Crystal fingerprint space – a novel paradigm for studying crystal-structure sets

The initial aim of the crystal fingerprint project was to solve a very specific problem: to classify and remove duplicate crystal structures from the results generated by the evolutionary crystal-structure predictor USPEX. These duplications decrease the genetic diversity of the population used by the evolutionary algorithm, potentially leading to stagnation and, after a certain time, reducing the likelihood of predicting essentially new structures. After solving the initial problem, the approach led to unexpected discoveries: unforeseen correlations, useful derived quantities and insight into the structure of the overall set of results. All of these were facilitated by the project's underlying idea: to transform the structure sets from the physical configuration space to an abstract, high-dimensional space called the fingerprint space. Here every structure is represented as a point whose coordinates (fingerprint) are computed from the crystal structure. Then the space's distance measure, interpreted as structure `closeness', enables grouping of structures into similarity classes. This model provides much flexibility and facilitates access to knowledge and algorithms from fields outside crystallography, e.g. pattern recognition and data mining. The current usage of the fingerprint-space model is revealing interesting properties that relate to chemical and crystallographic attributes of a structure set. For this reason, the mapping of structure sets to fingerprint space could become a new paradigm for studying crystal-structure ensembles and global chemical features of the energy landscape.