research papers
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 (C32N3O6H53) with 17 variable torsion angles.
Keywords: powder diffraction; structure envelope; electron density distribution; computer programs; phase estimation with low-resolution data; zeolites; simulated annealing.
Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S0021889802001759/ks0109sup1.cif | |
Rietveld powder data file (CIF format) https://doi.org/10.1107/S0021889802001759/ks0109sup2.rtv |
CCDC reference: 214225
Computing details top
(peptide) top
Crystal data top
C32H53N3O6 | β = 90° |
Mr = ? | γ = 90° |
?, ? | V = ? Å3 |
a = 61.0155 (9) Å | Z = 1 |
b = 11.1836 (1) Å | Cu Kα1 radiation, λ = ? Å |
c = 5.0827 (1) Å | ?, ? × ? × ? mm |
α = 90° |
Data collection top
Stoe STADI diffractometer | Scan method: step |
Radiation source: sealed X-ray tube | 2θmin = 2°, 2θmax = 42°, 2θstep = 0.02° |
Crystal data top
C32H53N3O6 | β = 90° |
Mr = ? | γ = 90° |
?, ? | V = ? Å3 |
a = 61.0155 (9) Å | Z = 1 |
b = 11.1836 (1) Å | Cu Kα1 radiation, λ = ? Å |
c = 5.0827 (1) Å | ?, ? × ? × ? mm |
α = 90° |
Data collection top
Stoe STADI diffractometer | 2θmin = 2°, 2θmax = 42°, 2θstep = 0.02° |
Scan method: step |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
x | y | z | Biso*/Beq | ||
C1 | 1.0120 (3) | 0.850 (2) | 0.396 (4) | ||
C2 | 1.0237 (4) | 0.751 (3) | 0.484 (6) | ||
C3 | 1.0393 (5) | 0.698 (2) | 0.321 (9) | ||
C4 | 1.0447 (6) | 0.751 (3) | 0.083 (7) | ||
C5 | 1.0344 (5) | 0.857 (3) | 0.007 (5) | ||
C6 | 1.0172 (5) | 0.902 (2) | 0.156 (5) | ||
C7 | 0.9955 (4) | 0.911 (3) | 0.578 (7) | ||
O8 | 0.9741 (4) | 0.854 (3) | 0.563 (4) | ||
C9 | 0.9659 (4) | 0.841 (2) | 0.810 (4) | ||
O10 | 0.9727 (6) | 0.906 (4) | 0.989 (7) | ||
C11 | 0.9450 (3) | 0.774 (2) | 0.849 (4) | ||
C12 | 0.9493 (5) | 0.639 (2) | 0.869 (7) | ||
C13 | 0.9298 (3) | 0.800 (2) | 0.621 (4) | ||
C14 | 0.9223 (4) | 0.937 (2) | 0.625 (6) | ||
C15 | 0.9043 (3) | 0.961 (2) | 0.840 (5) | ||
C16 | 0.8824 (4) | 0.915 (3) | 0.745 (8) | ||
C17 | 0.9020 (6) | 1.097 (2) | 0.884 (7) | ||
N18 | 0.9108 (4) | 0.722 (2) | 0.635 (4) | ||
C19 | 0.9037 (2) | 0.661 (1) | 0.428 (3) | ||
O20 | 0.9116 (5) | 0.673 (3) | 0.204 (3) | ||
C21 | 0.8884 (2) | 0.559 (1) | 0.487 (4) | ||
C22 | 0.9000 (4) | 0.452 (2) | 0.397 (8) | ||
C23 | 0.8660 (3) | 0.569 (1) | 0.349 (4) | ||
C24 | 0.8529 (4) | 0.654 (3) | 0.504 (7) | ||
N25 | 0.8551 (4) | 0.454 (2) | 0.376 (4) | ||
C26 | 0.8445 (3) | 0.403 (1) | 0.178 (4) | ||
O27 | 0.8481 (6) | 0.427 (3) | −0.056 (4) | ||
C28 | 0.8300 (2) | 0.298 (2) | 0.250 (4) | ||
C29 | 0.8437 (4) | 0.186 (2) | 0.270 (8) | ||
C30 | 0.8106 (3) | 0.278 (1) | 0.061 (4) | ||
C31 | 0.7907 (3) | 0.338 (2) | 0.176 (6) | ||
C32 | 0.7972 (5) | 0.406 (4) | 0.421 (8) | ||
C33 | 0.7812 (5) | 0.424 (4) | −0.026 (8) | ||
N34 | 0.8059 (4) | 0.151 (1) | 0.045 (5) | ||
C35 | 0.7932 (3) | 0.105 (1) | −0.142 (4) | ||
O36 | 0.7965 (6) | 0.121 (3) | −0.380 (4) | ||
O37 | 0.7776 (3) | 0.030 (2) | −0.060 (7) | ||
C38 | 0.7856 (2) | −0.091 (1) | −0.064 (5) | ||
C39 | 0.7979 (7) | −0.115 (4) | 0.196 (9) | ||
C40 | 0.7666 (4) | −0.177 (2) | −0.086 (9) | ||
C41 | 0.8008 (7) | −0.106 (3) | −0.303 (9) |
Experimental details
Crystal data | |
Chemical formula | C32H53N3O6 |
Mr | ? |
Crystal system, space group | ?, ? |
Temperature (K) | ? |
a, b, c (Å) | 61.0155 (9), 11.1836 (1), 5.0827 (1) |
α, β, γ (°) | 90, 90, 90 |
V (Å3) | ? |
Z | 1 |
Radiation type | Cu Kα1, λ = ? Å |
Specimen shape, size (mm) | ?, ? × ? × ? |
Data collection | |
Diffractometer | Stoe STADI diffractometer |
Specimen mounting | ? |
Data collection mode | ? |
Scan method | Step |
2θ values (°) | 2θmin = 2 2θmax = 42 2θstep = 0.02 |
Refinement | |
R factors and goodness of fit | Rp = ?, Rwp = 0.128, Rexp = 0.045, χ2 = NOT FOUND |
No. of data points | ? |
No. of parameters | 124 |
No. of restraints | 111 |