Solving Structures from Powder Data in Direct Space - State of the Art -

1
Solving Structures from Powder Data in Direct
Space - State of the Art - Armel Le
Bail Université du Maine, Laboratoire des oxydes
et Fluorures, CNRS UMR 6010, Avenue O. Messiaen,
72085 Le Mans Cedex 9, France. Email
alb_at_cristal.org
2
CONTENT Introduction Computer Programs DASH EAGE
R ENDEAVOUR ESPOIR FOX OCTOPUS POWDERSOLVE P
SSP SAFE SA (Simulated Annealing) TOPAS Conclus
ions / Advertisements / Tests with ESPOIR
3
Introduction The final SDPD step is always the
Rietveld method application. Going to this last
step needs at least an approximate model to be
improved by the Rietveld refinement and
eventually completed by further Fourier
difference synthesis. How can be obtained this
starting approximate (or sometimes complete)
model by a direct space approach is the only
question considered here. Not to mention that
before that structure solution step, you must
have yet recorded a powder pattern (so you must
have a sample), established that the structure is
unknown, indexed the powder pattern, proposed a
space group, and you must possess some chemical
knowledge of the sample.
4
The SDPD maze From the bookStructure
Determination from Powder Diffraction Data IUCr
Monographs on Crystallography 13 Oxford Science
Publications (2002)
5
Chemical Information Chemical knowledge is
indispensable to the application of the direct
space methods since they consist in placing
atoms, either independent or as a whole molecule,
at some positions in the cell, generally wrong
positions at the beginning of the process, and
moving them by translations (as well as rotations
for a molecule or polyhedron) up to obtain a
satisfying fit to the powder pattern or to a
mathematical representation of that pattern.
Going from wrong atomic positions to the final
roughly correct ones is made by a process called
global optimization which can be realized by
different but finally similar procedures Monte
Carlo (MC), Monte Carlo with simulated annealing
(SA) or/and with parallel tempering (PT), genetic
algorithm (GA). These processes present a
similarity in the use of random number sequences
atoms and molecules realize a random walk.
6
Some Definitions Sometimes the "direct space
methods" (not to be confused with the direct
methods) are called "global optimization methods"
or "model building methods", and even sometimes
"real space methods". "Direct space" was the
definition retained in the pioneering papers.
"Direct space" as opposed to "reciprocal space"
has an adequate crystallographic structural
sense, and should be preferred to "real space",
which, opposed to "imaginary" would call to mind
both parts of the diffusion factors. "Global
optimization" has a large sense and designates
the task of finding the absolutely best set of
parameters in order to optimize an objective
function, a task not at all limited to
crystallography.
7
Direct Space Pioneering PapersAlready an old
story M. W. Deem and J. M. Newsam, Nature 342 
(1989) 260-262M. W. Deem and J. M. Newsam, J.
Am. Chem. Soc. 114  (1992) 7189-7198J.W.
Newsam, M.W. Deem C.M. Freeman, Accuracy in
Powder Diffraction II, NIST Special Publication
846 (1992) 80-91. L.A. Solovyov S.D. Kirik,
Mat. Sci. Forum 133-136 (1993) 195-200. K.D.M.
Harris, M. Tremayne, P. Lightfoot P.G. Bruce,
J. Am. Chem. Soc. 116 (1994) 3543-3547. D.
Ramprasad, G.P. Pez, B.H. Toby, T.J. Markley
R.M. Pearlstein, J. Amer. Chem. Soc. 117 (1995)
10694-10701.
8
For instance J.W. Newsam, M.W. Deem C.M.
Freeman, Accuracy in Powder Diffraction II, NIST
Special Publication 846 (1992) 80-91.
