Abstract
The suitability of the generalized Langevin equation (GLE) for a realistic description of the behavior of a system of interacting particles in solution is discussed. This study is focused on the GLE for a system of non-Brownian particles, i.e., the masses and the sizes of the solute particles are similar to those of the bath particles. The random and frictional forces on the atoms of the solute due to their collisions with the solvent atoms are characterized from molecular dynamics simulations of simple dense liquid mixtures. The required effective memory functions, which are dependent on the concentration of solute, are obtained by solving a generalized Volterra equation. The validity of the usual assumptions on the statistical properties of the random forces is carefully analyzed, paying special attention to their Gaussianity. The reliability of stochastic simulations based on the GLE is also discussed.
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References
P. Turq, F. Lantelme, and H. L. Friedman,J. Chem. Phys. 66:3039 (1977).
M. P. Allen and D. J. Tildesley,Computer Simulation of Liquids (Clarendon Press, Oxford, 1987), Chapter 9.
H. L. Friedman,A Course in Statistical Mechanics (Prentice Hall, New Jersey, 1985), Chapter 4.
J. M. Deutch and I. Oppenheim,J. Chem. Phys. 54:3547 (1971);Faraday Disc. Chem. Soc. 83:1 (1987).
H. Mori,Prog. Theor. Phys. 33:423 (1965);34:399 (1965).
B. J. Berne and R. Pecora,Dynamic Light Scattering (Wiley, New York, 1976), Chapter 11.
G. Ciccotti and J. P. Ryckaert,J. Stat. Phys. 26:73 (1981).
F. J. Vesely and H. A. Posch,Mol. Phys. 64:97 (1988).
G. Bossis, B. Quentrec, and J. P. Boon,Mol. Phys. 45:191 (1982).
E. Guàrdia, J. L. Gómez-Estévez, and J. A. Padró,J. Chem. Phys. 86:6438 (1987).
J. A. Padró, E. Guàrdia, and G. Sesé,Mol. Phys. 63:355 (1988).
M. Canales and J. A. Padró,Mol. Simul. 1:403 (1988).
J. A. Padró and M. Canales,Mol. Phys. 68:423 (1989).
B. J. Berne and G. D. Harp,Adv. Chem. Phys. 17:63 (1970).
U. Balucani, V. Tognetti, R. Vallauri, P. Grigolini, and P. Marin,Z. Phys. B. 49:181 (1982).
R. Zwanzig,Annu. Rev. Phys. Chem. 16:67 (1965).
R. Vogelsang and C. Hoheisel,J. Stat. Phys. 47:193 (1987).
R. Vogelsang and C. Hoheisel,J. Stat. Phys. 54:315 (1989).
P. G. Wolynes,Annu. Rev. Phys. Chem. 31:345 (1980).
J. P. Bergsma, J. R. Reimers, K. R. Wilson, and J. T. Hynes,J. Chem. Phys. 85:5625 (1986).
M. A. Wilson, A. Pohorille, and L. R. Pratt,J. Chem. Phys. 83:5382 (1985).
M. Berkowitz and W. Wan,J. Chem. Phys. 86:376 (1987).
H. A. Posch, U. Balucani, and R. Vallauri,Physica 123A:516 (1984).
E. Guàrdia and J. A. Padró,J. Chem. Phys. 83:1917 (1985).
F. J. Vesely,Mol. Phys. 53:505 (1984).
W. F. van Gunsteren and H. J. C. Berendsen,Mol. Phys. 47:721 (1982).
J. P. Hansen and I. R. McDonald,Theory of Simple Liquids (Academic Press, London, 1986), Chapter 7.
M. Ferrario, P. Grigolini, A. Tani, R. Vallauri, and B. Zambon,Adv. Chem. Phys. 62:389 (1985); D. Bertolini, M. Casserattari, P. Grigolini, G. Salvetti, and A. Tani,J. Mol. Liquids 41:251 (1989).
D. Beeman,J. Comput. Phys. 20:130 (1976).
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Sesé, G., Guàrdia, E. & Padró, J.A. On the description of atomic motions in dense fluids by the generalized Langevin equation: statistical properties of random forces. J Stat Phys 60, 501–518 (1990). https://doi.org/10.1007/BF01314933
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DOI: https://doi.org/10.1007/BF01314933