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.
Cuts near this
Carbon Nucleus
This Carbon Nucleus
lies out of this plane
Stout & Jensen X-Ray Structure Determination
(1968)
K Penicillin
K+ Penicillin-
3-D map onplastic sheets
(1949)
K
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!
“Seeing” Bondswith
Difference Density Maps
(Observed e-Density) – (Atomic e-Density)experimental calculated
sometimes calledDeformation Density Maps
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)
Triene
plane of page
C Ccross section
(round)
C Ccross section
(oval)
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)
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
^
Bonding Densityis about
1/20th of a “Lewis”
Tetrafluorodicyanobenzene
CC
C
C
F
NC C
C
C
F
N
F
F
Dunitz, Schweitzer, & Seiler (1983)
unique
C
CC
C
F
N
TFDCBC
CC
C
F
N
is roundnot clover-leafnor diamond!
C N Triple Bond?
C C “Aromatic” Bond
C C Single Bond
TFDCB
Where is theC-F Bond?
C
CC
C
F
N
Unshared Pair!
TheSecond
KeyQuestion
See web page
for videoThe Beiderbeck Affair (1985)
©19
84 G
rana
da T
elev
isio
n
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
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”.
Dunitz et al. (1981)
End of Lecture 6Sept 13, 2010
Copyright © J. M. McBride 2009-2010. Some rights reserved. Except for cited third-party materials, and those used by visiting speakers, all content is licensed under a Creative Commons License (Attribution-NonCommercial-ShareAlike 3.0).
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