Moments of the probability density function ofR2approachedviaconditional probabilities. III. Models containing correctly as well as incorrectly placed atoms in the space groupsP1 andP\overline{1}
W. K. L. Van Havere, Albert T. H. Lenstra · Acta Crystallographica Section A Foundations of Crystallography · 1983
First and second moments of P(R2) are evaluated for models containing correctly as well as incorrectly placed atoms, denoted symbolically by {g, f}. Formulas are derived, valid for the space groups P1 and P{\bar 1}, using explicitly the set of observed reflections. Extrapolation through the introduction of an averaged structure allows some general conclusions to be drawn concerning possible strategies used in automated structure determinations. A select elimination of data points from the R2 check on the correctness of an atomic position severely limits the usefulness of the R2 criterion. A check based on Rn2 has no better characteristics than one based on R2. An R2 criterion together with a zero-atom strategy has better chances of being successful than a random-atom approach.