Space-group recognition with the modified library program ACMM

This program finds all solutions (including multiple solutions) of R_vx_i + v_v = x_j for given atom positions x_i and given rotation part R_v of the symmetry operations (R_v, v_v). The translation part v_v depends on the arbitrary origin O and is therefore decomposed into the screw or glide part w_v and the location part t_v. Certain components of w_v are independent of O. With these, together with the set of v and their multiplicity, 226 space groups can be recognized uniquely. The remaining four space groups also require information from t_v. When the general positions given in International Tables for Crystallography [Vol. A (1987), edited by T. Hahn. Dordrecht: Kluwer Academic Publishers] are chosen as x_j, all the w_v and t_v given therein are reproduced exactly.