITIONS; CONSERVATION OF ENERGY; EQUALISATION; ON THE FLIES; PARTIAL CHARGE TRANSFER;

BIOINFORMATICS;

EID: 84926135997     PISSN: 08927022     EISSN: 10290435     Source Type: Journal    
DOI: 10.1080/08927022.2014.911870     Document Type: Article

References (306)

1. Ayton GS, Noid WG, Voth GA. Multiscale modeling of biomolecular systems: in serial and in parallel. Curr Opin Struct Biol. 2007;17:192-198.
2. Sherwood P, Brooks BR, Sansom MSP. Multiscale methods for macromolecular simulations. Curr Opin Struct Biol. 2008;18:630-640.
3. Tozzini V. Multiscale modeling of proteins. Acc Chem Res. 2010;43:220-230.
4. Elliott JA. Novel approaches to multiscale modelling in materials science. Int Mater Rev. 2011;56:207-225.
5. Kamerlin SCL, Vicatos S, Dryga A, Warshel A. Coarse-grained (multiscale) simulations in studies of biophysical and chemical systems. Annu Rev Phys Chem. 2011;62:41-64.
6. Woodcock HL, Miller BT, Hodoscek M, Okur A, Larkin JD, Ponder JW, Brooks BR. MSCALE: a general utility for multiscale modeling. J Chem Theory Comput. 2011;7:1208-1219.
7. Kirchner B, Vrabec J, editors. Multiscale molecular methods in applied chemistry. Topics in current chemistry. Heidelberg: Springer; 2012.
8. Meier K, Choutko A, Dolenc J, Eichenberger AP, Riniker S, van Gunsteren WF. Multi-resolution simulation of biomolecular systems: a review of methodological issues. Angew Chem Int Ed. 2013;52:2820-2834.
9. Warshel A, Levitt M. Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme. J Mol Biol. 1976;103:227-249.
10. Singh UC, Kollmann PA. A combined ab initio quantum mechanical and molecular mechanical method for carrying out simulations on complex molecular systems: applications to the CH3Cl + Cl2 exchange reaction and gas phase protonation of polyethers. J Comput Chem. 1986;7:718-730.
11. Field MJ, Bash PA, Karplus M. A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations. J Comput Chem. 1990;11:700-733.
12. Gao J. Methods and applications of combined quantum mechanical and molecular mechanical potentials. Rev Comput Chem. 1996;7:119-185.
13. Mordasini T, Thiel W. Computational chemistry column: combined quantum mechanical and molecular approaches. Chimia. 1998;52:288-291.
14. Hillier IH. Chemical reactivity studied by hybrid QM/MM methods. THEOCHEM. 1999;463:45-52.
15. Monard G, Merz KM Jr. Combined quantum mechanical/molecular mechanical methodologies applied to biomolecular systems. Acc Chem Res. 1999;32:904-911.
16. Hammes-Schiffer S. Theoretical perspectives on proton-coupled electron transfer reactions. Acc Chem Res. 2000;34:273-281.
17. Sherwood P. Hybrid quantum mechanics/molecular mechanics approaches. In: Grotendorst J, editor. Modern methods and algorithms of quantum chemistry. Jülich: John von Neumann-Instituts; 2000. p. 285-305.
18. Gao J, Truhlar DG. Quantum mechanical methods for enzyme kinetics. Annu Rev Phys Chem. 2002;53:467-505.
19. Morokuma K. New challenges in quantum chemistry: quests for accurate calculations for large molecular systems. Philos Trans R Soc Lond A. 2002;360:1149-1164.
20. Lin H, Truhlar DG. QM/MM: what have we learned, where are we, and where do we go from here Theory Chem Acc. 2007;117:185-199.
21. Senn HM, Thiel W. QM/MM methods for biological systems. Top Curr Chem. 2007;268:173-290.
22. Hu H, Yang W. Free energies of chemical reactions in solution and in enzymes with ab initio quantum mechanics/molecular mechanics methods. Annu Rev Phys Chem. 2008;59:573-601.
23. Bernstein N, Kermode JR, Csányi G. Hybrid atomistic simulation methods for materials systems. Rep Prog Phys. 2009;72: 026501/1-25.
24. Senn HM, Thiel W. QM/MM methods for biomolecular systems. Angew Chem Int Ed. 2009;48:1198-1229.
25. Acevedo O, Jorgensen WL. Advances in quantum and molecular mechanical (QM/MM) simulations for organic and enzymatic reactions. Acc Chem Res. 2010;43:142-151.
26. Sabin JR, Brändas E, editors. Combining quantum mechanics and molecular mechanics. Some recent progresses in QM/MM methods. Advances in quantum chemistry. New York: Academic Press; 2010.
27. Yohsuke H, Masaru T. Recent advances in jointed quantum mechanics and molecular mechanics calculations of biological macromolecules: schemes and applications coupled to ab initio calculations. J Phys Condens Matter. 2010;22:413101/1-7.
28. Ferrer S, Ruiz-Pernia J, Marti S, Moliner V, Tunon I, Bertran J, Andres J. Hybrid schemes based on quantum mechanics/molecular mechanics simulations: goals to success, problems, and perspectives. In: Christov C, editor. Advances in protein chemistry and structural biology: computational chemistry methods in structural biology. Vol 85. San Diego: Elsevier; 2011. p. 81-142.
29. Menikarachchi LC, Gascon JA. QM/MM approaches in medicinal chemistry research. Curr Top Med Chem. 2010;10:46-54.
30. Wallrapp FH, Guallar V. Mixed quantum mechanics and molecular mechanics methods: looking inside proteins. Wiley Interdiscip Rev Comput Mol Sci. 2011;1:315-322.
31. Chung LW, Hirao H, Li X, Morokuma K. The ONIOM method: its foundation and applications to metalloenzymes and photobiology. Wiley Interdiscip Rev Comput Mol Sci. 2012;2:327-350.
32. Keil FJ. Multiscale modelling in computational heterogeneous catalysis. In: Kirchner B, Vrabec J, editors. Multiscale molecular methods in applied chemistry. Heidelberg: Springer; 2012. p. 69-107.
33. Lonsdale R, Harvey JN, Mulholland AJ. A practical guide to modelling enzyme-catalysed reactions. Chem Soc Rev. 2012;41:3025-3038.
34. Monari A, Rivail J-L, Assfeld X. Theoretical modeling of large molecular systems. Advances in the local self consistent field method for mixed quantum mechanics/molecular mechanics calculations. Acc Chem Res. 2012;46:596-603.
35. Site L, Holm C, Vegt NA. Multiscale approaches and perspectives to modeling aqueous electrolytes and polyelectrolytes. In: Kirchner B, Vrabec J, editors. Multiscale molecular methods in applied chemistry. Berlin: Springer; 2012. p. 251-294.
36. Wu R, Cao Z, Zhang Y. Computational simulations of zinc enzyme: challenges and recent advances. Prog Chem. 2012;24:1175-1184.
37. Yockel S, Schatz G. Dynamic QM/MM: a hybrid approach to simulating gas-liquid interactions. In: Kirchner B, Vrabec J, editors. Multiscale molecular methods in applied chemistry. Heidelberg: Springer; 2012. p. 43-67.
38. Mennucci B. Modeling environment effects on spectroscopies through QM/classical models. Phys Chem Chem Phys. 2013;15:6583-6594.
39. Kussmann J, Beer M, Ochsenfeld C. Linear-scaling self-consistent field methods for large molecules. Wiley Interdiscip Rev Comput Mol Sci. 2013;3:614-636.
40. Zhang Y, Lin H. Flexible-boundary QM/MM calculations: II. Partial charge transfer across the QM/MM boundary that passes through a covalent bond. Theory Chem Acc. 2010;126:315-322.
