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X-ray Crystallography

Fundamental Concepts · X-rays are diffracted by electrons · 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: discovered by William Röentgen; called x-rays · 1912: von Laue, Friedrich, and Knipping: "Interference Effects with Röentgen Rays" Experiment: passed x-rays through crystal of sphalerite (zinc sulfide); distinct diffraction pattern observed Conclusions: (a) Crystals cause distinct x-ray diffraction patterns due to atoms. (b) Crystals are composed of periodic arrays of atoms. · 1914: English physicists Sir William Henry Bragg and his son Sir William Lawrence Bragg showed that the scattering of x-rays could 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 Structure Determination: A Simplified Tour For diffraction to be observed, the wavelength () of radiation must be about equal to the distances between the atoms (about 0-5 Å; 1 Å = 10-10 m); so-called "hard" x-rays correspond to x-rays or neutrons

bond length

crest

amplitude

Lecture Supplement: X-ray Crystallography

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Diffraction observed when waves scatter and interfere:

Constructive interference: troughs and crests in phase wave amplitude magnified

+

Destructive interference: troughs and crests out of phase wave amplitude decreased

+

Partial interference: Complex patterns result

+

A collection of atoms produces complex interference pattern depending upon bond lengths, angles, etc.:

Electron clouds cause diffraction Detector

x-ray photon flight paths

significant diffraction

little diffraction

Interfere occurs where waves meet

Allows determination of atomic positions within regular crystal lattice 44 Lecture Supplement: X-ray Crystallography

Diffraction pattern detected

Crystals for x-ray diffraction must be: · perfect no twinning 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. Instrumentation · mount crystal · measure intensity and position of diffraction spots · rotate crystal · repeat data collection

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Results: The Diffraction Pattern

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Lecture Supplement: X-ray Crystallography

Results: The Electron Density Map · Atoms with higher atomic numbers have more electrons and therefore scatter x-rays more effectively · Hydrogen atoms often not located exactly due to large thermal motion and small size · Electron density map provides location of atoms relative to each other · Bond angles, bond lengths may be determined

N M N

N

N

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Example: Determination of Unknown Stereochemistry

Br

Br + SH K2CO3, DMF SN2 O single diastereomer; 86% yield S S

O ~3:1 mixture of diastereomers

X-ray structure of product: ORTEP (Oak Ridge Thermal Ellipsoid Plot) drawing

Conclusion: Actual product is....

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Lecture Supplement: X-ray Crystallography

Example: Structure of DNA 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

Advantages and Disadvantages over Spectroscopy · Advantage: Most precise method of structure determination. (Some modern NMR methods are getting close.) Disadvantage: Requires crystals.

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