School on glass formers and glasses
David Wales Lectures

6 January, 2010

Energy landscape approach

Abstract

These lectures will treat the exploration and characterisation of potential energy and enthalpy landscapes for glass-forming systems [1]. A coarse-grained framework for treating structure, dynamics and thermodynamics in terms of stationary points will be introduced, including algorithms for global optimisation [1,11] and characterising transition states and pathways [9,8,12]. The superposition approach will be described for global thermodynamics [1,13] and visualisation of the landscape is achieved using disconnectivity graphs [1,3].

This approach has recently provided a direct decomposition of the energy landscape into regions separated by cage-breaking events [2,3] for a locally ergodic dynamical trajectory [7]. Analysis of such trajectories on different time scales has previously been used to explain super-Arrhenius diffusion in terms of correlation effects, which implicitly include heterogeneity [5,6]. Equilibrium densities of states for the binary Lennard-Jones system [4] will be compared with simple models, which treat ergodicity-breaking via partition functions that depend upon the observation time [13]. To achieve a consistent model of fragility for thermodynamic and kinetic properties requires a correlation between the energy density of local minima and the corresponding normal mode frequencies. This correlation can be explained using catastrophe theory [10].

References and suggested reading

  1. Energy Landscapes by D.J. Wales, Cambridge University Press (Cambridge) 2003; D.J. Wales et al., Adv. Chem. Phys., 115, 1, (2000)
  2. V.K. de Souza and D.J. Wales, J. Chem. Phys., 130, 194508 (2009)
  3. V.K. de Souza and D.J. Wales, J. Chem. Phys., 129, 164507 (2008)
  4. F. Calvo, T.V. Bogdan, V.K. de Souza and D.J. Wales, J. Chem. Phys., 127, 044508 (2007)
  5. V.K. de Souza and D.J. Wales, Phys. Rev. B, 74, 134202 (2006).
  6. V.K. de Souza and D.J. Wales, Phys. Rev. Lett., 96, 057802 (2006).
  7. V.K. de Souza and D.J. Wales, J. Chem. Phys., 123, 134504 (2005).
  8. D.J. Wales and J.P.K. Doye, J. Chem. Phys., 119, 12409-12416 (2003)
  9. T.F. Middleton and D.J. Wales, J. Chem. Phys., 118, 4583-4593 (2003)
  10. D. J. Wales, Science, 293, 2067-2070 (2001)
  11. T.F. Middleton, J. Hernandez-Rojas, P.N. Mortenson and D.J. Wales, Phys. Rev. B, 64, 184201 (2001)
  12. T. F. Middleton and D.J. Wales, Phys. Rev. B, 64, 024205 (2001)
  13. D.J. Wales and J.P.K. Doye, Phys. Rev. B, 63, 214204 (2001)