Optimal Symbolic Phase Determination

Abstract

In spite of various differences, direct-method programs have one procedure in common. After normalizing the structure factors and generating the phase relations, a convergence procedure (Germain, Main & Woolfson, 1970) is invoked in order to get a (small) set of starting reflections. After fixing the origin with a subset of the starting set reflections, the remaining starting set reflections are assigned either various numerical trial values or symbolic phase values. In a second step all other phases are expressed successively in terms of the starting set phases, taking into account the statistical weights of the newly phased reflections. A drawback of this phasing technique may be the fixed starting set. The statistical weights can not be incorporated in the convergence procedure as they are calculated during and propagating throughout the phasing process. Therefore, a fixed starting set does not guarantee the most efficient starting set nor the best possible order of phasing reflections. A more effective procedure, in which both the starting set and the order of phasing reflections are flexible, can be based on the dynamic programming technique (Bellman, 1957).