Introduction to Sir2011

1. Introduction to Sir2011 Giovanni Luca Cascarano CNR- Istituto di Cristallografia – Bari - Italy

2. The crystalstructuresolution To solve a crystal structure, i.e. to obtain the atomic coordinates, different methods are available. We’ll focus our attention on Direct Methods, very popular and effective, able to give in a short time and in automatic way the solution to our problem: to compute the phases lost during the diffraction experiment (the so called Phase Problem). Once the phases are available it is possible to apply the Fourier Transform and get the electron density map whose maxima correspond to the atomic positions.

3. The crystalstructuresolution The phaseproblem Esperiment Crystallization I = |F|2  = ? Beam (X rays, electrons) Crystal Diffraction pattern Atomicmodel CrystallographicMethodologies Software Electron density map

4. The crystalstructuresolution The phaseproblem Esperiment Crystallization I = |F|2  = ? Beam (X rays, electrons) Crystal Diffraction pattern Atomicmodel CrystallographicMethodologies Software Electron density map

5. The crystalstructuresolution The phaseproblem Esperiment Crystallization I = |F|2  = ? Beam (X rays, electrons) Crystal Diffraction pattern Atomicmodel CrystallographicMethodologies Software Electron density map

6. The crystalstructuresolution The phaseproblem Esperiment Crystallization I = |F|2  = ? Beam (X rays, electrons) Crystal Diffraction pattern Atomicmodel CrystallographicMethodologies Software Electron density map

7. The phaseproblem If we define the structure factor Fh with indices h=(hkl) the electron density (r) for every point r in the unit cell is defined as: In this formula the |Fh| value is known from experiment, the phase of the structure factor h has to be recovered.

8. The structuralcomplexity • In Sir2011 the parameterrelatedto the structuralcomplexitygovernsmostof the algorithmsusedfor the automaticstructuresolution. • In the programthereis the followingclassification: • Verysmallsizestructures: up to 6 non-Hatoms in asymmetricunit • Smallsizestructures: 6-80 non-Hatoms in asymmetricunit • Mediumsizestructures: 81-300 non-Hatoms in asymmetricunit • Largesizestructures: more than 300 non-Hatoms in asymmetricunit

9. Program flow chart WILSON METHOD  (K, B) STRUCTURE FACTORS NORMALIZATION (|F||E|) STRUCTURE INVARIANTS CALCULATION (TRIPLETS AND QUARTETS) TANGENT FORMULA AND FIGURES OF MERIT DIRECT SPACE REFINEMENT AUTOMATIC STRUCTURE MODEL REFINEMENT

10. The multisolution approach Usually random phase values are assigned to a subset of strong reflections (those with the higher of |E|); by means of the triplets and of the tangent formula almost all the strong reflections can be phased. This procedure is repeated n times changing the values of the random phases and, for every obtained set of phases a suitable Figure of Merit (eFOM) is computed. Higher is the eFOM value, more likely the corresponding phase set is correct. These trials, sorted with respect to the eFom value, will be submitted to the automatic Direct Space Refinement (DSR).

11. Program flow chart WILSON METHOD  (K, B) STRUCTURE FACTORS NORMALIZATION (|F||E|) STRUCTURE INVARIANTS CALCULATION (TRIPLETS AND QUARTETS) TANGENT FORMULA AND FIGURES OF MERIT DIRECT SPACE REFINEMENT AUTOMATIC STRUCTURE MODEL REFINEMENT

12. Direct space refinement The number of reflections phased by the tangent formula is, in general, a small percentage of all reflections available. To extend and refine for all suitable reflections (i.e. those for which Fobs > 3(Fobs)) an iterative procedure is used, the Direct Space Refinement. The procedure is constituted by n cycles  where is the electron density map andis the set of calculated phases.

13. Direct space refinement The electron density maps are calculated by using a number of reflections cyclically increasing; a small fraction of  is used during the inversion of the electron density map, the remaining part is set to zero. To process a trial, EDM is applied a number of times, depending on structural complexity.

14. Program flow chart WILSON METHOD  (K, B) STRUCTURE FACTORS NORMALIZATION (|F||E|) STRUCTURE INVARIANTS CALCULATION (TRIPLETS AND QUARTETS) TANGENT FORMULA AND FIGURES OF MERIT DIRECT SPACE REFINEMENT AUTOMATIC STRUCTURE MODEL REFINEMENT

15. The DLSQ procedure Peaks are labelledin termsofatomicspeciesaccordingtotheirintensityand to the chemicalcontentof the unitcell; the atomiccoordinates and the isotropicthermalfactor are refinedusing a diagonalleastsquaresalgorithm. New valuesofphases and weights are computed and usedto produce a new electron density mapusing (2Fobs-Fcalc) coefficients. The DLSQ procedure stopswhen the crystallographicresidualRincreases.

16. The DLSQ procedure The DLSQ procedure stopswhen the crystallographicresidualRincreases. R = | |Fobs| – |Fcalc| | / |Fobs| Diagonal LeastSquares Fourier Recycling

17. The Directspacerefinement The DirectSpaceRefinement procedure stopswhen the R factorissmallerthan a giventhreshold (default value 25%)

18. What’s new Sir2011 is the latest product of the Sir family, in beta version at the moment. It includes many new features that will be described in the following slides.

19. What’s new • VLD procedure • Fourier map in a small volume • New features for electron diffraction data • New procedure to select the space group • Simulated Annealing • Integration with Jav, the new visualizer in 3D

20. The VLD procedure • Thisis a newcyclicphasingalgorithmwhichdoesnotuseDirect or Pattersonmethods: itisbasedonly on propertiesof a newdifference electron density and of the observed Fourier synthesis. Owingto the centralroleof the difference Fourier synthesis the methodhasbeencalled VLD (vive la différence) . • In sinergywith the RELAX procedure, ithasbeenappliedwith success bothtosmall/medium sizemolecules and toatomicresolutionproteins.

