Hexagonal “benzene” masks and Franklin’s X-ray pattern of DNA explain how a diffraction pattern in “reciprocal space” relates to the distribution of electrons in molecules and to the repetition of molecules in a crystal lattice. Electron difference density maps reveal bonds, and unshared electron pairs, and show that they are only 1/20 th as dense as would be expected for Lewis shared pairs. Anomalous difference density in the carbon-fluorine bond raises the course’s second key question, “Compared to what?” Chemistry 125: Lecture 6 Sept. 13, 2010 Seeing Bonds by Electron Difference Density For copyright notice see final page of this file
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Hexagonal “benzene” masks and Franklin’s X-ray pattern of DNA explain how a diffraction pattern in “reciprocal space” relates to the distribution of electrons.
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Hexagonal “benzene” masks and Franklin’s X-ray pattern of DNA explain how a diffraction
pattern in “reciprocal space” relates to the distribution of electrons in molecules and to the
repetition of molecules in a crystal lattice. Electron difference density maps reveal bonds, and
unshared electron pairs, and show that they are only 1/20th as dense as would be expected
for Lewis shared pairs. Anomalous difference density in the carbon-fluorine bond raises the
course’s second key question, “Compared to what?”
Chemistry 125: Lecture 6Sept. 13, 2010
Seeing Bonds byElectron Difference Density
For copyright notice see final page of this file
Smoothly Modulated Scattering from a Pair.
(Slight change in deflection changes phase difference only slightly)
Long-Range Regular Repetition “Focuses” the
Scattered Intensity.
Repetition of Pairs “Focuses” their Smoothly-Varying
Intensity.
Understanding CrystalX-Ray Diffraction
as a “Convolution” ofPattern and Lattice
as a “Convolution” ofPattern and Lattice
Benzene Snowflake Slide with Randomly positioned
but Oriented"Benzenes"
(Random position-ing generates the
same diffraction as a single pattern,
but more intense.)
Benzene Snowflake
Isolated“Benzene”
Look for e-density onevenly spaced planes.
(or near)
Greater spacing gives smaller
angles.
Benzene Snowflake
Isolated“Benzene”
Greater spacing gives smaller
angles.
Look for e-density on (or near)evenly spaced planes.
High-angle reflections are weak, because finite size
of scatters gives substantial electron density between
closely-spaced planes
Benzene Snowflake
Slide with regular lattice of “benzenes"
Lattice repeat concentrates the
benzene snowflake scattering into
tightly-focussedspots
Molecule (row)Two rows (cosine)
consider vertical
scattering only
Lattice (precise angles)
Pegboard
Diffraction from 2D Lattice
of“Benzenes”
Molecular snowflake pattern viewed through lattice “pegboard” and
amplified to give same total intensity
“Direct” or “Real” Space
“Unit Cell” Structure Fuzzy Pattern
Crystal Lattice Viewing Holes
Decreasing Spacing Increasing Spacing
Crystal
“Diffraction” or “Reciprocal” Space
Diffraction Photo
(intensity)
(location)
Filament
Light BulbFilament(helix)
Filament
Light BulbFilament(helix)
X angle tellshelix pitch
Spot spacingtells scale
Spot spacingtells scale
Spots weakensuccessively (because of finitewire thickness)
(given &
slide-screendistance)
HELIXw
S
Svw
SCuriousIntensitySequence
B-DNAR. Franklin
(1952)
EvenDouble Helix
wouldcancel
every other“reflection”
(planes twice as close)
OffsetDouble Helix
repeated pair pattern Much more
electron density near planes than
in between.
BASE STACKING
B-DNAR. Franklin
(1952)
wS
Svw
S
MAJOR& MINORGROOVES
HELIX DIAMETER
Using pretty heavy-duty math, (that earned a Nobel Prize,
but is now a canned program)
one can go the other way.
Knowing the molecule’s electron density, it is
straightforward to calculate a crystal’s diffraction pattern.
X-Ray Diffraction
Old-StyleElectronDensity
Map(one slice)Contours drawn by
hand to connect points of equivalent electron density on computer printout.
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