1. Advanced Crystallography: Refinement of Disordered Structures
November 13, 2012
Disorder Webinar

2. This Webinar is being broadcast from our Madison, Wisconsin, USA, facility
November 13, 2012
Disorder Webinar

3. Charles Campana, Ph.D.
Senior Applications Scientist at Bruker AXS, Madison, WI, USA
BS, Chemistry (1970), Montana State University, Bozeman, Montana
PhD (1975), Inorganic Chemistry (with L. F. Dahl), University of Wisconsin, Madison, Wisconsin
Assistant Professor (1976 – 1980), University of New Mexico University, Albuquerque, New Mexico
Senior Applications Scientist ( present) Single-Crystal X-ray Diffraction, Nicolet, Siemens and Bruker;
Crystallographic co-author on several hundred scientific papers.
November 13, 2012
Disorder Webinar

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November 13, 2012

5. Introduction
Modern X-ray crystallographic systems with automatic features have made it possible for synthetic chemists with limited crystallographic training to obtain publication-quality crystal structures quickly and easily for routine structures.
While the automated structure routines perform well on straight-forward molecular compounds, these routines are not capable of automatically modeling various disorder problems.
In these cases, the user must utilize some of the advanced SHELXL/XL instructions involving the use of free variables, constraints and restraints to successfully refine and publish his / her results.
All of these techniques involve editing the SHELXL/XL output (*.res) file, with either a text editor or a specialized graphical editor, to produce a new, modified SHELXL/XL input (*.ins) file.
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6. George Sheldrick
Professor of Structural Chemistry and part-time programming technician at the University of Göttingen
PhD (1966) University of Cambridge with E.A.V. Ebsworth; thesis entitled "NMR Studies of Inorganic Hydrides"
: University Lecturer and Fellow of Jesus College, Cambridge
Since 1978 Professor at the University of Göttingen
Since 2011 Niedersachsen Professor at the University of Göttingen (emeritus)
Author of about 800 scientific papers and of a computer program called SHELX (
Sheldrick, GM (2008) A short history of SHELX. Acta Crystallogr., A64: (open access) This paper is currently the most highly cited scientific paper of the last five years in all subjects.
November 13, 2012
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7. SHELX References
A short history of SHELX, Sheldrick, GM (2008) (
SHELX Manual (
Crystal Structure Refinement: A Crystallographer's Guide to SHELXL (International Union of Crystallography Texts on Crystallography)
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8. SHELXTL vs. SHELX* http://shelx.uni-ac.gwdg.de/SHELX/index.html
SHELXTL (Bruker AXS)
XPREP XS XM XE XL
XPRO
XWAT XP
XSHELL
XCIF
SHELX (Public Domain)*
None
SHELXS
SHELXD
SHELXE
SHELXL
SHELXPRO
SHELXWAT
CIFTAB
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Disorder Webinar

9. Peter Müller, MIT Director of the Diffraction Facility
MIT Department of Chemistry
Cambridge, Massachusetts
November 13, 2012
Disorder Webinar

