Insightful classification of crystal structures using distance functions

After a generating a structure using DFT or measuring a structure from experiment, we typically want to determine geometric properties of the structure, such as the Bravais lattice type, space group, dimensionality, and the primitive unit cell. Since the input structures are rarely perfect, most geometric analysis tools require the user to specify a tolerance which defines the extent of the geometric equality operator, i.e. when two slightly different atomic coordinates or lattice vectors should be considered identical. A common approach for tolerance selection is to use trial and error, repeatedly testing different values until the ‘right’ result is found. Rather than operating blindly in this manner, it would be beneficial to define a function which measures distances from each target class. By measuring distances from all target classes we build a complete view of the structural landscape. A good classification can then be made, a posteriori, and informed by the available options. Here I will presented some examples of recently developed distance functions. These include distances functions for the determination of the local structure in molecular dynamics simulations, determination of material dimensionality, classification of Bravais lattice. Preliminary work on the development of a distance-based space group classifier will also be discussed.