Topographies and Dynamics of Many-Dimensional Potential Surfaces
Multidimensional potential surfaces pose a variety of problems, not least of which is that it is now possible to obtain more information about the minima and other stationary points of such surfaces than we know how to use. This discussion describes a succession of steps to interpreting the topographies of such surfaces and of inferring the nature of the dynamics driven by those topographies. The procedure begins with a statistical search for minima and the saddles that link them. The topography lends itself to an analysis and categorization of local minima into large basins, including the primary basin, secondary and higher-order basins. From a representative sample of minima and saddles, one can construct inter-well rate coefficients and, from them, a master equation governing the flows on the surface. The flows can be categorized into intra-well and inter-well, and comparisons of the rates of these can be made, as the systems change temperature. A preliminary interpretation of the way the features of the topography govern the focusing or glassforming character of the surface.
KeywordsGlobal Minimum Potential Surface Master Equation Monotonic Sequence Distinct Minimum
Unable to display preview. Download preview PDF.
- 5.Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterling, W.T. (1986) Numerical Recipes, Cambridge University Press, Cambridge.Google Scholar
- 7.Pancik, J. (1975) Calculation of the Least Energy Path on the Energy Hypersurface, ColI. Czech. Chern. Comm. 40, 1112–1118.Google Scholar
- 8.Hilderbrandt, R.L. (1977) Application of Newton-Raphson optimization techniques in molecular mechanics calculations, Cornput. Chern. 1, 179–186.Google Scholar
- 28.Murrell, J.N., Carter, S., Farantos, S.C., Huxley, P. and Varandas, A.I.C. (1984) Molecular Potential Energy Functions, Wiley, New York.Google Scholar
- 36.Hoare, M.R. and Pal, P. (1972) Nature 230, 5.Google Scholar
- 46.Kunz, R.E., Astakhova, T. and Berry, R.S. (1995) Using Clusters to Relate Topography and Dynamics of Multidimensional Potentials, Surf. Rev. Lett. (in press).Google Scholar
- 48.Doye, J.P.K., Wales, DJ. and Berry, R.S. (1995) The effect of the range of the potential on the Structures of Clusters, J. Chem. Phys. (in press).Google Scholar
- 50.Bryngelson, J.D., Onuchic, J.N., Socci, N.D. and Wolynes, P.G. (1995) Funnels, Pathways and the Energy Landscape of Protein Folding, (submitted) Google Scholar
- 56.Beynon, J.H. and Gilbert, J.R. (1984) Application of Transition. State Theory to Unimolecular Reactions: An Introduction, Wiley, Chichester.Google Scholar
- 57.Robinson, P.J. and Holbrook, K.A. (1972) Unimolecular Reactions, WileyInterscience, London.Google Scholar
- 58.Jarrold, M.F. (1994) Introduction to Statistical Reaction Rate Theories, in H. Haberland (ed.), Clusters ofAtoms and Molecules, Springer-Verlag, Berlin.Google Scholar