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

References

• AytonGS, NoidWG, VothGA. Multiscale modeling of biomolecular systems: in serial and in parallel. Curr Opin Struct Biol. 2007;17:192–198.
   PubMed Web of Science ®Google Scholar
• SherwoodP, BrooksBR, SansomMSP. Multiscale methods for macromolecular simulations. Curr Opin Struct Biol. 2008;18:630–640.
   PubMed Web of Science ®Google Scholar
• TozziniV. Multiscale modeling of proteins. Acc Chem Res. 2010;43:220–230.
   PubMed Web of Science ®Google Scholar
• ElliottJA. Novel approaches to multiscale modelling in materials science. Int Mater Rev. 2011;56:207–225.
   Web of Science ®Google Scholar
• KamerlinSCL, VicatosS, DrygaA, WarshelA. Coarse-grained (multiscale) simulations in studies of biophysical and chemical systems. Annu Rev Phys Chem. 2011;62:41–64.
   PubMed Web of Science ®Google Scholar
• WoodcockHL, MillerBT, HodoscekM, OkurA, LarkinJD, PonderJW, BrooksBR. MSCALE: a general utility for multiscale modeling. J Chem Theory Comput. 2011;7:1208–1219.
   PubMedGoogle Scholar
• KirchnerB, VrabecJ, editors. Multiscale molecular methods in applied chemistry. Topics in current chemistry. Heidelberg: Springer; 2012.
   Google Scholar
• MeierK, ChoutkoA, DolencJ, EichenbergerAP, RinikerS, van GunsterenWF. Multi-resolution simulation of biomolecular systems: a review of methodological issues. Angew Chem Int Ed. 2013;52:2820–2834.
   PubMed Web of Science ®Google Scholar
• WarshelA, LevittM. 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.
   PubMed Web of Science ®Google Scholar
• SinghUC, KollmannPA. A combined ab initio quantum mechanical and molecular mechanical method for carrying out simulations on complex molecular systems: applications to the CH3Cl+Cl−  exchange reaction and gas phase protonation of polyethers. J Comput Chem. 1986;7:718–730.
   Web of Science ®Google Scholar
• FieldMJ, BashPA, KarplusM. A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations. J Comput Chem. 1990;11:700–733.
   Web of Science ®Google Scholar
• GaoJ. Methods and applications of combined quantum mechanical and molecular mechanical potentials. Rev Comput Chem. 1996;7:119–185.
   Google Scholar
• MordasiniT, ThielW. Computational chemistry column: combined quantum mechanical and molecular approaches. Chimia. 1998;52:288–291.
   Web of Science ®Google Scholar
• HillierIH. Chemical reactivity studied by hybrid QM/MM methods. THEOCHEM. 1999;463:45–52.
   Web of Science ®Google Scholar
• MonardG, MerzKMJr. Combined quantum mechanical/molecular mechanical methodologies applied to biomolecular systems. Acc Chem Res. 1999;32:904–911.
   Web of Science ®Google Scholar
• Hammes-SchifferS. Theoretical perspectives on proton-coupled electron transfer reactions. Acc Chem Res. 2000;34:273–281.
   Web of Science ®Google Scholar
• SherwoodP. Hybrid quantum mechanics/molecular mechanics approaches. In: GrotendorstJ, editor. Modern methods and algorithms of quantum chemistry. Jülich: John von Neumann-Instituts; 2000. p. 285–305.
   Google Scholar
• GaoJ, TruhlarDG. Quantum mechanical methods for enzyme kinetics. Annu Rev Phys Chem. 2002;53:467–505.
   PubMed Web of Science ®Google Scholar
• MorokumaK. New challenges in quantum chemistry: quests for accurate calculations for large molecular systems. Philos Trans R Soc Lond A. 2002;360:1149–1164.
   PubMed Web of Science ®Google Scholar
• LinH, TruhlarDG. QM/MM: what have we learned, where are we, and where do we go from here?Theory Chem Acc. 2007;117:185–199.
   Web of Science ®Google Scholar
• SennHM, ThielW. QM/MM methods for biological systems. Top Curr Chem. 2007;268:173–290.
   Web of Science ®Google Scholar
• HuH, YangW. 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.
   PubMed Web of Science ®Google Scholar
• BernsteinN, KermodeJR, CsányiG. Hybrid atomistic simulation methods for materials systems. Rep Prog Phys. 2009;72:026501/1-25.
   Web of Science ®Google Scholar
• SennHM, ThielW. QM/MM methods for biomolecular systems. Angew Chem Int Ed. 2009;48:1198–1229.
   PubMed Web of Science ®Google Scholar
• AcevedoO, JorgensenWL. Advances in quantum and molecular mechanical (QM/MM) simulations for organic and enzymatic reactions. Acc Chem Res. 2010;43:142–151.
   PubMed Web of Science ®Google Scholar
• SabinJR, BrändasE, editors. Combining quantum mechanics and molecular mechanics. Some recent progresses in QM/MM methods. Advances in quantum chemistry. New York: Academic Press; 2010.
   Google Scholar
• YohsukeH, MasaruT. 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.
   Google Scholar
• FerrerS, Ruiz-PerniaJ, MartiS, MolinerV, TunonI, BertranJ, AndresJ. Hybrid schemes based on quantum mechanics/molecular mechanics simulations: goals to success, problems, and perspectives. In: ChristovC, editor. Advances in protein chemistry and structural biology: computational chemistry methods in structural biology. Vol 85. San Diego: Elsevier; 2011. p. 81–142.
   Google Scholar
• MenikarachchiLC, GasconJA. QM/MM approaches in medicinal chemistry research. Curr Top Med Chem. 2010;10:46–54.
   PubMed Web of Science ®Google Scholar
• WallrappFH, GuallarV. Mixed quantum mechanics and molecular mechanics methods: looking inside proteins. Wiley Interdiscip Rev Comput Mol Sci. 2011;1:315–322.
   Web of Science ®Google Scholar
• ChungLW, HiraoH, LiX, MorokumaK. The ONIOM method: its foundation and applications to metalloenzymes and photobiology. Wiley Interdiscip Rev Comput Mol Sci. 2012;2:327–350.
   Web of Science ®Google Scholar
• KeilFJ. Multiscale modelling in computational heterogeneous catalysis. In: KirchnerB, VrabecJ, editors. Multiscale molecular methods in applied chemistry. Heidelberg: Springer; 2012. p. 69–107.
   Google Scholar
• LonsdaleR, HarveyJN, MulhollandAJ. A practical guide to modelling enzyme-catalysed reactions. Chem Soc Rev. 2012;41:3025–3038.
   PubMed Web of Science ®Google Scholar
• MonariA, RivailJ-L, AssfeldX. 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.
   PubMed Web of Science ®Google Scholar
• SiteL, HolmC, VegtNA. Multiscale approaches and perspectives to modeling aqueous electrolytes and polyelectrolytes. In: KirchnerB, VrabecJ, editors. Multiscale molecular methods in applied chemistry. Berlin: Springer; 2012. p. 251–294.
   Google Scholar
• WuR, CaoZ, ZhangY. Computational simulations of zinc enzyme: challenges and recent advances. Prog Chem. 2012;24:1175–1184.
   Web of Science ®Google Scholar
• YockelS, SchatzG. Dynamic QM/MM: a hybrid approach to simulating gas–liquid interactions. In: KirchnerB, VrabecJ, editors. Multiscale molecular methods in applied chemistry. Heidelberg: Springer; 2012. p. 43–67.
   Google Scholar
• MennucciB. Modeling environment effects on spectroscopies through QM/classical models. Phys Chem Chem Phys. 2013;15:6583–6594.
