Friedif Calculator
The Friedif value of Flack and Shmueli: how much resonant-scattering contrast a composition offers at a given radiation — the signal an absolute structure determination would have to work with, computed before the crystal is on the diffractometer.
- You supply
- A chemical formula — brackets and charges included, as on the CHN page — and one or more radiations. It is a property of the composition, so no cell or density is required.
- Reading it
- 80 or more indicates few absolute-structure problems; 34 or lower means difficulty reaching an e.s.d. on the Flack parameter below 0.1. The references below give the thresholds in full.
Worked examples: a nickel complex · an organic cation · C6H5SeCH3 just above the selenium K edge
See also: Absorption Coefficient Calculator · Space Group Reflection Conditions · Refinement Statistics and R Factors
Input
Results
| Formula as entered | C6H5SeCH3 |
|---|---|
| Read as | C7H8Se |
| Friedif(Mo): | 711 at 17.445 keV |
| Friedif(0.97625 Å): | 1206 at 12.7 keV |
The scattering factors behind it
Mo — 17.445 keV, 0.71073 Å
| element | Z | f′ | f″ | nearest edge below |
|---|---|---|---|---|
| C | 6 | 0.0051 | 0.0016 | — |
| H | 1 | 0.0000 | 0.0000 | — |
| Se | 34 | -0.0246 | 2.2229 | K at 12.658 keV |
0.97625 Å — 12.7 keV, 0.97625 Å
| element | Z | f′ | f″ | nearest edge below |
|---|---|---|---|---|
| C | 6 | 0.0089 | 0.0033 | — |
| H | 1 | 0.0000 | 0.0000 | — |
| Se | 34 | -4.8005 | 3.7999 | K at 12.658 keV |
f′ and f″ are Chantler’s relativistic tabulation (NIST FFAST, J. Phys. Chem. Ref. Data 24 (1995) 71 and 29 (2000) 597); the absorption coefficient is f″ through the optical theorem plus the tabulated scattering term. Compilations of these quantities differ from one another by a few per cent, and that is the accuracy to read them at.
Notes and references
- What the number is about. Far from an absorption edge an atom’s scattering factor is real, and I(hkl) = I(−h−k−l) for every structure whether or not it has a centre of symmetry — that is Friedel’s law, and while it holds a diffraction pattern cannot tell a structure from its mirror image. Near an edge the factor becomes complex, f = f0 + f′ + if″, and the imaginary part f″ breaks it: the two members of a Friedel pair come out with measurably different intensities, and that difference — the Bijvoet difference — is the whole of the information an absolute structure is determined from. Friedif scores how much of it a given composition offers at a given wavelength, which is why the answer changes so much between Cu, Mo and Cr for the same formula, and why it can be computed before the crystal is on the diffractometer. The structure factor page builds F without any of this, so everything there obeys Friedel’s law exactly.
- It is a property of the composition and the radiation, and so an estimate of the signal available rather than a prediction of the outcome. What is actually achieved also depends on resolution, redundancy, the absorption correction, crystal quality, inversion twinning and where the resonant scatterers sit in the cell.
- This is an implementation of an Excel spreadsheet calculation which was created by Flack and Shmueli; their paper is linked at the foot of this page.
- A Friedif value of 80 or more indicates few problems in determining the absolute structure. A Friedif value of 34 or lower indicates difficulties to reach an e.s.d. on the Flack parameter less than 0.1. (see H. D. Flack, Acta Chim. Slov., 2008, 55, 689–691.)
- The quality of an absolute structure determination is often derived from the Flack parameter x along with its associated e.s.d. u, thus x(u). u < 0.04 is associated with a strong inversion-distinguishing power, 0.04 < u < 0.1 means enantiopure-sufficient inversion-distinguishing power. A reliable absolute structure determination requires u < 0.04 and |x| < 2u. If there is a priori biological, chemical, or physical evidence for true enantiopurity of the compound of interest, 0.04 < u < 0.1 and |x| < 2u is also acceptable. These are Flack and Bernardinelli’s criteria; their paper is linked at the foot of this page.
Where this comes from
- The mean-square Friedel intensity difference in P1 with a centrosymmetric substructure
H. D. Flack and U. Shmueli, Acta Cryst. A 2007, 63, 257–265 · doi:10.1107/S0108767307002802
Friedif itself — the quantity this page computes is defined here, along with what it is for: judging in advance whether a given radiation can settle a structure’s absolute configuration. - XrayDB
Matthew Newville and contributors · on the reading list under “The tables this site computes from”
Where f′ and f″ come from — Chantler’s relativistic tabulation, read at whatever energy is asked for. Until August 2026 this page read three columns of f″ out of a database table instead, at Cu, Mo and Cr Kα and nowhere else, and had no f′ at all. - Relativistic calculation of anomalous scattering factors for X rays
D. T. Cromer and D. Liberman, J. Chem. Phys. 1970, 53, 1891–1898 · doi:10.1063/1.1674266
Where f″ comes from. The Friedel differences ranked here are a function of that one column, which is why changing the radiation changes the answer so much. - Reporting and evaluating absolute-structure and absolute-configuration determinations
H. D. Flack and G. Bernardinelli, J. Appl. Cryst. 2000, 33, 1143–1148 · doi:10.1107/S0021889800007184
What to do with the answer: the criteria on the Flack parameter and its standard uncertainty that the notes above quote, and what counts as a determination rather than a hope.