chem 125 lecture 7 9/14/05 projected material this material is for the exclusive use of chem 125...
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Chem 125 Lecture 79/14/05
Projected material
This material is for the exclusive use of Chem 125 students at Yale and may not
be copied or distributed further.
It is not readily understood without reference to notes from the lecture.
Rubofusarin
No H?
long
short
Highe-Density
No : !
Stout & Jensen "X-Ray Structure Determination (1968)
5 e/Å3
7 e/Å3
No : Bonds!
Spherical Atoms
Visualizing Bondswith
Difference Density Maps
Observed e-Density - Atomic e-Density(experimental) (calculated)
sometimes calledDeformation Density Maps
SphericalCarbon Atoms
Subtracted fromExperimental
Electron Density(H not subtracted)
Triene
7
6 5
4
~0.2 e
~0.2 e
~0.2 e
~0.1 e
H ~1 e
Lew
is B
ookk
eepi
ng
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)
Compared to what?What d'you think of him?
Exactly!
Compared with what, sir?
1) RESONANCE STABILIZATION
2) DIFFERENCE DENSITY
TFDCB
Where is theC-F Bond?
C
CC
C
F
N
Unshared Pair!
Need to subtract Finstead of
“unbiased”spherical F
••••
•••
Dunitz et al. (1981)
Pathological Bonding
0.002 Å !
for averagepositions
Typically vibratingby ±0.050 Åin the crystal
Lone "Pair"of N atom
Dunitz et al. (1981)
Pathological Bonding
Bond Cross SectionsMissing Bond?
H
H
H
H
HH
Lewis Pairs/Octets provide a pretty good bookkeeping device
for keeping track of valencebut 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).
www.uni-leipzig.de/ ~gasse/gesch1.html
"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 pro-perly 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."
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?
Well, I have found one."
"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:
H = E
Felix Bloch & Erich Hückel on 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.
(1926)
Function of What?
Named by "quantum numbers"(e.g. n,l,m ; 1s ; 3dxy ;
Function of Particle Position(s)[and time and "spin"]
We focus first on one dimension,then three dimensions (one e),
then many e atoms, then many atoms.
N particles 3N arguments![sometimes 4N+1]
Solving a Quantum ProblemGiven : a set of particles
their masses & their potential energy law
[ e.g. 1 Particle/1 Dimension : 1 amu & Hooke's Law ]
To Find : a Function of the position(s) of the particle(s)Such that H/ is the same (E) everywhere
Reward : Knowledge of EverythingAt least everything knowable to experiment
Allowed Es, Structure (probability of)All Chemical & Physical Properties
=
H = E
Kinetic Energy + Potential Energy = Total Energy
Given - Nothing to do with Hold your breath!
H = E