Chem 125 Lecture 89/22/06

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.

Exam 1 - Friday, Sept. 29 !Covers Lectures through next Wednesday

Including:

Functional GroupsX-Ray Diffraction

1-Dimensional Quantum Mechanics(Sections I-IV of webpage

& Erwin Meets Goldilocks)IMPORTANT PROBLEMS therein due Wednesday

Get-aquainted session this afternoon 4-5:30 in Lecture Room

Exam Review 7-9 pm Tuesday, Room WLH 208

Other Help Available Wednesday 8-10 PM, RTBAThursday 7-10:30 PM, RTBA

HELIXw

S

Svw

SCuriousIntensitySequence

B-DNAR. Franklin

(1952)

OffsetDouble Helix

repeated pair pattern

BASE STACKING

B-DNAR. Franklin

(1952)

wS

Svw

S

MAJOR& MINORGROOVES

HELIX DIAMETER

X-Ray Diffraction

Old-StyleElectronDensity

Map

Contours connect points of equivalent

density.

K Penicillin

K Penicillin3-D Map(1949)

K

1 e/Å3

contours

Rubofusarin

No H?

Highe-DensityNo :

on O!

Stout & Jensen "X-Ray Structure Determination (1968)

5 e/Å3

7 e/Å3

long

short

intermediate

No : Bonds!

Spherical Atoms

“Seeing” 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 electron),

then many-electron atoms, then many atoms,

& finally functional groups.

N particles 3N arguments![sometimes 4N+1]

Schrödinger Equation

H = E

(for “stationary” states)time-independent

=

H = E

Kinetic Energy + Potential Energy = Total Energy

Given - Nothing to do with (Couloumb is just fine)

Hold your breath!

H = E

Kinetic Energy?mi vi

2i

Const

Kinetic Energy!2

xi2

2

yi2

2

zi2

+ +1mi

i

h2

82

d2

dx21

mC

One particle; One dimension:

Kinetic Energy!2

xi2

2

yi2

2

zi2

+ +1mi

i

h2

82

d2

dx21

mC

C

Curvature of

m

One particle; One dimension:

Solving a Quantum Problem

Given : a set of particlestheir 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

AND remains finite(single-valued, continuous, 2 integrable)

Much Harder for Many Particles

Is it worth our effort?

Reward for Finding

Knowledge of Everythinge.g.

Allowed EnergiesStructureDynamicsBonding

Reactivity

The Jeopardy Approach

Answer Problem

= sin (x)

= sin (ax)

= ex

KineticEnergy

= e-x

C/mparticle infree space

a2 C/m shorter wave higher energy

’’

-C/m

-C/m

Const PE > TE

’’(actually appears for electrons bound to nucleiat large distance, where 1/r ceases changing much!)

Rearranging Schrödinger to give a formula for curve tracing.

C

Curvature of

m

+ V = E

CCurvature of

m

(V- E)=Curves away from 0 for V>E; toward 0 for V<E.

Since m, C, V(x) are given, this recipe allows tracing (x) in steps, from initial (0) [= 1], with initial slope [0], and a guessed E.

reward

ForFinding

www.nlc-bnc.ca/explorers/ kids