   PubMed Web of Science ®Google Scholar
• KussmannJ, BeerM, OchsenfeldC. Linear-scaling self-consistent field methods for large molecules. Wiley Interdiscip Rev Comput Mol Sci. 2013;3:614–636.
   Web of Science ®Google Scholar
• ZhangY, LinH. 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.
   Web of Science ®Google Scholar
• LinH, TruhlarDG. Redistributed charge and dipole schemes for combined quantum mechanical and molecular mechanical calculations. J Phys Chem A. 2005;109:3991–4004.
   PubMed Web of Science ®Google Scholar
• ZhangY, LinH, TruhlarDG. 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.
   Web of Science ®Google Scholar
• ZhangY, LinH. 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.
   PubMed Web of Science ®Google Scholar
• PezeshkiS, LinH. 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.
   Web of Science ®Google Scholar
• HeydenA, LinH, TruhlarDG. 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.
   PubMed Web of Science ®Google Scholar
• AntesI, ThielW. On the treatment of link atoms in hybrid methods. ACS Symp Ser. 1998;712:50–65.
   Google Scholar
• BentzienJ, FlorianJ, GlennonTM, WarshelA. Quantum mechanical-molecular mechanical approaches for studying chemical reactions in proteins and solution. ACS Symp Ser. 1998;712:16–34.
   Google Scholar
• MerzKMJr. Quantum mechanical-molecular mechanical coupled potentials. ACS Symp Ser. 1998;712:2–15.
   Google Scholar
• WooTK, MarglPM, DengL, CavalloL, ZieglerT. Combined QM/MM and ab initio molecular dynamics modeling of homogeneous catalysis. ACS Symp Ser. 1999;721:173–186.
   Google Scholar
• BakowiesD, ThielW. Hybrid models for combined quantum mechanical and molecular mechanical approaches. J Phys Chem. 1996;100:10580–10594.
   Web of Science ®Google Scholar
• MurphyRB, PhilippDM, FriesnerRA. 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.
   Web of Science ®Google Scholar
• RiccardiD, LiGH, CuiQ. Importance of van der Waals interactions in QM/MM simulations. J Phys Chem B. 2004;108:6467–6478.
   PubMed Web of Science ®Google Scholar
• FreindorfM, ShaoY, FurlaniTR, KongJ. Lennard–Jones parameters for the combined QM/MM method using the B3LYP/6-31G*/AMBER potential. J Comput Chem. 2005;26:1270–1278.
   PubMed Web of Science ®Google Scholar
• GieseTJ, YorkDM. 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.
   Web of Science ®Google Scholar
• JinY, JohnsonER, HuX, YangW, HuH. Contributions of pauli repulsions to the energetics and physical properties computed in QM/MM methods. J Comput Chem. 2013;34:2380–2388.
   PubMed Web of Science ®Google Scholar
• SinghUC, KollmanPA. An approach to computing electrostatic charges for molecules. J Comput Chem. 1984;5:129–145.
   Web of Science ®Google Scholar
• BeslerBH, MerzKMJr., KollmanPA. Atomic charges derived from semi-empirical methods. J Comput Chem. 1990;11:431–439.
   Web of Science ®Google Scholar
• FranclMM, CareyC, ChirlianLE, GangeDM. Charges fit to electrostatic potentials. II: can atomic charges be unambiguously fit to electrostatic potentials?J Comput Chem. 1996;17:367–383.
   Web of Science ®Google Scholar
• ZhangY, LiuH, YangW. 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.
   Web of Science ®Google Scholar
• KästnerJ, SennHM, ThielS, OtteN, ThielW. QM/MM free-energy perturbation compared to thermodynamic integration and umbrella sampling: application to an enzymatic reaction. J Chem Theory Comput. 2006;2:452–461.
   PubMed Web of Science ®Google Scholar
• DoniniO, DardenT, KollmanPA. 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.
   Web of Science ®Google Scholar
• RodTH, RydeU. Accurate QM/MM free energy calculations of enzyme reactions: methylation by catechol O-methyltransferase. J Chem Theory Comput. 2005;1:1240–1251.
   PubMed Web of Science ®Google Scholar
• RodTH, RydeU. Quantum mechanical free energy barrier for an enzymatic reaction. Phys Rev Lett. 2005;94:138302/1-4.
   Web of Science ®Google Scholar
• ValievM, GarrettBC, TsaiM-K, KowalskiK, KathmannSM, SchenterGK, DupuisM. Hybrid approach for free energy calculations with high-level methods: application to the SN2 reaction of CHCl3 and OH−  in water. J Chem Phys. 2007;127:051102/1-4.
   Web of Science ®Google Scholar
• ValievM, BylaskaEJ, DupuisM, TratnyekPG. 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.
   PubMed Web of Science ®Google Scholar
• Martins-CostaMTC, AngladaJM, FranciscoJS, Ruiz-LopezMF. Reactivity of volatile organic compounds at the surface of a water droplet. J Am Chem Soc. 2012;134:11821–11827.
   PubMed Web of Science ®Google Scholar
• PolyakI, BenighausT, BoulangerE, ThielW. Quantum mechanics/molecular mechanics dual Hamiltonian free energy perturbation. J Chem Phys. 2013;139:064105/1-11.
   Web of Science ®Google Scholar
• JensenKP, RydeU. How the Co–C bond is cleaved in coenzyme B12 enzymes: a theoretical study. J Am Chem Soc. 2005;127:9117–9128.
   PubMed Web of Science ®Google Scholar
• KwiecienRA, KhavrutskiiIV, MusaevDG, MorokumaK, BanerjeeR, PanethP. Computational insights into the mechanism of radical generation in B12-dependent methylmalonyl-CoA mutase. J Am Chem Soc. 2006;128:1287–1292.
   PubMed Web of Science ®Google Scholar
• MacKerellADJr., BashfordD, BellottM, DunbrackRL, EvanseckJD, FieldMJ, FischerS, GaoJ, GuoH, HaS, Joseph-McCarthyD, KuchnirL, KuczeraK, LauFTK, MattosC, MichnickS, NgoT, NguyenDT, ProdhomB, ReiherWE III, RouxB, SchlenkrichM, SmithJC, StoteR, StraubJ, WatanabeM, Wiorkiewicz-KuczeraJ, YinD, KarplusM.All-atom empirical potential for molecular modeling and dynamics studies of proteins. J Phys Chem B. 1998;102:3586–3616.
   PubMed Web of Science ®Google Scholar
• SherwoodP, De VriesAH, CollinsSJ, GreatbanksSP, BurtonNA, VincentMA, HillierIH. Computer simulation of zeolite structure and reactivity using embedded cluster methods. Faraday Discuss. 1997;106:79–92.
   Web of Science ®Google Scholar
• DayPN, JensenJH, GordonMS, WebbSP, StevensWJ, KraussM, GarmerD, BaschH, CohenD. An effective fragment method for modeling solvent effects in quantum mechanical calculations. J Chem Phys. 1996;105:1968–1986.
   Web of Science ®Google Scholar
• FreitagMA, GordonMS, JensenJH, StevensWJ. Evaluation of charge penetration between distributed multipolar expansions. J Chem Phys. 2000;112:7300–7306.
   Web of Science ®Google Scholar
• DasD, EureniusKP, BillingsEM, SherwoodP, ChatfieldDC, HodoscekM, BrooksBR. 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.
   Web of Science ®Google Scholar
• AmaraP, FieldMJ. Evaluation of an ab initio quantum mechanical/molecular mechanical hybrid-potential link-atom method. Theory Chem Acc. 2003;109:43–52.
   Web of Science ®Google Scholar
• CisnerosGA, PiquemalJ-P, DardenTA. Quantum mechanics/molecular mechanics electrostatic embedding with continuous and discrete functions. J Phys Chem B. 2006;110:13682–13684.
