Diffraction Basics: What You Really Need To Know

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Diffraction Basics What You Really Need To Know!
Diffraction Basics What You Really Need To Know!
Published in The New Yorker December 28, 1987
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X-ray Diffraction Nobel Prizes 1901 W. C.
Roentgen discovery of x-rays. 1914 M. von
Laue x-ray diffraction from crystals. 1915 W.
H. Bragg and W. L. Bragg crystal structure
derived from x-ray diffraction. 1917 C. G.
Barkla radiation of elements. 1924 K. M. G.
Siegbahn x-ray spectroscopy. 1927 A. H.
Compton scattering of x-rays by electrons. 1936
P. Debye diffraction of x-rays and electrons in
gases. 1937 C.J. Davisson and G.P. Thomson
diffraction of x-rays by electrons. 1954
L. Pauling the chemical bond and structures of
complex substances. 1962 J. Watson, M.
Wilkins, F. Crick structure of DNA. 1964 D.
Hodgkin structure of important biomolecules.
1976 B. Lipscomb structure of boron hydrides.
1979 A.M. Cormack and G.N. Hounsfield axial
tomography. 1981 K. M. Siegbahn electron
spectroscopy. 1982 A. Klug structures of
nucleic acid-protein complexes. 1985 H.
Hauptman, J. Karle direct methods. 1987 J.
Deisenhofer, R. Huber, M. Michel structural
evidence of a photosynthetic reaction
center. 1988 J. Deisenhofer, R. Huber, Michel
proteins. 1997 B. Brockhouse, C. Shull neutron
diffraction
Sir William Henry Bragg pioneered the
determination of crystal structure by X-ray
diffraction methods (1915)
Clinton J. Davisson (with George P. Thomson)
discovered that electrons can be diffracted like
light waves (1937)
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The Process An Overview
Crystal growth (0.5 hr to ?)
Crystal selection and mounting (15 to 60 min.)
Data collection (4 hours to 1 week)
Structure solution and refinement (0.5 hr to ?)
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X-ray Crystallography and Protein Structures
R. Franklin X-ray data L. Pauling Triple
helix J. Watson/F. Crick Double helix (1962)
Concepts of Genetics, Prentice Hall 2000.
Sir William Henry Bragg pioneered the
determination of crystal structure by X-ray
diffraction methods (1915)
Clinton J. Davisson (with George P. Thomson)
discovered that electrons can be diffracted like
light waves (1937)
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X-ray Crystallography and Protein Structures
R. Franklin X-ray data L. Pauling Triple
helix J. Watson/F. Crick Double helix (1962)
Concepts of Genetics, Prentice Hall 2000.

• HIV - Dana-Farber Cancer Institute (1998)
• Crystallize an important protein involved in
  the HIV viral invasion process.
• Protein GP120 demonstrates a two lock
  mechanism.
• GP120 has an identical region found in all HIV
  variants.
• Indicated the cavity in all HIV variants were
  potentially susceptible to highly specific drug
  regimes.

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X-ray Crystallography and Protein Structures
R. Franklin X-ray data L. Pauling Triple
helix J. Watson/F. Crick Double helix (1957)
Concepts of Genetics, Prentice Hall 2000.
EBOLA X-ray crystallographic analysis indicates
Ebo-74, a protein found on the outer membrane of
the Ebola virus, is similar to other structures
found in HIV, SIV (HIV for monkeys) and Influenza.
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X-ray Crystallography and Small Molecules

• PSEUDOEPHEDRINE STUDIES
• Pseudoephedrine is the active ingredient found
  in over-the-counter antihistamines such as
  Sudafed and Nyquil.
• The X-ray structures of this system provide
  detailed conformational information.
• The larger the R group, the more distorted the
  angle of the carbonyls becomes. Knowing such
  structural details helps to predict the
  properties, including potential drug
  characteristics, and the mechanism for
  synthesizing other similar molecules.
• J. Org. Chem. 67 (2002) 8871-8876.

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Clinton J. Davisson (with George P. Thomson)
discovered that electrons can be diffracted like
light waves (1937)
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X-ray Crystallography vs. NMR

• X-ray
• must crystallize
• molecules may be large
• better resolution
• structure modified by crystal packing
• oxidation states of metals, etc., may be
  difficult to determine
• In principle, the structure can be determined in
  the absence of any additional information

• NMR
• must be soluble
• limitations to molecular size
• less accurate
• can capture motion
• spin of the nucleus
• complex structure determination difficult.

