On the estimation of |E| values of the squared structure on the basis of quartet invariants

Expressions for the estimation of the |G_H| values, the | E_H values of the squared structure, on the basis of all quartets in which H is a cross-term vector are presented for the space groups P1 and P. A reliable estimation procedure was developed employing the quartets with highest quartet product only. It appears that in this way |E| values of strong or weak reflections outside the limiting sphere could be predicted. An implication of this is that for quartets with only two cross terms in the measured area of reciprocal space, the E's of which are both either large or small, the |E| of the third cross term is more likely to be large or small respectively. It is further shown that the estimated |G| values sharpen the Patterson synthesis; however, at its present state this technique does not offer advantages over other sharpening procedures.