41. Lin H, Truhlar DG. Redistributed charge and dipole schemes for combined quantum mechanical and molecular mechanical calculations. J Phys Chem A. 2005;109:3991-4004.
42. Zhang Y, Lin H, Truhlar DG. Self-consistent polarization of the boundary in the redistributed charge and dipole scheme for combined quantum-mechanical and molecular-mechanical calculations. J Chem Theory Comput. 2007;3:1378-1398.
43. Zhang Y, Lin H. Flexible-boundary quantum-mechanical/molecular-mechanical calculations: partial charge transfer between the quantum-mechanical and molecular-mechanical subsystems. J Chem Theory Comput. 2008;4:414-425.
44. Pezeshki S, Lin H. Adaptive-partitioning redistributed charge and dipole schemes for QM/MM dynamics simulations: on-the-fly relocation of boundaries that pass through covalent bonds. J Chem Theory Comput. 2011;7:3625-3634.
45. Heyden A, Lin H, Truhlar DG. Adaptive partitioning in combined quantum mechanical and molecular mechanical calculations of potential energy functions for multiscale simulations. J Phys Chem B. 2007;111:2231-2241.
46. Antes I, Thiel W. On the treatment of link atoms in hybrid methods. ACS Symp Ser. 1998;712:50-65.
47. Bentzien J, Florian J, Glennon TM, Warshel A. Quantum mechanical-molecular mechanical approaches for studying chemical reactions in proteins and solution. ACS Symp Ser. 1998;712:16-34.
48. Merz KM Jr. Quantum mechanical-molecular mechanical coupled potentials. ACS Symp Ser. 1998;712:2-15.
49. Woo TK, Margl PM, Deng L, Cavallo L, Ziegler T. Combined QM/MM and ab initio molecular dynamics modeling of homogeneous catalysis. ACS Symp Ser. 1999;721:173-186.
50. Bakowies D, Thiel W. Hybrid models for combined quantum mechanical and molecular mechanical approaches. J Phys Chem. 1996;100:10580-10594.
51. Murphy RB, Philipp DM, Friesner RA. A mixed quantum mechanics/molecular mechanics (QM/MM) method for large-scale modeling of chemistry in protein environments. J Comput Chem. 2000;21:1442-1457.
52. Riccardi D, Li GH, Cui Q. Importance of van der Waals interactions in QM/MM simulations. J Phys Chem B. 2004;108:6467-6478.
53. Freindorf M, Shao Y, Furlani TR, Kong J. Lennard-Jones parameters for the combined QM/MM method using the B3LYP/6-31G/AMBER potential. J Comput Chem. 2005;26:1270-1278.
54. Giese TJ, York DM. Charge-dependent model for many-body polarization, exchange, and dispersion interactions in hybrid quantum mechanical/molecular mechanical calculations. J Chem Phys. 2007;127:194101/1-11.
55. Jin Y, Johnson ER, Hu X, Yang W, Hu H. Contributions of pauli repulsions to the energetics and physical properties computed in QM/MM methods. J Comput Chem. 2013;34:2380-2388.
56. Singh UC, Kollman PA. An approach to computing electrostatic charges for molecules. J Comput Chem. 1984;5:129-145.
57. Besler BH, Merz KM Jr., Kollman PA. Atomic charges derived from semi-empirical methods. J Comput Chem. 1990;11:431-439.
58. Francl MM, Carey C, Chirlian LE, Gange DM. Charges fit to electrostatic potentials. II: can atomic charges be unambiguously fit to electrostatic potentials J Comput Chem. 1996;17:367-383.
59. Zhang Y, Liu H, Yang W. Free energy calculation on enzyme reactions with an efficient iterative procedure to determine minimum energy paths on a combined ab initio QM/MM potential energy surface. J Chem Phys. 2000;112:3483-3492.
60. Kästner J, Senn HM, Thiel S, Otte N, Thiel W. QM/MM freeenergy perturbation compared to thermodynamic integration and umbrella sampling: application to an enzymatic reaction. J Chem Theory Comput. 2006;2:452-461.
61. Donini O, Darden T, Kollman PA. QM-FE calculations of aliphatic hydrogen abstraction in citrate synthase and in solution: reproduction of the effect of enzyme catalysis and demonstration that an enolate rather than an enol is formed. J Am Chem Soc. 2000;122:12270-12280.
62. Rod TH, Ryde U. Accurate QM/MM free energy calculations of enzyme reactions: methylation by catechol O-methyltransferase. J Chem Theory Comput. 2005;1:1240-1251.
63. Rod TH, Ryde U. Quantum mechanical free energy barrier for an enzymatic reaction. Phys Rev Lett. 2005;94:138302/1-4.
64. Valiev M, Garrett BC, Tsai M-K, Kowalski K, Kathmann SM, Schenter GK, Dupuis M. Hybrid approach for free energy calculations with high-level methods: application to the SN2 reaction of CHCl3 and OH2 in water. J Chem Phys. 2007;127:051102/1-4.
65. Valiev M, Bylaska EJ, Dupuis M, Tratnyek PG. Combined quantum mechanical and molecular mechanics studies of the electron-transfer reactions involving carbon tetrachloride in solution. J Phys Chem A. 2008;112:2713-2720.
66. Martins-Costa MTC, Anglada JM, Francisco JS, Ruiz-Lopez MF. Reactivity of volatile organic compounds at the surface of a water droplet. J Am Chem Soc. 2012;134:11821-11827.
67. Polyak I, Benighaus T, Boulanger E, Thiel W. Quantum mechanics/molecular mechanics dual Hamiltonian free energy perturbation. J Chem Phys. 2013;139:064105/1-11.
68. Jensen KP, Ryde U. How the CoZC bond is cleaved in coenzyme B12 enzymes: a theoretical study. J Am Chem Soc. 2005;127:9117-9128.
69. Kwiecien RA, Khavrutskii IV, Musaev DG, Morokuma K, Banerjee R, Paneth P. Computational insights into the mechanism of radical generation in B12-dependent methylmalonyl-CoA mutase. J Am Chem Soc. 2006;128:1287-1292.
70. MacKerell AD Jr., Bashford D, Bellott M, Dunbrack RL, Evanseck JD, Field MJ, Fischer S, Gao J, Guo H, Ha S, Joseph-McCarthy D, Kuchnir L, Kuczera K, Lau FTK, Mattos C, Michnick S, Ngo T, Nguyen DT, Prodhom B, Reiher WE III, Roux B, Schlenkrich M, Smith JC, Stote R, Straub J, Watanabe M, Wiorkiewicz-Kuczera J, Yin D, Karplus M. All-Atom empirical potential for molecular modeling and dynamics studies of proteins. J Phys Chem B. 1998;102:3586-3616.
71. Sherwood P, De Vries AH, Collins SJ, Greatbanks SP, Burton NA, Vincent MA, Hillier IH. Computer simulation of zeolite structure and reactivity using embedded cluster methods. Faraday Discuss. 1997;106:79-92.
72. Day PN, Jensen JH, Gordon MS, Webb SP, Stevens WJ, Krauss M, Garmer D, Basch H, Cohen D. An effective fragment method for modeling solvent effects in quantum mechanical calculations. J Chem Phys. 1996;105:1968-1986.
73. Freitag MA, Gordon MS, Jensen JH, Stevens WJ. Evaluation of charge penetration between distributed multipolar expansions. J Chem Phys. 2000;112:7300-7306.
74. Das D, Eurenius KP, Billings EM, Sherwood P, Chatfield DC, Hodoscek M, Brooks BR. Optimization of quantum mechanical molecular mechanical partitioning schemes: Gaussian delocalization of molecular mechanical charges and the double link atom method. J Chem Phys. 2002;117:10534-10547.
