Table 2.3.2.2

Rossmann, M. G.; Arnold, E.

doi:10.1107/97809553602060000556

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

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

Table 2.3.2.2

M. G. Rossmann^a ^* and E. Arnold^b

^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: mgr@indiana.bio.purdue.edu

Table 2.3.2.2 | top | pdf |
Square matrix representation of vector interactions in a Patterson of a crystal with M crystallographic asymmetric units each containing N atoms

Peak positions $[{\bf u}_{m1n1, \, m2n2}]$ correspond to vectors between the atoms $[{\bf x}_{m1n1}]$ and $[{\bf x}_{m2n2}]$ where $[{\bf x}_{mn}]$ is the nth atom in the mth crystallographic asymmetric unit. The corresponding weights are $[w_{n1} w_{n2}]$ . The outlined blocks I1 and IM represent vector interactions between atoms in the same crystallographic asymmetric units (there are M such blocks). The off-diagonal blocks IIM1 and II1M represent vector interactions between atoms in crystal asymmetric units 1 and M; there are [M(M - 1)] blocks of this type. The significance of diagonal elements of block IIM1 is that they represent Harker-type interactions between symmetry-equivalent atoms (see Section 2.3.2.2).

	$[{\bf x}_{11}, w_{1}]$	$[{\bf x}_{12}, w_{2}]$	…	$[{\bf x}_{1N}, w_{N}]$	…	$[{\bf x}_{M1}, w_{1}]$	$[{\bf x}_{M2}, w_{2}]$
$[{\bf x}_{11}, w_{1}]$	0, $[w_{1}^{2}]$	$[{\bf u}_{11, \, 12}, w_{1} w_{2}]$	…	$[{\bf u}_{11, \, 1N}, w_{1} w_{N}]$
$[{\bf x}_{12}, w_{2}]$		0, $[w_{2}^{2}]$	…	$[{\bf u}_{12, \, 1N}, w_{2} w_{N}]$
$[\vdots]$		$[\ddots]$		$[\vdots]$	…
$[{\bf x}_{1N}, w_{N}]$				0, $[w_{N}^{2}]$
	Block I1					Block II1M
$[\vdots]$		$[\vdots]$			$[\ddots]$		$[\vdots]$
$[{\bf x}_{M1}, w_{1}]$	$[{\bf u}_{M1, \, 11}, w_{1}^{2}]$	$[{\bf u}_{M1, \, 12}, w_{1} w_{2}]$
$[{\bf x}_{M2}, w_{2}]$	$[{\bf u}_{M2, \, 11}, w_{2} w_{1}]$	$[{\bf u}_{M2, \, 12}, w_{2}^{2}]$
$[\vdots]$		$[\ddots]$			…
$[{\bf x}_{MN}, w_{N}]$				$[{\bf u}_{MN, \, 1N}, w_{N}^{2}]$
	Block IIM1					Block IM