The aims of this module are: (1) to provide instruction on the methods and basis for determining low molecular weight crystal structures using X-ray Crystallography; (2) to enable interpretative assessment of the results of crystal structure analysis to be carried out; and (3) to guide students through several actual analyses using the SHELX-program suite implemented on Pentium PC's. An introduction to Macromolecular Crystallography is provided at the end of the course in preparation for this module. Having undertaken the course students should be prepared to undertake extended project work using the methods covered in the course and are encouraged to do so at a later stage.

The objectives of each lecture are given below:

• Lecture 1
  To introduce the necessary concepts of diffraction theory in the context of single crystals. X-ray scattering from a single atom and from arrays of atoms, leading up to the formulation of the Structure Factor F(hkl) for centrosymmetric and non-centrosymmetric crystals.
• Lecture 2
  To introduce the concept and formulation of Fourier series as used in X-ray crystallography. Practical aspects of electron density calculations and interpretation in structural terms. The phase problem enunciated. To introduce the concept of the Patterson function, its calculation and properties, in particular when a structure contains an outstandingly heavy atom.
• Lecture 3
  To demonstrate the use of SHELX programs for calculating the Patterson function for a heavy atom containing crystal, and interpretation in terms of heavy atom positions. Hands-on use of the program package. Centrosymmetric case. Calculation of molecular geometry and chemical significance of bond lengths, bond angles and other geometrical features such as planarity.
• Lecture 4
  To continue with the analysis started in Lecture 3, to expand the structure using Fourier and difference Fourier methods. Use of graphics programs to interpret the results.
• Lecture 5
  To repeat the ground covered in previous lectures for a moderatly complex non-centrosymmetrical structure.
• Lecture 6
  To provide the theoretical basis of Direct Methods of stucture determination. Concept of and rules for origin fixing. Practical examples for various centrosymmetric space groups.
• Lecture 7
  To intoduce the triple product sign relationship and expansion into the sigma2 formula. Symbolic addition and multi-solution methods for phase determination. The use of figures of merit for descrimination between phase sets.
• Lecture 8
  Practical applications of direct methods for structure solution. Use of SHELX-S and graphics programs. Non-centrosymmetrical structures.
• Lecture 9
  Expansion and completion of trial crystal structures from Patterson or direct methods. The use of Fourier methods and least-squares refinement. Isotropic and anisotropic models for atomic thermal vibrations. Pit-falls and precautions necessary in practice. Practicals and demonstrations.
• Lecture 10
  Methods for locating and/or calculating and refining H-atom positions. Determination of absolute configuration. More practicals.
• Lecture 11
  Introduction to macromolecular Crystallography. Isomorphous replacement and molecular replacement, basic concepts.