Quantifying Atomistic Similarity of Carbon Allotropes for Structural Comparison and Classification

The expedited discovery of carbon allotropes and the rising attention to novel amorphous carbonaceous solids urge innovations in their effective classification with reference to their structural traits. The present report proposes a new in silico similarity-quantification scheme of carbon allotropes that reflects the exact atomic coordinates via reduction and clustering techniques. It allows for the evaluation of pairwise structural relevance and the fine-grained classification of known carbon allotropes. In practice, 511 known crystalline carbon allotropes are adopted to construct an exemplary training set of the proposed method. Evidently, the resultant taxonomic trees adequately separate structural motifs and group structurally alike allotropes into coherent taxa. In addition, examples are shown to support that mapping external allotropes, both crystalline and amorphous in nature, to their structurally alike counterparts in the training set is effective in revealing structural characteristics of external allotropes.