75. Amara P, Field MJ. Evaluation of an ab initio quantum mechanical/molecular mechanical hybrid-potential link-Atom method. Theory Chem Acc. 2003;109:43-52.
76. Cisneros GA, Piquemal J-P, Darden TA. Quantum mechanics/molecular mechanics electrostatic embedding with continuous and discrete functions. J Phys Chem B. 2006;110:13682-13684.
77. Cisneros GA, Tholander SN-I, Parisel O, Darden TA, Elking D, Perera L, Piquemal JP. Simple formulas for improved point-charge electrostatics in classical force fields and hybrid quantum mechanical/molecular mechanical embedding. Int J Quant Chem. 2008;108:1905-1912.
78. Wang B, Truhlar DG. Including charge penetration effects in molecular modeling. J Chem Theory Comput. 2010;6:3330-3342.
79. Alvarez-Ibarra A, Köster AM, Zhang R, Salahub DR. Asymptotic expansion for electrostatic embedding integrals in QM/MM calculations. J Chem Theory Comput. 2012;8:4232-4238.
80. Nam K, Gao J, York DM. An efficient linear-scaling Ewald method for long-range electrostatic interactions in combined QM/MM calculations. J Chem Theory Comput. 2005;1:2-13.
81. Riccardi D, Schaefer P, Cui Q. pKa calculations in solution and proteins with QM/MM free energy perturbation simulations: a quantitative test of QM/MM protocols. J Phys Chem B. 2005;109:17715-17733.
82. Schaefer P, Riccardi D, Cui Q. Reliable treatment of electrostatics in combined QM/MM simulation of macromolecules. J Chem Phys. 2005;123:014905/1-14.
83. Meier K, Schmid N, van Gunsteren WF. Interfacing the GROMOS (bio)molecular simulation software to quantum-chemical program packages. J Comput Chem. 2012;33:2108-2117.
84. Dinner AR, Lopez X, Karplus M. A charge-scaling method to treat solvent in QM/MM simulations. Theory Chem Acc. 2003;109:118-124.
85. Gao J, Alhambra C. A hybrid semiempirical quantum mechanical and lattice-sum method for electrostatic interactions in fluid simulations. J Chem Phys. 1997;107:1212-1217.
86. Laino T, Mohamed F, Laio A, Parrinello M. An efficient linearscaling electrostatic coupling for treating periodic boundary conditions in QM/MM simulations. J Chem Theory Comput. 2006;2:1370-1378.
87. Walker RC, Crowley MF, Case DA. The implementation of a fast and accurate QM/MM potential method in Amber. J Comput Chem. 2008;29:1019-1031.
88. Nakano H, Yamamoto T. Accurate and efficient treatment of continuous solute charge density in the mean-field QM/MM free energy calculation. J Chem Theory Comput. 2012;9:188-203.
89. Gregersen BA, York DM. Variational electrostatic projection (VEP) methods for efficient modeling of the macromolecular electrostatic and solvation environment in activated dynamics simulations. J Phys Chem B. 2005;109:536-556.
90. Riccardi D, Cui Q. pKa Analysis for the zinc-bound water in human carbonic anhydrase II: benchmark for 'multiscale' QM/MM simulations and mechanistic implications. J Phys Chem A. 2007;111:5703-5711.
91. Benighaus T, Thiel W. Efficiency and accuracy of the generalized solvent boundary potential for hybrid QM/MM simulations: implementation for semiempirical Hamiltonians. J Chem Theory Comput. 2008;4:1600-1609.
92. Heimdal J, Kaukonen M, Srnec M, Ruĺsek L, Ryde U. Reduction potentials and acidity constants of Mn superoxide dismutase calculated by QM/MM free-energy methods. ChemPhysChem. 2011;12:3337-3347.
93. Boulanger E, Thiel W. Solvent boundary potentials for hybrid QM/MM computations using classical Drude oscillators: a fully polarizable model. J Chem Theory Comput. 2012;8:4527-4538.
94. Lu X, Cui Q. Charging free energy calculations using the generalized solvent boundary potential (GSBP) and periodic boundary condition: a comparative analysis using ion solvation and oxidation free energy in proteins. J Phys Chem B. 2013;117:2005-2018.
95. Ojeda-May P, Pu J. Isotropic periodic sum treatment of long-range electrostatic interactions in combined quantum mechanical and molecular mechanical calculations. J Chem Theory Comput, 2013. DOI: 10.1021/ct400724d
96. Humbel S, Sieber S, Morokuma K. The IMOMO method: integration of different levels of molecular orbital approximations for geometry optimization of large systems: test for n-butane conformation and SN2 reaction: RCl + Cl2. J Chem Phys. 1996;105:1959-1967.
97. Dapprich S, Komiromi I, Byun KS, Morokuma K, Frisch MJ. A new ONIOM implementation in Gaussian98. Part I: the calculation of energies, gradients, vibrational frequencies and electric field derivatives. THEOCHEM. 1999;461-462:1-21.
98. Waszkowycz B, Hillier IH, Gensmantel N, Payling DW. Combined quantum mechanical-molecular mechanical study of catalysis by the enzyme phospholipase A2: an investigation of the potential energy surface for amide hydrolysis. J Chem Soc Perkin Trans. 1991;2:2025-2032.
99. Eurenius KP, Chatfield DC, Brooks BR, Hodoscek M. Enzyme mechanisms with hybrid quantum and molecular mechanical potentials. I. Theoretical considerations. Int J Quant Chem. 1996;60:1189-1200.
100. Lyne PD, Hodoscek M, Karplus M. A hybrid QM-MM potential employing Hartree-Fock or density functional methods in the quantum region. J Phys Chem A. 1999;103:3462-3471.
101. Lev B, Zhang R, de la Lande A, Salahub D, Noskov SY. The QM-MM interface for CHARMM-deMon. J Comput Chem. 2010;31:1015-1023.
102. Sinclair PE, de Vries A, Sherwood P, Catlow CRA, van Santen RA. Quantum-chemical studies of alkene chemisorption in chabazite: a comparison of cluster and embedded-cluster models. J Chem Soc Faraday Trans. 1998;94:3401-3408.
103. de Vries AH, Sherwood P, Collins SJ, Rigby AM, Rigutto M, Kramer GJ. Zeolite structure and reactivity by combined quantumchemical-classical calculations. J Phys Chem B. 1999;103: 6133-6141.
104. Sherwood P, de Vries AH, Guest MF, Schreckenbach G, Catlow CRA, French SA, Sokol AA, Bromley ST, Thiel W, Turner AJ, Billeter S, Terstegen F, Thiel S, Kendrick J, Rogers SC, Casci J, Watson M, King F, Karlsen E, Sjovoll M, Fahmi A, Schafer A, Lennartz C. QUASI: a general purpose implementation of the QM/MM approach and its application to problems in catalysis. THEOCHEM. 2003;632:1-28.
105. König PH, Hoffmann M, Frauenheim T, Cui Q. A critical evaluation of different QM/MM frontier treatments with SCCDFTB as the QM method. J Phys Chem B. 2005;109:9082-9095.
106. Zhang Y, Lee T-S, Yang W. A pseudobond approach to combining quantum mechanical and molecular mechanical methods. J Chem Phys. 1999;110:46-54.
107. Abarenkov IV, Tupitsyn II. A new separable potential operator for representing a chemical bond and other applications. J Chem Phys. 2001;115:1650-1660.
108. Poteau R, Ortega I, Alary F, Solis AR, Barthelat JC, Daudey JP. Effective group potentials: 1. Method. J Phys Chem A. 2001;105:198-205.
109. DiLabio GA, Hurley MM, Christiansen PA. Simple one-electron quantum capping potentials for use in hybrid QM/MM studies of biological molecules. J Chem Phys. 2002;116:9578-9584.