10. Objectives of this presentation
Use of text editors or graphical editors to insert additional instructions into SHELXL / XL input instruction (*.ins) files.
Introduction to the concepts of constraints and restraints in crystal structure refinement.
Introduction to the internal atom connectivity concept and PART n and PART –n instructions.
Introduction to the use of free variables in constraints and restraints.
Examples of commonly used instructions for applying a variety of constraints and restraints to the refinement of disordered structures.
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11. Constraints and Restraints
In crystal structure refinement, there is an important distinction between a 'constraint' and a 'restraint'.
A constraint enables one or more least-squares variables to be expressed exactly in terms of other variables or constants, and hence eliminated.
A restraint takes the form of additional information which is not exact but is subject to a probability distribution; for example we could restrain two chemically but not crystallographically equivalent bonds to be approximately equal.
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12. Constraints and Restraints in SHELXL
The following general categories of constraints and restraints are available using SHELXL:
Constraints for the coordinates and anisotropic displacement parameters for atoms on special positions: these are generated automatically by the program for ALL special positions in ALL space groups, in conventional settings or otherwise.
Floating origin restraints: these are generated automatically by the program, so the user should not attempt to fix the origin in such cases by fixing the coordinates of a heavy atom.
Two or more atoms sharing the same site: the xyz and Uij parameters may be equated using the EXYZ and EADP constraints respectively (or by using 'free variables'). The occupation factors may be expressed in terms of a 'free variable' so that their sum is constrained to be constant (e.g. 1.0). If more than two different chemical species share a site, a linear free variable restraint (SUMP) is required to restrain the sum of occupation factors.
Geometrical constraints: these include rigid-group refinements (AFIX 6), variable-metric rigid-group refinements (AFIX 9) and various riding models (AFIX/HFIX) for hydrogen atom refinement, for example torsional refinement of a methyl group about the local threefold axis.
November 13, 2012
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13. Constraints and Restraints in SHELXL
Fragments of known geometry may be fitted to target atom, and the coordinates generated for any missing atoms. Four standard groups are available: regular pentagon, regular hexagon, naphthalene and pentamethylcyclopentadienyl. Other groups may be used simply by specifying orthogonal or fractional coordinates in a given cell (AFIX mn with m > 16 and FRAG...FEND).
Geometrical restraints: a particularly useful restraint is to make chemically but not crystallographically equivalent distances equal without having to invent a value for this distance (SADI). The SAME instruction can be used to generate such restraints automatically, e.g. when chemically identical molecules or residues are present. This has the same effect as making equivalent bond lengths and angles but not torsion angles equal. The FLAT instruction restrains a group of atoms to lie in a plane (but the plane is free to move and rotate).
Restraints on anisotropic displacement parameters: three different types of restraint may be applied to Uij values. DELU applies a 'rigid-bond' restraint to Uij of two bonded (or 1,3) atoms; the anisotropic displacement components of the two atoms along the line joining them are restrained to be equal. Isolated atoms may be restrained to be approximately isotropic (ISOR). Similarly, the assumption of 'similar' Uij values for spatially adjacent atoms (SIMU) is useful for partially overlapping atoms of disordered groups.
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14. Types of constraints in SHELXL
Constraints for special positions: the necessary constraints on co-ordinates, occupancies and Uij are derived automatically.
Rigid groups (AFIX 6 … AFIX 0): the 3 positional parameters per atom are replaced by 3 rotations and 3 translations for the whole rigid group. Atoms may not be in more than one rigid group.
Riding hydrogen atoms (AFIX mn): xH = xC + x – no extra positional parameters.
Fixed parameters: add 10 to x, y, z, occ, U etc. Typically occupancies are fixed at 1.0 by adding 10, i.e. given as 11.0
Free variables: can be used to add extra linear constraints to the usual refinement parameters and also be used instead of restraint target values. This provides a convenient way of getting target values with esd’s for use as restraints in other structures.
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15. Special position constraints
Example: Atom on twofold axis in space group C2. The two positions related by the twofold axis (x,y,z: -x,y,-z) coincide when x = 0 and z = 0. Since we still wish to sum over all symmetry operators in the structure factor calculation, the occupancy is fixed at The probability ellipsoid used to describe the anisotropic motion should not be changed by the 180º rotation.
[U11, U22, U33, U23, U13, U12]  [U11, U22, U33, -U23, U13, -U12] which is only true if U23 = 0 and U12 = 0. All these constraints are generated automatically by SHELXL for all special positions in all space groups.
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16. Rigid group constraints
In SHELXL, rigid groups are defined by three rotations about the first atom in the group and by three translations of the group as a whole. Special position constraints may be applied to the first atom and restraints and riding hydrogen atoms are allowed on all atoms in the group. Note that the esd’s of bond lengths and angles but not of co-ordinates within a rigid group come out as zero from the L.S. matrix algebra.
AFIX rigid group – all AFIX 9 variable metric
… bond lengths and … rigid group - angles
atoms angles fixed atoms fixed, bond lengths
… … multiplied by the
AFIX AFIX 0 same factor
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17. The connectivity list
The connectivity list is used for the automatic generation of hydrogen atoms and some restraints. Non-hydrogen atoms i and j are considered to be ‘bonded’ if:
dij < ri + rj Å
The CONN instruction may be used to modify r and to set a maximum connectivity for an atom (e.g. 0 for water). A shell of symmetry equivalents is generated automatically around the unique atoms. Bonds may be added with BIND or deleted with FREE.
PART N controls the generation of bonds for disordered groups. Most atoms have N = 0; multiple conformations have N = 1, 2 etc. Bonds are generated only when the N are equal or one N is zero. If N is negative, bonds are not made to symmetry equivalents.
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Disorder Webinar

