Elser Veit
Department of Physics, Cornell University, Ithaca, NY 14853-2501, USA.
Acta Crystallogr A. 2003 May;59(Pt 3):201-9. doi: 10.1107/s0108767303002812. Epub 2003 Apr 25.
An algorithm for determining crystal structures from diffraction data is described which does not rely on the usual reciprocal-space formulations of atomicity. The new algorithm implements atomicity constraints in real space, as well as intensity constraints in reciprocal space, by projections that restore each constraint with the minimal modification of the scattering density. To recover the true density, the two projections are combined into a single operation, the difference map, which is iterated until the magnitude of the density modification becomes acceptably small. The resulting density, when acted upon by a single additional operation, is by construction a density that satisfies both intensity and atomicity constraints. Numerical experiments have yielded solutions for atomic resolution X-ray data sets with over 400 non-hydrogen atoms, as well as for neutron data, where positivity of the density cannot be invoked.
本文描述了一种从衍射数据确定晶体结构的算法，该算法不依赖于通常的原子性倒易空间公式。新算法通过投影在实空间中实现原子性约束，并在倒易空间中实现强度约束，这些投影以对散射密度的最小修改来恢复每个约束。为了恢复真实密度，将这两个投影组合成一个单一操作，即差值图，迭代该操作直到密度修改的幅度变得足够小。通过构建，当对所得密度执行单个附加操作时，它是一个同时满足强度和原子性约束的密度。数值实验已经得到了含有超过400个非氢原子的原子分辨率X射线数据集以及中子数据的解决方案，其中密度的正值性无法被调用。
