Sine-enhanced Shake-and-Bake: the theoretical basis and applications to Se-atom substructures

Shake-and-Bake is a dual-space direct-methods procedure for crystal structure determination capable of providing ab initio solutions for structures containing as many as 1200 independent non-H atoms, as well as for heavy-atom substructures containing as many as 160 Se atoms in the asymmetric unit. In traditional Shake-and-Bake, phase refinement in reciprocal space utilizes the technique of parameter shift to reduce the value of a minimal function that considers only the mean-square differences between the current values of the cosine structure invariants and their expected values. A new type of minimal function, termed the sine-enhanced minimal function, considers both cosine and sine values of the structure invariants. Exhaustive tests on six Se-atom substructures, ranging in size from 12 to 160 Se atoms in the asymmetric unit, have shown that a two- to eightfold increase in the percentage of trials that converge to solution is attainable with the technique of sine-enhanced parameter shift. The corresponding sine-enhanced Shake-and-Bake, with suitable default parameter values, is being incorporated into a new distributed version of the SnB computer program.