Mondal Swastik, Prathapa Siriyara Jagannatha, van Smaalen Sander
Laboratory of Crystallography, University of Bayreuth, 95440 Bayreuth, Germany.
Acta Crystallogr A. 2012 Sep;68(Pt 5):568-81. doi: 10.1107/S0108767312029005. Epub 2012 Aug 2.
It is shown that the dynamic electron density corresponding to a structure model can be computed by inverse Fourier transform of accurately calculated structure factors, employing the method of fast Fourier transform. Maps free of series-termination effects are obtained for resolutions better than 0.04 Å in direct space, corresponding to resolutions larger than 6 Å(-1) in reciprocal space. Multipole (MP) models of α-glycine and D,L-serine at different temperatures have been determined by refinement against X-ray diffraction data obtained from the scientific literature. The successful construction of dynamic electron densities is demonstrated by their topological properties, which indicate local maxima and bond-critical points (BCPs) at positions expected on the basis of the corresponding static electron densities, while non-atomic maxima have not been found. Density values near atomic maxima are much smaller in dynamic than in static electron densities. Static and low-temperature (∼20 K) dynamic electron-density maps are found to be surprisingly similar in the low-density regions. Especially at BCPs, values of the ∼20 K dynamic density maps are only slightly smaller than values of the corresponding static density maps. The major effect of these zero-point vibrations is a modification of the second derivatives of the density, which is most pronounced for values at the BCPs of polar C-O bonds. Nevertheless, dynamic MP electron densities provide an estimate of reasonable accuracy for the topological properties at BCPs of the corresponding static electron densities. The difference between static and dynamic electron densities increases with increasing temperature. These differences might provide information on temperature-dependent molecular or solid-state properties like chemical stability and reactivity. In regions of still lower densities, like in hydrogen bonds, static and dynamic electron densities have similar appearances within the complete range of temperatures that have been considered (20-298 K), providing similar values of both the density and its Laplacian at BCPs in static and dynamic electron densities at all temperatures.
结果表明，利用快速傅里叶变换方法，通过对精确计算的结构因子进行傅里叶逆变换，可以计算出与结构模型对应的动态电子密度。对于直接空间中分辨率优于0.04 Å的情况，可获得无级数终止效应的图谱，这对应于倒易空间中大于6 Å⁻¹的分辨率。通过对从科学文献中获得的X射线衍射数据进行精修，确定了不同温度下α-甘氨酸和D,L-丝氨酸的多极（MP）模型。动态电子密度的成功构建通过其拓扑性质得到了证明，这些拓扑性质表明在基于相应静态电子密度预期的位置处存在局部最大值和键临界点（BCP），而未发现非原子最大值。动态电子密度中原子最大值附近的密度值比静态电子密度中的小得多。发现静态和低温（约20 K）动态电子密度图在低密度区域惊人地相似。特别是在BCP处，约20 K动态密度图的值仅略小于相应静态密度图的值。这些零点振动的主要影响是密度二阶导数的改变，这在极性C - O键的BCP处的值最为明显。然而，动态MP电子密度为相应静态电子密度的BCP处的拓扑性质提供了合理准确的估计。静态和动态电子密度之间的差异随温度升高而增加。这些差异可能提供有关温度依赖性分子或固态性质（如化学稳定性和反应性）的信息。在密度更低的区域，如氢键中，在考虑的整个温度范围（20 - 298 K）内，静态和动态电子密度具有相似的外观，在所有温度下静态和动态电子密度的BCP处提供相似的密度及其拉普拉斯算子值。
