This document summarizes Peter Zavalij's presentation on using restraints and constraints in the structure refinement program Reflex. It discusses how Reflex allows motion groups and torsion angles to reduce parameters during refinement. Examples are presented of using these to refine structures with motion groups in special positions and rigid fragments. Demonstrations show refinement with a motion group in FePO4, motion groups in special positions of Li[B(C2O4)2], a motion group and torsion angle in VO(C6H5PO3), and restraints in large molecules like azithromycin.

1. ACA 2005, Workshop WK.01
Structure Solution and Refinement
of Difficult Structures
Using Powder Diffraction
Peter Y. Zavalij
Department of Chemistry and Biochemistry
University of Maryland, College Park, MD
Restrained refinement using Reflex

2.  What is Reflex
 Restrains & Constraints
 Constraints in Reflex
 Examples of Restrained Refinement:
- Motion group (rigid-body) in FePO4
- Motion groups in special positions, Li & Na [B(C2O4)2]
- Motion group & torsion angle in VO(C6H5PO3)
- Restrains in large molecules
 Demonstration - Reflex restrained refinement
Outlines

3. Materials Studio / Relex
Materials Studio
provides wide range of computational methods on the desktop
in structural and computational chemistry and materials science
offering expert-level modeling and simulation
still in an easy-to-learn environment.
Accelrys Inc. (www.accelrys.com)
Materials Visualizer
- construction & manipulation of models/structures
Reflex
- powder pattern simulation
- ab initio indexing (ITO, TREOR, DICVOL & X-Cell1
)
- full pattern decomposition
- automatic space group determination
- structure refinement (the Rietveld method)
- determination of crystal structures (Reflex +)
Reflex works with any radiation and medium- to high-quality powder diffraction data.
1. Neumann, M. X-Cell - A Novel Indexing Algorithm for Routine Tasks and Difficult Cases, J. Appl. Cryst., 36, 356

4. Constraints
Constraints
• specify exact relationship between atomic or geometric parameters
• reduce number of variable parameters
For example:
- special relationship between atomic coordinate and displacement parameters
for atoms in special position,
e.g. atom on diagonal mirror plane (1 1 0 ) has x=y
- relationship between occupation factors,
e.g. 2 different atoms (or group) occupying the same position (space)
- H atoms in the fixed groups,
e.g. CH group in aromatic rings, -CH3 group, etc.
- rigid-body groups or molecules,
e.g. fixed geometry benzene rind

5. Restrains
Restrains
• specify approximate (desirable) relationship between geometric parameters
• increase number of variable parameters
For example:
- restrained composition (content of specific element in the unit cell)
- approximately equal distances or angles of the same type
- approximately flat groups
- approximately isotropic displacement parameters
- others

6. Constraints in Reflex
- Constraints on fractional atom positions and other geometric constraints are ignored
- Atoms that not included in a motion group or a torsion object are considered to be fixed
- Limits on the variation of a degree of freedom cannot be specified.
All degrees of freedom are either completely flexible or fixed
1
Relex automatically imposes symmetry constraints on:
• Lattice parameters
• Parameters of atoms in special positions
• Motion groups or torsion angles
Reflex allows only two type of constraints :
• Motion groups (rigid-body)
- a whole molecule, a molecular fragment or a single atom
• Torsion angles
- torsions of the molecular fragments within a motion group
• Individual atoms can be refined when defined as motion groups

7. Constraints in Reflex 2
From Reflex help:
Tip. Although Reflex allows you to define only translations, rotations, and intra-molecular torsions as degrees
of freedom, these types of degrees of freedom are sufficient to refine any desired degree of freedom, including
bond lengths and angles.
Degrees of Freedom of Motion Groups in special positions:
1
This column also shows degree of freedom of individual atoms
Symmetry Translation1
Rotation Total
1 3 3 6
-1 0 3 3
m 2 1 3
2 1 1 2
2/m 0 1 1
mm2 1 0 1
mmm, 222 0 0 0

8. 0
1000
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Intensity
2-theta
Rietveld Refinement: Rwp = 8.03% Rwp(w/o bck) = 8.63% Rp = 6.33%
Motion group in FePO4
• Monoclinic, P21/n
2 motion groups:
- PO4
3-
ion, general site – 6 parameters
- Fe atom, general site – 3 parameters
w/o constraints: 6 atoms – 24 parameters

9. 0
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Libob2.pro
2-theta
Bis-Oxalato-Borate (BOB)
BOB-
Ion
Max. symmetry4m2
Li Salt - Li[B(C2O4)2]
• Orthorhombic, Pnma
Pseudo-hexagonal lattice parameters

10. 0
1000
2000
3000
4000
5000
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7000
8000
9000
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10 20 30 40 50 60
Intensity
2-theta
Rietveld Refinement: Rwp = 12.59% Rwp(w/o bck) = 15.78% Rp = 10.00%
Li[B(C2O4)2]
m
• Orthorhombic, Pnma
2 motion groups:
- BOB ion, symmetry .m. – 3 parameters
- Li atom, same symmetry – 2 parameters
• w/o constraints (8×2+3×3) – 33 parameters

11. 0
10000
20000
30000
40000
50000
60000
70000
10 20 30 40 50 60 70 80
Intensity
2-theta
Rietveld Refinement: Rwp = 13.84% Rwp(w/o bck) = 18.43% Rp = 10.41%
NaBOB & KBOB
• Orthorhombic, Cmcm
2 motion groups:
- BOB ion, symmetry m2m – 1 parameter
- Metal atom, same symmetry – 1 parameter
• w/o constraints (2×1+12×2) – 26 parameters

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Title =
2-theta
Motion group & Torsion angle in VO(PhPO3)
• Monoclinic, C2
• 2 motion groups:
- PhPO3
2-
, general site – 6 parameters
and
- O atom, general site – 3 parameters
- V atom, general site – 2 parameters
or
- vanadyl V=O motion group
(if V-O distance is known)
• w/o constraints – 36 parameters

13. 0
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Intensity
2-theta
Rietveld Refinement: Rwp = 15.94% Rwp(w/o bck) = 22.62% Rp = 11.77%
Motion group & Torsion angle in VO(PhPO3)
• Monoclinic, C2
• 2 motion groups:
- PhPO3
2-
, general site – 6 parameters
- O atom, general site – 3 parameters
- V atom, general site – 2 parameters
• Torsion: – 1 parameter
- – Ph –– PO3 – torsion angle defining
orientation of PO3 group
• w/o constraints – 36 parameters

14. Azithromycin – Degrees of Freedom
• Orthorhombic, P212121
• 3 motion groups:
- Azithromycin molecule – 6 parameters
- 2 Water molecules (2×6) – 12 parameters
• Torsions: – 7 parameters
• w/o constraints (3×54) – 162 parameters
Courtesy Dr. Srebri Petrov, U. of Toronto

15. Azithromycin – Groups & Torsions
• Orthorhombic, P212121
• 3 motion groups:
- Azithromycin molecule – 6 parameters
- 2 Water molecules (2×6) – 12 parameters
• Torsions: – 7 parameters
• w/o constraints (3×54) – 162 parameters

16. Demonstration
1. Motion group in FePO4
2. Motion group in .m. site, Li[B(C2O4)2]
3. Motion group in mm2 site, Na[B(C2O4)2]
4. Motion group & torsion angle in VO(C6H5PO3)
5. Restrains in large molecules

17. Instead of Conclusions
Special thanks to Accelrys
for providing full version
of the Materials Studio
Rigid-Body in Torsion

18. Reflex References
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