1. Charles Campana Bruker AXS Inc.
Crystal Structure Determination and Refinement Using the Bruker AXS SMART APEX II System
Charles Campana
Bruker AXS Inc.

2. Flowchart for Method Adapted from William Clegg
“Crystal Structure Determination”
Oxford 1998.

3. Crystal Growing Techniques
Slow evaporation
Slow cooling
Vapor diffusion
Solvent diffusion
Sublimation

4. Examples of Crystals

5. Growing Crystals
Kirsten Böttcher and Thomas Pape

6. Select and Mount the Crystal
Use microscope
Size: ~0.4 (±0.2) mm
Transparent, faces, looks single
Epoxy, caulk, oil, grease to affix
Glass fiber, nylon loop, capillary

7. What are crystals ?

8. Crystallographic Unit Cell
Unit Cell Packing Diagram - YLID

9. 7 Crystal Systems - Metric Constraints
Triclinic - none
Monoclinic -  =  = 90,   90
Orthorhombic -  =  =  = 90
Tetragonal -  =  =  = 90, a = b
Cubic -  =  =  = 90, a = b = c
Trigonal -  =  = 90,  = 120, a = b (hexagonal setting) or  =  =  , a = b = c (rhombohedral setting)
Hexagonal -  =  = 90,  = 120, a = b

10. X-Ray Diffraction Pattern from Single Crystal
Rotation Photograph

11. X-Ray Diffraction X-ray beam   1Å (0.1 nm) ~ (0.2mm)3 crystal
As crystallographers we are quite demanding. what we want is not only crystals. What we really want is 10^15 molecules all in the same conformation and all locked in that conformation for the time of our experiment about 1hours. If this is not the case we call it disorder.
From biophysical experiments we know that proteins have a very complex energy-landscape and that they can be in many energetically very similar states.
If such states are separated by a large energy barrier, the corresponding disorder would be called static, if there is no energybarrier or only a small one that is frequently crossed, we call it dynamic.
~ (0.2mm)3 crystal
~1013 unit cells, each ~ (100Å)3
Diffraction pattern on
CCD or image plate

12. n = 2d sin() Bragg’s law d  
We can think of diffraction as reflection at sets of planes running through the crystal. Only at certain angles 2 are the waves diffracted from different planes a whole number of wavelengths apart, i.e. in phase. At other angles the waves reflected from different planes are out of phase and cancel one another out.

13. Reflection Indices z y x Planes 3 -1 2 (or -3 1 -2)
These planes must intersect the cell edges rationally, otherwise the diffraction from the different unit cells would interfere destructively.
We can index them by the number of times h, k and l that they cut each edge.
The same h, k and l values are used to index the X-ray reflections from the planes. x
Planes (or )

14. Diffraction Patterns
Two successive CCD detector images with a crystal rotation of one degree per image
For each X-ray reflection (black dot) indices h,k,l can be assigned and an intensity I = F 2 measured

15. Reciprocal space
The immediate result of the X-ray diffraction experiment is a list of X-ray reflections hkl and their intensities I.
We can arrange the reflections on a 3D-grid based on their h, k and l values. The smallest repeat unit of this reciprocal lattice is known as the reciprocal unit cell; the lengths of the edges of this cell are inversely related to the dimensions of the real-space unit cell.
This concept is known as reciprocal space; it emphasizes the inverse relationship between the diffracted intensities and real space.

16. The structure factor F and electron density 
Fhkl =  V xyz exp[+2i(hx+ky+lz)] dV
xyz = (1/V) hkl Fhkl exp[-2i(hx+ky+lz)]
F and  are inversely related by these Fourier transformations. Note that  is real and positive but F is a complex number: in order to calculate the electron density from the diffracted intensities I = F2 we need the PHASE ( ) of F. Unfortunately it is almost impossible to measure  directly!

17. The Crystallographic Phase Problem

18. The Crystallographic Phase Problem
In order to calculate an electron density map, we require both the intensities I = F 2 and the phases  of the reflections hkl.
The information content of the phases is appreciably greater than that of the intensities.
Unfortunately, it is almost impossible to measure the phases experimentally !
This is known as the crystallographic phase problem and would appear to be insoluble

19. Real Space and Reciprocal Space
Unit Cell (a, b, c, , , )
Electron Density, (x, y, z)
Atomic Coordinates – x, y, z
Thermal Parameters – Bij
Bond Lengths (A)
Bond Angles (º)
Crystal Faces
Reciprocal Space
Diffraction Pattern
Reflections
Integrated Intensities – I(h,k,l)
Structure Factors – F(h,k,l)
Phase – (h,k,l)

20. Goniometer Head

21. 3-Axis Rotation (SMART)

22. 3-Axis Goniometer

23. SMART APEX II System
What you always wanted to know about protein structure but never dared to ask.

24. SMART APEX System

25. SMART APEX II System

26. APEX II detector

27. CCD Chip Sizes X8 APEX, SMART APEX, 6000, 6500 4K CCD 62x62 mm
Kodak 1K CCD 25x25 mm SMART 1000, 1500
& MSC Mercury
SITe 2K CCD 49x49 mm
SMART 2000

28. APEX II detector transmission of fiber-optic taper depends on 1/M2
APEX with direct 1:1 imaging
1:1 is 6x more efficient than 2.5:1
improved optical transmission by almost an order of magnitude
allowing data on yet smaller micro-crystals or very weak diffractors.
original SMART e/Mo photon APEX e/Mo ph.

29. project database
SMART
setup
sample screening
data collection
ASTRO
data collection strategy
default settings
detector calibration
SAINTPLUS
new project
change parameters
SAINT:
integrate
SADABS:
scale & empirical absorption correction
SHELXTL
new project
XPREP:
space group determination
XS:
structure solution
XL:
least squares refinement
XCIF:
tables, reports

30.                                                    
George M. Sheldrick
Professor, Director of Institute and part-time programming technician : student at Jesus College and Cambridge University, PhD (1966)    with Prof. E.A.V. Ebsworth entitled "NMR Studies of Inorganic Hydrides" : University Demonstrator and then Lecturer at Cambridge University; Fellow of Jesus College, Cambridge Meldola Medal (1970),  Corday-Morgan Medal (1978) 1978-now: Professor of Structural Chemistry at the University of Goettingen Royal Society of Chemistry Award for Structural Chemistry (1981) Leibniz Prize of the Deutsche Forschungsgemeinschaft  (1989) Member of the Akademie der Wissenschaften zu Goettingen (1989) Patterson Prize of the American Crystallographic Association (1993)
Author of more than 700 scientific papers and of a program called SHELX
Interested in methods of solving and refining crystal structures (both small molecules and proteins) and in structural chemistry fax:  

31. SHELXTL vs. SHELX* http://shelx.uni-ac.gwdg.de/SHELX/index.html
SHELXTL (Bruker Nonius)
XPREP XS XM XE XL
XPRO
XWAT XP
XSHELL
XCIF
SHELX (Public Domain)*
None
SHELXS
SHELXD
SHELXE
SHELXL
SHELXPRO
SHELXWAT
CIFTAB