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.