Difference between revisions of "R factor"
From Online Dictionary of Crystallography
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| + | <font color="blue">Facteur ''R''</font> (''Fr''). <font color="red">R-Faktor, Übereinstimmungsfaktor</font> (''Ge''). <font color="black">Fattore ''R''</font> (''It''). <font color="purple">R 因子</font> (''Ja''). <font color="brown">R-фактор</font> (''Ru''). <font color="green">Factor R</font> (''Sp''). | ||
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== Definition == | == Definition == | ||
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a measure of agreement between the amplitudes of the [[structure factor]]s calculated from a crystallographic model and those from the original X-ray diffraction data. The ''R'' factor is calculated during each cycle of least-squares structure refinement to assess progress. The final ''R'' factor is one measure of model quality. | a measure of agreement between the amplitudes of the [[structure factor]]s calculated from a crystallographic model and those from the original X-ray diffraction data. The ''R'' factor is calculated during each cycle of least-squares structure refinement to assess progress. The final ''R'' factor is one measure of model quality. | ||
| − | More generally, a variety of ''R'' factors may be determined to measure analogous residuals during least-squares optimization procedures. Where the refinement attempts to minimize the deviates of the squares of the structure factors (refinement | + | More generally, a variety of ''R'' factors may be determined to measure analogous residuals during least-squares optimization procedures. Where the refinement attempts to minimize the deviates of the squares of the structure factors (refinement based on <math>F^2</math>), the ''R'' factor based on <math>F^2</math> is used to monitor the progress of refinement: |
<math>R(F^2) = {{\sum | F^2_{obs} - F^2_{calc} | } \over {\sum |F^2_{obs} |}}</math>. | <math>R(F^2) = {{\sum | F^2_{obs} - F^2_{calc} | } \over {\sum |F^2_{obs} |}}</math>. | ||
| − | Likewise, refinement | + | Likewise, refinement based on ''I'' can be tracked using the [[Bragg R factor|Bragg ''R'' factor]] |
<math>R_B = {{\sum | I_{obs} - I_{calc} | } \over {\sum |I_{obs} |}}</math>. | <math>R_B = {{\sum | I_{obs} - I_{calc} | } \over {\sum |I_{obs} |}}</math>. | ||
| − | Even for refinement | + | Even for refinement based on <math>F^2</math> or ''I'', the 'conventional' ''R'' factor may be calculated and quoted as a measure of model quality, in order to compare the resulting quality of models calculated at different times and with different refinement strategies. |
The ''R'' factor is sometimes described as the '''discrepancy index'''. | The ''R'' factor is sometimes described as the '''discrepancy index'''. | ||
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(''Y'' being ''F'', <math>F^2</math> or ''I''). The general term for a weighted residual is | (''Y'' being ''F'', <math>F^2</math> or ''I''). The general term for a weighted residual is | ||
| − | <math>wR = ({{\sum |w |Y_o - Y_c|^2|}\over{\sum |wY^2_o}|})^{1/2}</math> | + | <math>wR = \Big({{\sum |w |Y_o - Y_c|^2|}\over{\sum |wY^2_o}|}\Big)^{1/2}</math>. |
The sum is usually computed over all reflections measured in the experiment. However, occasionally reflections are omitted from the calculation, either because they are believed to result from a systematic experimental error or are recorded with an intensity small compared with background noise. Any such selection may introduce statistical artefacts, and must always be described when reporting ''R'' factors. | The sum is usually computed over all reflections measured in the experiment. However, occasionally reflections are omitted from the calculation, either because they are believed to result from a systematic experimental error or are recorded with an intensity small compared with background noise. Any such selection may introduce statistical artefacts, and must always be described when reporting ''R'' factors. | ||
[[Category:Structure determination]] | [[Category:Structure determination]] | ||
Latest revision as of 10:32, 15 December 2017
Facteur R (Fr). R-Faktor, Übereinstimmungsfaktor (Ge). Fattore R (It). R 因子 (Ja). R-фактор (Ru). Factor R (Sp).
Definition
The term R factor in crystallography is commonly taken to refer to the 'conventional' R factor
[math]R = {{\sum | F_{obs} - F_{calc} | } \over {\sum |F_{obs} |}}[/math],
a measure of agreement between the amplitudes of the structure factors calculated from a crystallographic model and those from the original X-ray diffraction data. The R factor is calculated during each cycle of least-squares structure refinement to assess progress. The final R factor is one measure of model quality.
More generally, a variety of R factors may be determined to measure analogous residuals during least-squares optimization procedures. Where the refinement attempts to minimize the deviates of the squares of the structure factors (refinement based on [math]F^2[/math]), the R factor based on [math]F^2[/math] is used to monitor the progress of refinement:
[math]R(F^2) = {{\sum | F^2_{obs} - F^2_{calc} | } \over {\sum |F^2_{obs} |}}[/math].
Likewise, refinement based on I can be tracked using the Bragg R factor
[math]R_B = {{\sum | I_{obs} - I_{calc} | } \over {\sum |I_{obs} |}}[/math].
Even for refinement based on [math]F^2[/math] or I, the 'conventional' R factor may be calculated and quoted as a measure of model quality, in order to compare the resulting quality of models calculated at different times and with different refinement strategies.
The R factor is sometimes described as the discrepancy index.
R factor as a measure of structure quality
Theoretical values of R range from zero (perfect agreement of calculated and observed intensities) to about 0.6 for a set of measured intensities compared against a set of random intensities. R factors greater than 0.5 indicate very poor agreement between observed and calculated intensities, and many models with [math]R \ge 0.5[/math] will not respond to attempts at improvement. An early model with [math]R \le 0.4[/math] can usually be improved during refinement. A desirable target R factor for a protein model refined with data to 2.5 Å is considered to be [math]\sim 0.2[/math]. Small organic molecules commonly refine to [math]R \lt 0.05[/math]. However, the R factor must always be treated with caution, as an indicator of precision and not accuracy. Partially incorrect structures have been reported with R values below 0.1; many imprecise but essentially correct structures have been reported with higher R values.
Weighted R factors
In practice, weighted R factors are more often used to track least-squares refinement, since the functions minimized are weighted according to estimates of the precision of the measured quantity Y: [math]\sum w (Y_o - Y_c)^2[/math] (Y being F, [math]F^2[/math] or I). The general term for a weighted residual is
[math]wR = \Big({{\sum |w |Y_o - Y_c|^2|}\over{\sum |wY^2_o}|}\Big)^{1/2}[/math].
The sum is usually computed over all reflections measured in the experiment. However, occasionally reflections are omitted from the calculation, either because they are believed to result from a systematic experimental error or are recorded with an intensity small compared with background noise. Any such selection may introduce statistical artefacts, and must always be described when reporting R factors.