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

Transcription

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

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

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 ( ), 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 3

4 Audience Poll Please use your mouse to answer the question on your screen: What is your experience level? I have not done any crystal structures I have done only routine structures I have done problem structures I m a crystallographer November 13,

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. November 13, 2012 Disorder Webinar 5

6 George Sheldrick Professor of Structural Chemistry and parttime 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 Disorder Webinar 6

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) November 13, 2012 Disorder Webinar 7

8 SHELXTL vs. SHELX* SHELXTL (Bruker AXS) XPREP XS XM XE XL XPRO XWAT XP XSHELL XCIF SHELX (Public Domain)* None SHELXS SHELXD SHELXE SHELXL SHELXPRO SHELXWAT None None CIFTAB November 13, 2012 Disorder Webinar 8

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

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. November 13,

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. November 13, 2012 Disorder Webinar 11

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), variablemetric 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 Disorder Webinar 12

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. November 13, 2012 Disorder Webinar 13

14 Types of constraints in SHELXL Constraints for special positions: the necessary constraints on co-ordinates, occupancies and U ij 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): x H = x C + 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. November 13, 2012 Disorder Webinar 14

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 0.5. The probability ellipsoid used to describe the anisotropic motion should not be changed by the 180º rotation. [U 11, U 22, U 33, U 23, U 13, U 12 ] [U 11, U 22, U 33, -U 23, U 13, -U 12 ] which is only true if U 23 = 0 and U 12 = 0. All these constraints are generated automatically by SHELXL for all special positions in all space groups. November 13, 2012 Disorder Webinar 15

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 6 rigid group all AFIX 9 variable metric bond lengths and rigid group - angles atoms angles fixed atoms fixed, bond lengths multiplied by the AFIX 0 AFIX 0 same factor November 13, 2012 Disorder Webinar 16

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: d ij < r i + r j 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. November 13, 2012 Disorder Webinar 17

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 (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). November 13, 2012 Disorder Webinar 18

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 November 13, 2012 Disorder Webinar 19

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.) November 13, 2012 Disorder Webinar 20

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 November 13, 2012 Disorder Webinar 21

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 November 13, 2012 Disorder Webinar 22

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 U ij, so it may be necessary to supplement them with the less accurate but more numerous SIMU and ISOR restraints with larger esd s. November 13, 2012 Disorder Webinar 23

24 Restraints on ADP's November 13, 2012 Disorder Webinar 24

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 CH 3 ). 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 C7 (generates 6H with occupancies of 0.25) November 13, 2012 Disorder Webinar 25

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 = AFIX 43 H17D AFIX 0 PART 0 November 13, 2012 Disorder Webinar 26

27 Use of PART 1, PART 2 and SAME Part 1 Part 2 Parts 1 & 2 November 13, 2012 Disorder Webinar 27

28 The image part with relationship ID rid2 was not found in the file. Ethyl acetate disordered about a 2-fold axis FVAR C = O = SAME C1 > O6 PART -1 C1' = AFIX 0 O6' = PART 0 November 13, 2012 Disorder Webinar 28

29 Disordered t-butyl group November 13,

30 Disorder between Cl and C November 13,

31 Disorder of a cyclopentadienyl ring November 13,

32 November 13, 2012 Disorder Webinar 32

33 Disorder of a chloroform molecule on a mirror plane November 13, 2012 Disorder Webinar 33

34 DMSO disordered over three positions November 13, 2012 Disorder Webinar 34

35 Example 1 - Os 3 (CO) 10 (PPh 2 ~PPh 2 ) 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 ) November 13,

36 Example 1 - Os 3 (CO) 10 (PPh 2 ~PPh 2 ) preliminary structure chelating phosphine ligand November 13,

37 Example 1 - Os 3 (CO) 10 (PPh 2 ~PPh 2 ) 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 November 13,

38 Example 1 - Os 3 (CO) 10 (PPh 2 ~PPh 2 ) three large difference peaks November 13,

39 Example 1 - Os 3 (CO) 10 (PPh 2 ~PPh 2 ) L.S. 4 BOND FMAP 2 PLAN 99 WGHT FVAR PART 1 ANIS 3 OS OS OS PART 2 ANIS 3 OS OS OS PART 1 C1A O1A C2A O2A C9A O9A C10A O10A PART 0 ANIS 2 P P C C November 13,