9
Computer Programs - Nowadays
Selection of programs applying direct space
methods for the structure solution from powder
diffraction data Program Access GO
Data Example DoF DASH C S
A P Capsaicin 16 EAGER
A GA WP Ph2P(O)(CH2)7P(O)Ph2
18 ENDEAVOUR C SA I Ag2PdO2
45 ESPOIR O MC
L Gormanite 54 FOX O S
A WP Al2(CH3PO3)3 24 OCTOPUS A
MC WP Red Fluorescein 7 POWDERSO
LVE C MC WP Docetaxel 29 PSSP
O SA L Malaria Pigment Beta
Haematin 14 SAFE A SA WP C32N3O6H
53 23 SA A SA WP (CH
2CH2O)6LiAsF6 79 TOPAS C SA W
P Caffeine Anhydrous 93 Access C
Commercial with academic prices, O Open access,
A contact the authorsGO Global Optimization
MC Monte Carlo, SA MCSimulated Annealing,
GA Genetic AlgorithmData P Pawley, L Le
Bail, I Integrated intensities, WP Whole
PatternDoF degrees of freedom corresponding to
the example
10
Degrees of Freedom (DoF) Irrespectively to the
number of atoms, a molecule can be located easily
in a cell, as a rigid body, corresponding to 3
positional and 3 orientational degrees of freedom
(DoF), by checking the fit quality on, say, the
first 50 peaks of the diffraction pattern. But
the number of DoFs will increase by one for every
added free torsion angle, and more complications
arise if several independent molecules have to be
located altogether or/and if water molecules or
chlorine/sulphur/etc atoms are involved. For
inorganic compounds, in principle an atom in
general position corresponds to 3 DoFs (the three
xyz atomic coordinates), however, chemistry may
say if some polyhedra are to be expected, then an
octahedron for instance, instead of corresponding
to 7x321 DoFs when described by the atomic
coordinates, can be translated and rotated as a
whole polyhedron, corresponding to only 6 DoFs.
11
Flexibility Most of these computer programs are
also able to start from a complete set of
independent atoms, at random at the beginning,
and then will try to find their positions, moving
them while matching to the data. Combinations of
(several) molecules (or polyhedra) together with
independent atoms are of course possible.
Limitation The main difficulty may come finally
at the Rietveld refinement stage, if the powder
pattern quality becomes too low compared to the
number of parameters, then it will be necessary
to apply some constraints and/or restraints. And
it may be difficult to complete the structure
12
These computer programs are obtaining more and
more success, surpassing in number the solutions
by traditional approaches (Patterson or Direct
methods as applied in computer programs like
SHELXS - etc - or adapted to powder data in
EXPO). Nevertheless, the number of SDPD per year
remains quite small (close to 100, to be compare
to 30000 from single crystal data).
Cumulated histogram of the total number of
published SDPD. Picture from the SDPD Database
http//www.cristal.org/iniref.html
13
Comments
The following details about the direct space
computer programs were gathered and presented by
Yuri G. Andreev at the EPDIC-8 congress (Uppsala,
Suède, 2002), obtained from the authors
themselves. Things have not changed a lot after
two years.Note that EXPO2004/5 adds also now the
direct space approach to its traditional way to
solve structures (direct methods especially
adapted to powder data), and even can mix the two
approaches. To this list of programs may be
added a few others which have special abilities
for zeolites (ZEFSA-II, FOCUS, GRINSP).
14
DASH W.I.F. David and K. Shankland
Rutherford Appleton Laboratory,
further developed by J. Cole and J. van de Streek
CCDC, UK
SA
Correlated integrated intensities
Chem. Commun. 931 (1998)
Capsaicin - most complex structure in terms of
number of variables Chem. Commun. 931 (1998) 10
torsions and 6 external DoF.
Telmisartan forms A and B - fairly typical
structure J. Pharm. Sci. 89, 1465 (2000) 7
torsions and 6 external DoF.
Academics receive a 95 discount
15
EAGER K.D.M. Harris, R.L. Johnston, D. Albesa
Jové, M.H. Chao, E.Y. Cheung, S. Habershon, B.M.
Kariuki, O.J. Lanning, E. Tedesco, G.W.
Turner University of Birmingham, UK
Genetic Algorithm
Full profile
Acta Cryst. A, 54, 632 (1998)
Heptamethylene-1,7-bis(diphenylphosphane oxide)
Ph2P(O)(CH2)7P(O)Ph2 - typical structure. B.M.
