Quantum cluster equilibrium theory of liquids: Illustrative application to water

Journal of Chemical Physics

Volumn 109, Issue 2, 1998, Pages 373-384

  Weinhold, F ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346257938     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.476574     Document Type: Article

References (54)

1. F. Franks, Water, A Comprehensive Treatise, Vol. 1 (Plenum, New York, 1972), p. 18.
2. F. Weinhold, J. Chem. Phys. 109, 367 (1998), preceding paper.
3. A. R. Leach, Molecular Modelling, Principles and Applications (Addison Wesley Longman, Essex, England, 1996), Chap. 6.
4. For an authoritative description of the standard notation for quantum chemical methods and basis sets, see W. J. Hehre, L. Radom, P. v. R. Schleyer, and J. A. Pople, Ab Initio Molecular Orbital Theory (Wiley, New York, 1986).
5. GAUSSIAN 94, M. J. Frisch, G. W. Trucks, H. B. Schlegel, P. M. W. Gill, B. G. Johnson, M. A. Robb, J. R. Cheeseman, T. Keith, G. A. Petersson, J. A. Montgomery, K. Raghavachari, M. A. Al-Laham, V. G. Zakrzewski, J. V. Ortiz, J. B. Foresman, J. Cioslowski, B. B. Stefanov, A. Nanayakkara, M. Challacombe, C. Y. Peng, P. Y. Ayala, W. Chen, M. W. Wong, J. L. Andres, E. S. Replogle, R. Gomperts, R. L. Martin, D. J. Fox, J. S. Binkley, D. J. Defrees, J. Baker, J. P. Stewart, M. Head-Gordon, C. Gonzalez, and J. A. Pople, Gaussian, Inc., Pittsburgh PA, 1995.
6. D. A. McQuarrie, Statistical Mechanics (Harper & Row, New York, 1976).
7. (a) Among recent theoretical studies: E. P. F. Lee and J. M. Dyke, Mol. Phys. 73, 3755 (1991);
8. R. Knochenmuss and S. Leutwyler, J. Chem. Phys. 96, 5233 (1992);
9. S. S. Xantheas and T. H. Dunning, J. Chem. Phys. 99, 8774 (1993);
10. J. van Duijneveldt-dan de Rijdt and F. B. van Duijneveldt, Chem. Phys. 175, 271 (1993);
11. C. J. Tsai and K. D. Jordan, Chem. Phys. Lett. 213, 181 (1993);
12. L. A. Burke, J. O. Jensen, and P. N. Kirshnan, Chem. Phys. Lett. 206, (1993);
13. K. Lasonen, M. Parrinello, R. Car, L. Changoil, and D. Vanderbilt, Chem. Phys. Lett. 207, 208 (1993);
14. L. S. Sremaniak, L. Perera, and M. L. Berkowitz, Chem. Phys. Lett. 218, 377 (1994);
15. K. Kim, K. K. Jordan, and T. S. Zwier, J. Am. Chem. Soc. 116, 11568 (1994).
16. (b) Experimental studies: T. R. Dyke, J. Chem. Phys. 66, 492 (1977);
17. T. R. Dyke, K. M. Mack, and J. S. Muenter, J. Chem. Phys. 66, 498 (1977);
18. J. Farges, M. F. de Feraudy, B. Rault, and G. Torchet, Adv. Chem. Phys. 70, 45 (1988);
19. L. F. Sukhodub, Y. V. Telezhenko, and V. S. Shelkovskii, Zh. Strukt. Khim. 29, 89094 (1988);
20. N. Pugliano and R. S. Saykally, Science 257, 1937 (1992);
21. K. Liu, J. D. Cruzan, and R. J. Saykally, Science 271, 929 (1996);
22. 272, 929 (1966).
23. Ref. 4, p. 229ff.
24. I. Levine, Quantum Chemistry (Prentice-Hall, Englewood Cliffs, NJ, 1991), p. 603;
25. P. Hobza and R. Zahradnik, Chem. Rev. 88, 871 (1988).
26. S. F. Boys and F. Bernardi, Mol. Phys. 19, 553 (1970).
27. R. Ludwig, T. C. Farrar, and F. Weinhold, J. Chem. Phys. 103, 6941 (1995).
28. E. Silla, I. Tunon, and J. L. Pascual-Ahuir, J. Comput. Chem. 12, 1077 (1991).
29. All experimental water properties are from the CRC Handbook of Chemistry and Physics.
