Direct phase determination of triple products from Bijvoet inequalities. II. A probabilistic approach

Probability calculations confirm a recently proposed formula for the calculation of sin _hk from Bijvoet inequalities, where _hk is the average phase of the triple products F_hF_kF and F, FF [paper I: Kroon, Spek & Krabbendam (1977), Acta Cryst. A33, 382-3851. In paper I it was shown that _hk could be calculated quite accurately without knowledge of the positions of the anomalous scatterers, provided an appropriate scaling procedure was applied. If the magnitudes of the individual structure factors are considered in addition to the magnitudes of the triple products, an improved formula is obtained which leads to even better results without any scaling procedure. The efficacy of the improved formula is demonstrated by test calculations for the same structure as in paper I (space group P1, two Br ions): (i) the phases of 5139 triple products formed from 322 reflexions (observed) with |E| > 1.2 are calculated with a mean error in _hk of 16° (paper I: 21°), (ii) the phases of 3832 triple products formed from 258 reflexions (calculated) with |E| > 1.2 are calculated with a mean error in _hk of 8° (paper I: 14°). 447