110. Laio A, VandeVondele J, Röthlisberger U. A Hamiltonian electrostatic coupling scheme for hybrid Car-Parrinello molecular dynamics simulations. J Chem Phys. 2002;116:6941-6947.
111. Bessac F, Alary F, Carissan Y, Heully J-L, Daudey J-P, Poteau R. Effective group potentials: a powerful tool for hybrid QM/MM methods THEOCHEM. 2003;632:43-59.
112. Yasuda K, Yamaki D. Simple minimum principle to derive a quantum-mechanical/molecular-mechanical method. J Chem Phys. 2004;121:3964-3972.
113. DiLabio GA, Wolkow RA, Johnson ER. Efficient silicon surface and cluster modeling using quantum capping potentials. J Chem Phys. 2005;122:044708/1-5.
114. von Lilienfeld OA, Tavernelli I, Rothlisberger U, Sebastiani D. Variational optimization of effective atom centered potentials for molecular properties. J Chem Phys. 2005;122:014113/1-6.
115. Zhang Y. Improved pseudobonds for combined ab initio quantum mechanical/molecular mechanical methods. J Chem Phys. 2005;122:024114/1-7.
116. Carissan Y, Bessac F, Alary F, Heully J-L, Poteau R. What can we do with an effective group potential Int J Quant Chem. 2006;106:727-733.
117. Slavicek P, Martinez TJ. Multicentered valence electron effective potentials: a solution to the link atom problem for ground and excited electronic states. J Chem Phys. 2006;124:084107/1-10.
118. Zhang Y. Pseudobond ab initio QM/MM approach and its applications to enzyme reactions. Theory Chem Acc. 2006;116:43-50.
119. Dogel IA, Dogel SA, Pitters JL, DiLabio GA, Wolkow RA. Chemical methods for the hydrogen termination of silicon dangling bonds. Chem Phys Lett. 2007;448:237-242.
120. Nakamura Y, Takahashi N, Okamoto M, Uda T, Ohno T. Link molecule method for quantum mechanical/molecular mechanical hybrid simulations. J Comput Phys. 2007;225:1985-1993.
121. Xiao C, Zhang Y. Design-Atom approach for the quantum mechanical/molecular mechanical covalent boundary: a designcarbon atom with five valence electrons. J Chem Phys. 2007;127:124102/1-9.
122. DiLabio GA. Accurate treatment of van der Waals interactions using standard density functional theory methods with effective core-type potentials: application to carbon-containing dimers. Chem Phys Lett. 2008;455:348-353.
123. Jardillier N, Goursot A. One-electron quantum capping potential for hybrid QM/MM studies of silicate molecules and solids. Chem Phys Lett. 2008;454:65-69.
124. Raynaud C, Rosal I, Jolibois F, Maron L, Poteau R. Multicentered effective group potentials: ligand-field effects in organometallic clusters and dynamical study of chemical reactivity. Theory Chem Acc. 2010;126:151-163.
125. Exner TE. Critical investigation on the pseudobond approach for QM/MM and fragment-based QM methods. Int J Quant Chem. 2011;111:1002-1012.
126. Ihrig AC, Schiffmann C, Sebastiani D. Specific quantum mechanical/molecular mechanical capping-potentials for biomolecular functional groups. J Chem Phys. 2011;135:214107/1-7.
127. Schiffmann C, Sebastiani D. Artificial bee colony optimization of capping potentials for hybrid quantum mechanical/molecular mechanical calculations. J Chem Theory Comput. 2011;7:1307-1315.
128. Shao Y, Kong J. YinYang atom: a simple combined ab initio quantum mechanical molecular mechanical model. J Phys Chem A. 2007;111:3661-3671.
129. Field MJ, Albe M, Bret C, Martin FP-D, Thomas A. The dynamo library for molecular simulations using hybrid quantum mechanical and molecular mechanical potentials. J Comput Chem. 2000;21:1088-1100.
130. Ferré N, Olivucci M. The amide bond: pitfalls and drawbacks of the link atom scheme. THEOCHEM. 2003;632:71-82.
131. Antes I, Thiel W. Adjusted connection atoms for combined quantum mechanical and molecular mechanical methods. J Phys Chem A. 1999;103:9290-9295.
132. Eichinger M, Tavan P, Hutter J, Parrinello M. A hybrid method for solutes in complex solvents: density functional theory combined with empirical force fields. J Chem Phys. 1999;110:10452-10467.
133. Woodcock HL, Hodoscek M, Gilbert ATB, Gill PMW, Schaefer HF, Brooks BR. Interfacing Q-Chem and CHARMM to perform QM/MM reaction path calculations. J Comput Chem. 2007;28:1485-1502.
134. Thery V, Rinaldi D, Rivail J-L, Maigret B, Ferenczy GG. Quantum-mechanical computations on very large molecular systems: the local self-consistent field method. J Comput Chem. 1994;15:269-282.
135. Assfeld X, Rivail J-L. Quantum chemical computations on parts of large molecules: the ab initio local self consistent field method. Chem Phys Lett. 1996;263:100-106.
136. Monard G, Loos M, Thery V, Baka K, Rivail J-L. Hybrid classical quantum force field for modeling very large molecules. Int J Quant Chem. 1996;58:153-159.
137. Ferré N, Assfeld X, Rivail J-L. Specific force field parameters determination for the hybrid ab Initio QM/MM LSCF method. J Comput Chem. 2002;23:610-624.
138. Fornili A, Loos P-F, Sironi M, Assfeld X. Frozen core orbitals as an alternative to specific frontier bond potential in hybrid quantum mechanics/molecular mechanics methods. Chem Phys Lett. 2006;427:236-240.
139. Philipp DM, Friesner RA. Mixed ab initio QM/MM modeling using frozen orbitals and tests with alanine dipeptide and tetrapeptide. J Comput Chem. 1999;20:1468-1494.
140. Murphy RB, Philipp DM, Friesner RA. Frozen orbital QM/MM methods for density functional theory. Chem Phys Lett. 2000;321:113-120.
141. Gao J, Amara P, Alhambra C, Field MJ. A generalized hybrid orbital (GHO) method for the treatment of boundary atoms in combined QM/MM calculations. J Phys Chem A. 1998;102:4714-4721.
142. Amara P, Field MJ, Alhambra C, Gao J. The generalized hybrid orbital method for combined quantum mechanical/molecular mechanical calculations: formulation and tests of the analytical derivatives. Theory Chem Acc. 2000;104:336-343.
143. Garcia-Viloca M, Gao J. Generalized hybrid orbital for the treatment of boundary atoms in combined quantum mechanical and molecular mechanical calculations using the semiempirical parameterized model 3 method. Theory Chem Acc. 2004;111:280-286.
144. Pu J, Gao J, Truhlar DG. Generalized hybrid orbital (GHO) method for combining ab initio Hartree-Fock wave functions with molecular mechanics. J Phys Chem A. 2004;108:632-650.
145. Pu J, Gao J, Truhlar DG. Combining self-consistent-charge density-functional tight-binding (SCC-DFTB) with molecularmechanics by the generalized hybrid orbital (GHO) method. J Phys Chem A. 2004;108:5454-5463.
146. Pu J, Gao J, Truhlar DG. Generalized hybrid-orbital method for combining density functional theory with molecular mechanicals. ChemPhysChem. 2005;6:1853-1865.
147. Wang B, Truhlar DG. Combined quantum mechanical and molecular mechanical methods for calculating potential energy surfaces: tuned and balanced redistributed-charge algorithm. J Chem Theory Comput. 2010;6:359-369.
148. Wang B, Truhlar DG. Geometry optimization using tuned and balanced redistributed charge schemes for combined quantum mechanical and molecular mechanical calculations. Phys Chem Chem Phys. 2011;13:10556-10564.
