Density modification is a general standard technique which may be used to improve electron density derived from experimental phasing and also to refine densities obtained by ab initio approaches. Here, a novel method to expand density modification is presented, termed the Phantom derivative technique, which is based on non-existent structure factors and is of particular interest in molecular replacement. The Phantom derivative approach uses randomly generated ancil structures with the same unit cell as the target structure to create non-existent derivatives of the target structure, called phantom derivatives, which may be used for ab initio phasing or for refining the available target structure model. In this paper, it is supposed that a model electron density is available: it is shown that ancil structures related to the target obtained by shifting the target by origin-permissible translations may be employed to refine model phases. The method enlarges the concept of the ancil, is as efficient as the canonical approach using random ancils and significantly reduces the CPU refinement time. The results from many real test cases show that the proposed methods can substantially improve the quality of electron-density maps from molecular-replacement-based phases.
Keywords: Phantom derivative approach; phase refinement; phasing.