18. Free variables
Free variables are an extremely concise but effective way of applying linear constraints to atom parameters (especially occupancies), restraint targets etc. The parameter x is given as (10m+p), which is interpreted as follows:
m = 0: refine normally, starting at value p
m = 1: fix at value p
m > 1: x = p* fv(m)
m <-1: x = p* [fv(–m) – 1]
e.g., (m = 3, p = 0.25) means 0.25*[fv(3)] and –30.25 (m = –3, p = –0.25) means 0.25*[1 – fv(3)], which could be used to constrain two occupancies to add up to 0.25 (only one parameter, free variable #3, is refined). The starting values for the free variables are given on the FVAR instruction (but free variable #1 is the overall scale factor).
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19. Standard SHELX Instructions
TITL YLID in P2(1)2(1)2(1)
CELL
ZERR
LATT -1
SYMM 0.5-X, -Y, 0.5+Z
SYMM -X, 0.5+Y, 0.5-Z
SYMM 0.5+X, 0.5-Y, -Z
SFAC C H O S
UNIT
TEMP
SIZE
L.S. 4
BOND
FMAP 2
PLAN 20
FVAR S C C O C C C C C C O C C C
HKLF 4
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20. Graphical Editors for SHELXL/XL files
XP (Bruker AXS Inc.)
XShell (Bruker AXS Inc.)
APEX2 (Bruker AXS Inc.)
WinGX (L. Farrugia)
Crystals (D. Watkin et al.)
X-Seed (L. Barbour)
shelXle (C. Hubschle et al.)
OLEX2 (O. Dolomanov et al.)
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21. Two cations sharing the same site
The best strategy is to constrain the positions and displacement parameters to be the same, and refine the occupancies so that their sum is constrained to be unity:
EXYZ MG CA
EADP MG CA
FVAR ..
PART 1 MG
PART 2 CA
PART 0
If the cations were sharing a special position on a twofold axis, their occupancies would be specified as 20.5 and – For three atoms (or molecules) sharing a site, it is better to tether each occupancy to a free variable (e.g. by 31, 41 and 51) and to restrain the sum of these free variables to unity:
SUMP
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22. DFIX or SADI?
The DFIX restraint is able to restrain bond lengths to target values but sometimes the target is uncertain. For example the P―O distance in a phosphate may vary with the pH and the extent of libration. SADI can be very useful in such cases, e.g.
SADI P O1 P O2 P O3 P O4
SADI O1 O2 O1 O3 O1 O4 O2 O3 O2 O4 O3 O4
ensures that the phosphate will be a regular tetrahedron, but allow the bond length to refine.
The same can however be achieved by an AFIX 9 constraint or by using DFIX with a free variable, e.g.
FVAR …… …… 1.55
DFIX 31 P O1 P O2 P O3 P O4
DFIX O1 O2 O1 O3 O1 O4 O2 O3 O2 O4 O3 O4
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23. The rigid-bond restraint DELU
In SHELXL, the DELU restraint is a strict rigid-bond restraint, i.e. the components of the anisotropic motion of two atoms along the line joining them are restrained to be equal.
Although DELU is a reliable restraint and so can be given a small esd, there are not as many DELU restraints as Uij, so it may be necessary to supplement them with the less accurate but more numerous SIMU and ISOR restraints with larger esd’s.
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24. Restraints on ADP's
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25. Toluene on an inversion center
Toluene is a good solvent for growing crystals because of its long liquid range, but it simply cannot resist inversion centers:
This can be handled with one complete toluene molecule with occupancies of 10.5 (fixed at 0.5) and PART -1. Equivalent 1,2- and 1,3-distances can be restrained to be equal with SADI and a FLAT restraint applied to all 7 carbons, or a rigid hexagon can be used for the 6-membered ring (plus two SADI and one CHIV for the CH3). SIMU and DELU are recommended. The hydrogen atoms should be set with HFIX in a later job:
HFIX 43 C1 > C5 (generates 5H with occupancies of 0.5)
HFIX 123 C (generates 6H with occupancies of 0.25)
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26. Use of PART 1, PART 2 and SAME
ISOR
DELU
WGHT
FVAR
PART 1
C1A = .
C17A =
AFIX 43
H17A
AFIX 0
PART 2
SAME C1A > C17A
C1B =
C17D =
H17D
PART 0
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27. Use of PART 1, PART 2 and SAME
Part Part Parts 1 & 2
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28. Ethyl acetate disordered about a 2-fold axis
FVAR
C = .
O =
SAME C1 > O6
PART -1
C1' =
AFIX 0
