Multiple isomorphous replacement method

Vijayan, M.; Ramaseshan, S.

doi:10.1107/97809553602060000557

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

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International Tables for Crystallography (2006). Vol. B. ch. 2.4, p. 265 | 1 | 2 |

Section 2.4.2.3. Multiple isomorphous replacement method

M. Vijayan^a ^* and S. Ramaseshan^b ^‡

^a Molecular 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

2.4.2.3. Multiple isomorphous replacement method

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The ambiguity in $[\alpha_{N}]$ in a noncentrosymmetric crystal can be resolved only if at least two crystals isomorphous to it are available (Bokhoven et al., 1951). We then have two equations of the type (2.4.2.5), namely, $[\alpha_{N} = \alpha_{H1} \pm \varphi_{1} \quad \hbox{ and } \quad \alpha_{N} = \alpha_{H2} \pm \varphi_{2}, \eqno(2.4.2.7)]$ where subscripts 1 and 2 refer to isomorphous crystals 1 and 2, respectively. This is demonstrated graphically in Fig. 2.4.2.3 with the aid of the Harker (1956) construction. A circle is drawn with $[F_{N}]$ as radius and the origin of the vector diagram as the centre. Two more circles are drawn with $[F_{NH1}]$ and $[F_{NH2}]$ as radii and the ends of vectors $[- {\bf F}_{H1}]$ and $[- {\bf F}_{H2}]$ , respectively as centres. Each of these circles intersects the $[F_{N}]$ circle at two points corresponding to the two possible solutions. One of the points of intersection is common and this point defines the correct value of $[\alpha_{N}]$ . With the assumption of perfect isomorphism and if errors are neglected, the phase circles corresponding to all the crystals would intersect at a common point if a number of isomorphous crystals were used for phase determination.

Figure 2.4.2.3 | top | pdf |

Harker construction when two heavy-atom derivatives are available.

References

Bokhoven, C., Schoone, J. C. & Bijvoet, J. M. (1951). The Fourier synthesis of the crystal structure of strychnine sulphate pentahydrate. Acta Cryst. 4, 275–280.Google Scholar

Harker, D. (1956). The determination of the phases of the structure factors of non-centrosymmetric crystals by the method of double isomorphous replacement. Acta Cryst. 9, 1–9.Google Scholar

International Tables for Crystallography (2006). Vol. B. ch. 2.4, p. 265