FINDSYM: program for identifying the space‐group symmetry of a crystal

Given the lattice parameters of a crystal and the positions of atoms in the unit cell, it is often useful to identify the space-group symmetry of the crystal in a standard setting along with the Wyckoff positions to which the atoms belong. This can be a very difficult problem to do by hand, especially if the unit cell is given in a non-standard setting or if there are many atoms in the unit cell. The aim of this program is to identify the space-group symmetry and give the lattice parameters and Wyckoff positions of the atoms in a standard setting, no matter what setting the original information is given in. We have compared FINDSYM with other programs that address the same general problem. MISSYM (Le Page, 1987) and its implementation as ADDSYM in the program PLATON (Spek, 2003) searches for possibly missed additional symmetry in a given coordinate set. Two examples of its use are given at the internet site for ADDSYM (1998). FINDSYM failed in both cases to find the additonal symmetry found by ADDSYM. FINDSYM requires that all atomic positions be reasonably close to their idealized positions in the space-group symmetry we are seeking. TRS, RGS and SFND implemented in the program KPLOT (Hannemann et al., 1998; Hundt et al., 1999) use algorithms very similar to those in FINDSYM. Two examples of its function are given by Hannemann et al. (1998) and two more by Hundt et al. (1999). Each of these four examples consists of structures found during the investigation of the energy landscape of a system using global optimization techniques. In each of the four examples, FINDSYM successfully found the same space-group symmetry as that found by the KPLOT routines (this required using a tolerance of 0.03–0.06 Å). FINDSYM was not developed for the purpose of extracting a space-group symmetry from noisey data, although it can accomplish this if the data are not too noisey, as illustrated by its success with the KPLOT examples. Its limitations in this regard are illustrated by its failure with the ADDSYM examples. The main strength of FINDSYM is its ease of use. It can be run over the internet by filling out a simple and user-friendly html form. 2. Method of solution