   PubMed Web of Science ®Google Scholar
• CisnerosGA, TholanderSN-I, PariselO, DardenTA, ElkingD, PereraL, PiquemalJP. 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.
   PubMed Web of Science ®Google Scholar
• WangB, TruhlarDG. Including charge penetration effects in molecular modeling. J Chem Theory Comput. 2010;6:3330–3342.
   Web of Science ®Google Scholar
• Alvarez-IbarraA, KösterAM, ZhangR, SalahubDR. Asymptotic expansion for electrostatic embedding integrals in QM/MM calculations. J Chem Theory Comput. 2012;8:4232–4238.
   PubMed Web of Science ®Google Scholar
• NamK, GaoJ, YorkDM. An efficient linear-scaling Ewald method for long-range electrostatic interactions in combined QM/MM calculations. J Chem Theory Comput. 2005;1:2–13.
   PubMed Web of Science ®Google Scholar
• RiccardiD, SchaeferP, CuiQ. 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.
   PubMed Web of Science ®Google Scholar
• SchaeferP, RiccardiD, CuiQ. Reliable treatment of electrostatics in combined QM/MM simulation of macromolecules. J Chem Phys. 2005;123:014905/1-14.
   Web of Science ®Google Scholar
• MeierK, SchmidN, van GunsterenWF. Interfacing the GROMOS (bio)molecular simulation software to quantum-chemical program packages. J Comput Chem. 2012;33:2108–2117.
   PubMed Web of Science ®Google Scholar
• DinnerAR, LopezX, KarplusM. A charge-scaling method to treat solvent in QM/MM simulations. Theory Chem Acc. 2003;109:118–124.
   Web of Science ®Google Scholar
• GaoJ, AlhambraC. A hybrid semiempirical quantum mechanical and lattice-sum method for electrostatic interactions in fluid simulations. J Chem Phys. 1997;107:1212–1217.
   Web of Science ®Google Scholar
• LainoT, MohamedF, LaioA, ParrinelloM. An efficient linear-scaling electrostatic coupling for treating periodic boundary conditions in QM/MM simulations. J Chem Theory Comput. 2006;2:1370–1378.
   PubMed Web of Science ®Google Scholar
• WalkerRC, CrowleyMF, CaseDA. The implementation of a fast and accurate QM/MM potential method in Amber. J Comput Chem. 2008;29:1019–1031.
   PubMed Web of Science ®Google Scholar
• NakanoH, YamamotoT. 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.
   Web of Science ®Google Scholar
• GregersenBA, YorkDM. 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.
   PubMed Web of Science ®Google Scholar
• RiccardiD, CuiQ. 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.
   PubMed Web of Science ®Google Scholar
• BenighausT, ThielW. 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.
   Web of Science ®Google Scholar
• HeimdalJ, KaukonenM, SrnecM, RulíšekL, RydeU. Reduction potentials and acidity constants of Mn superoxide dismutase calculated by QM/MM free-energy methods. ChemPhysChem. 2011;12:3337–3347.
   PubMed Web of Science ®Google Scholar
• BoulangerE, ThielW. Solvent boundary potentials for hybrid QM/MM computations using classical Drude oscillators: a fully polarizable model. J Chem Theory Comput. 2012;8:4527–4538.
   Web of Science ®Google Scholar
• LuX, CuiQ. 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.
   PubMed Web of Science ®Google Scholar
• Ojeda-MayP, PuJ. Isotropic periodic sum treatment of long-range electrostatic interactions in combined quantum mechanical and molecular mechanical calculations. J Chem Theory Comput, 2013. 10.1021/ct400724d.
   Web of Science ®Google Scholar
• HumbelS, SieberS, MorokumaK. 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+Cl− . J Chem Phys. 1996;105:1959–1967.
   Web of Science ®Google Scholar
• DapprichS, KomiromiI, ByunKS, MorokumaK, FrischMJ. 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.
   Web of Science ®Google Scholar
• WaszkowyczB, HillierIH, GensmantelN, PaylingDW. 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.
   Google Scholar
• EureniusKP, ChatfieldDC, BrooksBR, HodoscekM. Enzyme mechanisms with hybrid quantum and molecular mechanical potentials. I. Theoretical considerations. Int J Quant Chem. 1996;60:1189–1200.
   Web of Science ®Google Scholar
• LynePD, HodoscekM, KarplusM. A hybrid QM–MM potential employing Hartree–Fock or density functional methods in the quantum region. J Phys Chem A. 1999;103:3462–3471.
   Web of Science ®Google Scholar
• LevB, ZhangR, de la LandeA, SalahubD, NoskovSY. The QM–MM interface for CHARMM-deMon. J Comput Chem. 2010;31:1015–1023.
   PubMed Web of Science ®Google Scholar
• SinclairPE, de VriesA, SherwoodP, CatlowCRA, van SantenRA. 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.
   Google Scholar
• de VriesAH, SherwoodP, CollinsSJ, RigbyAM, RiguttoM, KramerGJ. Zeolite structure and reactivity by combined quantum-chemical-classical calculations. J Phys Chem B. 1999;103:6133–6141.
   Web of Science ®Google Scholar
• SherwoodP, de VriesAH, GuestMF, SchreckenbachG, CatlowCRA, FrenchSA, SokolAA, BromleyST, ThielW, TurnerAJ, BilleterS, TerstegenF, ThielS, KendrickJ, RogersSC, CasciJ, WatsonM, KingF, KarlsenE, SjovollM, FahmiA, SchaferA, LennartzC. QUASI: a general purpose implementation of the QM/MM approach and its application to problems in catalysis. THEOCHEM. 2003;632:1–28.
   Web of Science ®Google Scholar
• KönigPH, HoffmannM, FrauenheimT, CuiQ. A critical evaluation of different QM/MM frontier treatments with SCC-DFTB as the QM method. J Phys Chem B. 2005;109:9082–9095.
   PubMed Web of Science ®Google Scholar
• ZhangY, LeeT-S, YangW. A pseudobond approach to combining quantum mechanical and molecular mechanical methods. J Chem Phys. 1999;110:46–54.
   Web of Science ®Google Scholar
• AbarenkovIV, TupitsynII. A new separable potential operator for representing a chemical bond and other applications. J Chem Phys. 2001;115:1650–1660.
   Web of Science ®Google Scholar
• PoteauR, OrtegaI, AlaryF, SolisAR, BarthelatJC, DaudeyJP. Effective group potentials: 1. Method. J Phys Chem A. 2001;105:198–205.
   Web of Science ®Google Scholar
• DiLabioGA, HurleyMM, ChristiansenPA. Simple one-electron quantum capping potentials for use in hybrid QM/MM studies of biological molecules. J Chem Phys. 2002;116:9578–9584.
   Web of Science ®Google Scholar
• LaioA, VandeVondeleJ, RöthlisbergerU. A Hamiltonian electrostatic coupling scheme for hybrid Car–Parrinello molecular dynamics simulations. J Chem Phys. 2002;116:6941–6947.
   Web of Science ®Google Scholar
• BessacF, AlaryF, CarissanY, HeullyJ-L, DaudeyJ-P, PoteauR. Effective group potentials: a powerful tool for hybrid QM/MM methods?THEOCHEM. 2003;632:43–59.
   Web of Science ®Google Scholar
• YasudaK, YamakiD. Simple minimum principle to derive a quantum-mechanical/ molecular-mechanical method. J Chem Phys. 2004;121:3964–3972.
   PubMed Web of Science ®Google Scholar
• DiLabioGA, WolkowRA, JohnsonER. Efficient silicon surface and cluster modeling using quantum capping potentials. J Chem Phys. 2005;122:044708/1-5.
