The Estradiol·Urea Complex and 6α-Fluorocortisol; Two-Dimensional Invariants

Abstract

Experience has shown that a sufficiently accurate and large set of phases used as input to the tangent formula usually results in extension of the set of known phases. For moderately complex structures (20 to 40 independent non-hydrogen atoms) which have appreciable overlap in the Patterson synthesis it is desirable to determine some 40 to 60 phases correctly before applying the tangent formula. (In contrast, 6 – 8 phases often suffice in the multiple solution technique because these are non-interacting among themselves but interact strongly with others.) In the structures of estriol and two androstane derivatives the correct phasing of this basis set was achieved through the least-squares analysis of the cosine invariants cos(ø₁+ø₂+ø₃) which were evaluated by the modified triple product formula (§2.1, Chapter V).