David J. Wales
The energy landscape approach to structure, dynamics and thermodynamics holds the key to resolving both the Levinthal and Kauzmann paradoxes in protein folding and glass physics. Using eigenvector-following based methods we have characterised large samples of transition states, rearrangement pathways and connected minima to map out the potential energy surface. These studies extend to systems containing hundreds of atoms and both empirical and quantum mechanical potentials. For small systems it is possible to characterise all the important minima and the transition states that link them, and deduce tunneling splitting patterns, for example. For large systems, the objective is to understand why some molecules are able to locate their global minima easily, whilst others are readily trapped as glasses. For both large and small systems disconnectivity graphs can be helpful in visualising the connection between the underlying potential energy surface and thermodynamic and dynamic properties. Such insight can also suggest new approaches to global optimisation.