The Gram-Charlier and multipole expansions in accurate X-ray diffraction studies: can they be distinguished?
The Gram-Charlier and multipole expansions in accurate X-ray diffraction studies: can they be distinguished?
复制标题
精确 X 射线衍射研究中的 Gram-Charlier 展开式和多极展开式：它们可以区分吗？
DOI：
10.1107/s0108767387012558
复制
发表时间：
1988
期刊：
影响因子：
--
通讯作者：
Coppens,P
中科院分区：
文献类型：
--
作者：
Mallinson,PR;Koritsanszky,T;Elkaim,E;Li,N;Coppens,P
的Gram-Charlier温度因子形式主义已被应用到一组准确的低温数据双（吡啶）（meso-tetraphenylporphinato）铁（II），和一套理论的静态结构因子的hexaaquairon（II）离子。由于化学键合原子的非球面性的多极处理的细化进行了比较。在只考虑铁原子非球面性的实验数据的处理中，“热运动”形式主义在解释观测结果方面与多极形式主义一样有效。当应用于静态理论数据时，它的效率略低，尽管基于两种处理的模型图非常相似。卟啉数据的高阶Gram-Charlier细化，随后是所有数据的多极细化，其中Gram-Charlier参数最初是固定的，后来改变，表明同时细化非谐波和非球面效应是可能的，尽管所得分离可能不准确。一个组合的Gram-Charlier多极细化的静态数据，但是，导致不显着的热参数。它的结论是，统计Gram-Charlier形式主义是非常成功的表示键合效应的价电荷密度，如果这些不具体占在散射形式主义。统计非谐热运动形式主义应仅用于X射线数据分析结合的形式主义占原子电荷密度上的键合的效果。
The Gram-Charlier temperature factor formalism has been applied to a set of accurate low-temperature data on bis(pyridine)(meso-tetraphenylporphinato)iron(II), and to a theoretical set of static structure factors on the hexaaquairon(lI) ion. The refinements are compared with the multipole treatment for atomic asphericity due to chemical bonding. In a treatment of the experimental data in which only the iron atom asphericity is considered, the 'thermal motion' formalism is as efficient as the multipole formalism in accounting for the observations. It is slightly less efficient when applied to the static theoretical data, though model maps based on the two treatments are remarkably similar. A high-order Gram-Charlier refinement of the porphyrin data, followed by a multipole refinement of all data with the Gram-Charlier parameters initially fixed, and later varied, shows that simultaneous refinement of anharmonic and aspherical effects is possible, though the resulting separation may not be accurate. A combined Gram-Charlier multipole refinement on the static data, however, leads to non-significant thermal parameters. It is concluded that the statistical Gram-Charlier formalism is remarkably successful in representing bonding effects in the valence charge density if these are not specifically accounted for in the scattering formalism. Statistical anharmonic thermal motion formalisms should only be used for X-ray data analysis in combination with a formalism accounting for the effect of bonding on the atomic charge density.