A heuristic study of neighborhoods of the structure seminvariants in the space groupP\overline{1}
Herbert A. Hauptman · Acta Crystallographica Section A · 1976
The first two neighborhoods of each of the structure seminvariants ϕh, ϕh + ϕk, ϕh + ϕk + ϕl, ϕh + ϕk + ϕl + ϕm in the space group P{\bar 1} are found. Not only do these neighborhoods identify the magnitudes of the normalized structure factors |E| most intimately related to the value of the associated structure seminvariant, but the analysis suggests in a qualitative way what the nature of this relation must be. Thus the stage is set for determining the conditional probability distribution of a structure seminvariant, given the magnitudes |E| of a corresponding neighborhood (or an appropriate subset), and this leads in turn to a probabilistic estimate for the seminvariant in terms of a suitably chosen small set of magnitudes.