Charge flipping in superspace, Aperiodic 2006, 21.9.2006 Structure solution of modulated structures by charge flipping in superspace Lukas Palatinus EPFL

Charge flipping in superspace, Aperiodic 2006, 21.9.2006

Structure solution of modulated structures by

charge flipping in superspaceLukas PalatinusEPFL Lausanne

Switzerland


• The principle of charge flipping

• Superspace

• Limitations and how to overcome them

• Implementation and demonstration


• 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.)


Flow chart

structure factors

electron density

“flipped” electron density

“flipped” structure factors

random phases

+experimental amplitudes

inverse FT

flip all charge below a (small) threshold δ

FT

Combine phases of the flipped SF with amplitudes of the experi-mental SF


structure factors

electron density

“flipped” electron density

“flipped” structure factors

random phases

+experimental amplitudes

inverse FT

flip all charge below a (small) threshold δ

FT

Combine phases of the flipped SF with amplitudes of the experi-mental SF

Flow chart


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 -> lower effectivity.

Advantage: No need to know the symmetry, symmetry can be read out from the result

Disadvantage: The structure is randomly shifted in the cell -> it is necessary to locate the origin


Charge flipping does not use “atomicity” -> no problem to apply to superspace densities:

• The 3D density is replaced by a (3+d)D superspace density sampled using a (3+d)D grid

• The structure factors are indexed by (3+d) integer indices. They represent the coefficients of the Fourier transform of the superspace density.

No need to know the average structure!


All tested modulated structures could be solved by charge flipping:

structure symmetry composition VUC atoms

tantalum germanium telluride Pnma(00γ)s00 TaGe0.354Te2 347.3 16

lanthanum niobium sulphide F′m2m(α00)00s (LaS)1.14NbS2 439.9 5.32

4,4’-azoxyphenetole I2(α0γ)0 C16H18N2O3 1457.0 42

quininium (R)-mandelate P21(α0γ)0 C20H25N2O2+·C8H7O3

- 1214.6 70

tetraphenylphosphonium hexabromotellurate-(IV) bis{dibromoselenate(I)}

C2/m(α0γ)0s [(C6H5)4P]2

[TeBr6(Se2Br2)2]

2913.9 130

hexamethylenetetramine sebacate P21(α0γ)0 N4(CH2)6·(CH2)8(COOH)2 942.1 48

hexamethylenetetramine resorcinol I′mcm(0β0)s0s N4(CH2)6·C6H4(OH)2 1232.4 32

chromium(II) diphosphate C2/m(α β0)0s Cr2P2O7 258.7 24

Ce13Cd58 Amma(00γ)s00 Ce13Cd58 6692.3 77

d-QC AlCoNi 105/mmc Al70Co15Ni15

d-QC AlIrOs 105mc Al70Ir14.5Os12.5

i-QC AlPdMn Fm-3-5


tetraphenylphosphonium hexabromotellurate(IV)bis{dibromoselenate(I)}

<-CF

Br1

Fourier->

<-CF

C5

Fourier->

4086 out of 4247 reflections correctly phased (~96%)


published sectionfinal structure

as obtained from charge flipping

d-QC Al-Co-Ni, Steurer et al., Acta Cryst. B49, 1993


Requirements on the data:• Atomic resolution dmin=<1.0 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)


• Atomic resolution dmin=<1.0 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)




i-QC AlPdMn, unpublished neutron data provided by Marc de Boissieu

Solution: flip everything between - and + (Oszlanyi & Sütö, ECM23)




0

20

40

60

80

100

0.00 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

proportion of missing reflections

located atoms [%]

original charge flipping charge flipping with enhanced data

from Palatinus & Steurer, in preparation

Solution: extrapolate the missing reflections by MEM


-2 0 2 4 6 8 10 12

correct histogram histogram of partial solution



Two techniques to overcome this problem:

a) Repartitioning of the overlapping reflections according to the “flipped” structure factors (Wu et al. (2006), Nature Mater.)

b) Repartitioning using histogram matching (Baerlocher, McCusker & Palatinus (2006), submitted)


-2 0 2 4 6 8 10 12

correct histogram histogram of partial solution



Two techniques to overcome this problem:

a) Repartitioning of the overlapping reflections according to the “flipped” structure factors (Wu et al. (2006), Nature Mater.)

b) Repartitioning using histogram matching (Baerlocher, McCusker & Palatinus (2006), submitted)


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 δ

• Automatic search for the origin of the (super)space group

• Support for the histogram-matching procedure and

intensity repartitioning

• Continuous development

Palatinus & Chapuis (2006), http://superspace.epfl.ch/superflip


EDMA

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

Palatinus & van Smaalen, University of Bayreuth


s

d


s

d

d = (I-R).s


d = (I-R).s

How to find d?

Patterson function:

Symmetry correlation function:

S will have the “origin peak” at d


Example of a solution of a modulated structure:

QuickTime™ and aCinepak decompressor

are needed to see this picture.


δ determines the amount of the flipped density.If δ is too small, the perturbation of the density is too

small and the iteration does not converge.

If δ 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 δ can be determined easily by trial and error.

Parameter δ

Documents

Charge flipping in superspace, Aperiodic 2006, 21.9.2006 Structure solution of modulated structures by charge flipping in superspace Lukas Palatinus EPFL