Towards the enantiomorph specific probabilistic theory of the structure invariants

It is now generally recognized that the availability of single wavelength anomalous scattering (SAS) diffraction data greatly increases the power of the direct method. This enhancement of the direct method is undoubtedly due to the fact that, in contrast to the usual case, the observed data in the SAS case serve to fix the enantiomorph. It is now proposed to reach the same goal, even when SAS data are not available, by a suitable probabilistic approach which yields relationships among the structure invariants which respect the enantiomorph, that is to say, which are valid for fixed choice of enantiomorph. Specifically, this approach will derive relationships among the sines of the triplets, the value of any one of which is not uniquely determined by the diffraction intensities (in sharp contrast to the cosines) but is determined by the crystal structure, i.e. by either one of the two enantiomorphs permitted by the measured intensities. Only a brief summary of the final results is given here.