Abstract.
To understand the properties of a complex system it is often illuminating to perform a comparison with a simpler, even idealised one. A prototypical application of this approach is the calculation of free energies and chemical potentials in liquids, which can be decomposed in the sum of ideal and excess contributions. In the same spirit, in computer simulations it is possible to extract useful information on a given system making use of setups where two models, an accurate one and a simpler one, are concurrently employed and directly coupled. Here, we tackle the issue of coupling atomistic or, more in general, interacting models of a system with the corresponding idealised representations: for a liquid, this is the ideal gas, i.e. a collection of non-interacting particles; for a solid, we employ the ideal Einstein crystal, a construct in which particles are decoupled from one another and restrained by a harmonic, exactly integrable potential. We describe in detail the practical and technical aspects of these simulations, and suggest that the concurrent usage and coupling of realistic and ideal models represents a promising strategy to investigate liquids and solids in silico.
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References
R.P. Feynman, Int. J. Theor. Phys. 21, 467 (1982)
D. Frenkel, J.-P. Hansen, Phys. World 9, 35 (1996)
W.F. van Gunsteren, A.E. Mark, J. Chem. Phys. 108, 6109 (1998)
W.G. Hoover, 50 Years of Computer Simulation -- a Personal View, arXiv:0812.2086v2 (2008)
M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids (Clarendon Press, Oxford, 1987)
D. Frenkel, B. Smit, Understanding Molecular Simulation: From Algorithms to Applications (Elsevier, 2001)
M. Praprotnik, L. Delle Site, K. Kremer, Annu. Rev. Phys. Chem. 59, 545 (2008)
K. Kremer, Soft and fragile matter non equilibrium dynamics, metastability and flow, in SUSSP Proceedings Vol. 53 (IOP Publishing Ltd., 2000) pp. 145--184
A. Mulero (Editor), Theory and Simulation of Hard-Sphere Fluids and Related Systems (Springer, Berlin, Heidelberg, 2008)
K. Kremer, F. Müller-Plathe, MRS Bull. 26, 205 (2001)
R.E. Caflisch, G. Ceder, K. Kremer, T. Pollock, M. Scheffler, E.G. Wang (Editors), Focus on Novel Materials Discovery, New J. Phys. (IOP, 2013 and 2014)
C. Micheletti, P. Carloni, A. Maritan, Proteins 55, 635 (2004)
W.G. Noid, J. Chem. Phys. 139, 090901 (2013)
F. Pontiggia, A. Zen, C. Micheletti, Biophys. J. 95, 5901 (2008)
M. Karplus, J. McCammon, Nature 277, 578 (1979)
M. Karplus, Acc. Chem. Res. 35, 321 (2002)
A. Pérez, F.J. Luque, M. Orozco, Acc. Chem. Res. 45, 196 (2012)
P. Ballone, Entropy 16, 322 (2014)
J. Kirkwood, J. Chem. Phys. 3, 300 (1935)
P. Raiteri, A. Laio, F.L. Gervasio, C. Micheletti, M. Parrinello, J. Phys. Chem. B 110, 3533 (2006)
M.E. Tuckerman, Statistical Mechanics: Theory and Molecular Simulation (Oxford University Press, 2010)
M. Praprotnik, L. Delle Site, K. Kremer, Phys. Rev. E 73, 066701 (2006)
M. Praprotnik, L. Delle Site, K. Kremer, J. Chem. Phys. 126, 134902 (2007)
S. Fritsch, S. Poblete, C. Junghans, G. Ciccotti, L. Delle Site, K. Kremer, Phys. Rev. Lett. 108, 170602 (2012)
