Improved Monte Carlo sampling in a real space approach to the crystallographic phase problem

A real space approach has been proposed to solve the x-ray phase problem formulated as a minimization problem. The cost function consists of two parts: one represents the usual crystallographical residual while the other enforces the probability distribution of the invariant phase triplets. Starting from a random real space structure, the atoms are moved one by one to gradually reduce the cost function (simulated annealing). In addition, the atoms are encouragd to preferentially sample the high density regions in space determined by an approximate density map which in turn is updated and modified by averaging and Fourier synthesis. Such a reduction of the configurational space has led to considerable improvement of the algorithm compared to an earlier version. Trial calculations for structures including hexadecaisoleucinomycin (HEXIL) and a collagenlike peptide (PPG) are presented.