Structure solution of modulated structures by charge flipping in superspace

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Structure solution of modulated structures by
charge flipping in superspace

• Lukas Palatinus
• EPFL Lausanne
• Switzerland

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• The principle of charge flipping
• Superspace
• Limitations and how to overcome them
• Implementation and demonstration

Overview
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• Published by Oszlanyi Sütö (2004), Acta Cryst A
• Iterative algorithm
• Requires only lattice parameters and reflection
  intensities
• The output is an approximate scattering density
  of the structure sampled on a discrete grid
• No use of atomicity, only of the sparseness of
  the electron density
• No use of symmetry apart from the input
  intensities
• Related to the LDE (low density elimination)
  method (Shiono Woolfson (1992), Acta Cryst. A
  Takakura et al. (2001), Phys.Rev.Lett.)

The principle
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• Flow chart

The principle
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• Flow chart

The principle
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• Charge flipping reconstructs the density always
  in P1
• Reason in P1 the maxima can appear anywhere in
  the cell. In higher symmetry the choice is
  limited -gt lower effectivity.

The principle
Advantage No need to know the symmetry, symmetry
can be read out from the result Disadvantage
The structure is randomly shifted in the cell -gt
it is necessary to locate the origin
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• Charge flipping does not use atomicity -gt no
  problem to apply to superspace densities
• The 3D density is replaced by a (3d)D
  superspace density sampled using a (3d)D grid
• The structure factors are indexed by (3d)
  integer indices. They represent the coefficients
  of the Fourier transform of the superspace
  density.
• No need to know the average structure!

Superspace
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• All tested modulated structures could be solved
  by charge flipping

Superspace
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tetraphenylphosphonium hexabromotellurate(IV)bisd
ibromoselenate(I)
lt-CF Br1 Fourier-gt
Superspace
lt-CF C5 Fourier-gt
4086 out of 4247 reflections correctly phased
(96)
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d-QC Al-Co-Ni, Steurer et al., Acta Cryst. B49,
1993
Superspace
published section final structure
as obtained from charge flipping
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• Requirements on the data
• Atomic resolution dminlt1.0 A
• Small to medium-sized structure (below ca 1000
  atoms in the unit cell)
• X-ray diffraction data
• Complete dataset
• Individual intensities are known (no powder, no
  twins)

The limitations
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• Atomic resolution dminlt1.0 A
• Small to medium-sized structure (below ca 1000
  atoms in the cell)
• X-ray diffraction data
• Complete dataset
• Individual intensities are known (no powder, no
  twins)

The limitations
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• Atomic resolution dminlt1.0 A
• Small to medium-sized structure (below ca 1000
  atoms in the cell)
• X-ray diffraction data
• Complete dataset
• Individual intensities are known (no powder, no
  twins)

Solution flip everything between -? and ?
(Oszlanyi Sütö, ECM23)
The limitations
i-QC AlPdMn, unpublished neutron data provided by
Marc de Boissieu
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• Atomic resolution dminlt1.0 A
• Small to medium-sized structure (below ca 1000
  atoms in the cell)
• X-ray diffraction data
• Complete dataset
• Individual intensities are known (no powder, no
  twins)

Solution extrapolate the missing reflections by
MEM
The limitations
from Palatinus Steurer, in preparation
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• Atomic resolution dminlt1.0 A
• Small to medium-sized structure (below ca 1000
  atoms in the cell)
• X-ray diffraction data
• Complete dataset
• Individual intensities are known (no powder, no
  twins)

• Two techniques to overcome this problem
• Repartitioning of the overlapping reflections
  according to the flipped structure factors (Wu
  et al. (2006), Nature Mater.)
• Repartitioning using histogram matching
  (Baerlocher, McCusker Palatinus (2006),
  submitted)

The limitations
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• Atomic resolution dminlt1.0 A
• Small to medium-sized structure (below ca 1000
  atoms in the cell)
• X-ray diffraction data
• Complete dataset
• Individual intensities are known (no powder, no
  twins)

• Two techniques to overcome this problem
• Repartitioning of the overlapping reflections
  according to the flipped structure factors (Wu
  et al. (2006), Nature Mater.)
• Repartitioning using histogram matching
  (Baerlocher, McCusker Palatinus (2006),
  submitted)

The limitations
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Superflip
Palatinus Chapuis (2006), http//superspace.epfl
.ch/superflip

• Superflip charge FLIPping in SUPERspace
• Program for application of charge flipping in
  arbitrary dimension
• Some properties
• Keyword driven free-format input file
• Automatic search for d
• Automatic search for the origin of the
  (super)space group
• Support for the histogram-matching procedure and
  intensity repartitioning
• Continuous development

Implementation
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EDMA
Palatinus van Smaalen, University of Bayreuth

• EDMA Electron Density Map Analysis (part of the
  BayMEM suite)
• Program for analysis of discrete electron density
  maps
• Originally developed for the MEM densities
• Analysis of periodic and incommensurately
  modulated structures
• Location of atoms and tentative assignment of
  chemical type based on a qualitative composition
• Export of the structure in Jana2000 format (SHELX
  and CIF formats in preparation)
• Writes out the modulation functions in a form of
  a x4-xi table

Implementation
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Symmetry
s
d
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Symmetry
s
d
d (I-R).s
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d (I-R).s
Symmetry
How to find d?
Patterson function
Symmetry correlation function S will have
the origin peak at d
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Example of a solution of a modulated structure
Superspace
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Parameter d
d determines the amount of the flipped
density. If d is too small, the perturbation of
the density is too small and the iteration does
not converge. If d is too large, too much of the
density is flipped. In an extreme case all the
density is flipped, which leads to no change of
the amplitude of the structure factors. In
practice d can be determined easily by trial and
error.
The principle