Kariuki, P. Calcagno, K.D.M. Harris, D. Philp,
R.L. Johnston. Angew. Chem. Int. Ed.
38, 831 (1999). 35 non-H atoms in the a.u. 18 DoF
including 12 torsion angles.
Under active development
16
ENDEAVOUR K. Brandenburg and H. Putz, Crystal
Impact, Bonn, Germany
Combined global optimization of R-factor and
potential energy using SA
Integrated intensities
J.Appl.Cryst. 32, 864 (1999)
Ag2NiO2 - typical structure Schreyer and Jansen,
Sol. State Sci. 3(1-2), 25, (2001). 15 atoms in
the a.u. of P1. 45 DoF.
Available from Crystal Impact at reduced price
for academic users.
17
ESPOIR A. Le Bail, Universite du Maine, France
Reverse Monte Carlo and pseudo SA
Integrated intensities or full profile on a
pseudo powder pattern regenerated from extracted
Fobs
Mat. Sci. Forum 378-381, 65 (2001).
Souzalite/Gormanite Le Bail, Stephens and
Hubert, European J. Mineralogy 15 (2003) 719. 19
atoms in the a.u. of P-1. Fe at 0,0,0 54 DoF.
Free and Open - all available executable as
well as Fortran and Visual C source code (GPL -
GNU Public Licence).Web site http//www.cristal.
org/sdpd/espoir/
18
FOX V. Favre-Nicolin and R. Cerny, University of
Geneva, Switzerland (Free Objects for
Xtallography)
Parallel Tempering or SA. Automatic correction of
special positions and of sharing of atoms between
polyhedra, without any a priori knowledge
multi-pattern
Full profile, integrated intensities, partial
integrated intensities
J.Appl.Cryst. 35 (2002) 734.
Aluminum methylphosphonate Al2(CH3PO3)3 - most
complex structure Edgar et al. Chem. Commun. 808,
(2002). 3 molecules and 2 Al atoms in the
a.u. 24 DoF including bond lengths and bond
angles.
Free, open-source published under the GPL license
http//objcryst.sourceforge.net/
19
OCTOPUS K.D.M. Harris, M. Tremayne and B.M.
Kariuki University of
Birmingham, UK
Monte Carlo
Full profile
J. Am. Chem. Soc. 116, 3543 (1994).
Red fluorescein - typical structure. Tremayne,
Kariuki and Harris. Angew. Chem. Int. Ed. 36, 770
(1997). 25 non-H atoms in the a.u. 7 DoF
including 1 torsion angle.
Under active development
20
POWDERSOLVE (part of Reflex Plus integrated
package) G. Engel, S. Wilke, D. Brown, F.
Leusen, O. Koenig, M. Neumann, C.
Conesa-Morarilla Accelrys Ltd., Cambridge, UK
Monte Carlo SA and Monte Carlo parallel tempering
(Falcioni and Deem. J. Chem. Phys. 110
(1999)1754.)
Full profile
J. Appl.Cryst. 32, 1169 (1999)
Docetaxel (C43H53NO143H2O) - most complex
structure L. Zaske, M.-A. Perrin and F.
Leveiller, J. Phys. IV, Pr10, 221 (2001) 29 DoF
including 3 rotations, 12 translations and 14
torsion angles.
Can be purchased from Accelrys Inc., generous
discounts given to academic researchers
21
PSSP P. Stephens and S. Pagola State
University of New York, Stony Brook, (Powder
Structure Solution Program) USA
SA
Integrated intensities (Le Bail) with novel
handling of peak overlap
Submitted to J.Appl.Cryst. Preprint available on
http//powder.physics.sunysb.edu
Malaria Pigment Beta Haematin - most complex
structure. Pagola, Stephens, Bohle, Kosar, and
Madsen. Nature 404 307(2000) 43 non-H atoms in
the a.u. 14 DoF.
Free, including open source. Available at
http//powder.physics.sunysb.edu
22
SAFE S. Brenner, L.B. McCusker and Ch. Baerlocher
ETH Zentrum, Zurich, Switzerland (Simulated
Annealing and Fragment search within an Envelope)
Tri-?-peptide C32N3O6H53 - the most complex
structure. Brenner, McCusker and Baerlocher
J.Appl.Cryst. 35, 243 (2002) 17 torsion angles
and 6 positional and orientational DoF.
