Overall values of conventional discrepancy indices for crystals with heavy atoms. Part I—Results for a triclinic crystal when the model consists of the heavy atoms and a part of light atoms

Abstract

The joint probability density functions of the normalized structure amplitudes of the structure and the model (i.e.,yN andypc) are derived for triclinic crystals containing heavy atoms (1, 2 and many) by taking the model to consist of the heavy atoms and a part of the light atoms in the unit cell. These functions are derived for the two cases where the model is completely correct (i.e., the related case) and where the model is completely wrong (i.e., the unrelated case) in terms of the fractional contributions to the local mean intensity from the heavy atoms and all known atoms (i.e., σ1h/2 and σ12) as parameters. These functions are then used to obtain the theoretical local values of 〈yN〉 and 〈|yNn − σ1n(yPc)n|〉,n=1, 2. A method of using these results to compute the theoretical overall values ofR(F) andR(I) for the related and unrelated cases is briefly described. A comparison of the observed values of these indices with their theoretical values for the related and unrelated cases would help in determining the correctness of the proposed trial structure.