149. Tuned and balanced redistributed charge scheme for combined quantum mechanical and molecular mechanical (QM/MM) methods and fragment methods: tuning based on the CM5 charge model. J Chem Theory Comput. 2012;9:1036-1042.
150. Dick BG Jr., Overhauser AW. Theory of the dielectric constants of alkali halide crystals. Phys Rev. 1958;112:90-103.
151. Stillinger FH, David CW. Polarization model for water and its ionic dissociation products. J Chem Phys. 1978;69:1473-1484.
152. Sprik M, Klein ML. A polarizable model for water using distributed charge sites. J Chem Phys. 1988;89:7556-7560.
153. Dang LX, Rice JE, Caldwell J, Kollman PA. Ion solvation in polarizable water: molecular dynamics simulations. J Am Chem Soc. 1991;113:2481-2486.
154. Dang LX. The nonadditive intermolecular potential for water revised. J Chem Phys. 1992;97:2659-2660.
155. Rick SW, Stuart SJ,BerneBJ.Dynamicfluctuating charge forcefields: application to liquid water. J Chem Phys. 1994;101:6141-6156.
156. Kowall T, Foglia F, Helm L, Merbach AE. Molecular dynamics simulation study of lanthanide ions Ln3+ in aqueous solution including water polarization. Change in coordination number from 9 to 8 along the series. J Am Chem Soc. 1995;117:3790-3799.
157. Banks JL, Kaminski GA, Zhou R, Mainz DT, Berne BJ, Friesner RA. Parameterizing a polarizable force field from ab initio data. I. The fluctuating point charge model. J Chem Phys. 1999;110:741-754.
158. Stern HA, Kaminski GA, Banks JL, Zhou R, Berne BJ, Friesner RA. Fluctuating charge, polarizable dipole, and combined models: parameterization from ab initio quantum chemistry. J Phys Chem B. 1999;103:4730-4737.
159. Martinez JM, Hernandez-Cobos J, Saint-Martin H, Pappalardo RR, Ortega-Blake I, Marcos ES. Coupling a polarizable water model to the hydrated ion-water interaction potential: a test on the Cr3+ hydration. J Chem Phys. 2000;112:2339-2347.
160. Wang J, Cieplak P, Kollman PA. How well does a restrained electrostatic potential (RESP) model perform in calculating conformational energies of organic and biological molecules J Comput Chem. 2000;21:1049-1074.
161. Cieplak P, Caldwell J, Kollman P. Molecular mechanical models for organic and biological systems going beyond the atom centered two body additive approximation: aqueous solution free energies of methanol and N-methyl acetamide, nucleic acid base, and amide hydrogen bonding and chloroform/water partition coefficients of the nucleic acid bases. J Comput Chem. 2001;22:1048-1057.
162. Rick SW, Stuart SJ. Potentials and algorithms for incorporating polarizability in computer simulations. Rev Comput Chem. 2002;18:89-146.
163. Lamoureux G, MacKerell AD, Roux B. A simple polarizable model of water based on classical Drude oscillators. J Chem Phys. 2003;119:5185-5197.
164. Ponder JW, Case DA. Force fields for protein simulations. Adv Protein Chem. 2003;66:27-85.
165. Kaminski GA, Stern HA, Berne BJ, Friesner RA. Development of an accurate and robust polarizable molecular mechanics force field from ab initio quantum chemistry. J Phys Chem A. 2004;108:621-627.
166. Patel S, Brooks CL III. CHARMM fluctuating charge force field for proteins: I parameterization and application to bulk organic liquid simulations. J Comput Chem. 2004;25:1-15.
167. Patel S, Mackerell AD Jr., Brooks CL III. CHARMM fluctuating charge force field for proteins: II protein/solvent properties from molecular dynamics simulations using a nonadditive electrostatic model. J Comput Chem. 2004;25:1504-1514.
168. Anisimov VM, Lamoureux G, Vorobyov IV, Huang N, Roux B, MacKerell AD. Determination of electrostatic parameters for a polarizable force field based on the classical Drude oscillator. J Chem Theory Comput. 2005;1:153-168.
169. Vorobyov IV, Anisimov VM, MacKerell AD Jr. Polarizable empirical force field for alkanes based on the classical Drude oscillator model. J Phys Chem B. 2005;109:18988-18999.
170. Wang Z-X, Zhang W, Wu C, Lei H, Cieplak P, Duan Y. Strike a balance: optimization of backbone torsion parameters of AMBER polarizable force field for simulations of proteins and peptides. J Comput Chem. 2006;27:781-790.
171. Kaminski GA, Stern HA, Berne BJ, Friesner RA, Cao YX, Murphy RB, Zhou R, Halgren TA. Development of a polarizable force field for proteins via ab initio quantum chemistry: first generation model and gas phase tests. J Comput Chem. 2002;23:1515-1531.
172. Ren P, Ponder JW. Consistent treatment of inter-And intramolecular polarization in molecular mechanics calculations. J Comput Chem. 2002;23:1497-1506.
173. Sefcik J, Demiralp E, Cagin T, Goddard WA. Dynamic charge equilibration-Morse stretch force field: application to energetics of pure silica zeolites. J Comput Chem. 2002;23:1507-1514.
174. Grossfield A, Ren P, Ponder JW. Ion solvation thermodynamics from simulation with a polarizable force field. J Am Chem Soc. 2003;125:15671-15682.
175. Ren P, Ponder JW. Polarizable atomic multipole water model for molecular mechanics simulation. J Phys Chem B. 2003;107:5933-5947.
176. Ma Y, Garofalini SH. Iterative fluctuation charge model: a new variable charge molecular dynamics method. J Chem Phys. 2006;124:234102/1-7.
177. Lopes PM, Roux B, MacKerell A Jr. Molecular modeling and dynamics studies with explicit inclusion of electronic polarizability: theory and applications. Theory Chem Acc. 2009;124:11-28.
178. Smalo HS, Astrand P-O, Jensen L. Nonmetallic electronegativity equalization and point-dipole interaction model including exchange interactions for molecular dipole moments and polarizabilities. J Chem Phys. 2009;131:044101/1-19.
179. Ponder JW. Current status of the AMOEBA polarizable force field. J Phys Chem B. 2010;114:2549-2564.
180. Ponomarev SY, Kaminski GA. Polarizable simulations with second-order interaction model (POSSIM) force field: developing parameters for alanine peptides and protein backbone. J Chem Theory Comput. 2011;7:1415-1427.
181. Ren P, Wu C, Ponder JW. Polarizable atomic multipole-based molecular mechanics for organic molecules. J Chem Theory Comput. 2011;7:3143-3161.
182. Kim WH, Rhee YM. Molecule-specific determination of atomic polarizabilities with the polarizable atomic multipole model. J Comput Chem. 2012;33:1662-1672.
183. Lamoureux G, Orabi EA. Molecular modelling of cation-p interactions. Mol Simul. 2012;38:704-722.
184. Cisneros GA, Karttunen M, Ren P, Sagui C. Classical electrostatics for biomolecular simulations. Chem Rev ASAP, 2013. dx.doi.org/10.1021/cr300461d
185. Baker CM, Best RB. Matching of additive and polarizable force fields for multiscale condensed phase simulations. J Chem Theory Comput. 2013;9:2826-2837.
186. Han J, Mazack MJM, Zhang P, Truhlar DG, Gao J. Quantum mechanical force field for water with explicit electronic polarization. J Chem Phys. 2013;139:054503/1-18.
187. Li X, Ponomarev SY, Sa Q, Sigalovsky DL, Kaminski GA. Polarizable simulations with second order interaction model (POSSIM) force field: developing parameters for protein sidechain analogues. J Comput Chem. 2013;34:1241-1250.
