Modeling The Structure of Ice as a Problem in Global Minimization

  • Jan Hermans
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 94)


The structure and properties of liquid water can be modeled with rigid H2O molecules that interact via a simple potential function containing 1/r 6 attractive, 1/r 12 repulsive terms and 1/r (electrostatic) attractive and repulsive terms. In ice I, each water molecule is tetrahedrally surrounded by 4 other water molecules; one OH bond points along each O...O vector. Minimization problem 1: given the molecular packing of ice I, find the low-energy arrangement(s) of OH bonds. Minimization problem 2: find low-energy crystal structures of water, including the one of lowest energy.


Water Molecule Minimization Problem Liquid Water IEEE Computer Society Pair Potential 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J.A. Board, Z.S. Hakura, W.D. Elliott, W.J. Blanke, D.C. Gray, and J.F. Leathrum, Scalable implementations of multipole-accelerated algorithms for molecular dynamics. In: Scalable high performance computing conference (SH-PCC’ 94). IEEE Computer Society, IEEE Computer Society Press, 1994, pp. 87–94.Google Scholar
  2. [2]
    T. Darden, D. York, and L. Pedersen, Particle mesh Ewald: An N logi N method for Ewald sums in large systems. J. Chem. Phys. 98, 10089–10092, 1993.CrossRefGoogle Scholar
  3. [3]
    K.S. Sharp and B. Honig, Electrostatic interactions in macromolecules: Theory and applications. Rev. Biophys. Biophys. Chem. 19, 301–332, 1990.CrossRefGoogle Scholar
  4. [4]
    H.J.C. Berendsen, J.P.M. Postma, W.F. van Gunsteren, and J. Hermans, Interaction Models for Water in Relation to Protein Hydration. Jerusalem Symposia on Quantum Chemistry and Biochemistry, 1981, Reidel, Dordrecht, Holland, 331–342.Google Scholar
  5. [5]
    H.J.C. Berendsen, J.R. Grigera, and T.P. Straatsma. J. Phys. Chem. 91, 6269–6271, 1987.CrossRefGoogle Scholar
  6. [6]
    W.L. Jorgensen, J. Chandrasekhar, J.D. Madura, R.W. Impey, and M.L. Klein. J. Chem. Phys. 79, 926–935, 1983.CrossRefGoogle Scholar
  7. [7]
    S. Kalat and J. Hermans, Melting of ice in computer models. In progress, 1995.Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Jan Hermans
    • 1
  1. 1.Department of Biochemistry and BiophysicsUniversity of North CarolinaChapel HillUSA

Personalised recommendations