O6' =
PART 0
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29. Disordered t-butyl group
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30. Disorder between Cl and C
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31. Disorder of a cyclopentadienyl ring
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32. November 13, 2012
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33. Disorder of a chloroform molecule on a mirror plane
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34. DMSO disordered over three positions
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35. Example 1 - Os3(CO)10(PPh2~PPh2)
Background
Sample from UCSD Summer School
Prof. Michael Richmond et al. (U. of North Texas)
NMR indicated dynamic equilibrium between two isomers
Structure was easily ‘solved’, but could not be refined
R1 = 16%
Many NPD atoms
Three very large difference peaks (‘Star of David’)
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36. Example 1 - Os3(CO)10(PPh2~PPh2)
preliminary structure – chelating phosphine ligand
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37. Example 1 - Os3(CO)10(PPh2~PPh2)
L.S. 4
BOND
FMAP 2
PLAN 99
WGHT
FVAR
ANIS 3 OS OS OS
C1A
O1A
C2A
O2A
C3A
O3A
C4A
O4A
C5A
O5A
C6A
O6A
C7A
O7A
C8A
O8A
C9A
O9A
C10A
O10A
ANIS 2 P P C C C
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38. Example 1 - Os3(CO)10(PPh2~PPh2)
three large difference peaks
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39. Example 1 - Os3(CO)10(PPh2~PPh2)
L.S. 4
BOND
FMAP 2
PLAN 99
WGHT
FVAR
PART 1
ANIS 3 OS OS OS
PART 2 OS OS OS
C1A
O1A
C2A
O2A
...
C9A
O9A
C10A
O10A
PART 0
ANIS 2 P P C C
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40. Example 1 - Os3(CO)10(PPh2~PPh2)
remaining carbonyl atoms revealed in difference map
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41. Example 1 - Os3(CO)10(PPh2~PPh2)
superposition of both isomers
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42. Example 1 - Os3(CO)10(PPh2RPPh2)
chelating phosphine ligand (85%)
bridging phosphine ligand
(15%)
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43. Example 1 - Os3(CO)10(PPh2~PPh2)
Crystallographic restraints (SADI, ISOR, SIMU, EADP) were used in initial refinement
Final refinement converged at R1 = 5.2%
Kandala, S.; Yang, L.; Campana, C. F.; Nesterov, V.; Wang, X.; Richmond, M. G. (2010) Isomerization of the diphosphine ligand 3,4-bis(diphenylphosphino)-5-methoxy-2(5H)-furanone (bmf) at a triosmium cluster and P-C bond cleavage in the unsaturated cluster 1,1-Os3(CO)9(bmf): Synthesis and x-ray diffraction structures of the isomeric Os3(CO)10(bmf) clusters and HOs3(CO)8(μ-C6H4)[μ-PhPC:C(Ph2P)CH(OMe)OC(O)]. Polyhedron, 29,
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44. Example 2 – Urea Host : Guest Complex
Background
Prof. Mark Hollingsworth et al. (Kansas State U.)
Urea host lattice with long-chain carboxylic acid in channels
Structure of urea lattice was ‘solved’, but carboxylic acid molecules could not be located
Apparent unit cell
Orthorhombic P212121
a = Å , b = Å , c = Å
12 Urea molecules, 4 carboxylic acid molecules per cell
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45. Example 2 – Urea Host : Guest Complex
projection down b-axis
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46. Example 2 – Urea Host : Guest Complex
Projection down a-axis
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47. Example 2 – Urea Host : Guest Complex
analysis of Q-peaks
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48. Example 2 – Urea Host : Guest Complex
analysis of Q-peaks
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49. Example 2 – Urea Host : Guest Complex
N2C
AFIX 93
H2CA
H2CB
AFIX 0
PART -1
C1S
O1S
O2S
AFIX 3
H2S
C2S
AFIX 23
H2SA
H2SB
....
C10S
H10A
H10B
C11S
O3S
O4S
H4S
PART 0
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50. Example 2 – Urea Host : Guest Complex
Anisotropic refinement of dicarboxylic acid
Final refinement
R1 = 3.83%
Temperature factors on hydrogen atoms refined
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51. Example 3 - Fe3(CO)12 Crystallographic Problem
Space group is P21/n with Z = 2
Each molecule must lie on a crystallographic center of symmetry
Successful refinement is difficult because it requires two half-weighted molecules superimposed on the center of symmetry

