Isomorphous replacement and isomorphous addition

Vijayan, M.; Ramaseshan, S.

doi:10.1107/97809553602060000557

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

pdf | chapter contents | chapter index | related articles

International Tables for Crystallography (2006). Vol. B. ch. 2.4, pp. 264-265 | 1 | 2 |

Section 2.4.2.1. Isomorphous replacement and isomorphous addition

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

2.4.2.1. Isomorphous replacement and isomorphous addition

| top | pdf |

Two crystals are said to be isomorphous if (a) both have the same space group and unit-cell dimensions and (b) the types and the positions of atoms in both are the same except for a replacement of one or more atoms in one structure with different types of atoms in the other (isomorphous replacement) or the presence of one or more additional atoms in one of them (isomorphous addition). Consider two crystal structures with identical space groups and unit-cell dimensions, one containing N atoms and the other M atoms. The N atoms in the first structure contain subsets P and Q whereas the M atoms in the second structure contain subsets P, Q′ and R. The subset P is common to both structures in terms of atomic positions and atom types. The atomic positions are identical in subsets Q and Q′, but at any given atomic position the atom type is different in Q and Q′. The subset R exists only in the second structure. If $[{\bf F}_{N}]$ and $[{\bf F}_{M}]$ denote the structure factors of the two structures for a given reflection, $[{\bf F}_{N} = {\bf F}_{P} + {\bf F}_{Q} \eqno(2.4.2.1)]$ and $[{\bf F}_{M} = {\bf F}_{P} + {\bf F}_{Q'} + {\bf F}_{R}, \eqno(2.4.2.2)]$ where the quantities on the right-hand side represent contributions from different subsets. From (2.4.2.1) and (2.4.2.2) we have $[{\bf F}_{M} - {\bf F}_{N} = {\bf F}_{H} = {\bf F}_{Q'} - {\bf F}_{Q} + {\bf F}_{R}. \eqno(2.4.2.3)]$ The above equations are illustrated in the Argand diagram shown in Fig. 2.4.2.1. $[{\bf F}_{Q}]$ and $[{\bf F}_{Q'}]$ would be collinear if all the atoms in Q were of the same type and those in Q′ of another single type, as in the replacement of chlorine atoms in a structure by bromine atoms.

Figure 2.4.2.1 | top | pdf |

Vector relationship between $[{\bf F}_{N}]$ and $[{\bf F}_{M}\ (\equiv {\bf F}_{NH})]$ .

We have a case of `isomorphous replacement' if $[{\bf F}_{R} = 0 \ ({\bf F}_{H} = {\bf F}_{Q'} - {\bf F}_{Q})]$ and a case of `isomorphous addition' if $[{\bf F}_{Q} = {\bf F}_{Q'} = 0 \ ({\bf F}_{H} = {\bf F}_{R})]$ . Once $[{\bf F}_{H}]$ is known, in addition to the magnitudes of $[{\bf F}_{N}]$ and $[{\bf F}_{M}]$ , which can be obtained experimentally, the two cases can be treated in an equivalent manner in reciprocal space. In deference to common practice, the term `isomorphous replacement' will be used to cover both cases. Also, in as much as $[{\bf F}_{M}]$ is the vector sum of $[{\bf F}_{N}]$ and $[{\bf F}_{H}]$ , $[{\bf F}_{M}]$ and $[{\bf F}_{NH}]$ will be used synonymously. Thus $[{\bf F}_{M} \equiv {\bf F}_{NH} = {\bf F}_{N} + {\bf F}_{H}. \eqno(2.4.2.4)]$

References

International Tables for Crystallography (2006). Vol. B. ch. 2.4, pp. 264-265