X-ray Crystallography

X-ray Crystallography
Reading: Atkins & Jones pages 196 - 197
Basis for Technique
• Electrons scatter x-rays.
• Diffraction: constructive or destructive interference of scattered waves.
• Pattern of diffracted x-rays useful to obtain orientation of atoms in space (molecular
structure).
History
• 1895: William Röentgen discovers x-rays.
• 1912: von Laue, Friedrich, and Knipping publish "Interference Effects with Röentgen
Rays.”
Experiment: passed x-rays beam through crystal of sphalerite (ZnS); distinct
diffraction pattern observed.
Conclusions: (a) Crystals are composed of periodic arrays of atoms.
(b) Crystals cause distinct x-ray diffraction patterns due to atoms.
• 1914: English physicists Sir William Henry Bragg and son Sir William Lawrence
Bragg show that the scattering of x-rays can be represented as a "reflection"
by successive planes of atoms within a crystal.


Implication: diffraction pattern can be used to determine relative positions of
atoms within a single crystal (i.e., molecular structure).


First single crystal structure: NaCl

• 1915: Braggs awarded Nobel Prize (http://nobelprize.org).
Structure Determination: A Simplified Tour
bond length
For diffraction to be observed, the wavelength (λ) of
λ
radiation must be about equal to the distances between
crest
the atoms (about 0-5 Å; 1 Å = 10-10 m)
amplitude
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Diffraction observed when scattered x-rays (waves) interfere (intensities add or subtract):
Constructive interference: troughs and crests
overlap in phase → wave amplitudes add
+
Wave
amplitude
Destructive interference: troughs and crests
overlap out of phase → wave amplitudes
+
cancel out
Partial interference: Complex patterns result
+
A collection of atoms produces complex interference pattern depending upon bond lengths,
angles, etc.:
Electron clouds
cause diffraction
Detector
significant
diffraction
e
t
e
c
t
e
d

d
x-ray photon
flight paths
t
t
e
r
n
a

p
n
c
t
i
o
little diffraction
i
f
f
r
a
D
Interference occurs where waves meet
Allows determination of atomic positions within regular crystal lattice
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Crystals for x-ray diffraction must be:
• perfect -- no twinning, inclusions or
other imperfections
• small (0.1 - 0.5 mm)
Growing crystals suitable for x-ray diffraction is a time-consuming art. "Small" molecules
are much easier to crystallize than larger ones, such as proteins, viruses, or DNA.
Procedure and Instrumentation
Procedure:
1. Mount crystal
2. Expose crystal to x-ray beam; measure intensity and position of diffraction spots
3. Rotate crystal
4. Repeat data collection
5. Analyze data
Basic operating priniciple of an x-ray diffractometer.
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Fundamental components of an x-ray diffractometer.
Results: The Diffraction Pattern
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Results: The Electron Density Map
• Atoms with higher atomic numbers (heavy atoms) have more electrons and therefore
diffract x-rays more effectively. Diffractive power example: Fe > C > H
• Hydrogen atoms often not located exactly due to small size and large thermal motion.
• Electron density map provides location of atoms relative to each other.
Smaller circle = higher electron density; center of circles = atom
• Bond angles, bond lengths may be determined → gives position of atoms in space.
• Connect the dots to get the molecular structure.
N
N
M
N
N
Electron density map
Molecular structure
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Application Example: Determination of Unknown Stereochemistry
A small molecule case
Starting dibromide is a mixture of diastereomers but product is a single diastereomer. What
is stereochemistry of product?
Br
Br
H
CH
3C
3
O
mixture of diastereomers
S
S
or
S
S
+
H
CH
3C
3
H
CH
3C
3
O
O
SH
Trans
Cis
(2R,4S) and (2S, 4R)
(meso)
IR doesn’t determine which isomer because...
NMR doesn’t determine which isomer because...
X-ray structure of product: ORTEP (Oak Ridge Thermal Ellipsoid Plot) drawing
Conclusion: Actual product is....
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Application Example: Structure of DNA
A large molecule case
X-ray diffraction data collected by Rosalind Franklin on Na salt of DNA:
• Helical structure, 20 Å diameter
• 3.4Å between nucleotides
• Guides Watson and Crick to double helix
Franklin’s Photo 51. The large X is characteristic of a helical structure.
Advantages and Disadvantages of X-ray Crystallography versus Spectroscopy
• Advantage: most precise method of structure determination. (Some modern NMR
methods are getting close.)
• Disadvantage: requires crystals.
Compared to MS, IR and NMR as tools for determination of molecular structure, x-ray
diffraction is more precise but more restricted in its application.
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