ACA 2005, Workshop WK.01 ACA 2005, Workshop WK.01

Structure Solution and Refinement of Difficult Structures

Using Powder Diffraction

Peter Y. Zavalij

Department of Chemistry and BiochemistryUniversity of Maryland, College Park, MD

Restrained refinement using Reflex

Restrained refinement using Reflex

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

OutlinesOutlines

Materials Studio / RelexMaterials 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 (2003).

ConstraintsConstraints

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

RestrainsRestrains

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

Constraints in ReflexConstraints 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

Constraints in ReflexConstraints 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

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Intensity

2-theta

Rietveld Refinement: Rwp = 8.03% Rwp(w/o bck) = 8.63% Rp = 6.33%

FePO4_MoKa (Sim) FePO4_MoKa (Exp) Observed Reflections

Motion group in FePO4Motion group in FePO4

• Monoclinic, P21/n

2 motion groups:

- PO43- ion, general site – 6 parameters

- Fe atom, general site – 3 parameters

w/o constraints: 6 atoms – 24 parameters

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Libob2.pro

2-theta

Legend

Intensity vs. 2Theta(Deg)

Bis-Oxalato-Borate (BOB) Bis-Oxalato-Borate (BOB)

BOB- Ion

Max. symmetry4m2

Li Salt - Li[B(C2O4)2]

• Orthorhombic, Pnma

Pseudo-hexagonal lattice parameters

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Rietveld Refinement: Rwp = 12.59% Rwp(w/o bck) = 15.78% Rp = 10.00%

LIBOB (Sim) LIBOB2 (Exp) Difference Observed Reflections

Li[B(C2O4)2]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 (82+33) – 33 parameters

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Rietveld Refinement: Rwp = 13.84% Rwp(w/o bck) = 18.43% Rp = 10.41%

NABOB (Sim) NABOB (Exp) Difference Observed Reflections

NaBOB & KBOBNaBOB & KBOB

• Orthorhombic, Cmcm

2 motion groups:

- BOB ion, symmetry m2m – 1 parameter

- Metal atom, same symmetry – 1 parameter

• w/o constraints (21+122) – 26 parameters

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Title =

2-theta

Legend

Intensity vs. 2Theta(Deg)

Motion group & Torsion angle in VO(PhPO3)

Motion group & Torsion angle in VO(PhPO3)

• Monoclinic, C2• 2 motion groups:

- PhPO32-, general site – 6

parametersand

- 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

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Rietveld Refinement: Rwp = 15.94% Rwp(w/o bck) = 22.62% Rp = 11.77%

REFINE (Sim) NEW_pattern (Exp) Difference Observed Reflections

Motion group & Torsion angle in VO(PhPO3)

Motion group & Torsion angle in VO(PhPO3)

• Monoclinic, C2• 2 motion groups:

- PhPO32-, 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

Azithromycin – Degrees of FreedomAzithromycin – Degrees of Freedom

• Orthorhombic, P212121

• 3 motion groups:- Azithromycin molecule – 6 parameters- 2 Water molecules (26) – 12 parameters

• Torsions: – 7 parameters• w/o constraints (354) – 162 parameters

Courtesy Dr. Srebri Petrov, U. of Toronto

Azithromycin – Groups & TorsionsAzithromycin – Groups & Torsions

• Orthorhombic, P212121

• 3 motion groups:- Azithromycin molecule – 6 parameters- 2 Water molecules (26) – 12 parameters

• Torsions: – 7 parameters• w/o constraints (354) – 162 parameters

DemonstrationDemonstration

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

Instead of ConclusionsInstead of Conclusions

Special thanks to Accelrysfor providing full version

of the Materials Studio

Rigid-Body in Torsion

Reflex ReferencesReflex References

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(1991) 5. Caglioti, G.; Paoletti, A.B.; Ricci, F.P. "Choice of collimators for a crystal spectrometer for neutron diffraction", Nucl. Instrum. Meth., 3, 223-228 (1958).6. Cromer, D.T.; Weber, J.T. International Tables for X-ray Crystallography, Vol. IV, Ibers, J.A.; Hamilton, W.C., Eds., The Kynoch Press: Birmingham, 99-101

