R-factors

Historically, R-factors were introduced by ...

Definitions

Data quality indicators

• R_sym and R_merge : the formula for both is

[math]\displaystyle{ R = \frac{\sum_{hkl} \sum_{j} \vert I_{hkl,j}-\langle I_{hkl}\rangle\vert}{\sum_{hkl} \sum_{j}I_{hkl,j}} }[/math]

where [math]\displaystyle{ \langle I_{hkl}\rangle }[/math] is the average of symmetry- (or Friedel-) related observations of a unique reflection, and the first summation is over all unique reflections with more than one observation.

• Redundancy-independant version of the above: R_meas
• measuring quality of averaged intensities/amplitudes: R_p.i.m. and R_mrgd-F

Model quality indicators

• R and R_free : the formula for both is

[math]\displaystyle{ R=\frac{\sum_{hkl_{unique}}\vert F_{hkl}^{(obs)}-F_{hkl}^{(calc)}\vert}{\sum_{hkl_{unique}} F_{hkl}^{(obs)}} }[/math]

where [math]\displaystyle{ F_{hkl}^{(obs)} }[/math] and [math]\displaystyle{ F_{hkl}^{(calc)} }[/math] have to be scaled w.r.t. each other. R and R_free differ in the set of reflections they are calculated from: R is calculated for the working set, whereas R_free is calculated for the test set.

what do R-factors try to measure, and how to interpret their values?

• relative deviation of

Data quality

• typical values: ...

what kinds of problems exist with these indicators?

- (R_sym / R_merge ) should not be used, R_meas should be used instead (explain why ?)

- R/R_free and NCS: reflections in work and test set are not independant