Tables for
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B, ch. 2.3, p. 236   | 1 | 2 |


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:

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Matrix representation of Patterson peaks

The [N\times N] matrix represents the position [{\bf u}_{ij}] and weights [w_{ij}] of atomic interactions in a Patterson arising from N atoms at [{\bf x}_{i}] and weight [w_{i}] in the real cell.

  [{\bf x}_{1}, w_{1}] [{\bf x}_{2}, w_{2}] [{\bf x}_{N}, w_{N}]
[{\bf x}_{1}, w_{1}] [{\bf u}_{11} = {\bf x}_{1} - {\bf x}_{1}], [{\bf u}_{12} = {\bf x}_{1} - {\bf x}_{2}], [{\bf u}_{1N} = {\bf x}_{1} - {\bf x}_{N}],
  [w_{11} = w_{1}^{2}] [w_{12} = w_{1} w_{2}]   [w_{1N} = w_{1} w_{N}]
[{\bf x}_{2}, w_{2}] [{\bf x}_{2} - {\bf x}_{1}, w_{2} w_{1}] 0, [w_{2}^{2}] [{\bf x}_{2} - {\bf x}_{N}, w_{2} w_{N}]
[\vdots] [\vdots] [\vdots] [\ddots] [\vdots]
[{\bf x}_{N}, w_{N}] [{\bf x}_{N} - {\bf x}_{1}, w_{N} w_{1}] [{\bf x}_{N} - {\bf x}_{2}, w_{N} w_{2}] 0, [w_{N}^{2}]