From Online Dictionary of Crystallography
Let R be a ring. R is a free module of rank one over itself (either as a left or right module); any unit element is a basis. More generally, If R is commutative, a nonzero ideal I of R is free if and only if it is a principal ideal generated by a nonzerodivisor, with a generator being a basis. ImagR is a free image converter for laser engraving. It was never easier before to prepare your photo for engraving. Five steps for the perfect picture, in under one minute work!
Facteur R libre (Fr). Freier R-Faktor (Ge). Fattore R libero (It). 自由Ｒ因子 (Ja). Factor R libre (Sp).
Definition
A residual function calculated during structure refinement in the same way as the conventional R factor, but applied to a small subset of reflections that are not used in the refinement of the structural model. The purpose is to monitor the progress of refinement and to check that the R factor is not being artificially reduced by the introduction of too many parameters.
Discussion
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Many macromolecular structure refinements now use the statistical cross-validation technique of monitoring a `free' R factor [math]R_textrm{free}[/math]. It is calculated in the same way as the conventional least-squares R factor
[math]R = {{sum F_{obs} - F_{calc} } over {sum F_{obs} }}[/math],
but uses a small subset of randomly selected reflections that are set aside from the beginning and not used in the refinement of the structural model. Thus [math]R_textrm{free}[/math] tests how well the model predicts experimental observations that are not themselves used to fit the model. A fixed percentage of the total number of reflections is usually assigned to the free group.
A weighted free R factor may also be calculated over the set of reflections not used in the refinement:
[math]wR = left( {sum w Y_o - Y_c ^2{ }over{sum wY^2_o} }right)^{1/2}[/math],
where Y represents F, [math]F^2[/math] or I.
After each cycle of refinement, the free R factor and the R factor for the working set of reflections are both calculated. However, as the refinement converges, the working and free R factors both approach stable values. It is common practice, particularly in structures at high resolution, to stop monitoring [math]R_textrm{free}[/math] at this point and to include all the reflections in the final rounds of refinement.
History
The idea of the free R factor was introduced by Brünger, A. T. [(1997). Methods Enzymol.277, 366–396.Free R value: cross-validation in crystallography.]
See also
- Validation of protein crystal structures. G. J. Kleywegt. International Tables for Crystallography (2006). Vol. F, ch. 21.1, pp. 497-506 doi:10.1107/97809553602060000707