   Web of Science ®Google Scholar
• von LilienfeldOA, TavernelliI, RothlisbergerU, SebastianiD. Variational optimization of effective atom centered potentials for molecular properties. J Chem Phys. 2005;122:014113/1-6.
   Web of Science ®Google Scholar
• ZhangY. Improved pseudobonds for combined ab initio quantum mechanical/molecular mechanical methods. J Chem Phys. 2005;122:024114/1-7.
   Google Scholar
• CarissanY, BessacF, AlaryF, HeullyJ-L, PoteauR. What can we do with an effective group potential?Int J Quant Chem. 2006;106:727–733.
   Web of Science ®Google Scholar
• SlavicekP, MartinezTJ. 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.
   Web of Science ®Google Scholar
• ZhangY. Pseudobond ab initio QM/MM approach and its applications to enzyme reactions. Theory Chem Acc. 2006;116:43–50.
   Web of Science ®Google Scholar
• DogelIA, DogelSA, PittersJL, DiLabioGA, WolkowRA. Chemical methods for the hydrogen termination of silicon dangling bonds. Chem Phys Lett. 2007;448:237–242.
   Web of Science ®Google Scholar
• NakamuraY, TakahashiN, OkamotoM, UdaT, OhnoT. Link molecule method for quantum mechanical/molecular mechanical hybrid simulations. J Comput Phys. 2007;225:1985–1993.
   Web of Science ®Google Scholar
• XiaoC, ZhangY. Design-atom approach for the quantum mechanical/molecular mechanical covalent boundary: a design-carbon atom with five valence electrons. J Chem Phys. 2007;127:124102/1-9.
   Google Scholar
• DiLabioGA. 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.
   Web of Science ®Google Scholar
• JardillierN, GoursotA. One-electron quantum capping potential for hybrid QM/MM studies of silicate molecules and solids. Chem Phys Lett. 2008;454:65–69.
   Web of Science ®Google Scholar
• RaynaudC, RosalI, JoliboisF, MaronL, PoteauR. Multicentered effective group potentials: ligand-field effects in organometallic clusters and dynamical study of chemical reactivity. Theory Chem Acc. 2010;126:151–163.
   Web of Science ®Google Scholar
• ExnerTE. Critical investigation on the pseudobond approach for QM/MM and fragment-based QM methods. Int J Quant Chem. 2011;111:1002–1012.
   Web of Science ®Google Scholar
• IhrigAC, SchiffmannC, SebastianiD. Specific quantum mechanical/molecular mechanical capping-potentials for biomolecular functional groups. J Chem Phys. 2011;135:214107/1-7.
   Web of Science ®Google Scholar
• SchiffmannC, SebastianiD. Artificial bee colony optimization of capping potentials for hybrid quantum mechanical/molecular mechanical calculations. J Chem Theory Comput. 2011;7:1307–1315.
   PubMed Web of Science ®Google Scholar
• ShaoY, KongJ. YinYang atom: a simple combined ab initio quantum mechanical molecular mechanical model. J Phys Chem A. 2007;111:3661–3671.
   PubMed Web of Science ®Google Scholar
• FieldMJ, AlbeM, BretC, MartinFP-D, ThomasA. The dynamo library for molecular simulations using hybrid quantum mechanical and molecular mechanical potentials. J Comput Chem. 2000;21:1088–1100.
   Web of Science ®Google Scholar
• FerréN, OlivucciM. The amide bond: pitfalls and drawbacks of the link atom scheme. THEOCHEM. 2003;632:71–82.
   Web of Science ®Google Scholar
• AntesI, ThielW. Adjusted connection atoms for combined quantum mechanical and molecular mechanical methods. J Phys Chem A. 1999;103:9290–9295.
   Web of Science ®Google Scholar
• EichingerM, TavanP, HutterJ, ParrinelloM. A hybrid method for solutes in complex solvents: density functional theory combined with empirical force fields. J Chem Phys. 1999;110:10452–10467.
   Web of Science ®Google Scholar
• WoodcockHL, HodoščekM, GilbertATB, GillPMW, SchaeferHF, BrooksBR. Interfacing Q-Chem and CHARMM to perform QM/MM reaction path calculations. J Comput Chem. 2007;28:1485–1502.
   PubMed Web of Science ®Google Scholar
• TheryV, RinaldiD, RivailJ-L, MaigretB, FerenczyGG. Quantum-mechanical computations on very large molecular systems: the local self-consistent field method. J Comput Chem. 1994;15:269–282.
   Web of Science ®Google Scholar
• AssfeldX, RivailJ-L. Quantum chemical computations on parts of large molecules: the ab initio local self consistent field method. Chem Phys Lett. 1996;263:100–106.
   Web of Science ®Google Scholar
• MonardG, LoosM, TheryV, BakaK, RivailJ-L. Hybrid classical quantum force field for modeling very large molecules. Int J Quant Chem. 1996;58:153–159.
   Web of Science ®Google Scholar
• FerréN, AssfeldX, RivailJ-L. Specific force field parameters determination for the hybrid ab Initio QM/MM LSCF method. J Comput Chem. 2002;23:610–624.
   PubMed Web of Science ®Google Scholar
• ForniliA, LoosP-F, SironiM, AssfeldX. 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.
   Web of Science ®Google Scholar
• PhilippDM, FriesnerRA. Mixed ab initio QM/MM modeling using frozen orbitals and tests with alanine dipeptide and tetrapeptide. J Comput Chem. 1999;20:1468–1494.
   Web of Science ®Google Scholar
• MurphyRB, PhilippDM, FriesnerRA. Frozen orbital QM/MM methods for density functional theory. Chem Phys Lett. 2000;321:113–120.
   Web of Science ®Google Scholar
• GaoJ, AmaraP, AlhambraC, FieldMJ. 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.
   Web of Science ®Google Scholar
• AmaraP, FieldMJ, AlhambraC, GaoJ. 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.
   Web of Science ®Google Scholar
• Garcia-VilocaM, GaoJ. 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.
   Web of Science ®Google Scholar
• PuJ, GaoJ, TruhlarDG. Generalized hybrid orbital (GHO) method for combining ab initio Hartree-Fock wave functions with molecular mechanics. J Phys Chem A. 2004;108:632–650.
   Web of Science ®Google Scholar
• PuJ, GaoJ, TruhlarDG. Combining self-consistent-charge density-functional tight-binding (SCC-DFTB) with molecular-mechanics by the generalized hybrid orbital (GHO) method. J Phys Chem A. 2004;108:5454–5463.
   Web of Science ®Google Scholar
• PuJ, GaoJ, TruhlarDG. Generalized hybrid–orbital method for combining density functional theory with molecular mechanicals. ChemPhysChem. 2005;6:1853–1865.
   PubMed Web of Science ®Google Scholar
• WangB, TruhlarDG. 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.
   Web of Science ®Google Scholar
• WangB, TruhlarDG. 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.
   PubMed Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• DickBGJr., OverhauserAW. Theory of the dielectric constants of alkali halide crystals. Phys Rev. 1958;112:90–103.
   Web of Science ®Google Scholar
• StillingerFH, DavidCW. Polarization model for water and its ionic dissociation products. J Chem Phys. 1978;69:1473–1484.
   Web of Science ®Google Scholar
• SprikM, KleinML. A polarizable model for water using distributed charge sites. J Chem Phys. 1988;89:7556–7560.
   Web of Science ®Google Scholar
• DangLX, RiceJE, CaldwellJ, KollmanPA. Ion solvation in polarizable water: molecular dynamics simulations. J Am Chem Soc. 1991;113:2481–2486.
   Web of Science ®Google Scholar
• DangLX. The nonadditive intermolecular potential for water revised. J Chem Phys. 1992;97:2659–2660.