188. Shi Y, Xia Z, Zhang J, Best R, Wu C, Ponder JW, Ren P. Polarizable atomic multipole-based AMOEBA force field for proteins. J Chem Theory Comput. 2013;9:4046-4063.
189. Thompson MA, Schenter GK. Excited states of the bacteriochlorophyll b dimer of Rhodopseudomonas viridis: a QM/MM study of the photosynthetic reaction center that includes MM polarization. J Phys Chem. 1995;99:6374-6386.
190. Thompson MA. Hybrid quantum mechanical/molecular mechanical force field development for large flexible molecules: a molecular dynamics study of 18-crown-6. J Phys Chem. 1995;99:4794-4804.
191. Bakowies D, Thiel W. Semiempirical treatment of electrostatic potentials and partial charges in combined quantum mechanical and molecular mechanical approaches. J Comput Chem. 1996;17:87-108.
192. York DM, Yang W. A chemical potential equalization method for molecular simulations. J Chem Phys. 1996;104:159-172.
193. Yang Z-Z, Wang C-S. Atom-bond electronegativity equalization method. 1. Calculation of the charge distribution in large molecules. J Phys Chem A. 1997;101:6315-6321.
194. Gao J. Energy components of aqueous solution: insight from hybrid QM/MM simulations using a polarizable solvent model. J Comput Chem. 1997;18:1061-1071.
195. Gao J, Byun K. Solvent effects on the n !p transition of pyrimidine in aqueous solution. Theory Chem Acc. 1997;96:151-156.
196. Gao J, Alhambra C. Solvent effects on the bond length alternation and absorption energy of conjugated compounds. J Am Chem Soc. 1997;119:2962-2963.
197. Itskowitz P, Berkowitz ML. Chemical potential equalization principle: direct approach from density functional theory. J Phys Chem A. 1997;101:5687-5691.
198. Bryce RA, Vincent MA, Malcolm NOJ, Hillier IH, Burton NA. Cooperative effects in the structuring of fluoride water clusters: ab initio hybrid quantum mechanical/molecular mechanical model incorporating polarizable fluctuating charge solvent. J Chem Phys. 1998;109:3077-3085.
199. Bultinck P, Langenaeker W, Lahorte P, De Proft F, Geerings P, Waroquier M, Tollenaere JP. The electronegativity equalization method I: parameterization and validation for atomic charge calculations. J Phys Chem AJ Phys. 2002;106:7887-7894.
200. Jensen L, van Duijnen PT, Snijders JG. A discrete solvent reaction field model within density functional theory. J Chem Phys. 2003;118:514-521.
201. Illingworth CJR, Gooding SR, Winn PJ, Jones GA, Ferenczy GG, Reynolds CA. Classical polarization in hybrid QM/MM methods. J Phys Chem A. 2006;110:6487-6497.
202. Geerke DP, Thiel S, Thiel W, van Gunsteren WF. Combined QM/MM molecular dynamics study on a condensed-phase SN2 reaction at nitrogen: the effect of explicitly including solvent polarization. J Chem Theory Comput. 2007;3:1499-1509.
203. Lin Y-L, Gao J. Solvatochromic shifts of the n !p transition of acetone from steam vapor to ambient aqueous solution: a combined configuration interaction QM/MM simulation study incorporating solvent polarization. J Chem Theory Comput. 2007;3:1484-1493.
204. Geerke DP, Thiel S, Thiel W, van Gunsteren WF. QM-MM interactions in simulations of liquid water using combined semiempirical/classical Hamiltonians. Phys Chem Chem Phys. 2008;10:297-302.
205. Illingworth CJR, Parkes KEB, Snell CR, Ferenczy GrG, Reynolds CA. Toward a consistent treatment of polarization in model QM/MM calculations. J Phys Chem A. 2008;112:12151-12156.
206. Illingworth CJR, Morris GM, Parkes KEB, Snell CR, Reynolds CA. Assessing the role of polarization in docking. J Phys Chem A. 2008;112:12157-12163.
207. Lu Z, Zhang Y. Interfacing ab initio quantum mechanical method with classical Drude oscillator polarizable model for molecular dynamics simulation of chemical reactions. J Chem Theory Comput. 2008;4:1237-1248.
208. Wanko M, Hoffmann M, Frähmcke J, Frauenheim T, Elstner M. Effect of polarization on the opsin shift in rhodopsins. 2. Empirical polarization models for proteins. J Phys Chem B. 2008;112:11468-11478.
209. Illingworth CJR, Furini S, Domene C. Computational studies on polarization effects and selectivity in K+ channels. J Chem Theory Comput. 2010;6:3780-3792.
210. Sneskov K, Schwabe T, Christiansen O, Kongsted J. Scrutinizing the effects of polarization in QM/MM excited state calculations. Phys Chem Chem Phys. 2011;13:18551-18560.
211. Sneskov K, Schwabe T, Kongsted J, Christiansen O. The polarizable embedding coupled cluster method. J Chem Phys. 2011;134:104108/1-15.
212. Wang Q, Bryce RA. Accounting for non-optimal interactions in molecular recognition: a study of ion-p complexes using a QM/MM model with a dipole-polarisable MM region. Phys Chem Chem Phys. 2011;13:19401-19408.
213. SchworerM, Breitenfeld B, Troster P, Bauer S, Lorenzen K, Tavan P, Mathias G. Coupling density functional theory to polarizable force fields for efficient and accurate Hamiltonian molecular dynamics simulations. J Chem Phys. 2013;138:244103/1-13.
214. Applequist J, Carl JR, Fung K-K. An atom dipole interaction model for molecular polarizability. Application to polyatomic molecules and determination of atom polarizabilities. J Am Chem Soc. 1972;94:2952-2960.
215. Thole BT. Molecular polarizabilities calculated with a modified dipole interaction. Chem Phys. 1981;59:341-350.
216. Stone AJ. Distributed polarizability. Mol Phys. 1985;56: 1065-1082.
217. Winn PJ, Ferenczy GG, Reynolds CA. Toward improved force fields: III polarization through modified atomic charges. J Comput Chem. 1999;20:704-712.
218. Mortier WJ, Van Genechten K, Gasteiger J. Electronegativity equalization: application and parameterization. J Am Chem Soc. 1985;107:829-835.
219. Mortier WJ, Ghosh SK, Shankar S. Electronegativity equalization method for the calculation of atomic charges in molecules. J Am Chem Soc. 1986;108:4315-4320.
220. Rappé AK, Goddard WA. Charge equilibration for molecular dynamics simulations. J Phys Chem. 1991;95:3358-3363.
221. Dewar MJS, Hashmall JA, Venier CG. Ground states of conjugated molecules. IX. Hydrocarbon radicals and radical ions. J Am Chem Soc. 1968;90:1953-1957.
222. Dewar MJS, Trinajstic N. Triplet states of aromatic hydrocarbons. J Chem Soc Chem Commun. 1970 :646-647.
223. Gogonea V, Merz KM Jr. A quantum mechanical-Poisson-Boltzmann equation approach for studying charge flow between ions and a dielectric continuum. J Chem Phys. 2000;112:3227-3235.
224. Gogonea V, Merz KM Jr. Charge flow between ions and a dielectric continuum. 2. Variational method for distributing charge into the dielectric. J Phys Chem B. 2000;104:2117-2122.
225. Perdew JP, Parr RG, Levy M, Balduz JL. Density-functional theory for fractional particle number: derivative discontinuities of the energy. Phys Rev Lett. 1982;49:1691-1694.
226. Zhang Y, Yang W. A challenge for density functionals: selfinteraction error increases for systems with a noninteger number of electrons. J Chem Phys. 1998;109:2604-2608.
227. Yang W, Zhang Y, Ayers PW. Degenerate ground states and a fractional number of electrons in density and reduced density matrix functional theory. Phys Rev Lett. 2000;84:5172-5175.
