How to quantify energy landscapes of solids

TL;DR

This paper introduces a set of tools and methods to quantitatively analyze the energy landscapes of solids, revealing structural rules and aiding in crystal structure prediction and property analysis.

Contribution

It develops new quantitative measures and representations for energy landscapes, enabling better understanding and rationalization of crystal structures and their properties.

Findings

Low-energy minima cluster in 'funnels' in configuration space.

Crystals tend to adopt simple structures consistent with their chemistry.

Analysis supports Pauling's fifth rule with thermodynamic justification.

Abstract

We explore whether the topology of energy landscapes in chemical systems obeys any rules and what these rules are. To answer this and related questions we use several tools: (i)Reduced energy surface and its density of states, (ii) descriptor of structure called fingerprint function, which can be represented as a one-dimensional function or a vector in abstract multidimensional space, (iii) definition of a ''distance'' between two structures enabling quantification of energy landscapes, (iv) definition of a degree of order of a structure, and (v) definitions of the quasi-entropy quantifying structural diversity. Our approach can be used for rationalizing large databases of crystal structures and for tuning computational algorithms for structure prediction. It enables quantitative and intuitive representations of energy landscapes and reappraisal of some of the traditional chemical notions and rules. Our analysis confirms the expectations that low-energy minima are clustered in compact regions of configuration space ("funnels") and that chemical systems tend to have very few funnels, sometimes only one. This analysis can be applied to the physical properties of solids, opening new ways of discovering structure-property relations. We quantitatively demonstrate that crystals tend to adopt one of the few simplest structures consistent with their chemistry, providing a thermodynamic justification of Pauling's fifth rule.