Theoretical frameworks used to qualitatively and quantitatively describe nuclear dynamics in solids are often based on the harmonic approximation. However, this approximation is known to become inaccurate or to break down completely in many modern functional materials. Interestingly, there is no reliable measure to quantify anharmonicity so far. Thus, a systematic classification of materials in terms of anharmonicity and a benchmark of methodologies that may be appropriate for different strengths of anharmonicity is currently impossible. In this work, we derive and discuss a statistical measure that reliably classifies compounds across temperature regimes and material classes by their degree of anharmonicity. This enables us to distinguish harmonic materials, for which anharmonic effects constitute a small perturbation on top of the harmonic approximation, from strongly anharmonic materials, for which anharmonic effects become significant or even dominant and the treatment of anharmonicity in terms of perturbation theory is more than questionable. We show that the analysis of this measure in real and reciprocal space is able to shed light on the underlying microscopic mechanisms, even at conditions close to, e.g., phase transitions or defect formation. Eventually, we demonstrate that the developed approach is computationally efficient and enables rapid high-throughput searches by scanning over a set of several hundred binary solids. The results show that strong anharmonic effects beyond the perturbative limit are not only active in complex materials or close to phase transitions, but already at moderate temperatures in simple binary compounds.
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