   Web of Science ®Google Scholar
• RickSW, StuartSJ, BerneBJ. Dynamic fluctuating charge force fields: application to liquid water. J Chem Phys. 1994;101:6141–6156.
   Web of Science ®Google Scholar
• KowallT, FogliaF, HelmL, MerbachAE. 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.
   Web of Science ®Google Scholar
• BanksJL, KaminskiGA, ZhouR, MainzDT, BerneBJ, FriesnerRA. Parameterizing a polarizable force field from ab initio data. I. The fluctuating point charge model. J Chem Phys. 1999;110:741–754.
   Web of Science ®Google Scholar
• SternHA, KaminskiGA, BanksJL, ZhouR, BerneBJ, FriesnerRA. Fluctuating charge, polarizable dipole, and combined models: parameterization from ab initio quantum chemistry. J Phys Chem B. 1999;103:4730–4737.
   Web of Science ®Google Scholar
• MartinezJM, Hernandez-CobosJ, Saint-MartinH, PappalardoRR, Ortega-BlakeI, MarcosES. 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.
   Web of Science ®Google Scholar
• WangJ, CieplakP, KollmanPA. 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.
   Web of Science ®Google Scholar
• CieplakP, CaldwellJ, KollmanP. 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.
   Web of Science ®Google Scholar
• RickSW, StuartSJ. Potentials and algorithms for incorporating polarizability in computer simulations. Rev Comput Chem. 2002;18:89–146.
   Web of Science ®Google Scholar
• LamoureuxG, MacKerellAD, RouxB. A simple polarizable model of water based on classical Drude oscillators. J Chem Phys. 2003;119:5185–5197.
   Web of Science ®Google Scholar
• PonderJW, CaseDA. Force fields for protein simulations. Adv Protein Chem. 2003;66:27–85.
   PubMedGoogle Scholar
• KaminskiGA, SternHA, BerneBJ, FriesnerRA. Development of an accurate and robust polarizable molecular mechanics force field from ab initio quantum chemistry. J Phys Chem A. 2004;108:621–627.
   Web of Science ®Google Scholar
• PatelS, BrooksCLIII. CHARMM fluctuating charge force field for proteins: I parameterization and application to bulk organic liquid simulations. J Comput Chem. 2004;25:1–15.
   PubMed Web of Science ®Google Scholar
• PatelS, MackerellADJr., BrooksCLIII. 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.
   PubMed Web of Science ®Google Scholar
• AnisimovVM, LamoureuxG, VorobyovIV, HuangN, RouxB, MacKerellAD. Determination of electrostatic parameters for a polarizable force field based on the classical Drude oscillator. J Chem Theory Comput. 2005;1:153–168.
   PubMed Web of Science ®Google Scholar
• VorobyovIV, AnisimovVM, MacKerellADJr. Polarizable empirical force field for alkanes based on the classical Drude oscillator model. J Phys Chem B. 2005;109:18988–18999.
   PubMed Web of Science ®Google Scholar
• WangZ-X, ZhangW, WuC, LeiH, CieplakP, DuanY. 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.
   PubMed Web of Science ®Google Scholar
• KaminskiGA, SternHA, BerneBJ, FriesnerRA, CaoYX, MurphyRB, ZhouR, HalgrenTA. 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.
   PubMed Web of Science ®Google Scholar
• RenP, PonderJW. Consistent treatment of inter- and intramolecular polarization in molecular mechanics calculations. J Comput Chem. 2002;23:1497–1506.
   PubMed Web of Science ®Google Scholar
• SefcikJ, DemiralpE, CaginT, GoddardWA. Dynamic charge equilibration-Morse stretch force field: application to energetics of pure silica zeolites. J Comput Chem. 2002;23:1507–1514.
   PubMed Web of Science ®Google Scholar
• GrossfieldA, RenP, PonderJW. Ion solvation thermodynamics from simulation with a polarizable force field. J Am Chem Soc. 2003;125:15671–15682.
   PubMed Web of Science ®Google Scholar
• RenP, PonderJW. Polarizable atomic multipole water model for molecular mechanics simulation. J Phys Chem B. 2003;107:5933–5947.
   Web of Science ®Google Scholar
• MaY, GarofaliniSH. Iterative fluctuation charge model: a new variable charge molecular dynamics method. J Chem Phys. 2006;124:234102/1-7.
   Google Scholar
• LopesPM, RouxB, MacKerellAJr. Molecular modeling and dynamics studies with explicit inclusion of electronic polarizability: theory and applications. Theory Chem Acc. 2009;124:11–28.
   PubMed Web of Science ®Google Scholar
• SmaloHS, AstrandP-O, JensenL. 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.
   Web of Science ®Google Scholar
• PonderJW. Current status of the AMOEBA polarizable force field. J Phys Chem B. 2010;114:2549–2564.
   PubMed Web of Science ®Google Scholar
• PonomarevSY, KaminskiGA. 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.
   PubMed Web of Science ®Google Scholar
• RenP, WuC, PonderJW. Polarizable atomic multipole-based molecular mechanics for organic molecules. J Chem Theory Comput. 2011;7:3143–3161.
   PubMed Web of Science ®Google Scholar
• KimWH, RheeYM. Molecule-specific determination of atomic polarizabilities with the polarizable atomic multipole model. J Comput Chem. 2012;33:1662–1672.
   PubMed Web of Science ®Google Scholar
• LamoureuxG, OrabiEA. Molecular modelling of cation–π interactions. Mol Simul. 2012;38:704–722.
   Web of Science ®Google Scholar
• CisnerosGA, KarttunenM, RenP, SaguiC. Classical electrostatics for biomolecular simulations. Chem Rev ASAP, 2013. 10.1021/cr300461d.
   Google Scholar
• BakerCM, BestRB. Matching of additive and polarizable force fields for multiscale condensed phase simulations. J Chem Theory Comput. 2013;9:2826–2837.
   PubMed Web of Science ®Google Scholar
• HanJ, MazackMJM, ZhangP, TruhlarDG, GaoJ. Quantum mechanical force field for water with explicit electronic polarization. J Chem Phys. 2013;139:054503/1-18.
   Google Scholar
• LiX, PonomarevSY, SaQ, SigalovskyDL, KaminskiGA. Polarizable simulations with second order interaction model (POSSIM) force field: developing parameters for protein side-chain analogues. J Comput Chem. 2013;34:1241–1250.
   PubMed Web of Science ®Google Scholar
• ShiY, XiaZ, ZhangJ, BestR, WuC, PonderJW, RenP. Polarizable atomic multipole-based AMOEBA force field for proteins. J Chem Theory Comput. 2013;9:4046–4063.
   PubMed Web of Science ®Google Scholar
• ThompsonMA, SchenterGK. 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.
   Web of Science ®Google Scholar
• ThompsonMA. 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.
   Web of Science ®Google Scholar
• BakowiesD, ThielW. Semiempirical treatment of electrostatic potentials and partial charges in combined quantum mechanical and molecular mechanical approaches. J Comput Chem. 1996;17:87–108.
   Web of Science ®Google Scholar
• YorkDM, YangW. A chemical potential equalization method for molecular simulations. J Chem Phys. 1996;104:159–172.
   Web of Science ®Google Scholar
• YangZ-Z, WangC-S. Atom-bond electronegativity equalization method. 1. Calculation of the charge distribution in large molecules. J Phys Chem A. 1997;101:6315–6321.
   Web of Science ®Google Scholar
• GaoJ. Energy components of aqueous solution: insight from hybrid QM/MM simulations using a polarizable solvent model. J Comput Chem. 1997;18:1061–1071.