P. Español, R. Delgado-Buscalioni, R. Everaers, R. Potestio, D. Donadio, K. Kremer, J. Chem. Phys. 142, 064115 (2015)
A.C. Fogarty, R. Potestio, K. Kremer, J. Chem. Phys. 142, 195101 (2015)
A.C. Fogarty, R. Potestio, K. Kremer, Proteins 84, 1902 (2016)
R. Fiorentini, K. Kremer, R. Potestio, A.C. Fogarty, J. Chem. Phys. 146, 244113 (2017)
T. Tarenzi, V. Calandrini, R. Potestio, A. Giorgetti, P. Carloni, J. Chem. Theory Comput. 13, 5647 (2017)
R. Potestio, S. Fritsch, P. Español, R. Delgado-Buscalioni, K. Kremer, R. Everaers, D. Donadio, Phys. Rev. Lett. 110, 108301 (2013)
R. Potestio, P. Español, R. Delgado-Buscalioni, R. Everaers, K. Kremer, D. Donadio, Phys. Rev. Lett. 111, 060601 (2013)
M. Heidari, K. Kremer, R. Cortes-Huerto, R. Potestio, Spatially resolved thermodynamic integration: An efficient method to compute chemical potentials of dense fluids, arXiv:1802.08045, submitted to J. Chem. Theory Comput
K. Kreis, A.C. Fogarty, K. Kremer, R. Potestio, Eur. Phys. J. ST 224, 2289 (2015)
M. Praprotnik, L. Delle Site, K. Kremer, J. Chem. Phys. 123, 224106 (2005)
J. Zavadlav, R. Podgornik, M. Melo, S. Marrink, M. Praprotnik, Eur. Phys. J. ST 225, 1595 (2016)
K. Kreis, R. Potestio, K. Kremer, A.C. Fogarty, J. Chem. Theory Comput. 12, 4067 (2016)
M. Heidari, R. Cortes-Huerto, D. Donadio, R. Potestio, Eur. Phys. J. ST 225, 1505 (2016)
D. Wolf, P. Keblinski, S.R. Phillpot, J. Eggebrecht, J. Chem. Phys. 110, 8254 (1999)
C.J. Fennell, J.D. Gezelter, J. Chem. Phys. 124, 234104 (2006)
H.J.C. Berendsen, J.R. Grigera, T.P. Straatsma, J. Phys. Chem. 91, 6269 (1987)
L.X. Dang, B.M. Pettitt, J. Phys. Chem. 91, 3349 (1987)
Y. Wu, H.L. Tepper, G.A. Voth, J. Chem. Phys. 124, 024503 (2006)
S. Plimpton, J. Comput. Phys. 117, 1 (1995)
J.D. Halverson, T. Brandes, O. Lenz, A. Arnold, S. Bevc, V. Starchenko, K. Kremer, T. Stuehn, D. Reith, Comput. Phys. Commun. 184, 1129 (2013)
K. Kreis, A.C. Fogarty, K. Kremer, R. Potestio, Eur. Phys. J. ST 224, 2289 (2015)
J. Kohanoff, Comput. Mater. Sci. 2, 221 (1994)
F. Pavia, W.A. Curtin, Model. Simul. Mater. Sci. Eng. 23, 055002 (2015)
R. Rudd, J. Broughton, Phys. Status Solidi B: Basic Res. 217, 251 (2000)
J. Rottler, S. Barsky, M.O. Robbins, Phys. Rev. Lett. 89, 148304 (2002)
G. Csanyi, T. Albaret, M.C. Payne, A.D. Vita, Phys. Rev. Lett. 93, 175503 (2004)
D. Jiang, E.A. Carter, Acta Mater. 52, 4801 (2004)
G. Lu, E.B. Tadmor, E. Kaxiras, Phys. Rev. B 73, 024108 (2006)
D. Frenkel, A.J.C. Ladd, J. Chem. Phys. 81, 3188 (1984)
J.M. Polson, E. Trizac, S. Pronk, D. Frenkel, J. Chem. Phys. 112, 5339 (2000)
M.A. van der Hoef, J. Chem. Phys. 113, 8142 (2000)
C. Vega, E.G. Noya, J. Chem. Phys. 127, 154113 (2007)
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Heidari, M., Cortes-Huerto, R., Kremer, K. et al. Concurrent coupling of realistic and ideal models of liquids and solids in Hamiltonian adaptive resolution simulations. Eur. Phys. J. E 41, 64 (2018). https://doi.org/10.1140/epje/i2018-11675-x
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DOI: https://doi.org/10.1140/epje/i2018-11675-x
Keywords
- Topical issue: Advances in Computational Methods for Soft Matter Systems