Uncertainties of recalculated bond lengths, angles and polyhedral volumes as implemented in the <i>Crystal Palace</i> program for parametric crystal structure analysis

Crystal Palace is a new Windows program for Parametric Analysis of Least-squares and Atomic Coordination with Estimated standard uncertainties (e.s.u.'s). The primary purpose of the program is to organize the refined structures from parametric structural studies (as a function of pressure or temperature or a series of compositions) for analysis of the structural trends, and the production of tables for publication without the risks associated with manual editing. The program reads structural information from one or more crystallographic information format (cif) files. It organizes the data by finding the structurally equivalent atoms in each structure and therefore can correctly organize structural information even if atom names or site occupancies are different, or the atom lists in the cif files are ordered differently. A major shortcoming of cif files as currently used is that they do not contain the full variance-covariance matrix from the structure refinement, but only the uncertainties of the individual positional parameters. Without the covariance of positional parameters, the e.s.u.'s of bond lengths and angles cannot be determined. Crystal Palace uses symmetry to estimate the major contributions to the covariance of atomic coordinates and thus realistic uncertainties of bond lengths, angles and polyhedral volumes. Crystal Palace also calculates various polyhedral distortion parameters and rigid-body corrections to bond lengths.