Some B_eq are more equivalent than others

Acta Cryst. (2011). A67, 512-516 (http://doi.org/g3d)

Mean fractional error in predicting the B_iso obtained from 1.0 Å isotropic re-refinement of PDB entry 1ot9. Atoms are sorted on anisotropy. Most atoms in the original structure have anisotropy in the range indicated by the bar.

Macromolecular crystal structures are typically refined with isotropic B factors, even though their atoms are substantially anisotropic. To evaluate whether a high-level model for the anisotropy, e.g. from TLS or Normal Mode analysis, adequately describes the structure, we must predict what value of B will in practice be refined for an atom with hidden parameters U^ij. Until now the approximation B_eq = 1/3trace(U^ij) has been used. This paper derives a more accurate predictor, B_est, which will allow construction of better TLS models from isotropic input.