In this method, only grids of smaller subunits are summed and used as subunits ( i.e. For very large structures, a hybrid method can be used. In the direct method, no grids are computed, and the scattering amplitude is directly computed by summing all the subunit contributions in the complex structure. The final scattering amplitude is obtained by repeating this process for all the leaves and nodes of the tree data structure. When moving up in the hierarchy, the reciprocal grids of larger structures are computed by interpolating precomputed lower-level reciprocal grids. In D+, F( q) can be calculated by computing the scattering amplitudes of the subunits on 3D reciprocal-space grids. Furthermore, K j, m is the number of real-space translations, R j, m, k, of object j with orientation A j, m. Is the number of unique orientations of an object of type j, given by the Tait–Bryan rotation matrices A j, m. The scattering amplitude of the entire structure, made of J unique subunits, is Repeating subunits are then docked into their assembly symmetries (the tree's nodes), containing the locations and orientations of repeating subunits. In D+, structures can be defined in hierarchical data-structure trees, using geometric or atomic model subunits forming the tree's leaves. As previously shown (Ginsburg et al., 2019, 2016 ), the analysis program D+ ( ), developed in our laboratory, can accurately and rapidly compute the expected solution small/wide-angle X-ray scattering intensity from highly complex and large structural models. With the evolution in the strength of computers came the evolution of X-ray technology, and the complexity of the experiments followed suit. Much effort has been devoted to scattering data analysis and modeling. The term, where θ q and ϕ q are the reciprocal ( q)-space polar and azimuthal angles, respectively.
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