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Chem 125 Lecture 7
9/14/05
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High
e-Density
long
No : !
No :
shortBonds!
5 e/Å3
7 e/Å3
Spherical Atoms
Rubofusarin
Stout & Jensen "X-Ray Structure Determination (1968)
No H?
Visualizing Bonds
with
Difference Density Maps
sometimes called
Deformation Density Maps
Observed e-Density - Atomic e-Density
(experimental)
(calculated)
H ~1 e
Triene
6
~0.2 e
7
Spherical
Carbon Atoms
Subtracted from
Experimental
Electron Density
(H not subtracted)
~0.2 e
5
~0.2 e
4
~0.1 e
Triene
plane of page
partial
double bond
cross section
~0.1 e
Leiserowitz
~0.2 e
~0.3 e
C
C
C
C
Bent bonds from
tetrahedral
C?
Why not?
Density (e)
Difference
Integrated
Bookkeeping
Lewis
How many electrons are there in a bond?
6
0.3
4
0.2
2
0.1
1.2
1.4
1.6
Bond Distance (Å)
Berkovitch-Yellin &
Leiserowitz (1977)
Bonding Density
is about
th
1/20 of a “Lewis”
F
F
C
C
C
C
C
C
C
F
Tetrafluorodicyanobenzene
C
N
unique
F
Dunitz, Schweitzer,
& Seiler (1983)
N
C
TFDCB
C
C
N
C N Triple Bond
is round
not clover-leaf
nor diamond!
C
F
C
TFDCB
C
C
N
Unshared Pair!
C
F
Where is the
C-F Bond?
The
Second
Great
Question
1) RESONANCE STABILIZATION
2) DIFFERENCE DENSITY
Exactly!
Compared
What
d'youwith
think
what,
of
him?
sir?
Compared
to
what?
C
TFDCB
C
C
N
Unshared Pair!
C
F
• ••
Where
Needistothe
subtract • F •
•
•
C-F Bond?
instead of
“unbiased”spherical F
Pathological Bonding
0.002 Å !
for average
positions
Typically vibrating
by ±0.050 Å
in the crystal
Dunitz et al. (1981)
Pathological Bonding
Surprising only for its beauty
Dunitz et al. (1981)
Pathological Bonding
Lone "Pair"
of N atom
H
H
H
H
H
H
Bond Cross Sections
Dunitz et al. (1981)
Missing Bond?
Pathological Bonding
Missing
Bond !
Dunitz et al. (1981)
Bent
Bonds !
Lewis Pairs/Octets provide a
pretty good bookkeeping device
for keeping track of valence
but they are hopelessly crude
when it comes to describing
actual electron distribution.
There is electron sharing (~5% of Lewis's prediction).
There are unshared "pairs" (<5% of Lewis's prediction).
Is there a Better Bond Theory,
maybe even a Quantitative one?
YES!
Chemical
Quantum
Mechanics
Erwin Schrödinger (Zurich,1925)
www.zbp.univie.ac.at/schrodinger
Felix Bloch, Physics Today (1976)
"Once at the end of a colloquium I heard Debye saying
something like: Schrödinger, you are not working right
now on very important problems anyway. Why don't you
tell us sometime about that thesis of de Broglie?
"So in one of the next colloquia, Schrödinger gave a
beautifully clear account of how de Broglie associated
a wave with a particle…When he had finished, Debye
casually remarked the he thought this way of talking
was rather childish… he had learned that, to deal properly with waves, one had to have a wave equation.
It sounded rather trivial and did not seem to make a
great impression, but Schrödinger evidently thought a
bit more about the idea afterwards."
www.uni-leipzig.de/ ~gasse/gesch1.html
"Just a few weeks later he gave
another talk in the colloquium,
which he started by saying: My
colleague Debye suggested that one
should have a wave equation:
Well, I have found one."
Hy = E y
Stockholm (1933)
Paul
Dirac
Werner
Heisenberg
Erwin
Schrödinger
www.th.physik.uni-frankfurt.de/~jr
Schrödinger Equation
Hy =Ey
Leipzig (1931)
Felix
Bloch
Victor
Weisskopf
Werner
Heisenberg
American Institute of Physics
Felix Bloch & Erich Hückel on
(1926)
y
Gar Manches rechnet Erwin schon
Mit seiner Wellenfunktion.
Nur wissen möcht man gerne wohl,
Was man sich dabei vorstell'n soll.
Erwin with his Psi can do
calculations, quite a few.
We only wish that we could glean
an inkling of what Psi could mean.
Y
Function of What?
Named by "quantum numbers"
(e.g. n,l,m ; 1s ; 3dxy ; s p p*)
Function of Particle Position(s)
[and time and "spin"]
N particles  3N arguments!
[sometimes 4N+1]
We focus first on one dimension,
then three dimensions (one e),
then many e atoms,
then many atoms.
Solving a Quantum Problem
Given : a set of particles
their masses & their potential energy law
[ e.g. 1 Particle/1 Dimension : 1 amu & Hooke's Law ]
To Find : Y
a Function of the position(s) of the particle(s)
Such that HY/Y is the same (E) everywhere
Reward : Knowledge of Everything
At least everything knowable to experiment
Allowed Es, Structure (probability of)
All Chemical & Physical Properties
Hy=Ey
Hy
=
y
=E
Kinetic Energy + Potential Energy = Total Energy
Hold your breath!
Given - Nothing to do with y
Kinetic Energy!
h2
8p2

i
1 2y 2y 2y
+
+
mi xi2
yi2 zi2
y
One particle; One dimension:
C
1 d2y
m dx2
y
C
m
Curvature of
y
y