228. Zhang Y, Yang W. Perspective on 'density-functional theory for fractional particle number: derivative discontinuities of the energy'. Theory Chem Acc. 2000;103:346-348.
229. Cohen AJ, Mori-Sanchez P, Yang W. Fractional spins and static correlation error in density functional theory. J Chem Phys. 2008;129:121104/1-4.
230. Zeng X, Hu H, Hu X, Cohen AJ, Yang W. Ab initio quantum mechanical/molecular mechanical simulation of electron transfer process: fractional electron approach. J Chem Phys. 2008;128:124510/1-10.
231. Cohen AJ, Mori-Sanchez P, Yang W. Second-order perturbation theory with fractional charges and fractional spins. J Chem Theory Comput. 2009;5:786-792.
232. Ess DH, Johnson ER, Hu X, Yang W. Singlet-triplet energy gaps for diradicals from fractional-spin density-functional theory. J Phys Chem A. 2011;115:76-83.
233. Steinmann SN, Yang W. Wave function methods for fractional electrons. J Chem Phys. 2013;139:074107/1-14.
234. Mayhall NJ, Raghavachari K. Molecules-in-molecules: an extrapolated fragment-based approach for accurate calculations on large molecules and materials. J Chem Theory Comput. 2011;7:1336-1343.
235. Elliott P, Cohen MH, Wasserman A, Burke K. Density functional partition theory with fractional occupations. J Chem Theory Comput. 2009;5:827-833.
236. Elliott P, Burke K, Cohen MH, Wasserman A. Partition densityfunctional theory. Phys Rev A. 2010;82:024501/1-4.
237. Tavernelli I, Vuilleumier R, Sprik M. Ab initio dynamics for molecules with variable numbers of electrons. Phys Rev Lett. 2002;88:213002/1-4.
238. Hall RJ, Hindle SA, Burton NA, Hillier IH. Aspects of hybrid QM/MM calculations: the treatment of the QM/MM interface region and geometry optimization with an application to chorismate mutase. J Comput Chem. 2000;21:1433-1441.
239. Reuter N, Dejaegere A, Maigret B, Karplus M. Frontier bonds in QM/MM methods: a comparison of different approaches. J Phys Chem A. 2000;104:1720-1735.
240. Nicoll RM, Hindle SA, MacKenzie G, Hillier IH, Burton NA. Quantum mechanical/molecular mechanical methods and the study of kinetic isotope effects: modeling the covalent junction region and application to the enzyme xylose isomerase. Theory Chem Acc. 2001;106:105-112.
241. Lennartz C, Schaefer A, Terstegen F, Thiel W. Enzymatic reactions of triosephosphate isomerase: a theoretical calibration study. J Phys Chem B. 2002;106:1758-1767.
242. Car R, Parrinello M. Unified approach for molecular dynamics and density-functional theory. Phys Rev Lett. 1985;55:2471-2474.
243. Woo TK, Cavallo L, Ziegler T. Implementation of the IMOMM methodology for performing combined QM/MM molecular dynamics simulations and frequency calculations. Theory Chem Acc. 1998;100:307-313.
244. Röthlisberger U, Carloni P, Doclo K, Parrinello M. A comparative study of galactose oxidase and active site analogs based on QM/MM Car-Parrinello simulations. J Bio Inorg Chem. 2000;5:236-250.
245. Woo TK, Blöchl PE, Ziegler T. Towards solvation simulations with a combined ab initio molecular dynamics and molecular mechanics approach. THEOCHEM. 2000;506:313-334.
246. Colombo MC. Hybrid QM/MM Car-Parrinello simulations of catalytic and enzymatic reactions. Chimia. 2002;56:13-19.
247. Woo TK, Margl P, Blochl PE, Ziegler T. Sampling phase space by a combined QM/MM ab initio Car-Parrinello molecular dynamics method with different (multiple) time steps in the quantum mechanical (QM) and molecular mechanical (MM) domains. J Phys Chem A. 2002;106:1173-1182.
248. Sulpizi M, Laio A, VandeVondele J, Cattaneo A, Röthlisberger U, Carloni P. Reaction mechanism of caspases: insights from QM/MM Car-Parrinello simulations. Proteins: Struct Funct Genet. 2003;52:212-224.
249. Raugei S, Cascella M, Carloni P. A proficient enzyme: insights on the mechanism of orotidine monophosphate decarboxylase from computer simulations. J Am Chem Soc. 2004;126:15730-15737.
250. Kerdcharoen T, Liedl KR, Rode BM. A QM/MM simulation method applied to the solution of Li+ in liquid ammonia. Chem Phys. 1996;211:313-323.
251. Kerdcharoen T, Morokuma K. ONIOM-XS: an extension of the ONIOM method for molecular simulation in condensed phase. Chem Phys Lett. 2002;355:257-262.
252. Kerdcharoen T, Morokuma K. Combined quantum mechanics and molecular mechanics simulation of Ca2+/ammonia solution based on the ONIOM-XS method: octahedral coordination and implication to biology. J Chem Phys. 2003;118:8856-8862.
253. Bulo RE, Ensing B, Sikkema J, Visscher L. Toward a practical method for adaptive QM/MM simulations. J Chem Theory Comput. 2009;5:2212-2221.
254. Guthrie MG, Daigle AD, Salazar MR. Properties of a method for performing adaptive, multilevel QM simulations of complex chemical reactions in the gas-phase. J Chem Theory Comput. 2009;6:18-25.
255. Nielsen SO, Bulo RE, Moore PB, Ensing B. Recent progress in adaptive multiscale molecular dynamics simulations of soft matter. Phys Chem Chem Phys. 2010;12:12401-12414.
256. Poma AB, Delle Site L. Classical to path-integral adaptive resolution in molecular simulation: towards a smooth quantumclassical coupling. Phys Rev Lett. 2010;104:250201/1-4.
257. Bernstein N, Varnai C, Solt I, Winfield SA, Payne MC, Simon I, FuxreiterM, Csanyi G. QM/MM simulation of liquid water with an adaptive quantum region. Phys Chem Chem Phys. 2012;14:646-656.
258. Park K, Gotz AW, Walker RC, Paesani F. Application of adaptive QM/MM methods to molecular dynamics simulations of aqueous systems. J Chem Theory Comput. 2012;8:2868-2877.
259. Takenaka N, Kitamura Y, Koyano Y, Nagaoka M. The numberadaptive multiscale QM/MM molecular dynamics simulation: application to liquid water. Chem Phys Lett. 2012;524:56-61.
260. Várnai C, Bernstein N, Mones L, Csányi G. Tests of an adaptive QM/MM calculation on free energy profiles of chemical reactions in solution. J Phys Chem B. 2013;117:12202-12211.
261. Rowley CN, Roux B. The solvation structure of Na+ and K+ in liquid water determined from high level ab initio molecular dynamics simulations. J Chem Theory Comput. 2012;8:3526-3535.
262. Shiga M, Masia M. Boundary based on exchange symmetry theory for multilevel simulations. I. Basic theory. J Chem Phys. 2013;139:044120/1-8.
263. Bulo RE, Michel C, Fleurat-Lessard P, Sautet P. Multiscale modeling of chemistry in water: are we there yet J Chem Theory Comput. 2013;9:5567-5577.
264. Stewart JP. Optimization of parameters for semiempirical methods V: modification of NDDO approximations and application to 70 elements. J Mol Model. 2007;13:1173-1213.
265. Korth M. Third-generation hydrogen-bonding corrections for semiempirical QM methods and force fields. J Chem Theory Comput. 2010;6:3808-3816.
266. Elstner M, Porezag D, Jungnickel G, Elsner J, Haugk M, Frauenheim T, Suhai S, Seifert G. Self-consistent-charge densityfunctional tight-binding method for simulations of complex materials properties. Phys Rev B. 1998;58:7260-7268.