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Simple Diffraction
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13,500 lines/inch 660 nm
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The New Yorker February 25, 1991
The New Yorker November 4, 2002
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Molecular Crystals
Unit Cells reproducible space in a crystal
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Unit Cells
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Unit Cells
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b
c
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Conditions For Diffraction
Clinton J. Davisson (with George P. Thomson)
discovered that electrons can be diffracted like
light waves (1937)
Changing Wavelength (?)
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Conditions For Diffraction
Changing Distance (d)
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Conditions For Diffraction
Changing Theta
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Braggs Law For Diffraction

• The difference between the length of wave 1 and
  2 CB BD

• Constructive interference (diffraction) will
  only occur if CB BD 2CB n?

sin? CB/d
CB n?/2
sin? (n?/2)/d
Braggs Law 2dsin? n?
sin? ? 1/d (reciprocal space)
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Consequences of sin? ? 1/d (Reciprocal Space)
1 size of crystal lattice ?
size of diffraction pattern
http//www.uni-wuerzburg.de/mineralogie/crystal/te
aching/
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Consequences of sin? ? 1/d (Reciprocal Space)
Square Lattice
Coordinates
Atomic (x,y,z)
Reflection (h,k,l)
http//www.uni-wuerzburg.de/mineralogie/crystal/te
aching/
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Consequences of sin? ? 1/d (Reciprocal Space)
Rectangular Lattice
http//www.uni-wuerzburg.de/mineralogie/crystal/te
aching/
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Consequences of sin? ? 1/d (Reciprocal Space)
Oblique Lattice
http//www.uni-wuerzburg.de/mineralogie/crystal/te
aching/
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Consequences of sin? ? 1/d (Reciprocal Space)
Oblique Lattice
Crystal Translation
http//www.uni-wuerzburg.de/mineralogie/crystal/te
aching/
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RECIPROCAL LATTICE - a set of imaginary points
constructed in such a way that the direction of a
vector from one point to another coincides with
the direction of a normal to the real space
planes and the separation of those points
(absolute value of the vector) is equal to the
reciprocal of the real interplanar distance.
Reciprocal Lattice
Crystal Lattice
(Imaginary)
0 2
2 2
-2 2
-2 0
2 0
-2 -2
2 -2
0 -2
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Reciprocal Lattice
Crystal Lattice
g 2?/d
N
d
0 2
2 2
-2 2
-2 0
2 0
g
-2 -2
2 -2
0 -2
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Reciprocal Lattice
Crystal Lattice
g 2?/d
d
N
0 2
2 2
-2 2
g
-2 0
2 0
-2 -2
2 -2
0 -2
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Reciprocal Lattice
Crystal Lattice
g 2?/d
d
N
0 2
2 2
-2 2
g
-2 0
2 0
-2 -2
2 -2
0 -2
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Reciprocal Lattice
Crystal Lattice
g 2?/d
d
N
0 2
2 2
-2 2
0 2
2 2
-2 2
g
2 0
-2 0
-2 0
2 0
-2 -2
2 -2
-2 -2
2 -2
0 -2
0 -2
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Reciprocal Lattice
Crystal Lattice
g 2?/d
0 2
0 2
2 2
2 2
-2 2
-2 2
N
d
g
2 0
-2 0
-2 0
2 0
-2 -2
-2 -2
2 -2
2 -2
0 -2
0 -2
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Reciprocal Lattice
Crystal Lattice
Reciprocal unit cell
c
Real unit cell
c
c
b
b
c
b
b
a
a
a
a
Real unit cell
Reciprocal unit cell
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http//phillips-lab.biochem.wisc.edu/software.html
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From Diffraction Patterns to Crystal Structures
(or visa versa)
X-ray diffraction data (h,k,l)
Fourier Series
Electron Density
Structure Factor
Complete description of a diffracted ray recorded
as reflection hkl (a wave equation)
Amplitude
Frequency
Phase
Contour map of electron density (x,y,z)
X-ray Source
? (Intensity)1/2
unknown
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Conclusions X-ray diffraction is not
magic It is
2dsin? n? (Braggs Law) Reciprocal space
2dsin? n? (Braggs Law) Reciprocal space
Waves (x-rays) interacting with the atomic
periodicity in the crystal
Waves (x-rays) interacting with the atomic
periodicity in the crystal
Each atom of a molecule contributing to every
reflection
Each atom of a molecule contributing to every
reflection
Predictable, calculable and useful for decoding
structural details of crystals
Predictable, calculable and useful for decoding
structural details of crystals
X-rays diffracting via electrons
X-rays diffracting via electrons