21. The VLD procedure • The VLD cycling processmaybedescribedby the followingsteps: • The difference Fourier q =  - psynthesisiscalculatedusing the following formula: • The differencemapissuitablymodified and inverted; the corresponding Fourier coefficients are combinedwith the normalizedstructurefactorsof the modelstructurebymeansof the tangent formula: • A newmapusing the observedstructurefactors and the phasesdefined in b) issubmittedto EDM cycles.

22. The VLD procedure DEDM Tangent NO Solution? EDM Stop YES

23. The VLD procedure DM vs VLD: results Averagetime in seconds and numberof test structures

24. The VLD procedure

25. The VLD procedure

26. The VLD procedure

27. What’s new • VLD procedure • Fourier map in a small volume • New features for electron diffraction data • New procedure to select the space group • Simulated Annealing • Integration with Jav, the new visualizer in 3D

28. Fourier map in part of the cell

29. Fourier map in part of the cell: Jav

30. Fourier map in part of the cell

31. Fourier map in part of the cell: Jav

32. What’s new • VLD procedure • Fourier map in a small volume • New features for electron diffraction data • New procedure to select the space group • Simulated Annealing • Integration with Jav, the new visualizer in 3D

33. New features for electron diffraction data If the crystal size is in the nanometric range, X-ray crystallography cannot be used because of both the weak interaction between X-ray and matter and the damage induced by high energy X-ray photons. Electrons interact with matter about 103-104 times stronger than X-ray and are therefore the ideal source to study such small single crystals. Electron diffraction can provide data up to 0.5 Å (and even more) but only 2D projections. A pseudo 3D set of reflections can be obtained by tilting the sample and merging different zone axes. Furthermore dynamical effects can reduce the reliability of the measured intensities.

34. New features for electron diffraction data The PED techniques reduce the number of reflections which are simultaneously excited and therefore allow to describe the scattering by few beam approximations, however 2-dimensional reflections from few well oriented zone axes are usually collected. More recently the combination of the ADT (Automated Diffraction Tomography) technique with PED has increased the data quality and completeness.

35. New features for electron diffraction data If PED techniques are used, the dynamical effects are no more dominant but still present. Two questions arise: 1) Is the average (over symmetry equivalent reflections) a good representative of the correct intensity? 2) In absence of a theoretical formulation establishing which of the equivalent reflections is less affected by dynamical scattering, can one use a practical criterion for selecting the best unique reflection?

36. New features for electron diffraction data BEAhas some similarity with a criterion used in powder crystallography during the phasing process: when a structural model is not available the experimental diffraction profile is decomposed according to LeBailor to Pawley algorithms; if a structural model is available, the experimental diffraction profile is partitioned in a way proportional to the calculated structure factors of the overlapping reflections.

37. New features for electron diffraction data In theBEA(Best Equivalent Amplitude)algorithm it is selected as unique reflection that one which better agrees with the current structural model. The effect is certainly cosmetic (the final RESID value may be much smaller than that obtained by using the average of the equivalent amplitudes). But it may also be substantial: i.e., the crystal structure solution becomes more straightforward and the final structural model may be more complete

38. New features for electron diffraction data Direct Methods applications, performed viathe last version of the program Sir2011including BEA, show that such algorithm is able to provide more complete structural models and better crystallographic residuals. More extended applications are needed to extrapolate the usefulness of BEA for the final refinement stages.

39. Test structure: Charoite89 atoms in a.u. I. Rozhdestvenskaya, E. Mugnaioli, M. Czank, W. Depmeier, U. Kolb, A. Reinholdt, T. Weirich, Mineralogical Magazine 74 (2010), 159-177.

40. What’s new • VLD procedure • Fourier map in a small volume • New features for electron diffraction data • New procedure to select the space group • Simulated Annealing • Integration with Jav, the new visualizer in 3D

41. New procedure to select the space group • A new algorithm has been developed for the automatic identification of the Laue group and of the extinction symbol from electron diffraction intensities. • The algorithm has a statistical basis, and tries to face the severe problems arising from the often non-kinematical nature of the diffraction intensities, from the limited accuracy of the lattice parameters determined via electron diffraction and from the limited amount of measured intensities.

42. New procedure to select the space group • First step • Since the accepted unit cell may show a lattice symmetry higher than the true one, all the crystal systems with unit cells compatible with that experimentally estimated (we will call them feasible systems) are taken into considerations for the next steps. • For example, in case of a cell with cubic geometry, tetragonal, orthorhombic, monoclinic and triclinic systems are considered feasible, hexagonal and trigonal are excluded. • Second step • The list of the Laue groups compatible with each feasible crystal system is automatically generated (denoted as admittedLaue groups).

43. New procedure to select the space group • Third step • For each feasible crystal system the admitted Laue group with minimal symmetry (say LGmin) is considered. For each i-th admitted Laue group the internal residual factor Rint(i) is calculated: • The probability of the i-thLaue group is:

44. New procedure to select the space group • The final probabilistic formula for identifying the most probable extinction symbol, and simultaneously, for confirming the most probable Laue group and crystal system is: • associated to the i-th admitted Laue group and the j-th extinction symbol

45. New procedure to select the space group Charoite Cell 31.91 19.64 7.09 90 9090 Space Group: P 21/m

46. New procedure to select the space group

47. What’s new • VLD procedure • Fourier map in a small volume • New features for electron diffraction data • New procedure to select the space group • Simulated Annealing • Integration with Jav, the new visualizer in 3D

48. Simulated Annealing

49. Simulated Annealing

50. Simulated Annealing