   Web of Science ®Google Scholar
• GaoJ, ByunK. Solvent effects on the n → π* transition of pyrimidine in aqueous solution. Theory Chem Acc. 1997;96:151–156.
   Web of Science ®Google Scholar
• GaoJ, AlhambraC. Solvent effects on the bond length alternation and absorption energy of conjugated compounds. J Am Chem Soc. 1997;119:2962–2963.
   Web of Science ®Google Scholar
• ItskowitzP, BerkowitzML. Chemical potential equalization principle: direct approach from density functional theory. J Phys Chem A. 1997;101:5687–5691.
   Web of Science ®Google Scholar
• BryceRA, VincentMA, MalcolmNOJ, HillierIH, BurtonNA. 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.
   Web of Science ®Google Scholar
• BultinckP, LangenaekerW, LahorteP, De ProftF, GeeringsP, WaroquierM, TollenaereJP. The electronegativity equalization method I: parameterization and validation for atomic charge calculations. J Phys Chem AJ Phys. 2002;106:7887–7894.
   Web of Science ®Google Scholar
• JensenL, van DuijnenPT, SnijdersJG. A discrete solvent reaction field model within density functional theory. J Chem Phys. 2003;118:514–521.
   Web of Science ®Google Scholar
• IllingworthCJR, GoodingSR, WinnPJ, JonesGA, FerenczyGG, ReynoldsCA. Classical polarization in hybrid QM/MM methods. J Phys Chem A. 2006;110:6487–6497.
   PubMed Web of Science ®Google Scholar
• GeerkeDP, ThielS, ThielW, van GunsterenWF. 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.
   Web of Science ®Google Scholar
• LinY-L, GaoJ. Solvatochromic shifts of the n → π* 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.
   Web of Science ®Google Scholar
• GeerkeDP, ThielS, ThielW, van GunsterenWF. QM–MM interactions in simulations of liquid water using combined semi-empirical/classical Hamiltonians. Phys Chem Chem Phys. 2008;10:297–302.
   PubMed Web of Science ®Google Scholar
• IllingworthCJR, ParkesKEB, SnellCR, FerenczyGrG, ReynoldsCA. Toward a consistent treatment of polarization in model QM/MM calculations. J Phys Chem A. 2008;112:12151–12156.
   PubMed Web of Science ®Google Scholar
• IllingworthCJR, MorrisGM, ParkesKEB, SnellCR, ReynoldsCA. Assessing the role of polarization in docking. J Phys Chem A. 2008;112:12157–12163.
   PubMed Web of Science ®Google Scholar
• LuZ, ZhangY. 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.
   PubMed Web of Science ®Google Scholar
• WankoM, HoffmannM, FrähmckeJ, FrauenheimT, ElstnerM. Effect of polarization on the opsin shift in rhodopsins. 2. Empirical polarization models for proteins. J Phys Chem B. 2008;112:11468–11478.
   PubMed Web of Science ®Google Scholar
• IllingworthCJR, FuriniS, DomeneC. Computational studies on polarization effects and selectivity in K+ channels. J Chem Theory Comput. 2010;6:3780–3792.
   Web of Science ®Google Scholar
• SneskovK, SchwabeT, ChristiansenO, KongstedJ. Scrutinizing the effects of polarization in QM/MM excited state calculations. Phys Chem Chem Phys. 2011;13:18551–18560.
   PubMed Web of Science ®Google Scholar
• SneskovK, SchwabeT, KongstedJ, ChristiansenO. The polarizable embedding coupled cluster method. J Chem Phys. 2011;134:104108/1-15.
   Web of Science ®Google Scholar
• WangQ, BryceRA. Accounting for non-optimal interactions in molecular recognition: a study of ion–π complexes using a QM/MM model with a dipole-polarisable MM region. Phys Chem Chem Phys. 2011;13:19401–19408.
   PubMed Web of Science ®Google Scholar
• SchworerM, BreitenfeldB, TrosterP, BauerS, LorenzenK, TavanP, MathiasG. Coupling density functional theory to polarizable force fields for efficient and accurate Hamiltonian molecular dynamics simulations. J Chem Phys. 2013;138:244103/1-13.
   Web of Science ®Google Scholar
• ApplequistJ, CarlJR, FungK-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.
   Web of Science ®Google Scholar
• TholeBT. Molecular polarizabilities calculated with a modified dipole interaction. Chem Phys. 1981;59:341–350.
   Web of Science ®Google Scholar
• StoneAJ. Distributed polarizability. Mol Phys. 1985;56:1065–1082.
   Web of Science ®Google Scholar
• WinnPJ, FerenczyGG, ReynoldsCA. Toward improved force fields: III polarization through modified atomic charges. J Comput Chem. 1999;20:704–712.
   Google Scholar
• MortierWJ, Van GenechtenK, GasteigerJ. Electronegativity equalization: application and parameterization. J Am Chem Soc. 1985;107:829–835.
   Web of Science ®Google Scholar
• MortierWJ, GhoshSK, ShankarS. Electronegativity equalization method for the calculation of atomic charges in molecules. J Am Chem Soc. 1986;108:4315–4320.
   Web of Science ®Google Scholar
• RappéAK, GoddardWA. Charge equilibration for molecular dynamics simulations. J Phys Chem. 1991;95:3358–3363.
   Web of Science ®Google Scholar
• DewarMJS, HashmallJA, VenierCG. Ground states of conjugated molecules. IX. Hydrocarbon radicals and radical ions. J Am Chem Soc. 1968;90:1953–1957.
   Web of Science ®Google Scholar
• DewarMJS, TrinajsticN. Triplet states of aromatic hydrocarbons. J Chem Soc Chem Commun. 1970 :646–647.
   Google Scholar
• GogoneaV, MerzKMJr. A quantum mechanical-Poisson–Boltzmann equation approach for studying charge flow between ions and a dielectric continuum. J Chem Phys. 2000;112:3227–3235.
   Web of Science ®Google Scholar
• GogoneaV, MerzKMJr. 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.
   Web of Science ®Google Scholar
• PerdewJP, ParrRG, LevyM, BalduzJL. Density-functional theory for fractional particle number: derivative discontinuities of the energy. Phys Rev Lett. 1982;49:1691–1694.
   Web of Science ®Google Scholar
• ZhangY, YangW. A challenge for density functionals: self-interaction error increases for systems with a noninteger number of electrons. J Chem Phys. 1998;109:2604–2608.
   Web of Science ®Google Scholar
• YangW, ZhangY, AyersPW. Degenerate ground states and a fractional number of electrons in density and reduced density matrix functional theory. Phys Rev Lett. 2000;84:5172–5175.
   PubMed Web of Science ®Google Scholar
• ZhangY, YangW. Perspective on ‘density-functional theory for fractional particle number: derivative discontinuities of the energy’. Theory Chem Acc. 2000;103:346–348.
   Web of Science ®Google Scholar
• CohenAJ, Mori-SanchezP, YangW. Fractional spins and static correlation error in density functional theory. J Chem Phys. 2008;129:121104/1-4.
   Web of Science ®Google Scholar
• ZengX, HuH, HuX, CohenAJ, YangW. Ab initio quantum mechanical/molecular mechanical simulation of electron transfer process: fractional electron approach. J Chem Phys. 2008;128:124510/1-10.
   Web of Science ®Google Scholar
• CohenAJ, Mori-SanchezP, YangW. Second-order perturbation theory with fractional charges and fractional spins. J Chem Theory Comput. 2009;5:786–792.
   PubMed Web of Science ®Google Scholar
• EssDH, JohnsonER, HuX, YangW. Singlet-triplet energy gaps for diradicals from fractional-spin density-functional theory. J Phys Chem A. 2011;115:76–83.
   PubMed Web of Science ®Google Scholar
• SteinmannSN, YangW. Wave function methods for fractional electrons. J Chem Phys. 2013;139:074107/1-14.
