Mining of effective local order parameters for classifying crystal structures: A machine learning study

Determining local structures of molecular systems helps the scientific and technological understanding of the function of materials. Molecular simulations provide microscopic information on molecular systems, but analyzing the resulting local structures is a non-trivial task. Many kinds of order parameters have been developed for detecting such local structures. Bond-orientational order parameters are promising for classifying local structures and have been used to analyze systems with such structures as body-centered cubic, face-centered cubic, hexagonal close-packed, and liquid. A specific set of order parameters derived from Lechner's definitional equation are widely used to classify complex local structures. However, there has been no thorough investigation of the classification capability of other Lechner parameters, despite their potential to precisely distinguish local structures. In this work, we evaluate the classification capability of 112 species of bond-orientational order parameters including Lechner's definitions. A total of 234 248 combinations of these parameters are also evaluated. The evaluation is systematically and automatically performed using machine learning techniques. To distinguish the four types of local structures, we determine the better set of two order parameters by comparing with a conventional set. A set of three order parameters is also suggested for better accuracy. Therefore, the machine learning scheme in the present study enables the systematic, accurate, and automatic mining of effective order parameters for classifying crystal structures.