On the handling of atomic anisotropic displacement parameters Page: 2 of 12
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As we show in section 2, a number of conventions for the representation of ADPs are
currently in use. A comprehensive overview is given by Trueblood et al. (1996). These
different conventions pose a significant potential for confusion. For example, the ADPs
found in files that follow the PDB format (http://www.rcsb.org/pdb/info.html) follow a
different convention than the ADPs found in files that follow the mmCIF format
(http://pdb.rutgers.edu/mmcif/). If this is not taken into account, there exists a possibility
that the ADPs can be misinterpreted, leading to incorrect analysis of a structure.
Therefore a library for the conversion between the different representations is a valuable
tool. We have implemented such a library by adding the ADP toolbox (adptbx) to the
Computational Crystallography toolbox (cctbx) (Grosse-Kunstleve et al., 2002). In
addition to the conversions the library facilitates the computation of Debye-Waller
factors, the handling of symmetry restrictions, and the determination of the eigenvalues
and eigenvectors of anisotropic displacement ellipsoids. The cctbx is organized as a
freely available Open Source library of reusable, object-oriented software components for
In general, the nomenclature that was adopted for the implementation of the adptbx
follows the recommendations of the IUCr Subcommittee on Atomic Displacement
Parameter Nomenclature (Trueblood et al., 1996). In the following sections we will
review the commonly used conventions for ADPs in the literature, computer programs
and databases. This is followed by a description of the adptbx. Further documentation is
available online (http://cctbx.sourceforge.net/).
2. Commonly used conventions for the representation of
atomic anisotropic displacement parameters
The mean-square displacements that define the probability density functions of atomic
displacements are commonly parameterized as a trivariate Gaussian. The effect of the
atomic displacements enters into the structure factor calculation as the Debye-Waller
factor T(h), where h is the Miller index (given as a column vector) of a Bragg reflection.
The fundamental expression for T(h) is (e.g. Trueblood et al., 1996)
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Grosse-Kunstleve, Ralf W. & Adams, Paul D. On the handling of atomic anisotropic displacement parameters, article, November 12, 2001; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc785745/m1/2/: accessed August 14, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.