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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.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0021889802001759/ks0109sup1.cif
Contains datablock peptide

rtv

Rietveld powder data file (CIF format) https://doi.org/10.1107/S0021889802001759/ks0109sup2.rtv
Contains datablock peptide

CCDC reference: 214225

Computing details top

Figures top
[Figure 1]
[Figure 2]
[Figure 3]
[Figure 4]
[Figure 5]
[Figure 6]
[Figure 7]
[Figure 8]
(peptide) top
Crystal data top
C32H53N3O6β = 90°
Mr = ?γ = 90°
?, ?V = ? Å3
a = 61.0155 (9) ÅZ = 1
b = 11.1836 (1) ÅCu 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 tube2θmin = 2°, 2θmax = 42°, 2θstep = 0.02°
Refinement top
Rp = ?? data points
Rwp = 0.128124 parameters
Rexp = 0.045111 restraints
χ2 = NOT FOUND
Crystal data top
C32H53N3O6β = 90°
Mr = ?γ = 90°
?, ?V = ? Å3
a = 61.0155 (9) ÅZ = 1
b = 11.1836 (1) ÅCu 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
Refinement top
Rp = ?? data points
Rwp = 0.128124 parameters
Rexp = 0.045111 restraints
χ2 = NOT FOUND
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
C11.0120 (3)0.850 (2)0.396 (4)
C21.0237 (4)0.751 (3)0.484 (6)
C31.0393 (5)0.698 (2)0.321 (9)
C41.0447 (6)0.751 (3)0.083 (7)
C51.0344 (5)0.857 (3)0.007 (5)
C61.0172 (5)0.902 (2)0.156 (5)
C70.9955 (4)0.911 (3)0.578 (7)
O80.9741 (4)0.854 (3)0.563 (4)
C90.9659 (4)0.841 (2)0.810 (4)
O100.9727 (6)0.906 (4)0.989 (7)
C110.9450 (3)0.774 (2)0.849 (4)
C120.9493 (5)0.639 (2)0.869 (7)
C130.9298 (3)0.800 (2)0.621 (4)
C140.9223 (4)0.937 (2)0.625 (6)
C150.9043 (3)0.961 (2)0.840 (5)
C160.8824 (4)0.915 (3)0.745 (8)
C170.9020 (6)1.097 (2)0.884 (7)
N180.9108 (4)0.722 (2)0.635 (4)
C190.9037 (2)0.661 (1)0.428 (3)
O200.9116 (5)0.673 (3)0.204 (3)
C210.8884 (2)0.559 (1)0.487 (4)
C220.9000 (4)0.452 (2)0.397 (8)
C230.8660 (3)0.569 (1)0.349 (4)
C240.8529 (4)0.654 (3)0.504 (7)
N250.8551 (4)0.454 (2)0.376 (4)
C260.8445 (3)0.403 (1)0.178 (4)
O270.8481 (6)0.427 (3)0.056 (4)
C280.8300 (2)0.298 (2)0.250 (4)
C290.8437 (4)0.186 (2)0.270 (8)
C300.8106 (3)0.278 (1)0.061 (4)
C310.7907 (3)0.338 (2)0.176 (6)
C320.7972 (5)0.406 (4)0.421 (8)
C330.7812 (5)0.424 (4)0.026 (8)
N340.8059 (4)0.151 (1)0.045 (5)
C350.7932 (3)0.105 (1)0.142 (4)
O360.7965 (6)0.121 (3)0.380 (4)
O370.7776 (3)0.030 (2)0.060 (7)
C380.7856 (2)0.091 (1)0.064 (5)
C390.7979 (7)0.115 (4)0.196 (9)
C400.7666 (4)0.177 (2)0.086 (9)
C410.8008 (7)0.106 (3)0.303 (9)

Experimental details

Crystal data
Chemical formulaC32H53N3O6
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
V3)?
Z1
Radiation typeCu Kα1, λ = ? Å
Specimen shape, size (mm)?, ? × ? × ?
Data collection
DiffractometerStoe STADI
diffractometer
Specimen mounting?
Data collection mode?
Scan methodStep
2θ values (°)2θmin = 2 2θmax = 42 2θstep = 0.02
Refinement
R factors and goodness of fitRp = ?, Rwp = 0.128, Rexp = 0.045, χ2 = NOT FOUND
No. of data points?
No. of parameters124
No. of restraints111

 

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