1. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.1 Perspective view of an unexpected Sm(II) reduction product [L 2 Sm{Al(CH 3 ) 4 } 2 ] of the reaction of Sm(III)[Al(CH 3 ) 4 ] 3 with a cyclic triamine ligand L = cyclo-(cyclohexyl-NCH 2 ) 3 [1]. The figure shows the experimental atom positions and the links between atoms represent chemical bonds, to facilitate identification of the components. The positions of the many hydrogen atoms have been omitted to clarify the picture.

2. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.2 (a) A scattering center hit by a planar wave-front emits a spherical wave. (b) and (c) Two scattering centers with different spacings emit spherical waves leading to observable interference patterns at a detector.

3. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.3 Interference patterns (thick lines) formed by the superposition of waves of the same wavelength but different phases (thin and dashed lines); (a) same phase, (b) slightly out of phase, (c) almost opposing phases, and (d) exactly opposing phases. The double arrows represent the phase differences.

4. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.4 Diffraction geometry for constructively interfering waves emerging from a double slit.

5. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.5 Variation of scattering power (the scattering amplitude f) with atomic number for (a) X-rays and (b) neutrons. (c) Variation with angle (expressed as sin  / ) for X-ray and neutron scattering by carbon.

6. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.6 (a) Schematic drawing of the GED apparatus and (b) photograph of the gas electron diffractometer located at the University of Bielefeld. Courtesy of University of Bielefeld.

7. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.7 Experimental diffraction patterns of benzene recorded (a) without and (b) with a rotating sector. (We thank Christian Reuter, Bielefeld, for performing the experiments and preparing the figures.) (c) The shape of a rotating sector with the opening angle  dependent on the distance r from the center of the disk.

8. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.8 Schematic drawing of scattering at a single center (atomic nucleus), showing the change of momentum s as a difference vector between the incoming and outgoing electron wave vectors k and k.

9. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.9 Total diffracted intensity I tot (s), and atomic I a (s) and molecular I m (s) scattering contributions (in arbitrary units) recorded in an electron diffraction experiment for tetrachloromethane, CCl 4. Courtesy of Dr Yuri Vishnevskiy, University of Bielefeld.

10. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.10 GED experimental results for P 4 and P 3 As, showing molecular intensity scattering curves for (a) P 4 and (c) P 3 As, along with their corresponding radial distribution curves in (b) and (d). The sticks in (b) and (d) indicate the positions of the refined interatomic distances and the lower trace curves are the difference curves (experiment – model), expressing the misfit between the experimental molecular intensity and that provided by the model.

11. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.11 (a) Molecular intensity curve and (b) corresponding radial distribution curve for PBrF 2 S.

12. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.12 (a) Molecular structure and (b) radial distribution curve of C 60. Drawn using data from [6].

13. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.13 Molecular structure and radial distribution curve for perchloric acid, HClO 4, showing the positions of the two Cl–O bonded distances and the two non-bonded O···O distances. Redrawn from [7] with permission of The Royal Society of Chemistry.

14. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.14 Structure and radial distribution curve of gallaborane, GaBH 6. The table lists some of the geometrical parameters (distances in Å, angles in degrees) obtained in the analysis of the GED data. Redrawn with permission from [12]. Copyright 2001 American Chemical Society.

15. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.15 Molecular structures and radial distribution curves of the two conformers, anti and gauche, of 1,4-disilabutane. Redrawn with permission from [14]. Copyright 1996 American Chemical Society.

16. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.16 The shrinkage effect illustrated by a linear triatomic molecule AB 2.

17. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.17 Selected parameters from the dynamic two-conformer structure model refinement of F 2 PN 3. The dynamical range of the N 3 group in the anti conformer is graphically displayed by a superposition of all pseudo-conformers. Adapted with permission from [15]. Copyright 2011 John Wiley & Sons.

18. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.18 Radial distribution curves for liquid gallium at different temperatures. Reprinted from [18]. Copyright 1977 American Institute of Physics.

19. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.19 (a) Total structure factor S(q) of liquid chlorine as obtained by X-ray diffraction and (b) radial distribution curve of liquid chlorine from X-ray diffraction data and corresponding neutron diffraction data. Redrawn with permission from [21]. Copyright 1994 Taylor & Francis.

20. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.20 Radial distribution curve of a 10:1 molar mixture of water and trimethylamine, a composition that gives a crystalline hydrate on cooling. The curve shows peaks corresponding to bonded and non-bonded intramolecular contacts, such as C — O, O — H, N — C and C···C, and intermolecular contacts, particularly between oxygen atoms of one water molecule and oxygen or nitrogen atoms of adjacent molecules. The solid line represents experimental data and the dotted line shows values calculated from a theoretical model of the structure. Adapted with permission from [22]. Copyright 1971, American Institute of Physics.

21. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.21 Alternative descriptions of a unit cell by three lattice vectors a, b and c, and by edge lengths a, b, c and angles ,  and . The axes are conventionally defined to be right-handed.

22. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.22 Examples of simple crystallographic symmetry elements denoted in Hermann-Mauguin notation.

23. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.23 Combination of inversion and rotation to give inversion-rotation symmetry operation. P int (–x, –y, z) is an intermediate point in the combined inversion and rotation operation.

24. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.24 (a) A screw axis. Object (1) is rotated about a 3-fold axis along a to a hypothetical intermediate position (2) (dashed) and then translated along a by a/3 to its screw-axis equivalent (3). Repetition of this combined action leads via intermediate (4) to (5), the second equivalent position. A third repetition of the screw axis operation leads to (6), the equivalent position in the next unit cell. (b) A glide plane. Object (1) is reflected into (2) and then translated along a by a/2 to its glide-plane equivalent (3). Repetition of this combined action leads via (4) to the equivalent position (5).

25. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.25 (a) Possible choices of unit cell in two dimensions; A is the most appropriate primitive cell. (b) A centered cell (D) is preferred, taking lattice symmetry into account. Adapted from [28]. Copyright 2007 Teubner.

26. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.26 The 14 Bravais lattices. Adapted from [28]. Copyright 2007 Teubner.

27. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.27 Constructive interference of X-rays reflected at two planes separated by a distance d (Bragg’s Law).

28. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.28 Lines of atoms in a two-dimensional lattice.

29. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.29 Miller indices for a set of three parallel lattice planes. The set of planes in this example has the indices h = 3, k = 4 and l = 2, defining the planes (3 4 2).

30. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.30 Packing of Se(CH 3 ) 2 molecules (H atoms omitted for clarity) in a crystal lattice, showing three different interpenetrating unit cells.

31. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.31 Schematic course of a single-crystal X-ray diffraction experiment.

32. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.32 Growth of a single crystal from a liquid. (a) Polycrystalline sample produced by freezing the liquid within a cryostream and then held just below the sample melting point; (b) melting almost all of the sample by application of an external heat source; (c) removal of the heat source, allowing a single crystal to grow from the seed.

33. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.33 (a) Schematic of a single-crystal four-circle X-ray diffractometer with an area detector. Shown are the X-ray source, the goniometer, which allows positioning of the crystal in any defined angular position relative to its center and the instrument, and the detector, which itself can be rotated about the diffraction point. The four circles of rotation are indicated: for positioning the crystal there are three rotations ( ,  and  ) and the detector can also be moved on a circle by an angle .

34. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.34 (a) A goniometer head, which holds the mounting pin with the crystal and allows fine adjustment of the crystal in x, y and z directions. (b–f) Five ways to mount a crystal on a diffractometer: (b) glued on top of a fiber, (c) sealed from the atmosphere within a drop of inert oil, (d) mounted within a thin- walled glass capillary, (e) mounted within a loop of fiber, and (f) mounted within a special tool made from thin plastic.

35. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.35 Some typical twinned crystals. (a) A ‘dovetail’ crystal, composed of two individuals just touching one another on one face; (b) a heavily inter-grown twin; (c) a layered twin.

36. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.36 (a) Section of a diffraction pattern of a twinned crystal. (b) Circles show positions of reflections calculated for one lattice orientation, but they account for only a proportion of the observed reflections. (c) Squares indicate positions of reflections calculated for a second lattice orientation. (d) Calculated reflection positions for both lattice orientations overlaid. Note that some spots represent overlaid reflections and are assigned to both lattices. Graphics courtesy of Dr Hans-Georg Stammler.

37. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.37 Structure of the carbyne aluminum-samarium complex [{cyclo-CyNCH 2 ) 3 }Sm{C(AlMe 3 ) 3 }] (Cy = cyclohexyl) containing atoms from four different periods of the periodic table, with associated structure parameters, whose standard deviations reflect more precise definition of the more electron-rich atoms. Adapted with permission from [1]. Copyright 2010 John Wiley & Sons.

38. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.38 Structure of the  phase of white phosphorus determined at 185  C by X-ray diffraction. (a) The unit cell, viewed along the a axis. (b) The asymmetric unit with three independent P 4 molecules. (c) List of 18 P — P distances (in Å ), showing that the spread of values is much larger than the standard deviations. Adapted from [34]. Copyright 1997 Wiley-VCH Verlag GmbH & Co. KGaA.

39. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.39 Synthesis, deuterolysis and structure of the complex aggregate Sm 3 Al 5 (tmtac)(CH 3 ) 16 (CH 2 ) 2 (C)] with a central six coordinate carbide ion, C 4–. Adapted from [35] with permission of The Royal Society of Chemistry.

40. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.40 (a) Molecules having no internal symmetry in a two-dimensional unit cell, related by a center of inversion. (b) If two planes of symmetry are assumed, the positions of the atoms must be slightly changed. (c) Two sets of disordered molecules, represented by solid and dashed lines. (d) If the disorder is ignored, the atoms will appear to be in average positions, with artificially large thermal ellipsoids.

41. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.41 Molecular structure of a trisila-allene showing disorder of the Si=Si=Si unit. (a) View of the whole molecule. (b) View along the Si(Si)Si axis. Adapted by permission from Macmillan Publishers Ltd: Nature [36], copyright 2003.

42. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.42 Molecular structure of the aminomethylgallium halide [Me 2 NCH 2 GaX 2 ] 2 (X = Cl, I) with statistically disordered iodine and chlorine positions for I(2) and Cl. Reprinted with permission from [37]. 2006 Verlag der Zeitschrift fu¨r Naturforschung.

43. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.43 Three representations of the structure of the [Li 4 (CH 3 ) 4 ] tetramers within the crystals of methyllithium.

44. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.44 The ‘nano-lemon’ [H x Mo 368 O 1032 (H 2 O) 240 (SO 4 ) 48 ] 48– cluster anion [38]. (Big dark balls are Mo, small white O, medium S.) The structure is mainly composed of MoO 6 octahedra, but some are pentagonal bipyramids, MoO 7. Courtesy of Dr Hartmut Bögge, University of Bielefeld.

45. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.45 Experimental deformation density map for dimolybdenum tetra-ethanoate, assuming that all atoms are neutral. The map is for a section through a plane formed by one Mo atom and four O atoms bonded to it. Negative contours are dotted. Reprinted with permission from [39]. Copyright 1981 IUCr.

46. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.46 Experimental deformation density maps for dimolybdenum tetra-ethanoate, with refined charges on all atoms. (a) Section through a plane formed by one Mo atom and four O atoms bonded to it. (b) Section through the Mo ≡ Mo bond and bisecting the two planes of the adjacent ethanoate groups. (c) Section through the Mo ≡ Mo bond and two ethanoate groups. (d) Cross-section through the middle of the Mo ≡ Mo bond. Reprinted with permission from [39]. Copyright 1981 IUCr.

47. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.47 Residual electron density maps in the C 6 ring plane of HP[CNS(C 6 H 4 )] 2 when described by multipole models of different order: (a) monopoles, (b) dipoles, (c) quadrupoles, (d) octapoles. Positive values are drawn as solid lines, negative as dashed, the zero contour is dotted, step size 0.1 e Å –3. Redrawn with permission from [41]. Copyright 2011 John Wiley & Sons.

48. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.48 Electron density plots of trans-diimine, HN=NH, as relief plots (a) in the plane of symmetry and (b) perpendicular to it,and the same represented as contour line plots (c) and (d). (e) Gradient vector field of the electron density of transdiimine, HN=NH. (f) Contour plot of the electron density with interatomic surface lines partitioning the molecular space into atomic basins (interatomic surfaces (IAS) and atomic interaction lines overlaid. All plots are based on calculations at the MP2/6-311G** level of theory.

49. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.49 3D representations of the N and H atoms in HN=NH defined by their interatomic surfaces (IAS) and one surface of constant electron density,  =0.001 au. Two different perspectives are shown for better visibility.

50. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.50 Examples of molecular graphs for some representative molecules. The nuclear positions are drawn as open circles, the bond critical points (BCP) as filled circles.

51. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.51 Contour map of  at the BCP perpendicular to the N — N AIL. The positions of the hydrogen atoms in front of and behind the plane indicate the molecular orientation.

52. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.52 A monotonically descending one-dimensional function f(x), and its first derivative and negative second derivative. Note the amplification of the seemingly hidden feature at point b in f(x) in the second derivative function. Adapted with permission from [48]. Copyright 1996 Wiley-VCH Verlag GmbH & Co. KGaA.

53. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.53 Plots of the negative Laplacian, L, of HN=NH in the molecular plane of symmetry. (a) Relief plot with regions of charge accumulation and depletion as positive and negative values. (b) Contour plot with positive values as bold lines and negative values as thin lines. The arrows indicate local bonding and nonbonding charge concentrations (CC). Also shown are the N–N and N–H AILs, with BCPs denoted as small black circles.

54. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.54 Contour plots of the negative Laplacian, L, of two covalently bonded molecules, C 2 H 6 and N 2, and two predominantly ionically bonded molecules, BeF 2 and BF 3. Bold contour lines represent positive values and dotted contour lines represent negative values. Also shown are the AILs and the BCPs (indicated as small black circles on the AILs). Adapted from [46]. Copyright 2001 Oxford University Press USA.

55. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.55 Electron density plots of NH 3, SiF 4 and the adduct H 3 N  SiF 4. Adapted with permission from [50]. Copyright 1992, American Institute of Physics.

56. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.56 Isovalue surfaces of L(r) = 0 for CO (left) and BH 3 (right) showing regions of valence-shell charge concentration (VSCC,inside surfaces) and depletion (VSCD, holes) that define the reactive surface and direction of interaction between a Lewis base and a Lewis acid. Adapted from ref. [42]. Copyright 1994 Oxford University Press USA.

57. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.57 Contour plot of L(r), based on experimental data, of S 4 N 4 in a plane showing parts of two molecules. The local charge concentrations of one approach the regions of charge depletion in the other. Reproduced from [53] with permission of The Royal Society of Chemistry.

58. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.58 Structures of the adducts Me 3 Al·OMe 2 and Me 3 Al·SMe 2, with values of parameters that are strongly phase-dependent. Two values for solid Me 3 Al·SMe 2 are due to two independent molecules in the unit cell.

59. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.59 (a) The structure of Me 3 SnONMe 2 in the crystalline phase. (b) The gas-phase structure (bold print), with the faded parts representing the structure in the crystal, showing the effects of a neighboring second molecule. The intermolecular O···Sn contact leads to two methyl groups being pushed up, while the rest of the structure remains almost unaltered.

60. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.60 Structure of the two independent molecules of decamethylsilicocene in the crystal (hydrogen atoms omitted). Adapted with permission from [58]. Copyright 1986 Wiley-VCH Verlag GmbH & Co. KGaA.

61. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.61 (a) The molecular structure of [{2-(Me 3 Si) 2 CLiC 5 H 4 N} 2 ], determined by single-crystal neutron diffraction. The symbol denotes a crystallographic inversion center. (b) An enlarged view of the part of the structure shaded in (a), to show the close proximity of the Li and H atoms. Distances in Å, angle in degrees. Adapted with permission from [65]. Copyright 2002 John Wiley & Sons.

62. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.62 (a) Molecular structure of the ion [H 2 Rh 13 (CO) 24 ] 3– as determined by single-crystal neutron diffraction. (b) and (c) Parts of the structure showing the square-pyramidal five coordination of the interstitial hydrogen atoms in [H 2 Rh 13 (CO) 24 ] 3– some selected Rh–H distances are given in Å. Data taken from ref. [66].

63. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.63 (a) Diffraction image of S 2 N 2, with the support for the beam stop clearly visible. (b) Extracted radial intensity as a function of the diffraction angle (upper trace), with a magnified inset; the middle trace represents a line pattern of the positions of the reflections of S 2 N 2 and the lower trace is the difference curve (experiment – model) after refinement. (c) Stack plot of the diffractogram changing with time; the trace at t = 0 s represents pure S 2 N 2. (d) Structures of S 2 N 2 and (SN) x. Adapted with permission from [68]. Copyright 1981 IUCr.

64. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.64 (a) Experimental diffractogram of the high-pressure form of nitrogen (dots), the idealized curve corresponding to the model of the structure (solid line) shown in (b) and (c), and some contributions of the cell material, cubic boron nitride (dotted line). The lowest trace shows a diffractogram at slightly lower pressure but the same temperature, where the sample is still dinitrogen, N 2. Adapted by permission from Macmillan Publishers Ltd: Nature Materials [70], copyright 2004.

65. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.65 X-ray absorption spectrum for the Fe(II) caperone protein yeast frataxin. The X-ray absorption near edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) regions are labeled. Reprinted from [71]. Copyright 2007 John Wiley & Sons.

66. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.66 The origin of EXAFS. The circles represent the photoelectron wave originating at the absorbing atom and back-scattered from neighboring atoms. In (a) the waves are in phase at the absorbing atom, but in (b) the photoelectron has a longer wavelength, and destructive interference occurs at the absorbing atom.

67. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.67 X-ray absorption spectrum (Co K edge) of the dicobalt complex [CpCoPPh 2 ] 2. Redrawn with permission from [73]. Copyright 1978 American Chemical Society.

68. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.68 (a) EXAFS data k 3  (  ) for the dicobalt complex [CpCoPPh 2 ] 2. The continuous line represents unfiltered data and the dashed line filtered data. (b) Radial distribution curve obtained by Fourier transformation of the unfiltered EXAFS data. Redrawn with permission from [73]. Copyright 1978 American Chemical Society.

69. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.69 Determination of the structure of [(NC) 5 PtTI(CN)] – in aqueous solution: (a) Pt L III -edge EXAFS spectrum with individual contributions of different single- and multiple-scattering paths originating at Pt; (b) Fourier transform and calculated contributions to this; (c) TI L III -edge EXAFS spectrum with individual contributions of diffrent single- and multiple-scattering paths originating at TI; (d) Fourier transform and calculated contributions to this; (e) structure of the molecular model and refined distances/Å ; (f) explanation of the various scattering paths within the molecule. Courtesy of Prof. Farideh Jalilehvand, University of Calgary. See also [74].

70. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.I

71. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Figure 10.II, III

72. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Discussion Problem Figure 10.24

73. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Discussion Problem Figure 10.25

74. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Discussion Problem Figure 10.30

75. Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A. Morrison @ 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd. Discussion Problem Figure 10.31