Graph invariants for periodic systems: Towards predicting physical properties from the hydrogen bond topology of ice

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 67, Issue 1 2, 2003, Pages 161141-1611418

  Kuo, Jer Lai ^a   Singer, Sherwin J ^a  

^a OHIO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BINDING ENERGY; CRYSTAL LATTICES; FREE ENERGY; HYDROGEN BONDS; ICE; MAGNETIC MOMENTS; MONTE CARLO METHODS; TIME VARYING SYSTEMS;

GRAPH INVARIANTS;

GRAPH THEORY;

EID: 0038394429     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (45)

1. L. Pauling, J. Am. Chem. Soc. 57, 2680 (1935).
2. W.F. Giauque and J.W. Stout, J. Am. Chem. Soc. 58, 1144 (1936)
3. J.D. Bernal and R.H. Fowler, J. Chem. Phys. 1, 515 (1933).
4. E.A. DiMarzio and F.H. Stillinger, J. Chem. Phys. 40, 1577 (1964).
5. J.F. Nagle, J. Math. Phys. 7, 1484 (1966).
6. R. Howe, J. Phys. (Paris) 48, C1 (1987).
7. J. Lekner, Physica B 252, 149 (1998).
8. V. Buch, P. Sandler, and J. Sadlej, J. Phys. Chem. B 102, 8641 (1998).
9. S. Kawada, J. Phys. Soc. Jpn. 32, 1442 (1972).
10. Y. Tajima, T. Matsuo, and H. Suga, Nature (London) 299, 810 (1982).
11. Y. Tajima, T. Matsuo, and H. Suga, J. Phys. Chem. Solids 45, 1135 (1984).
12. T. Matsuo, Y. Tajima, and H. Suga, J. Phys. Chem. Solids 47, 165 (1986).
13. T. Matsuo and H. Suga, J. Phys. Colloq. C1, 477 (1987).
14. R. Howe and R.W. Whitworth, J. Chem. Phys. 90, 4450 (1989).
15. S.M. Jackson, V.M. Nield, R.W. Whitworth, M. Oguro, and C.C. Wilson, J. Phys. Chem. B 101, 6142 (1997).
16. A.J. Leadbetter, R.C. Ward, J.W. Clark, P.A. Tucker, T. Matsuo, and H. Suga, J. Chem. Phys. 82, 424 (1985).
17. C.M.B. Line and R.W. Whitworth, J. Chem. Phys. 104, 10 008 (1996).
18. H. Fukazawa, S. Mae, S. Ikeda, and O. Watanabe, Chem. Phys. Lett. 294, 554 (1998).
19. G.P. Johari and S.J. Jones, J. Chem. Phys. 62, 4213 (1975).
20. M.J. Iedema, M.J. Dresser, D.L. Doering, J.B. Rowland, W.P. Hess, A.A. Tsekouras, and J.P. Cowin, J. Phys. Chem. B 102, 9203 (1998).
21. J.-L. Kuo, J.V. Coe, S.J. Singer, Y.B. Band, and L. Ojamäe, J. Chem. Phys. 114, 2527 (2001).
22. F. Harary, Michigan Math. J. 4, 221 (1957).
23. F. Harary and E. Palmer, Can. J. Math. 18, 853 (1966).
24. F. Harary, Graph Theory (Addison-Wesley, Reading, MA, 1969).
25. N. Bjerrum, Science 115, 386 (1952).
26. K.S. Pitzer and J. Polissar, J. Am. Chem. Soc. 60, 1140 (1956).
27. J.C. Li and D.K. Ross, Nature (London) 365, 327 (1993).
28. J.S. Tse and D.D. Klug, Phys. Lett. A 198, 464 (1995).
29. I. Morrison, J.-C. Li, S. Jenkins, S.S. Xantheas, and M.C. Payne, J. Phys. Chem. B 101, 6146 (1997).
30. D.J. McGinty, J. Chem. Phys. 55, 580 (1971).
31. J.J. Burton, J. Chem. Phys. 56, 3133 (1972).
32. M.R. Hoare, Adv. Chem. Phys. 40, 49 (1979).
33. F.H. Stillinger and T.A. Weber, Phys. Rev. A 25, 978 (1982).
34. F.H. Stillinger and T.A. Weber, Phys. Rev. A 28, 2408 (1983).
35. P.G. Mezey, Potential Energy Hypersurfaces, Studies in Physical and Theoretical Chemistry Vol. 53 (Elsevier, New York, 1987).
36. G. Franke, E.R. Hilf, and P. Borrmann, J. Chem. Phys. 98, 3496 (1993).
37. D.J. Wales, Mol. Phys. 78, 151 (1993).
38. J.P.K. Doye and D.J. Wales, J. Chem Phys. 102, 9659 (1995).
39. M.B. Boisen, Jr. and G.V. Gibbs, Mathematical Crystallography, 2nd ed., Reviews in Mineralogy Vol. 15 (Mineralogical Soc. of America, Washington, D.C., 1990).
40. A. Rahman and F.H. Stillinger, J. Chem. Phys. 57, 4009 (1972).
41. W.H. Bragg, Proc. Phys. Soc. London 34, 98 (1922).
42. W.H. Barnes, Proc. R. Soc. London, Ser. A 324, 127 (1929).
43. To provide examples of the meaning of cis and trans H bonds in ice-Ih, we note that all of the H bonds in the configuration of Fig. 4 are cis. In Fig. 6, two bonds along the c axis are shown in both structures. (Another two c axis bonds are part of the unit cell, but are not shown because they connect to atoms in adjoining cells.) The left of the two c axis bonds in both structures of Fig. 6 is trans, while the right one is cis. In the left-hand structure the bonds in the lower a-b plane are all trans, while two bonds in the upper a-b plane are cis and four are trans. In the right-hand structure the configurations of the a-b planes are reversed. Figure 9 provides two examples with very large fraction of trans H bonds.
44. J.A. Hayward and J.R. Reimers, J. Chem. Phys. 106, 1518 (1997).
45. E. Cota and W.G. Hoover, J. Chem. Phys. 67, 3839 (1977).