40 Example 1 - Os 3 (CO) 10 (PPh 2 ~PPh 2 ) remaining carbonyl atoms revealed in difference map November 13,

41 Example 1 - Os 3 (CO) 10 (PPh 2 ~PPh 2 ) superposition of both isomers November 13,

42 Example 1 - Os 3 (CO) 10 (PPh 2 RPPh 2 ) chelating phosphine ligand (85%) bridging phosphine ligand (15%) November 13, 2012 Disorder Webinar 42

43 Example 1 - Os 3 (CO) 10 (PPh 2 ~PPh 2 ) 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, November 13, 2012 Disorder Webinar 43

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 P a = Å, b = Å, c = Å 12 Urea molecules, 4 carboxylic acid molecules per cell November 13,

45 Example 2 Urea Host : Guest Complex projection down b-axis November 13,

46 Example 2 Urea Host : Guest Complex Projection down a-axis November 13,

47 Example 2 Urea Host : Guest Complex analysis of Q-peaks November 13,

48 Example 2 Urea Host : Guest Complex analysis of Q-peaks November 13,

49 Example 2 Urea Host : Guest Complex N2C AFIX 93 H2CA H2CB AFIX 0 PART -1 C1S O1S O2S AFIX 3 H2S AFIX 0 C2S AFIX 23 H2SA H2SB AFIX 0... C10S AFIX 23 H10A H10B AFIX 0 C11S O3S O4S AFIX 3 H4S PART 0 November 13,

50 Example 2 Urea Host : Guest Complex Anisotropic refinement of dicarboxylic acid Final refinement R1 = 3.83% Temperature factors on hydrogen atoms refined November 13,

51 Example 3 - Fe 3 (CO) 12 Crystallographic Problem Space group is P2 1 /n with Z = 2 Each molecule must lie on a crystallographic center of symmetry Successful refinement is difficult because it requires two halfweighted molecules superimposed on the center of symmetry

52 Example 3 - Fe 3 (CO) 12 Refinement Results 100K Data Resolution 0.40Å R1 = 3.82% wr2 = 9.14% Ind. Refl. 298K Data Resolution 0.65Å R1 = 5.11% wr2 = 13.45% 2989 Ind. Refl.

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

54 Example 3 - Fe 3 (CO) 12 - shelxle diagrams November 13, 2012 Disorder Webinar 54

55 50% Thermal Ellipsoids 100K 298K

56 Example 3 - Fe 3 (CO) 12 Bond Lengths 100K Fe(1) -Fe(2) (3) Å Fe(2)- Fe(3) (3) Å Fe(2)-Fe(3) (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) 2.013(4) Å Fe(2)-C(2) 1.985(4) Å Fe(3)-C(1) 1.989(4) Å Fe(3)-C(2) 2.020(4) Å Fe(2)-C(1) 2.095(8) Å Fe(2)-C(2) 2.042(8) Å Fe(3)-C(1) 2.063(8) Å Fe(3)-C(2) 2.129(8) Å

57 Example 3 - Fe 3 (CO) 12 Bond Lengths 100K Fe(1) -Fe(2) (3) Å Fe(2)- Fe(3) (3) Å Fe(2)-Fe(3) (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) 2.013(4) Å Fe(2)-C(2) 1.985(4) Å Fe(3)-C(1) 1.989(4) Å Fe(3)-C(2) 2.020(4) Å C(1)-O1) 1.161(3) Å C(2)-O(2) 1.163(3) Å Fe(2)-C(1) 2.095(8) Å Fe(2)-C(2) 2.042(8) Å Fe(3)-C(1) 2.063(8) Å Fe(3)-C(2) 2.129(8) Å C(1)-O1) 1.088(6) Å C(2)-O(2) 1.112(6) Å

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

59 Example 3 - Fe 3 (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 Fe 3 (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,

61 Questions and Answers Any questions? Please type any questions you may have for our speakers in the Q&A panel and click Send. How did we do? When you exit the webinar, please fill out our evaluation survey to let us know. We appreciate your feedback. Thank you! November 13, 2012 Disorder Webinar 61

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