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

Abstract

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.

Pathways for diffusion in the potential energy landscape of the network glass former SiO2

“…Both liquids have values of f in the characteristic range for multi-funnel energy landscapes, 102 as expected for glass formers. The silica database falls near the bottom of this range and is less frustrated than the BLJ database at all temperatures.…”

“…We use a recently proposed metric to quantify the degree of frustration in the potential energy landscapes of the two glass formers. 102 Here, "frustration" describes the existence of competing low-lying potential energy minima separated by high barriers. Highly frustrated landscapes have many such minima, which makes relaxation to the equilibrium zero-temperature structure relatively slow.…”

“…Good structure-seekers have low frustration, and glass formers have high frustration. 102 The frustration metric facilitates comparison of PELs for very different systems.…”

Exploring Energy Landscapes

“…The landscapes visualised for structural glass-formers correspond to multi-funnel systems, with many competing amorphous minima separated by high barriers (47)(48)(49)(50). Here another level of organisation has been identified by separating different regions of the landscape in terms of cage-breaking processes required for atomic or molecular diffusion.…”

The alchemical energy landscape for a pentameric cluster

“…Here we use a recently developed index based on the barrier heights between the global minimum and the other minima. 56 The frustration index f (T ) is…”