(1974).7. David, W.I.F. "Powder diffraction peak shapes. Parameterization of the pseudo-Voigt as a Voigt function", J.Appl.Cryst., 19, 63-64, (1986).8. Debye, P. Ann. Physik., 46, 809 (1915).9. Dollase, W.A. "Correction of intensities for preferred orientation in powder diffractometry: application of the March model", J. Appl. Cryst., 19, 267-272 (1986).10. Doyle, P.A.; Turner, P.S. "Relativistic Hartree-Fock X-ray and electron scattering factors", Acta Cryst., A24, 390 (1968).11. Engel, G.E.; Wilke, S.; Harris, K.D.M.; Leusen, F.J.J, J. Appl. Cryst. 32, 1169 (1999).12. Hermann, C. Z.Kristallogr., 68, 257-287 (1928). 13. Howard, C.J. "The Approximation of Asymmetric Neutron Powder Diffraction Peaks by Sums of Gaussians", J.Appl.Cryst. 15, 615 (1982).14. Finger, L.W.; Cox, D.E.; Jephcoat, A.P. "A Correction for Powder Diffraction Peak Asymmetry due to Axial Divergence" J. Appl. Cryst. 27, 892 (1994).15. Klug, H.P.; Alexander, L.E. X-ray Diffraction Procedures, 2nd Ed., John Wiley: New York (1974).16. Le Bail, A.; Duroy, H.; Forquet, J.L. Matter. Res. Bull. 23, 447-452 (1988). 17. Neumann, M. "X-Cell - A Novel Indexing Algorithm for Routine Tasks and Difficult Cases", J. Appl. Cryst., 36, 356 (2003). 18. Pawley, G.S. J. Appl. Cryst. 14, 357 (1981).19. Press, W.H.; Flannery, B.P.; Tuekolsky, S.A.; Vetterlin, W.T. Numerical Recipes , Cambridge University Press (1986).20. Rietveld, H.M. "A Profile Refinement Method for Nuclear and Magnetic Structures", J. Appl. Cryst., 2, 65-71 (1969).21. Scherrer, P. Gött. Nachr., 2, 98 (1918).22. Smith, G.S.; Snyder, R.L. J. Appl. Cryst. 12, 60-65 (1979). 23. Thompson, P.; Cox, D.E.; Hastings, J.B. "Rietveld Refinement of Debye-Scherrer Synchrotron X-ray Data from Al2O3", J.Appl.Cryst., 20, 79-83, (1987).24. Tomandl, R.L. Univ. Erlangen, Private Communication (1987).25. Toraya, H.; Marumo, F. Mineral. J., 10, 211 (1981).26. Visser, J.W. "A Fully Automatic Program for Finding the Unit Cell from Powder Data", J. Appl. Cryst., 2, 89 (1969). 27. Warren, B.E. X-ray Diffraction, Addison-Wesley: Reading (1969).28. Werner, P.E.; Eriksson, L.; Westdahl, M. "TREOR, a semiexhaustive trial-and-error powder indexing program for all symmetries", J. Appl. Cryst., 18, 367-370

(1985).29. Wilson, A.J.C. Mathematical theory of X-ray powder diffraction, Philips Technical Library: Eindhoven (1963).30. Yakimanski, A. V.; Kolb, U.; Matveeva, G. N.; Voigt-Martin, I. G.; Tenkovtsev, A. V. "The Use of Structure Analysis Methods in Combination with Semi-

empirical Quantum-Chemical Calculations for the Estimation of Quadratic Nonlinear Optical Coefficients of Organic Crystals", Acta. Cryst., A53, 603-614 (1997). 31. Young, R.A. The Rietveld Method , IUCr Monographies of Crystallography 5, Oxford University Press, Oxford (1993).