R factors in X‐ray fiber diffraction. IV. Analytic expressions for largest likely R factors

The largest likely R-factor is useful for evaluating the significance of R-factors obtained in structure determinations. Numerical expressions have been derived previously for calculating largest likely R-factors in fiber diffraction analyses. Analytical approximations to largest likely R-factors (R) in fiber diffraction are derived here that show the dependence on resolution (\hat \rho), helix symmetry (uo) and molecular radius (\hat r). The simplest approximation is R ∝ (u/{\hat r}{\hat \rho})1/2 which represents the overall behavior of R-factors reasonably well. More accurate approximations are also derived. These are applied to various structures and the dependence on different structural parameters is examined. These results provide insight into the behavior of R-factors in fiber diffraction and may be useful in further analysis.