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How to quantify energy landscapes of solids
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.Comment: Published in J. Chem. Phys. 130, 104504 (2009
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