From a random to the correct structure: the VLD algorithm

A recent probabilistic reformulation of the difference electron-density Fourier synthesis [Burla, Caliandro, Giacovazzo & Polidori (2010). Acta Cryst. A66, 347-361] suggested that the most suitable Fourier coefficients are the sum of the classical difference term (mF - DF_p) with a flipping term, depending on the model and on its quality. The flipping term is dominant when the model is poor and is negligible when the model is a good representation of the target structure. In the case of a random model the Fourier coefficient does not vanish and therefore could allow the recovery of the target structure from a random model. This paper describes a new phasing algorithm which does not require use of the concept of structure invariants or semi-invariants: it is based only on the properties of the new difference electron density and of the observed Fourier synthesis. The algorithm is cyclic and very easy to implement. It has been applied to a large set of small-molecule structures to verify the suitability of the approach.