The application of structure envelopes in structure determination from powder diffraction data

A structure envelope is a special type of periodic nodal surface that separates regions of high electron density from those of low electron density. Once such a surface has been generated, it can be used in combination with direct-space methods to facilitate structure solution from powder data. To generate an informative structure envelope, the phases of the structure factors of a few strong low-order reflections must be determined; an algorithm has been developed for this purpose. The program SayPerm combines ( a ) the use of error-correcting codes (e.c.c.'s) to sample phase space efficiently, ( b ) a pseudo-atom approximation of structure fragments to simulate atomic resolution at ca 2.5 Å, and ( c ) phase extension and phase set ranking using the Sayre equation. The effect of using a structure envelope in structure solution was first tested in combination with a subroutine for finding zeolite topologies in the program FOCUS . Then extension to molecular structures in combination with a simulated-annealing program was explored. This resulted in the development of the program Safe and the subsequent determination of the structure of a tri-β-peptide (C 32 N 3 O 6 H 53 ) with 17 variable torsion angles.