Tables for
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B. ch. 2.3, pp. 239-240   | 1 | 2 |

Section Finding heavy atoms

M. G. Rossmanna* and E. Arnoldb

aDepartment of Biological Sciences, Purdue University, West Lafayette, Indiana 47907, USA, and  bCABM & Rutgers University, 679 Hoes Lane, Piscataway, New Jersey 08854-5638, USA
Correspondence e-mail: Finding heavy atoms

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The previous two sections have developed some of the useful mechanics for interpreting Pattersons. In this section, we will consider finding heavy-atom positions, in the presence of numerous light atoms, from Patterson maps. The feasibility of structure solution by the heavy-atom method depends on a number of factors which include the relative size of the heavy atom and the extent and quality of the data. A useful rule of thumb is that the ratio [r = {\sum_{\rm heavy} Z^{2} \over \sum_{\rm light} Z^{2}}] should be near unity if the heavy atom is to provide useful starting phase information (Z is the atomic number of an atom). The condition that [r  \gt  1] normally guarantees interpretability of the Patterson function in terms of the heavy-atom positions. This `rule', arising from the work of Luzzati (1953)[link], Woolfson (1956)[link], Sim (1961)[link] and others, is not inviolable; many ambitious determinations have been accomplished via the heavy-atom method for which r was well below 1.0. An outstanding example is vitamin B12 with formula C62H88CoO14P, which gave an [r = 0.14] for the cobalt atom alone (Hodgkin et al., 1957[link]). One factor contributing to the success of such a determination is that the relative scattering power of Co is enhanced for higher scattering angles. Thus, the ratio, r, provides a conservative estimate. If the value of r is well above 1.0, the initial easier interpretation of the Patterson will come at the expense of poorly defined parameters of the lighter atoms.

A general strategy for determining heavy atoms from the Patterson usually involves the following steps.

  • (1) List the number and type of atoms in the cell.

  • (2) Construct the interaction matrix for the heaviest atoms to predict the positions and weights of the largest Patterson vectors. Group recurrent vectors and notice vectors with special properties, such as Harker vectors.

  • (3) Compute the Patterson using any desired modifications. Placing the map on an absolute scale [[P(000) = {\textstyle\sum} Z^{2}]] is convenient but not necessary.

  • (4) Examine Harker sections and derive trial atom coordinates from vector positions.

  • (5) Check the trial coordinates using other vectors in the predicted set. Correlate enantiomorphic choice and origin choice for independent sites.

  • (6) Include the next-heaviest atoms in the interpretation if possible. In particular, use the cross-vectors with the heaviest atoms.

  • (7) Use the best heavy-atom model to initiate phasing.

Detailed and instructive examples of using Pattersons to find heavy-atom positions are found in almost every textbook on crystal structure analysis [see, for example, Buerger (1959)[link], Lipson & Cochran (1966)[link] and Stout & Jensen (1968)[link]].

The determination of the crystal structure of cholesteryl iodide by Carlisle & Crowfoot (1945)[link] provides an example of using the Patterson function to locate heavy atoms. There were two molecules, each of formula C27H45I, in the [P2_{1}] unit cell. The ratio [r = 2.8] is clearly well over the optimal value of unity. The P(xz) Patterson projection showed one dominant peak at [\langle 0.434, 0.084\rangle] in the asymmetric unit. The equivalent positions for [P2_{1}] require that an iodine atom at [x_{\rm I}], [y_{\rm I}], [z_{\rm I}] generates another at [-x_{\rm I}, {1 \over 2} + y_{\rm I}, z_{\rm I}] and thus produces a Patterson peak at [\langle 2x_{\rm I}, {1 \over 2}, 2z_{\rm I}\rangle]. The iodine position was therefore determined as 0.217, 0.042. The y coordinate of the iodine is arbitrary for [P2_{1}] yet the value of [y_{\rm I} = 0.25] is convenient, since an inversion centre in the two-atom iodine structure is then exactly at the origin, making all calculated phases 0 or π. Although the presence of this extra symmetry caused some initial difficulties in the interpretation of the steroid backbone, Carlisle and Crowfoot successfully separated the enantiomorphic images. Owing to the presence of the perhaps too heavy iodine atom, however, the structure of the carbon skeleton could not be defined very precisely. Nevertheless, all critical stereochemical details were adequately illuminated by this determination. In the cholesteryl iodide example, a number of different yet equivalent origins could have been selected. Alternative origin choices include all combinations of [x \pm {1 \over 2}] and [z \pm {1 \over 2}].

A further example of using the Patterson to find heavy atoms will be provided in Section[link] on solving for heavy atoms in the presence of noncrystallographic symmetry.


First citation Buerger, M. J. (1959). Vector space and its application in crystal-structure investigation. New York: John Wiley.Google Scholar
First citation Carlisle, C. H. & Crowfoot, D. (1945). The crystal structure of cholesteryl iodide. Proc. R. Soc. London Ser. A, 184, 64–83.Google Scholar
First citation Hodgkin, D. C., Kamper, J., Lindsey, J., MacKay, M., Pickworth, J., Robertson, J. H., Shoemaker, C. B., White, J. G., Prosen, R. J. & Trueblood, K. N. (1957). The structure of vitamin B12. I. An outline of the crystallographic investigation of vitamin B12. Proc. R. Soc. London Ser. A, 242, 228–263.Google Scholar
First citation Lipson, H. & Cochran, W. (1966). The determination of crystal structures. Ithaca: Cornell University Press.Google Scholar
First citation Luzzati, V. (1953). Résolution d'une structure cristalline lorsque les positions d'une partie des atomes sont connues: traitement statistique. Acta Cryst. 6, 142–152.Google Scholar
First citation Sim, G. A. (1961). Aspects of the heavy-atom method. In Computing methods and the phase problem in X-ray crystal analysis, edited by R. Pepinsky, J. M. Robertson & J. C. Speakman, pp. 227–235. Oxford: Pergamon Press.Google Scholar
First citation Stout, G. H. & Jensen, L. H. (1968). X-ray structure determination. New York: Macmillan.Google Scholar
First citation Woolfson, M. M. (1956). An improvement of the `heavy-atom' method of solving crystal structures. Acta Cryst. 9, 804–810.Google Scholar

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