The previously proposed method [Fan, Han & Qian (1984). Acta Cryst. A40, 495-498;. Acta Cryst. A41, 280-284] has been improved and tested for ab initio phasing of the one-wavelength anomalous scattering data at 2 A, resolution from a known small protein, avian pancreatic polypeptide. Positions of the anomalous scatterers were found by the direct-method program SAPI and used to normalize the anomalous differences before calculating the phase doublets. 2108 independent reflections and about 790 000 Y~2 relationships were involved in the phase derivation. The 'best phases' and the figures of merit obtained from the direct method were used to calculate a Fourier map, which revealed the essential feature of the structure.

Optimization has been made of the program SAIl for automatic solution of structures having pseudotranslational symmetry. This includes: (1) floating default cutoff of E's; (2) automatic and user-adjustable balance between the number of systematically strong reflections and that of the systematically weak ones; (3) R factors for reflection subsets corresponding to the 'strong' group and the 'weak' groups. Examples on solving structures with pseudo-translational symmetry are discussed in detail. They include known as well as unknown structures and centrosymmetric as well as non-centrosymmetric structures, all of which can be solved starting from a default run of SAPI. IntroductionPseudo-translational symmetry often occurs in minerals and some important inorganic as well as organic crystals. Structures having pseudo-translational symmetry give rise to complicated positional ambiguity in real space or phase ambiguity in reciprocal space. Hence structure analysis of such kinds of crystals remains a difficult problem. The first example of applying direct methods to remove the phase ambiguity arising from pseudo-translational symmetry was given by Fan Hai-fu (1975). Since then the method has been greatly improved (Fan Hai-fu, He Luo, Qian Jin-zi & Liu Shi-xiang, 1978;Fan Hai-fu, Yao Jia-xing, Main & Woolfson, 1983) and finally incorporated into the program SAP! (Fan Hai-fu, 1986). For automatic discrimination of pseudo-translational symmetry and automatic grouping of the reflections accordingly, an additional subroutine AUTOGP is provided in SAPI (Fan Hai-fu, Yao Jia-xing & Qian Jin-zi, 1988). This enables structures having pseudo-translational symmetry, such as superstructures, to be solved in a fully automatic way. Apart from the above, optimization has also been made in SAPI to strengthen the power of dealing * Also in Department of Chemistry, Zhongshan University, Guangzhou, China.with structures having pseudo-translational symmetry. In this paper some treatments for the optimization are discussed and examples of practical applications are given. Default cutoff of E'sIn most direct-methods programs the default minimum value of normalized structure factors, E's, accepted for phase derivation is set to about 1.2. However, for structures having pseudo-translational symmetry, especially for superstructures, the total number of reflections will sometimes be much smaller than usual. In this case the number of E's accepted for phase derivation may not be enough to ensure a reliable result. In order to overcome this difficulty, the default minimum value of E's in SAIl is made automatically adjustable. The value 1.2 is used first; however it will be automatically changed by the program to 0.9 whenever the total number of input reflections is smaller than 500. Balance between 'strong' and 'weak' reflectionsOne special feature of structures having pseudo-translational symmetry is that the reflections can be classified into two categories, one systematically strong and the other systematically weak. In our method, thes...

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