267. Wu Y, Tepper HL, Voth GA. Flexible simple point-charge water model with improved liquid-state properties. J Chem Phys. 2006;124:024503/1-12.
268. Duin ACTv, Dasgupta S, Lorant F, Goddard WA. ReaxFF: a reactive force field for hydrocarbons. J Phys Chem A. 2001;105:9396-9409.
269. Kästner J, Thiel W. Bridging the gap between thermodynamic integration and umbrella sampling provides a novel analysis method: 'umbrella integration'. J Chem Phys. 2005;123:144104/1-5.
270. Carter EA, Ciccotti G, Hynes JT, Kapral R. Constrained reaction coordinate dynamics for the simulation of rare events. Chem Phys Lett. 1989;156:472-477.
271. Laio A, Parrinello M. Escaping free-energy minima. Proc Natl Acad Sci USA. 2002;99:12562-12566.
272. Darve E, Pohorille A. Calculating free energies using average force. J Chem Phys. 2001;115:9169-9183.
273. Steve ON, Carlos FL, Goundla S, Michael LK. Coarse grain models and the computer simulation of soft materials. J Phys Condens Matter. 2004;16:R481.
274. Shih AY, Arkhipov A, Freddolino PL, Schulten K. Coarse grained protein-lipid model with application to lipoprotein particles. J Phys Chem B. 2006;110:3674-3684.
275. Marrink SJ, Risselada HJ, Yefimov S, Tieleman DP, de Vries AH. The MARTINI force field: coarse grained model for biomolecular simulations. J Phys Chem B. 2007;111:7812-7824.
276. Clementi C. Coarse-grained models of protein folding: toy models or predictive tools Curr Opin Struct Biol. 2008;18:10-15.
277. Murtola T, Bunker A, Vattulainen I, Deserno M, Karttunen M. Multiscale modeling of emergent materials: biological and soft matter. Phys Chem Chem Phys. 2009;11:1869-1892.
278. Peter C, Kremer K. Multiscale simulation of soft matter systems-from the atomistic to the coarse-grained level and back. Soft Matter. 2009;5:4357-4366.
279. Wu Z, Cui Q, Yethiraj A. A new coarse-grained model for water: the importance of electrostatic interactions. J Phys Chem B. 2010;114:10524-10529.
280. Riniker S, van Gunsteren WF. A simple, efficient polarizable coarse-grained water model for molecular dynamics simulations. J Chem Phys. 2011;134:084110/1-12.
281. Takada S. Coarse-grained molecular simulations of large biomolecules. Curr Opin Struct Biol. 2012;22:130-137.
282. Noid WG. Perspective: coarse-grained models for biomolecular systems. J Chem Phys. 2013;139:090901/1-25.
283. Saunders MG, Voth GA. Coarse-graining methods for computational biology. Annu Rev Biophys. 2013;42:73-93.
284. Neri M, Anselmi C, Cascella M, Maritan A, Carloni P. Coarsegrained model of proteins incorporating atomistic detail of the active site. Phys Rev Lett. 2005;95:218102/1-4.
285. Shi Q, Izvekov S, Voth GA. Mixed atomistic and coarse-grained molecular dynamics: simulation of a membrane-bound ion channel. J Phys Chem B. 2006;110:15045-15048.
286. Michel J, Orsi M, Essex JW. Prediction of partition coefficients by multiscale hybrid atomic-level/coarse-grain simulations. J Phys Chem B. 2007;112:657-660.
287. Masella M, Borgis D, Cuniasse P. Combining a polarizable forcefield and a coarse-grained polarizable solvent model: application to long dynamics simulations of bovine pancreatic trypsin inhibitor. J Comput Chem. 2008;29:1707-1724.
288. Orsi M, Sanderson WE, Essex JW. Permeability of small molecules through a lipid bilayer: a multiscale simulation study. J Phys Chem B. 2009;113:12019-12029.
289. Masella M, Borgis D, Cuniasse P. Combining a polarizable forcefield and a coarse-grained polarizable solvent model. II. Accounting for hydrophobic effects. J Comput Chem. 2011;32:2664-2678.
290. Rzepiela AJ, Louhivuori M, Peter C, Marrink SJ. Hybrid simulations: combining atomistic and coarse-grained force fields using virtual sites. Phys Chem Chem Phys. 2011;13:10437-10448.
291. Riniker S, Eichenberger AP, van Gunsteren WF. Structural effects of an atomic-level layer of water molecules around proteins solvated in supra-molecular coarse-grained water. J Phys Chem B. 2012;116:8873-8879.
292. Darré L, Tek A, Baaden M, Pantano S. Mixing atomistic and coarse grain solvation models for MD simulations: let WT4 handle the bulk. J Chem Theory Comput. 2012;8:3880-3894.
293. Riniker S, van Gunsteren WF. Mixing coarse-grained and finegrained water in molecular dynamics simulations of a single system. J Chem Phys. 2012;137:044120/1-8.
294. Riniker S, Eichenberger A, van Gunsteren W. Solvating atomic level fine-grained proteins in supra-molecular level coarse-grained water for molecular dynamics simulations. Eur Biophys J. 2012;41:647-661.
295. Gonzalez HC, Darré L, Pantano S. Transferable mixing of atomistic and coarse-grained water models. J Phys Chem B. 2013;117: 14438-14448.
296. Lin Z, Riniker S, van Gunsteren WF. Free enthalpy differences between a-, p-, and 310-helices of an atomic level fine-grained alanine deca-peptide solvated in supramolecular coarse-grained water. J Chem Theory Comput. 2013;9:1328-1333.
297. Sokkar P, Choi SM, Rhee YM. Simple method for simulating the mixture of atomistic and coarse-grained molecular systems. J Chem Theory Comput. 2013;9:3728-3739.
298. Wassenaar TA, Ingólfsson HI, Prie M, Marrink SJ, Schäfer LV. Mixing MARTINI: electrostatic coupling in hybrid atomistic-coarse-grained biomolecular simulations. J Phys Chem B. 2013;117:3516-3530.
299. Ghysels A, Miller BT, Pickard FC, Brooks BR. Comparing normal modes across different models and scales: Hessian reduction versus coarse-graining. J Comput Chem. 2012;33:2250-2275.
300. Abrams CF. Concurrent dual-resolution Monte Carlo simulation of liquid methane. J Chem Phys. 2005;123:234101/1-13.
301. Praprotnik M, Delle Site L, Kremer K. Adaptive resolution molecular-dynamics simulation: changing the degrees of freedom on the fly. J Chem Phys. 2005;123:224106/1-14.
302. Ensing B, Nielsen SO, Moore PB, Klein ML, Parrinello M. Energy conservation in adaptive hybrid atomistic/coarse-grain molecular dynamics. J Chem Theory Comput. 2007;3:1100-1105.
303. Praprotnik M, Matysiak S, Site LD, Kremer K, Clementi C. Adaptive resolution simulation of liquid water. J Phys Condens Matter. 2007;19:292201/1-10.
304. Heyden A, Truhlar DG. Conservative algorithm for an adaptive change of resolution in mixed atomistic/coarse-grained multiscale simulations. J Chem Theory Comput. 2008;4:217-221.
305. Wang H, Schütte C, Delle Site L. Adaptive resolution simulation (AdResS): a smooth thermodynamic and structural transition from atomistic to coarse grained resolution and vice versa in a grand canonical fashion. J Chem Theory Comput. 2012;8:2878-2887.
306. Wang H, Hartmann C, Schütte C, Delle Site L. Grand-canonicallike molecular-dynamics simulations by using an adaptiveresolution technique. Phys Rev X. 2013;3:011018/1-16.