Burla Maria Cristina, Caliandro Rocco, Giacovazzo Carmelo, Polidori Giampiero
Department of Earth Sciences, University of Perugia, 06100 Perugia, Italy.
Acta Crystallogr A. 2010 May;66(Pt 3):347-61. doi: 10.1107/S010876731000365X. Epub 2010 Mar 31.
The joint probability distribution function P(E, E(p)), where E and E(p) are the normalized structure factors of the target and of a model structure, respectively, is a fundamental tool in crystallographic methods devoted to crystal structure solution. It plays a central role in any attempt for improving phase estimates from a given structure model. More recently the difference electron density rho(q) = rho - rho(p) has been revisited and methods based on its modifications have started to play an important role in combination with electron density modification approaches. In this paper new coefficients for the difference electron density have been obtained by using the joint probability distribution function P(E, E(p), E(q)) and by taking into account both errors in the model and in measurements. The first applications show the correctness of our theoretical approach and the superiority of the new difference Fourier synthesis, particularly when the model is a rough approximation of the target structure. The new and the classic difference syntheses coincide when the model represents the target structure well.
联合概率分布函数P(E, E(p))，其中E和E(p)分别是目标结构和模型结构的归一化结构因子，是致力于晶体结构解析的晶体学方法中的一个基本工具。在任何尝试从给定结构模型改进相位估计的过程中，它都起着核心作用。最近，差异电子密度ρ(q) = ρ - ρ(p) 被重新审视，基于其修正的方法开始与电子密度修正方法相结合发挥重要作用。在本文中，通过使用联合概率分布函数P(E, E(p), E(q))并考虑模型和测量中的误差，获得了差异电子密度的新系数。首次应用表明了我们理论方法的正确性以及新差异傅里叶合成的优越性，特别是当模型是目标结构的粗略近似时。当模型很好地代表目标结构时，新的和经典的差异合成是一致的。
