Theory of solutions in the energy representation. III. Treatment of the molecular flexibility

Journal of Chemical Physics

Volumn 119, Issue 18, 2003, Pages 9686-9702

  Matubayasi, Nobuyuki ^a   Nakahara, Masaru ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; CONFORMATIONS; ELECTRON ENERGY LEVELS; INTEGRAL EQUATIONS; MOLECULAR STRUCTURE; MOLECULAR VIBRATIONS; MONTE CARLO METHODS; ORGANIC SOLVENTS; PROBABILITY DISTRIBUTIONS; SOLUTIONS;

INTERMOLECULAR INTERACTION; INTRAMOLECULAR FLEXIBILITY; INTRAMOLECULAR STRUCTURE; SOLUTE-SOLVENT INTERACTION; SOLVATION FREE ENERGY;

MOLECULAR DYNAMICS;

EID: 0345529905     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1613938     Document Type: Article

References (42)

1. J. P. Hansen and I. R. McDonald, Theory of Simple Liquids (Academic, London, 1986).
2. A. Ben-Naim, Solvation Thermodynamics (Plenum, New York, 1987).
3. D. Chandler and L. R. Pratt, J. Chem. Phys. 65, 2925 (1976).
4. N. Matubayasi and M. Nakahara, J. Chem. Phys. 113, 6070 (2000).
5. N. Matubayashi and M. Nakahara, J. Chem. Phys. 117, 3605, (2002)
6. N. Matubayashi and M. Nakahara, J. Chem. Phys. 118, 2446 (2003).
7. In Refs. 4 and 5, we employed the terms "chemical potential" and "excess chemical potential" instead of "solvation free energy"
8. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford University Press, Oxford, 1987).
9. It is actually sufficient to suppose that only the solute-solvent interaction is pairwise additive
10. When the intramolecular degrees of freedom are present in the solvent molecule, the corresponding intramolecular coordinates are contained in x. The overall position and orientation of the solute molecule may also be incorporated into the coordinate ψ. Actually, the developments in the present paper are valid simply by defining x and ψ as collections of the variables that are enough to specify the solute-solvent interaction potential.
11. 0(ψ)exp(-ΒΔv(φ)).
12. C. H. Bennett, J. Comput. Phys. 22, 245 (1976).
13. K. S. Shing and K. E. Gubbins, Mol. Phys. 5, 1109 (1982).
14. 0(φ) at each φ.
15. 0(φ) are fixed, the extremization of Eq. (29) with respect to P(φ) leads to Eq. (28) under the normalization condition for P(φ).
16. K. Binder and A. P. Young, Rev. Mod. Phys. 58, 801 (1986).
17. W. G. Madden, J. Chem. Phys. 96, 5422 (1992).
18. J. A. Given, Phys. Rev. A 45, 816 (1992).
19. J. A. Given and G. Stell, J. Chem. Phys. 97, 4573 (1992).
20. J. A. Given and G. Stell, Physica A 209, 495 (1994).
21. A. Kovalenko and F. Hirata, J. Chem. Phys. 115, 8620 (2001).
22. Actually, Δμ̃ evaluated through Eqs. (35)-(39) is exact to second order in the solvent density and in the solute-solvent interaction for any choice of the weight factor α̃(ε).
23. A different choice of φ corresponds to a different form of approximation when Eqs. (29) and (35)-(40) are employed.
24. H. J. C. Berendsen, J. R. Grigera, and T. P. Straatsma, J. Phys. Chem. 91, 6269 (1987).
25. Of course, a negative value of distance r is not allowed in Eq. (44). In other words, the intramolecular potential function of the solute molecule is prohibitively large when r<0. Actually, the region of r≲ is not available in the practically used form of potential function between two sites. When the two sites are chemically bonded, K in Eq. (44) is much larger the ones employed in the preset work. A nonbonded pair of sites is subject to strong repulsion, typically in the Lennard-Jones form, at short distances. Our values of K are adopted simply to realize substantial fluctuation in the solute structure within the form of Eq. (44).
26. J. Chandrasekhar, D. C. Spellmeyer, and W. L. Jorgensen, J. Am. Chem. Soc. 106, 903 (1984).
27. When a molecule carries partial charges and the Ewald method is adopted, its "intramolecular" potential function depends slightly on the overall orientation.
28. 0(ψ)] is difficult.
29. P. B. Balbuena, K. P. Johnston, and P. J. Rossky, J. Phys. Chem. 99, 1554 (1995).
30. P. B. Balbuena, K. P. Johnston, and P. J. Rossky, J. Phys. Chem. 100, 2706 (1996).
31. R. E. Westacott, K. P. Johnston, and P. J. Rossky, J. Phys. Chem. B 105, 6611 (2001).
32. BT, as described in the Appendix of Ref. 5. In principle, when the discretization interval is sufficiently fine and the sampling statistics is good enough, the calculation of the solvation free energy does not involve a numerical trouble even in the original form of approximation. The difficulty in practice is that the important ψ region is sampled too rarely when the structure of the solute is largely affected by the solute-solvent interaction.
33. e(ε) need to beunity near ε=0.
34. The number of solvent molecules interacting with the solute varies in response to the change in the system configuration when the solute-solvent interaction is truncated in a finite region. It is not variable, in contrast, when the truncation is not applied and the number of solvent molecules is constant in the ensemble.
35. The presentation in Appendix B of Ref. 4 is not sufficiently careful at this point. The procedure to fix the additive constant needs to be supplemented to complete the arguments.
36. A similar argument to prove the one-to-one correspondence applies in the full coordinate representation.
37. N fluctuates in the grand canonical ensemble.
38. When the reference solute molecule is employed, ∫ d ε φ = N holds at each φ in addition to the counterpart of Eq. (C1), where <...) φ is given by Eq. (24).
39. In the present work, the energy distribution functions obtained from the simulations of the solution and pure solvent systems are stored in seven digits.
40. e is usually calculated to be zero numerically in the strongly unfavorable region of the solute-solvent interaction even when the corresponding value of the energy coordinate is finite.
41. p))/2.
42. e is zero, the numerical procedures described can be straightforwardly extended.