Chem 125 Lecture 7 9/14/05 Projected material This material is for the exclusive use of Chem 125 students at Yale and may not be copied or distributed.

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

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: