Use of negative quartet cosine invariants as a phasing figure of merit: NQEST

Recent theoretical advances in the identification of those cosine invariants cos (φ_h + φ_k + φ₁ + φ_m) which are probably negative suggest algorithms for the calculation of a figure of merit which is sensitive to the integrity of a phase set. The negative quartet figure of merit, NQEST, defined here is of particular utility in conjunction with fast multi-solution tangent formula techniques. Development of the methods and applications to both known and unknown crystal structures are presented.