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Erice 2011 Electron Crystallography – June 2-12 2011 Introduction to Sir2011 Giovanni Luca Cascarano CNR- Istituto di Cristallografia – Bari - Italy.

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Presentation on theme: "Erice 2011 Electron Crystallography – June 2-12 2011 Introduction to Sir2011 Giovanni Luca Cascarano CNR- Istituto di Cristallografia – Bari - Italy."— Presentation transcript:

1 Erice 2011 Electron Crystallography – June Introduction to Sir2011 Giovanni Luca Cascarano CNR- Istituto di Cristallografia – Bari - Italy

2 Erice 2011 Electron Crystallography – June 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. The crystal structure solution

3 Erice 2011 Electron Crystallography – June I = |F| 2  = ? The phase problem Esperiment Atomic model Crystallographic Methodologies Beam (X rays, electrons) Crystal Diffraction pattern Software Electron density map The crystal structure solution Crystallization

4 Erice 2011 Electron Crystallography – June I = |F| 2  = ? The phase problem Esperiment Atomic model Crystallographic Methodologies Beam (X rays, electrons) Crystal Diffraction pattern Software Electron density map The crystal structure solution Crystallization

5 Erice 2011 Electron Crystallography – June I = |F| 2  = ? The phase problem Esperiment Atomic model Crystallographic Methodologies Beam (X rays, electrons) Crystal Diffraction pattern Software Electron density map The crystal structure solution Crystallization

6 Erice 2011 Electron Crystallography – June I = |F| 2  = ? The phase problem Esperiment Atomic model Crystallographic Methodologies Beam (X rays, electrons) Crystal Diffraction pattern Software Electron density map The crystal structure solution Crystallization

7 Erice 2011 Electron Crystallography – June The phase problem If we define the structure factor F h with indices h=(hkl) the electron density  (r) for every point r in the unit cell is defined as: In this formula the |F h | value is known from experiment, the phase of the structure factor  h has to be recovered.

8 Erice 2011 Electron Crystallography – June The structural complexity In Sir2011 the parameter related to the structural complexity governs most of the algorithms used for the automatic structure solution. In the program there is the following classification:  Very small size structures: up to 6 non-H atoms in asymmetric unit  Small size structures: 6-80 non-H atoms in asymmetric unit  Medium size structures: non-H atoms in asymmetric unit  Large size structures: more than 300 non-H atoms in asymmetric unit

9 Erice 2011 Electron Crystallography – June TANGENT FORMULA AND FIGURES OF MERIT WILSON METHOD  (K, B) STRUCTURE FACTORS NORMALIZATION (|F|  |E|) STRUCTURE INVARIANTS CALCULATION (TRIPLETS AND QUARTETS) DIRECT SPACE REFINEMENT AUTOMATIC STRUCTURE MODEL REFINEMENT Program flow chart

10 Erice 2011 Electron Crystallography – June 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). The multisolution approach

11 Erice 2011 Electron Crystallography – June TANGENT FORMULA AND FIGURES OF MERIT WILSON METHOD  (K, B) STRUCTURE FACTORS NORMALIZATION (|F|  |E|) STRUCTURE INVARIANTS CALCULATION (TRIPLETS AND QUARTETS) DIRECT SPACE REFINEMENT AUTOMATIC STRUCTURE MODEL REFINEMENT Program flow chart

12 Erice 2011 Electron Crystallography – June 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 F obs > 3  (F obs )) 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 Erice 2011 Electron Crystallography – June 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. Direct space refinement

14 Erice 2011 Electron Crystallography – June TANGENT FORMULA AND FIGURES OF MERIT WILSON METHOD  (K, B) STRUCTURE FACTORS NORMALIZATION (|F|  |E|) STRUCTURE INVARIANTS CALCULATION (TRIPLETS AND QUARTETS) DIRECT SPACE REFINEMENT AUTOMATIC STRUCTURE MODEL REFINEMENT Program flow chart

15 Erice 2011 Electron Crystallography – June The DLSQ procedure Peaks are labelled in terms of atomic species according to their intensity and to the chemical content of the unit cell; the atomic coordinates and the isotropic thermal factor are refined using a diagonal least squares algorithm. New values of phases and weights are computed and used to produce a new electron density map using (2F obs -F calc ) coefficients. The DLSQ procedure stops when the crystallographic residual R increases.

16 Erice 2011 Electron Crystallography – June The DLSQ procedure The DLSQ procedure stops when the crystallographic residual R increases. R =  | |F obs | – |F calc | | /  |F obs | Fourier Recycling Diagonal Least Squares

17 Erice 2011 Electron Crystallography – June The Direct space refinement The Direct Space Refinement procedure stops when the R factor is smaller than a given threshold (default value 25%)

18 Erice 2011 Electron Crystallography – June 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. What’s new

19 Erice 2011 Electron Crystallography – June 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 Erice 2011 Electron Crystallography – June The VLD procedure This is a new cyclic phasing algorithm which does not use Direct or Patterson methods: it is based only on properties of a new difference electron density and of the observed Fourier synthesis. Owing to the central role of the difference Fourier synthesis the method has been called VLD (vive la différence). In sinergy with the RELAX procedure, it has been applied with success both to small/medium size molecules and to atomic resolution proteins.

