Defining and quantifying frustration in the energy landscape: Applications to atomic and molecular clusters, biomolecules, jammed and glassy systems.

The emergence of observable properties from the organisation of the underlying potential energy landscape is analysed, spanning a full range of complexity from self-organising to glassy and jammed systems. The examples include atomic and molecular clusters, a β-barrel protein, the GNNQQNY peptide dimer, and models of condensed matter that exhibit structural glass formation and jamming. We have considered measures based on several different properties, namely, the Shannon entropy, an equilibrium thermodynamic measure that uses a sample of local minima, and indices that require additional information about the connections between local minima in the form of transition states. A frustration index is defined that correlates directly with key properties that distinguish relaxation behaviour within this diverse set. The index uses the ratio of the energy barrier to the energy difference with reference to the global minimum. The contributions for each local minimum are weighted by the equilibrium occupation probabilities. Hence we obtain fundamental insight into the connections and distinctions between systems that cover the continuum from efficient structure-seekers to landscapes that exhibit broken ergodicity and rare event dynamics.