   Web of Science ®Google Scholar
• MayhallNJ, RaghavachariK. Molecules-in-molecules: an extrapolated fragment-based approach for accurate calculations on large molecules and materials. J Chem Theory Comput. 2011;7:1336–1343.
   PubMed Web of Science ®Google Scholar
• ElliottP, CohenMH, WassermanA, BurkeK. Density functional partition theory with fractional occupations. J Chem Theory Comput. 2009;5:827–833.
   Web of Science ®Google Scholar
• ElliottP, BurkeK, CohenMH, WassermanA. Partition density-functional theory. Phys Rev A. 2010;82:024501/1-4.
   Web of Science ®Google Scholar
• TavernelliI, VuilleumierR, SprikM. Ab initio dynamics for molecules with variable numbers of electrons. Phys Rev Lett. 2002;88:213002/1-4.
   Web of Science ®Google Scholar
• HallRJ, HindleSA, BurtonNA, HillierIH. 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.
   Web of Science ®Google Scholar
• ReuterN, DejaegereA, MaigretB, KarplusM. Frontier bonds in QM/MM methods: a comparison of different approaches. J Phys Chem A. 2000;104:1720–1735.
   Web of Science ®Google Scholar
• NicollRM, HindleSA, MacKenzieG, HillierIH, BurtonNA. 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.
   Web of Science ®Google Scholar
• LennartzC, SchaeferA, TerstegenF, ThielW. Enzymatic reactions of triosephosphate isomerase: a theoretical calibration study. J Phys Chem B. 2002;106:1758–1767.
   Web of Science ®Google Scholar
• CarR, ParrinelloM. Unified approach for molecular dynamics and density-functional theory. Phys Rev Lett. 1985;55:2471–2474.
   PubMed Web of Science ®Google Scholar
• WooTK, CavalloL, ZieglerT. Implementation of the IMOMM methodology for performing combined QM/MM molecular dynamics simulations and frequency calculations. Theory Chem Acc. 1998;100:307–313.
   Web of Science ®Google Scholar
• RöthlisbergerU, CarloniP, DocloK, ParrinelloM. 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.
   PubMed Web of Science ®Google Scholar
• WooTK, BlöchlPE, ZieglerT. Towards solvation simulations with a combined ab initio molecular dynamics and molecular mechanics approach. THEOCHEM. 2000;506:313–334.
   Web of Science ®Google Scholar
• ColomboMC. Hybrid QM/MM Car–Parrinello simulations of catalytic and enzymatic reactions. Chimia. 2002;56:13–19.
   Web of Science ®Google Scholar
• WooTK, MarglP, BlochlPE, ZieglerT. 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.
   Web of Science ®Google Scholar
• SulpiziM, LaioA, VandeVondeleJ, CattaneoA, RöthlisbergerU, CarloniP. Reaction mechanism of caspases: insights from QM/MM Car–Parrinello simulations. Proteins: Struct Funct Genet. 2003;52:212–224.
   PubMed Web of Science ®Google Scholar
• RaugeiS, CascellaM, CarloniP. A proficient enzyme: insights on the mechanism of orotidine monophosphate decarboxylase from computer simulations. J Am Chem Soc. 2004;126:15730–15737.
   PubMed Web of Science ®Google Scholar
• KerdcharoenT, LiedlKR, RodeBM. A QM/MM simulation method applied to the solution of Li+ in liquid ammonia. Chem Phys. 1996;211:313–323.
   Web of Science ®Google Scholar
• KerdcharoenT, MorokumaK. ONIOM-XS: an extension of the ONIOM method for molecular simulation in condensed phase. Chem Phys Lett. 2002;355:257–262.
   Web of Science ®Google Scholar
• KerdcharoenT, MorokumaK. 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.
   Web of Science ®Google Scholar
• BuloRE, EnsingB, SikkemaJ, VisscherL. Toward a practical method for adaptive QM/MM simulations. J Chem Theory Comput. 2009;5:2212–2221.
   PubMed Web of Science ®Google Scholar
• GuthrieMG, DaigleAD, SalazarMR. 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.
   Web of Science ®Google Scholar
• NielsenSO, BuloRE, MoorePB, EnsingB. Recent progress in adaptive multiscale molecular dynamics simulations of soft matter. Phys Chem Chem Phys. 2010;12:12401–12414.
   PubMed Web of Science ®Google Scholar
• PomaAB, Delle SiteL. Classical to path-integral adaptive resolution in molecular simulation: towards a smooth quantum-classical coupling. Phys Rev Lett. 2010;104:250201/1-4.
   Web of Science ®Google Scholar
• BernsteinN, VarnaiC, SoltI, WinfieldSA, PayneMC, SimonI, FuxreiterM, CsanyiG. QM/MM simulation of liquid water with an adaptive quantum region. Phys Chem Chem Phys. 2012;14:646–656.
   PubMed Web of Science ®Google Scholar
• ParkK, GotzAW, WalkerRC, PaesaniF. Application of adaptive QM/MM methods to molecular dynamics simulations of aqueous systems. J Chem Theory Comput. 2012;8:2868–2877.
   Web of Science ®Google Scholar
• TakenakaN, KitamuraY, KoyanoY, NagaokaM. The number-adaptive multiscale QM/MM molecular dynamics simulation: application to liquid water. Chem Phys Lett. 2012;524:56–61.
   Web of Science ®Google Scholar
• VárnaiC, BernsteinN, MonesL, CsányiG. Tests of an adaptive QM/MM calculation on free energy profiles of chemical reactions in solution. J Phys Chem B. 2013;117:12202–12211.
   PubMed Web of Science ®Google Scholar
• RowleyCN, RouxB. 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.
   PubMed Web of Science ®Google Scholar
• ShigaM, MasiaM. Boundary based on exchange symmetry theory for multilevel simulations. I. Basic theory. J Chem Phys. 2013;139:044120/1-8.
   Google Scholar
• BuloRE, MichelC, Fleurat-LessardP, SautetP. Multiscale modeling of chemistry in water: are we there yet?J Chem Theory Comput. 2013;9:5567–5577.
   PubMed Web of Science ®Google Scholar
• StewartJP. Optimization of parameters for semiempirical methods V: modification of NDDO approximations and application to 70 elements. J Mol Model. 2007;13:1173–1213.
   PubMed Web of Science ®Google Scholar
• KorthM. Third-generation hydrogen-bonding corrections for semiempirical QM methods and force fields. J Chem Theory Comput. 2010;6:3808–3816.
   Web of Science ®Google Scholar
• ElstnerM, PorezagD, JungnickelG, ElsnerJ, HaugkM, FrauenheimT, SuhaiS, SeifertG. Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties. Phys Rev B. 1998;58:7260–7268.
   Web of Science ®Google Scholar
• WuY, TepperHL, VothGA. Flexible simple point-charge water model with improved liquid-state properties. J Chem Phys. 2006;124:024503/1-12.
   Google Scholar
• DuinACTv, DasguptaS, LorantF, GoddardWA. ReaxFF: a reactive force field for hydrocarbons. J Phys Chem A. 2001;105:9396–9409.
   Web of Science ®Google Scholar
• KästnerJ, ThielW. Bridging the gap between thermodynamic integration and umbrella sampling provides a novel analysis method: ‘umbrella integration’. J Chem Phys. 2005;123:144104/1-5.
   Google Scholar
• CarterEA, CiccottiG, HynesJT, KapralR. Constrained reaction coordinate dynamics for the simulation of rare events. Chem Phys Lett. 1989;156:472–477.
   Web of Science ®Google Scholar
• LaioA, ParrinelloM. Escaping free-energy minima. Proc Natl Acad Sci USA. 2002;99:12562–12566.