21 Erice 2011 Electron Crystallography – June The VLD procedure The VLD cycling process may be described by the following steps: a)The difference Fourier  q =  -  p synthesis is calculated using the following formula: b)The difference map is suitably modified and inverted; the corresponding Fourier coefficients are combined with the normalized structure factors of the model structure by means of the tangent formula: c)A new map using the observed structure factors and the phases  defined in b) is submitted to EDM cycles.

22 Erice 2011 Electron Crystallography – June The VLD procedure Stop Tangent EDM Solution? YES NO DEDM

23 Erice 2011 Electron Crystallography – June The VLD procedure MethodSmall < 80Medium Macro > 200 Direct Methods5 (33/33)319 (23/23)1728 (16/35) VLD7 (33/33)246 (23/23)1844 (24/35) DM vs VLD: results Average time in seconds and number of test structures

24 Erice 2011 Electron Crystallography – June The VLD procedure

25 Erice 2011 Electron Crystallography – June The VLD procedure

26 Erice 2011 Electron Crystallography – June The VLD procedure

27 Erice 2011 Electron Crystallography – June 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 Erice 2011 Electron Crystallography – June Fourier map in part of the cell

29 Erice 2011 Electron Crystallography – June Fourier map in part of the cell: Jav

30 Erice 2011 Electron Crystallography – June Fourier map in part of the cell

31 Erice 2011 Electron Crystallography – June Fourier map in part of the cell: Jav

32 Erice 2011 Electron Crystallography – June 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 Erice 2011 Electron Crystallography – June 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 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 Erice 2011 Electron Crystallography – June 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 Erice 2011 Electron Crystallography – June 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 Erice 2011 Electron Crystallography – June New features for electron diffraction data BEA has 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 LeBail or 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 Erice 2011 Electron Crystallography – June New features for electron diffraction data In the BEA (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 Erice 2011 Electron Crystallography – June New features for electron diffraction data Direct Methods applications, performed via the last version of the program Sir2011 including 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 Erice 2011 Electron Crystallography – June Test structure: Charoite 89 atoms in a.u. I. Rozhdestvenskaya, E. Mugnaioli, M. Czank, W. Depmeier, U. Kolb, A. Reinholdt, T. Weirich, Mineralogical Magazine 74 (2010),

40 Erice 2011 Electron Crystallography – June 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 Erice 2011 Electron Crystallography – June 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 Erice 2011 Electron Crystallography – June Second step The list of the Laue groups compatible with each feasible crystal system is automatically generated (denoted as admitted Laue groups). 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.

43 Erice 2011 Electron Crystallography – June New procedure to select the space group Third step For each feasible crystal system the admitted Laue group with minimal symmetry (say LG min ) is considered. For each i-th admitted Laue group the internal residual factor R int (i) is calculated: The probability of the i-th Laue group is:

44 Erice 2011 Electron Crystallography – June 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 Erice 2011 Electron Crystallography – June New procedure to select the space group Charoite Cell Space Group: P 2 1 /m

46 Erice 2011 Electron Crystallography – June New procedure to select the space group

47 Erice 2011 Electron Crystallography – June 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 Erice 2011 Electron Crystallography – June Simulated Annealing

49 Erice 2011 Electron Crystallography – June Simulated Annealing

50 Erice 2011 Electron Crystallography – June Simulated Annealing

51 Erice 2011 Electron Crystallography – June 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

52 Erice 2011 Electron Crystallography – June Integration with Jav, the new visualizer in 3D

53 Erice 2011 Electron Crystallography – June Integration with Jav, the new visualizer in 3D

54 Erice 2011 Electron Crystallography – June Integration with Jav, the new visualizer in 3D

55 Erice 2011 Electron Crystallography – June Integration with Jav, the new visualizer in 3D

56 Erice 2011 Electron Crystallography – June Integration with Jav, the new visualizer in 3D

57 Erice 2011 Electron Crystallography – June Integration with Jav, the new visualizer in 3D

58 Erice 2011 Electron Crystallography – June Integration with Jav, the new visualizer in 3D

59 Erice 2011 Electron Crystallography – June Integration with Jav, the new visualizer in 3D

60 Erice 2011 Electron Crystallography – June Integration with Jav, the new visualizer in 3D

61 Erice 2011 Electron Crystallography – June Integration with Jav, the new visualizer in 3D

62 Erice 2011 Electron Crystallography – June Integration with Jav, the new visualizer in 3D

63 Erice 2011 Electron Crystallography – June Integration with Jav, the new visualizer in 3D

64 Erice 2011 Electron Crystallography – June The program This program will be available, free of charge for academic institutions, for Linux, Mac and MS Windows systems. J. Appl. Cryst. (2011), in preparation Sir2011: a new program for crystal structure solution M.C.Burla, R. Caliandro, M. Camalli, B. Carrozzini, G.L. Cascarano, C. Giacovazzo, A. Mazzone, G. Polidori, R. Spagna

65 Erice 2011 Electron Crystallography – June Thanks for your attention The authors R.Caliandro, B.Carrozzini, G.L.Cascarano, C.Giacovazzo, A. Mazzone Istituto di Cristallografia del CNR – Bari M.Camalli, R.Spagna Istituto di Cristallografia del CNR –Rome M.C.Burla, G.Polidori Dipartimento di Scienze della Terra, University of Perugia

66 Erice 2011 Electron Crystallography – June Tutorial Before the tutorial (june 8) please download from ERICE_SERVER \ Put Files Here the following files: barite.sir barite.doc barite.hkl Sir betaSetUp.exe


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