ELECTRON CRYSTALLOGRAPHY OF LINEAR-POLYMERS - DIRECT PHASE DETERMINATION FOR ZONAL DATA SETS

To facilitate fitting a conformational chain model to two-dimensional electron diffraction intensity data, the zonal crystal structures of five representative linear polymers have been determined by the probabilistic estimate of three-and four-phase structure invariant sums. For two examples where individual atomic positions can be resolved in projection (i.e., poly(ethylene sulfide) and gamma-poly(pivalolactone)), the structures can be refined further by Fourier techniques. In another example, alpha-poly[3,3-bis(chloromethyl)oxacyclobutane], on the other hand, one fails to find the position of a linkage methylene group in difference Fourier maps, even though the initial phase set is mostly correct. Two polysaccharide structures, mannan and anhydrous nigeran, can only be visualized as a molecular density envelope, undoubtedly due to the overlap of many projected atomic positions. In all cases the phase determination is best carried out as a multisolution technique, via one or two algebraic unknowns in phase, to circumvent false indications given by incorrectly predicted invariant sums.