International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B. ch. 2.4, pp. 268-269   | 1 | 2 |

Section 2.4.3.7. Treatment of anomalous scattering in structure refinement

M. Vijayana* and S. Ramaseshanb

aMolecular Biophysics Unit, Indian Institute of Science, Bangalore 560 012, India, and bRaman Research Institute, Bangalore 560 080, India
Correspondence e-mail:  mv@mbu.iisc.ernet.in

2.4.3.7. Treatment of anomalous scattering in structure refinement

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The effect of anomalous scattering needs to be taken into account in the refinement of structures containing anomalous scatterers, if accurate atomic parameters are required. The effect of the real part of the dispersion correction is largely confined to the thermal parameters of anomalous scatterers. This effect can be eliminated by simply adding f′ to the normal scattering factor of the anomalous scatterers.

The effects of the imaginary component of the dispersion correction are, however, more complex. These effects could lead to serious errors in positional parameters when the space group is polar, if data in the entire diffraction sphere are not used (Ueki et al., 1966[link]; Cruickshank & McDonald, 1967[link]). For example, accessible data in a hemisphere are normally used for X-ray analysis when the space group is P1. If the hemisphere has say h positive, the x coordinates of all the atoms would be in error when the structure contains anomalous scatterers. The situation in other polar space groups has been discussed by Cruickshank & McDonald (1967[link]). In general, in the presence of anomalous scattering, it is desirable to collect data for the complete sphere, if accurate structural parameters are required (Srinivasan, 1972[link]).

Methods have been derived to correct for dispersion effects in observed data from centrosymmetric and noncentrosymmetric crystals (Patterson, 1963[link]). The methods are empirical and depend upon the refined parameters at the stage at which corrections are applied. This is obviously an unsatisfactory situation and it has been suggested that the measured structure factors of Bijvoet equivalents should instead be treated as independent observations in structure refinement (Ibers & Hamilton, 1964[link]). The effect of dispersion corrections needs to be taken into account to arrive at the correct scale and temperature factors also (Wilson, 1975[link]; Gilli & Cruickshank, 1973[link]).

References

First citationCruickshank, D. W. J. & McDonald, W. S. (1967). Parameter errors in polar space groups caused by neglect of anomalous scattering. Acta Cryst. 23, 9–11.Google Scholar
First citationGilli, G. & Cruickshank, D. W. J. (1973). Effect of neglect of dispersion in centrosymmetric structures: results for OsO4. Acta Cryst. B29, 1983–1985.Google Scholar
First citationIbers, J. A. & Hamilton, W. C. (1964). Dispersion corrections and crystal structure refinements. Acta Cryst. 17, 781–782.Google Scholar
First citationPatterson, A. L. (1963). Treatment of anomalous dispersion in X-ray diffraction data. Acta Cryst. 16, 1255–1256.Google Scholar
First citationSrinivasan, R. (1972). Applications of X-ray anomalous scattering in structural studies. In Advances in structure research by diffraction methods, Vol. 4, edited by W. Hoppe & R. Mason, pp. 105–197. Braunschweig: Freidr. Vieweg & Sohn; and Oxford: Pergamon Press.Google Scholar
First citationUeki, T., Zalkin, A. & Templeton, D. H. (1966). Crystal structure of thorium nitrate pentahydrate by X-ray diffraction. Acta Cryst. 20, 836–841.Google Scholar
First citationWilson, A. J. C. (1975). Effect of neglect of dispersion on apparent scale and temperature parameters. In Anomalous scattering, edited by S. Ramaseshan & S. C. Abrahams, pp. 325–332. Copenhagen: Munksgaard.Google Scholar








































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