Solving structures with quartets: the least-squares analysis of quartet invariants in space group P1

A least-squares technique for extracting individual phase angles from a set of quartet invariants is described. For symmorphic space groups, this procedure offers the advantages of stability and, in noncentrosymmetric cases, a systematic way of defining the enantiomorph, in contrast with traditional direct methods employing triplets. The application to a phthalic anhydride derivative C₂₆H₁₆O₅ in space group P1 is described. The method is readily extended to other space groups.