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Translational and rotational diffusion in liquids. I. Translational single‐particle correlation functions
1.J. D. Weeks, D. Chandler, and H. C. Andersen, J. Chem. Phys. 54, 5237 (1971);
1.J. D. Weeks, D. Chandler, and H. C. Andersen, 55, 5422 (1971); , J. Chem. Phys.
1.D. Chandler and J. D. Weeks, Phys. Rev. Lett. 25, 149 (1970).
2.L. Verlet and J.‐J. Weis, Phys. Rev. A 5, 939 (1972).
3.S. Sung and D. Chandler, J. Chem. Phys. 56, 4989 (1972).
4.J. A. Barker and D. Henderson, J. Chem. Phys. 47, 4714 (1967);
4.J. A. Barker and D. Henderson, Acc. Chem. Res. 4, 303 (1971).
5.For a recent review, see J. A. Barker and D. Henderson, Ann. Rev. Phys. Chem. 23, 439 (1972).
6.H. C. Andersen, J. D. Weeks, and D. Chandler, Phys. Rev. A 4, 1597 (1971).
7.See S. Chapman and T. G. Cowling, Mathematical Theory of Non‐Uniform Gases (Cambridge U.P., Cambridge, England, 1970), 3rd ed., Chap. 16.
8.The list of publications along these lines is huge; Refs. 9–13 are meant to be representative, not comprehensive.
9.J. H. Dymond and B. J. Alder, J. Chem. Phys. 45, 2061 (1966);
9.J. H. Dymond and B. J. Alder, 48, 343 (1968); , J. Chem. Phys.
9.J. H. Dymond and B. J. Alder, 52, 923 (1970)., J. Chem. Phys.
10.D. Levesque and L. Verlet, Phys. Rev. A 2, 2514 (1970);
10.D. Levesque, L. Verlet, and J. Kürkijarvi, Phys. Rev. A 7, 1690 (1973)., Phys. Rev. A
11.S. A. Rice and P. Gray, Statistical Mechanics of Simple Liquids (Interscience, New York, 1965).
12.P. Protopapas, H. C. Andersen, and N. A. D. Parlee, J. Chem. Phys. 59, 15 (1973).
13.D. W. Condiff, Wei‐Kao Lu, and J. S. Dahler, J. Chem. Phys. 42, 3445 (1965);
13.B. J. McCoy, S. I. Sandler, and J. S. Dahler, J. Chem. Phys. 45, 3485 (1966)., J. Chem. Phys.
14.There are two extreme limits for rough hard sphere models. In one, the spheres are perfectly smooth, and as a result, collisions do not change the angular momentum of a particle. In the text we call such particles “smooth hard spheres.” In the other limit, the spheres are “perfectly rough” (see Sec. 11.6 of S. Chapman and T. G. Cowling, Refs. 7 and 13, and Appendix B for a precise definition and some detailed calculations). A realistic rough hard sphere model for nonspherical molecules is probably somewhere between these two extreme cases.
15.R. Zwanzig, Phys. Rev. 129, 486 (1963).
16.We list here a few references which we have found particularly useful: M. H. Ernst, J. R. Dorfman, W. R. Hoegy, and J. M. J. Van Leeuwen, Physica 45, 127 (1969);
16.W. R. Hoegy and J. V. Sengers, Phys. Rev. A 2, 2461 (1970);
16.J. R. Dorfman, (unpublished notes).
17.H. Mori, Progr. Theor. Phys. 33, 423 (1965).
18.B. J. Berne, in Physical Chemistry: An Advanced Treatise, VIIIB, edited by D. Henderson (Academic, New York, 1971).
19.R. Kubo, J. Phys. Soc. Japan 17, 1100 (1962).
20.R. G. Gordon, J. Chem. Phys. 44, 1830 (1966).
21.See, for example, P. C. Martin, Measurements and Correlation Functions (Gordon and Breach, New York, 1968), pp. 80–84.
22.K. Kim and D. Chandler (work in progress).
23.B. J. Alder and T. E. Wainwright, Phys. Rev. Lett. 18, 988 (1967);
23.B. J. Alder (unpublished tabulated results).
24.This assumption forms the basis of the theories presented in Refs. 1–5. A physical justification for the assumption is the following: For liquid states outside of the critical region, is so small that one estimates that molecules are crushed together to the extent that the average intermolecular force between nearest neighbors is repulsive. As a result, when a molecular position is altered, there is a large change in energy due to the harsh repulsive forces and a relatively small change in energy due to the more slowly varying attractions. Thus, at characteristic liquid densities, one expects the repulsive forces to dominate the liquid structure. A quantitative explanation of this structural phenomenon as it is related to the static correlation functions is obtained from the optimized cluster theory: H. C. Andersen and D. Chandler, J. Chem. Phys. 57, 1918 (1972);
24.H. C. Andersen, D. Chandler, and J. D. Weeks, J. Chem. Phys. 57, 2626 (1972); , J. Chem. Phys.
24.S. Sung and D. Chandler, Phys. Rev. A 9, 1688 (1974).
25.By estimating we require that For the Lennard‐Jones liquid,
26.K. Kim and D. Chandler, J. Chem. Phys. 59, 5215 (1973).
27.J. Kushick and B. J. Berne, J. Chem. Phys. 59, 3732 (1973).
28.By using the estimate we find that for argon, This number is considerably smaller than the typical time over which F(k, t) varies appreciably [ see Ref. 10]. For nitrogen, we consider the model studied by J. Barojas, D. Levesque, and B. Quentrec, Phys. Rev. A 7, 1092 (1973). We find The relevant time scale for nitrogen is Thus, the hard sphere model should be reliable to within 10% accuracy.
29.See Sec. 11.6 of S. Chapman and T. G. Cowling, Ref. 7.
30.A physical derivation of this formula can be obtained with a slight generalization of the calculation presented by Zwanzig in the Appendix to Ref. 15 (Zwanzig considers only the low density limit). For more formal derivations, see Ref. 16.
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