Largest likely values for R factors calculated after phase refinement by non-crystallographic symmetry averaging

The progress of phase refinement by non-crystallographic symmetry averaging is often described by the behavior of a crystallographic R factor expressing agreement between the observed structure factors and structure factors calculated from an averaged electron density map. An upper limit for this R factor is evaluated for the case of incorrectly positioned non-crystallographic symmetry operators. Depending on the degree of non-crystallographic symmetry, the upper limit on R varies from 0.29 to 0.3, for acentric structures. Incorrect structures with the correct non-crystallographic symmetry are anticipated to converge to even lower values of R. In all cases, R values calculated for incorrect structures will be significantly lower than the value of 0.586 characteristic of wrong structures lacking non-crystallographic symmetry [Wilson (1950). Acta Cryst. 3, 397-399].