**Anomalous X-ray Dispersion **

In the vicinity of the X-ray absorption edge(s) of an element the wavelength dependent
contributions *f'* and *f" *to the atomic X-ray scattering factor change rapidly with wavelength. This effect
can be exploited to obtain exceptional initial phases for a structure. Click on the icon
above for a mini synopsis.

**Atomic
scattering factors (basic)
Anomalous
X-ray scattering (Introduction, Ethan Merritt's site)
Table of absorption edges and eV <> wavelength conversion
Graph of absorption edges
Look at MAD maps (very pretty)**

**Estimating the anomalous scattering signal**

The changes in the intensities caused by the anomalous scattering are very small.
Differences of a few percent can be observed between *|F(hkl)|* and its Friedel opposite |*F(-hkl)|* at the same
wavelength (**Bijvoet **differences) and
the same *|F(hkl)|* at different wavelengths (**Dispersive**
differences). The question arises how to estimate these anomalous effects, and how
accurately do we need to measure the data to distinguish between actual dispersive signal
and just noise in the data?

We have a little program on this site that allows to estimate the anomalous signal
ratios for a given protein based on the number and kind of anomalous scatterers, the
number of residues, and the theoretical values for the anomalous scattering factors *f'*
and *f"* [1-4]. The anomalous scatterer is entered by element symbol. Ratios
for 5 wavelengths are used, the (optional) first one entered as an x-ray anode element (in
some cases even in-house data can deliver useful anomalous data) and the other 4 in
reference to the absorption edge. The format of the output follows closely Wayne's MADSYS:
The diagonal elements of the output matrix contain the
Bijvoet ratios, and the off-diagonal elements the dispersive
ratios between different wavelengths. To obtain a usable anomalous signal, the data
must be measured with a significantly better (lower) noise level, which can be determined
by deriving the Bijvoet ratios from measured centric
reflections (**centric** reflections do **not** contain any
Bijvoet differences, and the merging statistics for centrics thus reveal the statistical
noise in the data).

Like all other rules of thumb ('at least one Se for 17 kD'), favourable estimates do
not guarantee a good result. Wavelengths may be difficult to optimize for best dispersive
ratios; on the other hand, if you have a white line, the values for *f"* may
be higher. The success of MAD phasing critically depends on data quality and completeness,
and special collection techniques for Friedel opposites (inverse beam) etc. are
advantageous. Additional problems can arise from, for example, space group related
difficulties in solving the anomalous difference maps by Patterson or direct Methods. For
a quick review about MAD phasing see refs. [5,6].

**References**

[1] Cromer and Liberman, J. Chem. Phys. **53**,1891-1898 (1970)

[2] Cromer and Liberman, Acta Cryst. **A37**, 267-268 (1981)

[3] Kissel & Pratt, Acta Cryst. **A46**, 170-175 (1990)

[4] Don.T.Cromer, Program FPRIME

[5] E.Fanchon and W.A. Hendrickson, in Crystallographic Computing, Volume 5, Chapter 15,
IUCr/Oxford University Press (1991)

[6] H.M.Krishna Murthy, in Crystallographic Methods and Protocols, Chapter 5, Humana Press
(1996)

**Back to Introduction**

**This World Wide Web site conceived and maintained by
Bernhard Rupp**

Last revised
Dezember 27, 2009 01:40