   PubMed Web of Science ®Google Scholar
• DarveE, PohorilleA. Calculating free energies using average force. J Chem Phys. 2001;115:9169–9183.
   Web of Science ®Google Scholar
• SteveON, CarlosFL, GoundlaS, MichaelLK. Coarse grain models and the computer simulation of soft materials. J Phys Condens Matter. 2004;16:R481.
   Web of Science ®Google Scholar
• ShihAY, ArkhipovA, FreddolinoPL, SchultenK. Coarse grained protein-lipid model with application to lipoprotein particles. J Phys Chem B. 2006;110:3674–3684.
   PubMed Web of Science ®Google Scholar
• MarrinkSJ, RisseladaHJ, YefimovS, TielemanDP, de VriesAH. The MARTINI force field: coarse grained model for biomolecular simulations. J Phys Chem B. 2007;111:7812–7824.
   PubMed Web of Science ®Google Scholar
• ClementiC. Coarse-grained models of protein folding: toy models or predictive tools?Curr Opin Struct Biol. 2008;18:10–15.
   PubMed Web of Science ®Google Scholar
• MurtolaT, BunkerA, VattulainenI, DesernoM, KarttunenM. Multiscale modeling of emergent materials: biological and soft matter. Phys Chem Chem Phys. 2009;11:1869–1892.
   PubMed Web of Science ®Google Scholar
• PeterC, KremerK. Multiscale simulation of soft matter systems – from the atomistic to the coarse-grained level and back. Soft Matter. 2009;5:4357–4366.
   Web of Science ®Google Scholar
• WuZ, CuiQ, YethirajA. A new coarse-grained model for water: the importance of electrostatic interactions. J Phys Chem B. 2010;114:10524–10529.
   PubMed Web of Science ®Google Scholar
• RinikerS, van GunsterenWF. A simple, efficient polarizable coarse-grained water model for molecular dynamics simulations. J Chem Phys. 2011;134:084110/1-12.
   Web of Science ®Google Scholar
• TakadaS. Coarse-grained molecular simulations of large biomolecules. Curr Opin Struct Biol. 2012;22:130–137.
   PubMed Web of Science ®Google Scholar
• NoidWG. Perspective: coarse-grained models for biomolecular systems. J Chem Phys. 2013;139:090901/1-25.
   Web of Science ®Google Scholar
• SaundersMG, VothGA. Coarse-graining methods for computational biology. Annu Rev Biophys. 2013;42:73–93.
   PubMed Web of Science ®Google Scholar
• NeriM, AnselmiC, CascellaM, MaritanA, CarloniP. Coarse-grained model of proteins incorporating atomistic detail of the active site. Phys Rev Lett. 2005;95:218102/1-4.
   Web of Science ®Google Scholar
• ShiQ, IzvekovS, VothGA. Mixed atomistic and coarse-grained molecular dynamics: simulation of a membrane-bound ion channel. J Phys Chem B. 2006;110:15045–15048.
   PubMed Web of Science ®Google Scholar
• MichelJ, OrsiM, EssexJW. Prediction of partition coefficients by multiscale hybrid atomic-level/coarse-grain simulations. J Phys Chem B. 2007;112:657–660.
   PubMed Web of Science ®Google Scholar
• MasellaM, BorgisD, CuniasseP. Combining a polarizable force-field and a coarse-grained polarizable solvent model: application to long dynamics simulations of bovine pancreatic trypsin inhibitor. J Comput Chem. 2008;29:1707–1724.
   PubMed Web of Science ®Google Scholar
• OrsiM, SandersonWE, EssexJW. Permeability of small molecules through a lipid bilayer: a multiscale simulation study. J Phys Chem B. 2009;113:12019–12029.
   PubMed Web of Science ®Google Scholar
• MasellaM, BorgisD, CuniasseP. Combining a polarizable force-field and a coarse-grained polarizable solvent model. II. Accounting for hydrophobic effects. J Comput Chem. 2011;32:2664–2678.
   PubMed Web of Science ®Google Scholar
• RzepielaAJ, LouhivuoriM, PeterC, MarrinkSJ. Hybrid simulations: combining atomistic and coarse-grained force fields using virtual sites. Phys Chem Chem Phys. 2011;13:10437–10448.
   PubMed Web of Science ®Google Scholar
• RinikerS, EichenbergerAP, van GunsterenWF. 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.
   PubMed Web of Science ®Google Scholar
• DarréL, TekA, BaadenM, PantanoS. Mixing atomistic and coarse grain solvation models for MD simulations: let WT4 handle the bulk. J Chem Theory Comput. 2012;8:3880–3894.
   PubMed Web of Science ®Google Scholar
• RinikerS, van GunsterenWF. Mixing coarse-grained and fine-grained water in molecular dynamics simulations of a single system. J Chem Phys. 2012;137:044120/1-8.
   Web of Science ®Google Scholar
• RinikerS, EichenbergerA, van GunsterenW. Solvating atomic level fine-grained proteins in supra-molecular level coarse-grained water for molecular dynamics simulations. Eur Biophys J. 2012;41:647–661.
   PubMed Web of Science ®Google Scholar
• GonzalezHC, DarréL, PantanoS. Transferable mixing of atomistic and coarse-grained water models. J Phys Chem B. 2013;117:14438–14448.
   PubMed Web of Science ®Google Scholar
• LinZ, RinikerS, van GunsterenWF. Free enthalpy differences between α-, π-, 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.
   Web of Science ®Google Scholar
• SokkarP, ChoiSM, RheeYM. Simple method for simulating the mixture of atomistic and coarse-grained molecular systems. J Chem Theory Comput. 2013;9:3728–3739.
   Web of Science ®Google Scholar
• WassenaarTA, IngólfssonHI, PrießM, MarrinkSJ, SchäferLV. Mixing MARTINI: electrostatic coupling in hybrid atomistic–coarse-grained biomolecular simulations. J Phys Chem B. 2013;117:3516–3530.
   PubMed Web of Science ®Google Scholar
• GhyselsA, MillerBT, PickardFC, BrooksBR. Comparing normal modes across different models and scales: Hessian reduction versus coarse-graining. J Comput Chem. 2012;33:2250–2275.
   PubMed Web of Science ®Google Scholar
• AbramsCF. Concurrent dual-resolution Monte Carlo simulation of liquid methane. J Chem Phys. 2005;123:234101/1-13.
   Web of Science ®Google Scholar
• PraprotnikM, Delle SiteL, KremerK. Adaptive resolution molecular-dynamics simulation: changing the degrees of freedom on the fly. J Chem Phys. 2005;123:224106/1-14.
   Web of Science ®Google Scholar
• EnsingB, NielsenSO, MoorePB, KleinML, ParrinelloM. Energy conservation in adaptive hybrid atomistic/coarse-grain molecular dynamics. J Chem Theory Comput. 2007;3:1100–1105.
   Web of Science ®Google Scholar
• PraprotnikM, MatysiakS, SiteLD, KremerK, ClementiC. Adaptive resolution simulation of liquid water. J Phys Condens Matter. 2007;19:292201/1-10.
   Web of Science ®Google Scholar
• HeydenA, TruhlarDG. Conservative algorithm for an adaptive change of resolution in mixed atomistic/coarse-grained multiscale simulations. J Chem Theory Comput. 2008;4:217–221.
   Web of Science ®Google Scholar
• WangH, SchütteC, Delle SiteL. 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.
   Web of Science ®Google Scholar
• WangH, HartmannC, SchütteC, Delle SiteL. Grand-canonical-like molecular-dynamics simulations by using an adaptive-resolution technique. Phys Rev X. 2013;3:011018/1-16.
   Google Scholar