Chem 125 Lecture 79/14/05

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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

Triene

plane of page

cross sectionpartial

double bond

Leiserowitz~0.1 e

~0.3 e~0.2 e

C CC

C

Why not?Bent bonds from

tetrahedral C ?

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)

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

TFDCBC

CC

C

F

N

is roundnot clover-leafnor diamond!

C N Triple Bond

TFDCB

Where is theC-F Bond?

C

CC

C

F

N

Unshared Pair!

TheSecondGreat

Question

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

Dunitz et al. (1981)

Pathological Bonding

Surprising only for its beauty

Lone "Pair"of N atom

Dunitz et al. (1981)

Pathological Bonding

Bond Cross SectionsMissing Bond?

H

H

H

H

HH

Dunitz et al. (1981)

Pathological Bonding

MissingBond !

BentBonds !

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).

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

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

Stockholm (1933)

www.th.physik.uni-frankfurt.de/~jr

PaulDirac

WernerHeisenberg

ErwinSchrödinger

Schrödinger Equation

H = E

Leipzig (1931)

American Institute of Physics

WernerHeisenberg

FelixBloch

VictorWeisskopf

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

Kinetic Energy!2

xi2

2

yi2

2

zi2

+ +1mi

i

h2

82

d2

dx21

mC

C

Curvature of

m

One particle; One dimension: