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The most important result of this chapter is probably the introduction of an index to quantify the cooperativity of atomic rearrangements. With this new measure it becomes possible to correlate cooperativity and barrier heights, and to show that cooperative rearrangements generally have lower barriers and shorter path lengths. We hope that these results will shed new light on relaxation mechanisms in complex systems, such as glasses and biomolecules, in future applications. For example, in a peptide or protein a large geometrical change can result from a rearrangement that could be described in terms of a single dihedral angle. In glasses and supercooled liquids an important research goal is to understand how observed dynamical properties, such as atomic diffusion and correlation functions [183,171,174,182], are related to features of the underlying PES. The classification of elementary rearrangements as `cage-breaking' or `cage-preserving' [184,171], and the emergence of structures such as `megabasins' [186,184,185,171] can now be investigated more precisely in terms of localisation and cooperativity.
We have also demonstrated that cooperative rearrangements are relatively easy to characterise using double-ended transition state searching algorithms, since linear interpolation produces an effective initial guess. Uncooperative rearrangements are usually harder to find using such methods, and alternative initial guesses may be helpful in these cases.
Single-ended transition state searching has been used both in conjunction with double-ended methods, and as a way to sample potential energy surfaces for stationary points. Stationary point databases constructed using random perturbations followed by quenching are likely to be biased towards uncooperative rearrangements. We have therefore outlined a strategy for generating initial guesses appropriate to single-ended transition state searching algorithms, which instead favours cooperative rearrangements. This approach also includes a parameter that is likely to influence the degree of localisation.
Next: ENSEMBLES OF REARRANGEMENT PATHWAYS Up: PROPERTIES OF REARRANGEMENT PATHWAYS Previous: Applications to LJ and Contents Semen A Trygubenko 2006-04-10