hexagonal “benzene” masks and franklin’s x-ray pattern of dna explain how a diffraction...
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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
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Smoothly Modulated Scattering from a Pair.
(Slight change in deflection changes phase difference only slightly)
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Long-Range Regular Repetition “Focuses” the
Scattered Intensity.
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Repetition of Pairs “Focuses” their Smoothly-Varying
Intensity.
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Understanding CrystalX-Ray Diffraction
as a “Convolution” ofPattern and Lattice
as a “Convolution” ofPattern and Lattice
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Benzene Snowflake Slide with Randomly positioned
but Oriented"Benzenes"
(Random position-ing generates the
same diffraction as a single pattern,
but more intense.)
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Benzene Snowflake
Isolated“Benzene”
Look for e-density onevenly spaced planes.
(or near)
Greater spacing gives smaller
angles.
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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
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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)
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Pegboard
Diffraction from 2D Lattice
of“Benzenes”
Molecular snowflake pattern viewed through lattice “pegboard” and
amplified to give same total intensity
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“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)
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Filament
Light BulbFilament(helix)
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Filament
Light BulbFilament(helix)
X angle tellshelix pitch
Spot spacingtells scale
Spot spacingtells scale
Spots weakensuccessively (because of finitewire thickness)
(given &
slide-screendistance)
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HELIXw
S
Svw
SCuriousIntensitySequence
B-DNAR. Franklin
(1952)
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EvenDouble Helix
wouldcancel
every other“reflection”
(planes twice as close)
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OffsetDouble Helix
repeated pair pattern Much more
electron density near planes than
in between.
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BASE STACKING
B-DNAR. Franklin
(1952)
wS
Svw
S
MAJOR& MINORGROOVES
HELIX DIAMETER
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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.
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X-Ray Diffraction
Old-StyleElectronDensity
Map(one slice)Contours drawn by
hand to connect points of equivalent electron density on computer printout.
Cuts near this
Carbon Nucleus
This Carbon Nucleus
lies out of this plane
Stout & Jensen X-Ray Structure Determination
(1968)
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K Penicillin
K+ Penicillin-
3-D map onplastic sheets
(1949)
K
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1 e/Å3
contours
Rubofusarin (planar)
No H?
Highe-Density
Stout & Jensen "X-Ray Structure Determination (1968)
5 e/Å3
7 e/Å3
long
short
intermediate
No : Bonds!
Spherical Atoms
No : on O!
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“Seeing” Bondswith
Difference Density Maps
(Observed e-Density) – (Atomic e-Density)experimental calculated
sometimes calledDeformation Density Maps
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SphericalCarbon Atoms
Subtracted fromExperimental
Electron Density
Triene
7
6 5
4
~0.2 e
~0.2 e
~0.2 e
~0.1 e
H ~1 e
C C
C C
(H not subtracted)
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Triene
plane of page
C Ccross section
(round)
C Ccross section
(oval)
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Leiserowitz~0.1 e
~0.3 e~0.2 e
Why so littlebuild-up here? C
C
CC
as ifthere are
bent bonds from tetrahedral C atoms
Be patient(Quantum
Mechanics)
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Lew
is B
ookk
eepi
ng e
lect
rons
4
2
6
Inte
grat
ed D
iffer
ence
Den
sity
(e)
How many electrons are there in a bond?
Bond Distance (Å)1.2 1.4 1.6
0.2
0.1
0.3
Berkovitch-Yellin &Leiserowitz (1977)
more
^
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Bonding Densityis about
1/20th of a “Lewis”
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Tetrafluorodicyanobenzene
CC
C
C
F
NC C
C
C
F
N
F
F
Dunitz, Schweitzer, & Seiler (1983)
unique
C
CC
C
F
N
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TFDCBC
CC
C
F
N
is roundnot clover-leafnor diamond!
C N Triple Bond?
C C “Aromatic” Bond
C C Single Bond
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TFDCB
Where is theC-F Bond?
C
CC
C
F
N
Unshared Pair!
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TheSecond
KeyQuestion
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See web page
for videoThe Beiderbeck Affair (1985)
©19
84 G
rana
da T
elev
isio
n
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Compared to what?What d'you think of him?
Exactly!
Compared with what, sir?
1) SPECIAL “RESONANCE” STABILIZATION
/
2) DIFFERENCE ELECTRON DENSITY
Comparing observed (or calculated) energy to energy expected for a single Lewis structure
See webpage for dialogue and context
Comparing observed (or calculated) total e-density to the sum of e-densities for a set of undistorted atoms
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TFDCB
Where is theC-F Bond?
To avoid “Pauli” problemswe need to subtract not “unbiased” spherical
C
CC
C
F
N
C
which would start with 2.75 electrons in the bonding quadrants
(1 from C, 1.75 from F)
but rather
“valence prepared”
“Pauli Principle”
No more than two electrons in an “orbital”.
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Dunitz et al. (1981)
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End of Lecture 6Sept 13, 2010
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