Small Molecule Example – YLID Unit Cell Contents and Z Value Chemical formula is C11H10O2S Z value is determined to be 4.0 Density is calculated to be 1.381 The average non-H volume is calculated to be 17.7

Small Molecule Example – YLID Set Up File for Structure Solution

Structure Refinement with SHELX / SHELXTL George M. Sheldrick, Professor of Structural Chemistry at the Georg-August-Universität Göttingen and part-time programming technician. Author of public-domain SHELX and Bruker SHELXTL solution and refinement software and other programs. Sheldrick software is used in ca. 70% of all crystal structure refinements.

Structure Solution Once the structure factor amplitudes are known, the phase problem must be solved to find a self-consistent set of phases that can be combined with the structure factor amplitudes to obtain the electron density and thereby determine the structure of the crystal. A number of crystallographic techniques exist for obtaining the phases of diffracted waves; the most widely utilized approaches to the solution of phase problem involve the use of either vector methods based on |F(hkl)|2 or direct or statistical methods. Typically, the solution to the structure yields only a partial or approximate model, which must be improved by successive applications of Fourier-transform methods before the complete structure has been determined. Once the structure amplitudes are known, the phase problem must be solved to find a self-consistent set of phases that can be combined with the structure factor amplitudes to obtain the electron density and thereby determine the structure of the crystal. A number of crystallographic techniques exist for obtaining the phases of diffracted waves; the most widely utilized approaches to the solution of phase problem involve the use of either vector methods based on |F(hkl)|2 or direct or statistical methods. Typically, the solution to the structure yields only a partial or approximate model, which must be improved by successive applications of Fourier-transform methods before the complete structure has been determined.

Small Molecule Example – YLID Results for Direct Methods Solution 1 S atom + 13 Q-peaks

Small Molecule Example – YLID Assignment of Atom Types 1 S atom + 11 C atoms + 2 O atoms

X-ray Crystal Structure Determination Refinement of Structures

Refinement of Structures When a structure is “solved”, atom types are assigned to some of the electron density peaks from the three-dimensional “Fourier map”. The atomic scattering factors for these atoms are then used to calculate structure factors, F(calc), which are compared with the observed structure factors, F(obs), for the whole dataset. The agreement is measured by an R- factor. The fractional coordinates are then adjusted (refined) to obtain better agreement and to locate and assign additional electron density peaks.

Small Molecule Example – YLID First Refinement Run 1 S atom + 11 C atoms + 2 O atoms

Small Molecule Example – YLID First Refinement Run Isotropic Refinement R1 = 7.68%

Small Molecule Example – YLID First Refinement Run Anisotropic Refinement R1 = 4.33% Difference peaks assigned as H atoms

Refinement of Structures After the entire molecular structure has been determined, the approximate positions of the atoms are refined by nonlinear least-squares techniques to give the best fit between the calculated and observed intensity data for the specimen. Besides positional parameters (i.e., fractional coordinates), additional parameters are included in the refinement to model the thermal motion of individual atoms.

Small Molecule Example – YLID Final Refinement Run Final anisotropic refinement with H atoms R1 = 2.03% wR2 = 5.38% Shown as 50% thermal ellipsoids Flack x parameter = 0.0113 with esd of 0.0642 WGHT 0.0321 0.0906

Bond Lengths and Angles The refinement process yields very accurate values for atomic positions from which bond lengths, bond angles and other structural parameters may be calculated. The estimated standard deviations in the unit cell parameters and the measured intensities are used to estimated the standard deviations in bond length, bond angles and other derived structural parameters.

Small Molecule Example – YLID Bond Lengths and Angles

Small Molecule Example – YLID Reports

Small Molecule Example – YLID Structure Validation After the structural refinement process has been completed, an analysis of the complete structure is usually carried out with an independent validation program (e.g., PLATON, PublCIF) which checks the structure for missing information or inconsistent data. Warning messages are generated that allow the authors to address the error prior to publication.

Small Molecule Example – YLID Generation of CIF Files All of the crystallographic journals and most of the major chemical journals have now adopted the CIF (Crystal Information Format) for depositing and publishing crystallographic data. Most commercial and public-domain structure refinement programs now generate CIF files for validation and deposition.

Small Molecule Example – YLID Typical Crystal Structure Diagrams Ball-and-stick diagram of one molecule Unit-cell diagram showing the arrangement of four molecules within the cell

Summary of Part 2 Review of Part 1 Selection and Mounting of Samples Unit Cell Determination Intensity Data Collection Data Reduction Structure Solution and Refinement Analysis and Interpretation of Results We demonstrated these concepts by carrying out an X-ray crystal structure analysis on 2-Dimethylsufuranylidene-1,3-indanedione (YLID)* *Polymorphism and History of 2-Dimethylsufuranylidene-1,3-indanedione (YLID), Ilia A. Guzei, Galina A. Bikzhanova, Lara C. Spencer, Tatiana V. Timofeeva, Tiffany L. Kinnibrugh and Charles F. Campana, Crystal Growth & Design, Vol. 8, No. 7, 2008

Recommended Books J. P. Glusker and K. N. Trueblood, Crystal Structure Analysis: A Primer, Oxford Univ. Press 2nd Edition ,1985, ISBN 019-503543-7 W. Clegg, Crystal Structure Determination, Oxford Univ. Press, 1998, ISBN 019-855901-1 W. Massa, Crystal Structure Determination, 3. Auflage 2002, Teubner, ISBN 3-519-23527-7; 2nd Edition, 2004, Springer, ISBN 3-540-20644-2.

Single Crystal XRD Diffracted Incident Beam Beam Single crystal sample run on a powder diffractometer gives only one peak (maybe 2 or 3 orders) and very limited information. 22

Single Crystal XRD Each point represents Braggs law being satisfied for a different set of diffracting planes. Some of the planes belong to the same family, so their d-spacing is the same, but the orientation is different.

Definition of Powder Definition Powder diffraction is a method of X-ray diffraction analysis in which monochromatic X- rays are incident on a sample containing a large number of tiny crystals having random orientation, producing a diffraction pattern that is recorded with a point detector or an area detector.

Powder XRD Make the sample simultaneously consist of every possible orientation by grinding it into a fine powder. The powder will consist of tens of thousands of single-crystal grains that are randomly oriented with respect to one another. Every possible orientation is well-represented, and so every set of diffracting planes has crystallites oriented such that those planes are parallel to the sample surface.

Powder XRD Diffracted Beam Incident Beam

Diffracted Intensity of a Powder Sample

Powder XRD in Three Dimensions

Powder XRD Tens of thousands of single crystals that are oriented randomly with respect to one another. At any incident angle, there will be a sufficient number of crystallites with every possible set of diffracting planes oriented to Bragg diffract.