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

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