52. Example 3 - Fe3(CO)12 Refinement Results
100K Data
Resolution – 0.40Å
R1 = 3.82%
wR2 = 9.14%
12633 Ind. Refl.
298K Data
Resolution – 0.65Å
R1 = 5.11%
wR2 = %
2989 Ind. Refl.

53. Example 3 - Fe3(CO)12 November 13, 2012 Disorder Webinar PART -1
FE =
FE =
C =
O =
C =
O =
C =
O = .
C =
O =
C =
O =
PART 0
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Disorder Webinar

54. Example 3 - Fe3(CO)12 - shelXle diagrams
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55. 50% Thermal Ellipsoids
100K
298K

56. Example 3 - Fe3(CO)12 Bond Lengths
100K
Fe(1) -Fe(2) (3) Å
Fe(2)- Fe(3) (3) Å
Fe(2)-Fe(3) (4) Å
Fe(2)-C(1) (4) Å
Fe(2)-C(2) (4) Å
Fe(3)-C(1) (4) Å
Fe(3)-C(2) (4) Å
298K
Fe(1) -Fe(2) (11) Å
Fe(2)- Fe(3) (11) Å
Fe(2)-Fe(3) (12) Å
Fe(2)-C(1) (8) Å
Fe(2)-C(2) (8) Å
Fe(3)-C(1) (8) Å
Fe(3)-C(2) (8) Å

57. Example 3 - Fe3(CO)12 Bond Lengths
100K
Fe(1) -Fe(2) (3) Å
Fe(2)- Fe(3) (3) Å
Fe(2)-Fe(3) (4) Å
Fe(2)-C(1) (4) Å
Fe(2)-C(2) (4) Å
Fe(3)-C(1) (4) Å
Fe(3)-C(2) (4) Å
C(1)-O1) 1.161(3) Å
C(2)-O(2) 1.163(3) Å
298K
Fe(1) -Fe(2) (11) Å
Fe(2)- Fe(3) (11) Å
Fe(2)-Fe(3) (12) Å
Fe(2)-C(1) (8) Å
Fe(2)-C(2) (8) Å
Fe(3)-C(1) (8) Å
Fe(3)-C(2) (8) Å
C(1)-O1) 1.088(6) Å
C(2)-O(2) 1.112(6) Å

58. Example 3 - Fe3(CO)12 Comparison of 100K and 298K Structures

59. Example 3 - Fe3(CO)12 Conclusions
Collection of low temperature (100K) data to high resolution (0.40 Å) facilitates the separation of overlapped peaks in the disordered structure. The refinement of the structure using the PART -1 instruction in SHELX(TL) allows a stable refinement of the Fe3(CO)12 structure with no restraints. The final structure a 100K exhibits only minor deviations from idealized C2v molecular symmetry with symmetrically bridging carbonyl ligands. Although the results of the lower resolution (0.65 Å) dataset collected at room temperature are not as precise, both structures are nearly superimposable with the 100K structure.

60. Review and Conclusions
Use of text editors or graphical editors to insert additional instructions into SHELXL / XL input instruction (*.ins) files.
Introduction to the concepts of constraints and restraints in crystal structure refinement.
Introduction to the internal atom connectivity concept and PART n and PART –n instructions.
Introduction to the use of free variables in constraints and restraints.
Examples on commonly used instructions for applying a variety of constraints and restraints to the refinement of disordered structures.
November 13, 2012

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62. Available at www. bruker
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