30. See, e.g., H. S. Frank and W. Wen, Discuss. Faraday Soc. 24, 133 (1957);
31. P. L. Huyskens, W. A. P. Luck, and T. Zeegers-Huyskens, Intermolecular Forces (Springer, Berlin, 1991), pp. 251-280;
32. J. E. Del Bene and J. A. Pople, Chem. Phys. Lett. 4, 426 (1969);
33. H. Guo and M. Karplus, J. Phys. Chem. 98, 7104 (1994);
34. S. Suhai, Int. J. Quantum Chem. 52, 395 (1994);
35. B. F. King and F. Weinhold, J. Chem. Phys. 103, 333 (1995).
36. F. Weinhold, J. Mol. Struct.: THEOCHEM 399, 181 (1997).
37. The role of such clusters in the solid-liquid transition region are discussed in a forthcoming paper; R. Ludwig and F. Weinhold (unpublished).
38. For this reason, little numerical effect is seen when the w8c cluster is omitted from higher correlated treatments (MP2, B3LYP), where it is found not to be a distinct equilibrium species.
39. H. S. Frank and A. S. Quist, J. Chem. Phys. 34, 604 (1961);
40. M. S. Jhon, J. Grosh, T. Ree, and H. Eyring, J. Chem. Phys. 44, 1465 (1965).
41. (0) thermodynamic predictions.
42. However, the relative insensitivity of QCE thermodynamics to H-bond torsions would be altered by perturbations that are sensitive to this property. For example, the high-symmetry cyclic hexamer w6c [Fig. 1(e)] has no dipole moment and could thus differ significantly from other rotamers with respect to electric field effects.
43. As mentioned in the previous paper (footnote 1 of Ref. 2), empirical potential parameters are usually considered to include some "average" contribution from higher cooperative effects. The chosen "effective" bond energy may therefore not match the actual dimer bond energy. However, qualitatively similar (unphysical) behavior is found for many other possible bond energy values.
44. The few very modes that would have been shifted to negative frequencies by the softening procedure were set to +1 K.
45. P. M. Morse, Phys. Rev. 34, 57 (1929);
46. L. Pauling and E. B. Wilson Jr., Introduction to Quantum Mechanics (McGraw-Hill, New York, 1935), p. 271.
47. (0) model (with molar volume 10.7 mL) is composed of 0.3% monomer and 99.7% large cyclic clusters, whereas in the high-density phase of Fig. 8 the corresponding values are 0.7% and 99.3% (but with higher proportion of w8c to w5c,w6c in the latter case). The compositions of the gas phases in the two models are practically identical: w (98.1%), w5c (1.6%), w2 (0.2%), w6c (0.1%).
48. xv=1.32 model (with molar volume 18.3 mL) has composition w8c (87.5%), w5c (8.8%), w6c (3.1%), w (0.7%).
49. J. K. Badenhoop and F. Weinhold, J. Chem. Phys. 107, 5406 (1997).
50. C. H. Cho, S. Singh, and G. W. Robinson, J. Chem. Phys. 107, 7979 (1997).
51. Since the pressure dependence is so weak, the "infinitesimal" ΔP can be chosen rather arbitrarily in the range 5-50 atm with no appreciable loss of numerical accuracy (the plotted values were computed with ΔP=19atm).
52. vap=41.6kJ/mol. The surprisingly high accuracy of the simple RHF/3-21G treatment is presumably due to partial cancellation of errors due to neglect of electron correlation and incomplete CP-suppression of BSSE.
53. R. Ludwig, F. Weinhold, and T. C. Farrar, J. Chem. Phys. 107, 499 (1997);
54. R. Ludwig, T. C. Farrar, and F. Weinhold, Ber. Bunsenges. Phys. Chem. 102, 197,205 (1998).