What is the complexity of a crystal structure? The definition of complexity is a challenging and similarly fascinating subject, touching different scientific disciplines such as economy, informatics, biology, math, and chemistry amongst others. Instead of defining complexity per sé, it is in practice easier to ask which system is more complex, showing that the challenge of defining complexity is closely related to the identification of an appropriate scale to measure complexity. In this contribution, the Shannon entropy is used as measuring system as defined by information theory, providing us with a framework to differentiate between the complexity of crystal structures as initially introduced by S. Krivovichev.
In my presentation I discuss the opportunities and challenges that come with an information theory-based analysis of crystal structures as measure for complexity. I show that comparisons between Shannon entropy, crystal structure complexity and configurational entropy can be drawn, opening intriguing opportunities for the systematic assessment of configurational entropy of crystal structures with implications in the areas of crystal growth and chemical bond theory. Finally, and following on from recent developments in the field where theory development is in the centre, I introduce crystIT (crystallography & Information Theory), a python-based open-access program. crystIT calculates various information measures based on a *.cif file as input, providing an easy-to-use platform for an information theory-based crystal structure analysis.
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