How to quantify energy landscapes of solids

Abstract

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, (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 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 demostrate that crystals tend to adopt one of the few simplest structures consistent with their chemistry, providing a thermodynamic justification of Pauling's 5 th rule.

PLUMED 2: New feathers for an old bird

“…Furthermore, the mean will not necessarily separate all the structurally distinct configurations of a cluster or bulk solid. The average is not the only quantity one can calculate from a distribution of symmetry functions and there is strong evidence that calculating functions other than the average allows you to examine interesting phenomena [51,52,53]. Hence, within PLUMED 2 we provide tools to calculate the average of a distribution of symmetry functions, the moments of the distribution, the number of symmetry functions less than a certain value and so on all within the MultiColvar class.…”

Semimetallic Two-Dimensional Boron Allotrope with Massless Dirac Fermions

“…It can mix in-plane and out-of-plane states and can be thought of as a symmetryreducing distortion that enhances binding by opening a band gap or pseudogap [6]. 2D-boron is a frustrated system, which tends to have many complex near-groundstate structures, and such systems violate the correlation between the energy and geometric simplicity of crystal structures (simpler structures are statistically more stable) [34]. This is also one of the most important reasons to explain the dynamical instability of planar α-sheet.…”

Fine-grained optimization method for crystal structure prediction

“…We compared generated initial structures by calculating the fingerprint. 21 For each system, almost all of them are different each other. Although only two structures in Na 8 Cl 8 are the same, we performed local optimization for them as different structures.…”

“…In structure selection, a structure that is expected to have lower final energy is chosen by using the framework of BO based on structure data and their relaxed energies previously calculated. To perform the framework of BO, we adopted the fingerprint of Oganov and Valle 21 as the descriptor of structures in the previous work. 15 A fingerprint is a vector representation of a structure.…”