SA option of using a structure envelope.
Full-profile
Not ready for general distribution but will be in
public domain (still not by the end of 2004).
Verify at http//zeolites.ethz.ch/software/
J. Appl. Cryst. 35, 243 (2002)
23
Simulated Annealing Y. G. Andreev and P. G.
Bruce, University of St. Andrews
SA
Full-profile
J. Appl. Cryst. 30, 294 (1997)
Free, very user unfriendly. Requires changing of
the code for each new structure
determination. Customised molecular description
without Z-matrix input.
(CH2CH2O)6LiAsF6 - most complex structure.
MacGlashan, Andreev, and Bruce Nature 398
792(1999) 26 non-H atoms in the a.u. 79 DoF
including 15 torsion angles.
24
TOPAS A.A. Coelho, R.W.Cheary, A. Kern, T. Taut.
Bruker AXS GmbH,

Karlsruhe, Germany
SA (together with user definable penalty
functions, rigid bodies, various bond length
restraints and lattice energy minimization
techniques including user definable force fields)
Caffeine Anhydrous C8H10N4O2 Stowasser and
Lehmann, Abstract submitted to the XIX IUCr
Congress 5 molecules in the a.u. 93 DoF.
Full-profile or integrated intensities
J. Appl. Cryst. 33, 899 (2000)
Discounted price (500 ) for academic users.See
http//pws.prserv.net/Alan.Coelho/
25
Which software could solve the problems proposed
during two previous SDPD Round Robin ?
1998 SDPDRR DASH http//sdpd.univ-lemans.fr/SDPD
RR/ 2002 SDPDRR FOX and TOPAS http//www.crista
l.org/sdpdrr2/
26
CONCLUSIONS
The capacities for solving structures from powder
diffraction data have never been so efficient
than during the past 5-12 years evolutions. One
has to find his way in the SDPD maze and to
select the appropriate methods and computer
programs at each step of the problem
(identification - which should fail to establish
any relation with a known structure-, indexing,
whole pattern fitting with cell constraints,
structure solution, Rietveld refinement).
27
Advice
When a SDPD is decided, you know already the
complexity level. Then select the appropriate
radiation, a 3rd generation synchrotron pattern
being the best choice for complex cases. It is
better to wait a bit for a good pattern and to
solve the problem than to waste large time and
not to solve the problem. Applying direct space
methods requires generally much less data (3 to 5
intensities per degree of freedom may be
sufficient) than direct methods. However, big
organic or organometallic problems can be
completely solved only if one disposes of a
maximum of knowledge about the molecular formula
together with the most excellent data.
28
Use your common sense
Very complex molecules will present more serious
difficulties at the Rietveld structure refinement
stage the ratio of the effective number of
structure factors with the number of atomic
coordinates to refine may be as small as 3 or
less (because there is soon no accurate intensity
on the powder pattern at resolution d lt1.5 Å), so
that the model needs to be constrained/restrained.
This may lead to difficulties to locate some
additional water molecule, or to be absolutely
sure that there is not any misunderstanding
somewhere which could explain why the Bragg R
factor RB is going to be sometimes as large as 10
or 15. No need to say that some proposed H atom
positions will have sometimes a low credibility.
You will have to know  how much is too much ,
or your manuscript will be rejected (by a good
reviewer).
29
Advertisements
30
15 CD-ROM of this distance learning course are
available during this workshop (you may duplicate
them)
31
Sessions 1 and 2 are in free access, but after
that, you will not obtain the encrypted
solutions, nor help, nor the diploma, if you do
not pay the fees (250 for students in
developing countries)
32
This SDPD distance learning course provides
informations and guidance on the complete state
of the art, not only on a few selected
software. You will find inside of the CD-ROM
documents or internet links about everything
concerningStructure Determination by Powder
Diffractometry.
33
Next and ultimate (for today -) advertisement