Chemistry 125: Lecture 3Sept 3, 2010

Force Laws,Lewis Structures,

Resonance, Double Minima, and Earnshaw’s Theorem

For copyright notice see final page of this file

Does Newton’sChemical Force Law

Exist?

How far can you Stretcha Chain of Atomsbefore it Snaps?

Force Laws & Molecular StructureSpring (ut tensio sic vis) Electrical Charges (gravity, etc.)

Balanced minimum Balanced minimum !

F = -k x F = k / (x)2

Po

ten

tial

En

erg

y

Single Minimum Double Minimum

x

x

sum

sum

Slope = F

0

0

2nd Spring(weaker,

opposing)

3rd Stronger Body

E = k/2 (x)2 E = -k/(2 |x|)Direct Inverse

(but not with ions or magnets)

Thus with springs you might make a stable polyatomic

molecule from point atoms.

However, if bonds obeyed Hooke’s Law,

they could never break.

FixedNeighbor

Mathematically convenient approximation

for realistic bond energies(proposed 1929)

Sum

Morse Potential

Second Fixed

Neighbor

Morse Potential

Snaps atInflection Point

(Change from direct to inverse force)

What ARE bonds?

Demonstrationwith

Magnets

Valuable prize for balancing suspended magnet

between sets of attracting ma gnt!

Why do Elements Differ?

Figure from 1861

Different # for different atoms: H(1), C(4), O(2), N(3)

NH3 and NH4Cl

or 5?)

19th Century Experiments led to VALENCE numbers

Gertrude and Robert Robinson (1917)

Might Latent Valence Loop explain trivalence of pentavalent N?

What does the loop mean?

“partial dissociation”

Such slippery concepts “explain” so much that they convince you of nothing.

“latent” valence

loop

Why/When

?

Why/When ? reaction produc

t

Reaction Scheme

Might Partial Dissociation explain amine/HCl reactivity?

How Many?

ElectronDiscovered

1897

The Cubic Octet of G. N.

Lewis(1875-1946)

as Harvard Undergraduate

~1894

as Harvard Instructor~1902

© E

. S. L

ewis

, by

per

mis

sion

Octet to "Explain" Periodicity & Electron Transfer

(1902 teaching notes)

Octet Predicts Shared Pair Bonding

?

shared edge

shared face

Cubic Octet to Tetrahedral Octetto Tetrahedral Octet

N N::

(G. N. Lewis 1916)

Tetrahedral distribution of the bonds from C had

already been known in organic chemistry

for 40 years!

Good Theory should be Realistic & Simple

In regard to Factsit should allow:

PredictionSuggestion

Explanation

Classification& Remembering

as as possible

Postdiction:Realm of Lore

From Number of Valence Electronswe would like to predict:

Constitution (valence numbers for different atoms)

Structure (distances & angles)

Energy Content

Reactivity

Charge Distribution

Lewis Explains Constitution “the nature and sequence of bonds”

H ••B••

•

•C••

••

•N•• O

••••

•• F••

••••

•

1 233 4 1

H •N••

••••

•HH

Why Octet?

Why Pair for H / He?

(Electron # Valence # and Unshared Pairs)

H •

H•

H•N•

••

••+

H•H•

H•B•

••

HCNH • •

•C ••

Tetravalent N is positive.

N ••

••

•

••CH•

• ••• N••• C ••H N

Tetravalent B is negative.

NH3 BH3H3N-BH3

+

H •

H•

H•N ••

••

•H•

H•

H•B•

••

Bookkeeping of “Formal” Charges

(each atom is assignedhalf-interest in bonding pairs)

••

Puzzle:

2 BH3 B2H6 + ~40 kcal/molWhat is the “glue”? (Answer in Lecture 16)

Lewis had the idea of using : to denote

unshared pairs.

+ -

*) Energy of a proton on the “molecular surface”

Surface Potential* of H3N-BH3 (from Quantum-Mechanics)

HIGH(+ 25 kcal/mole)

(-41 kcal/mole)

LOWN end indeed bearspositive charge

and B end bearsnegative charge

Lewis Explains “Pentavalent” N.Actually Tetravalent - thus Charged.

NH

HHH

+Cl

Amine

R •

R•

R•N ••

••

•

SR •

R••

••

Sulfide

•

••

O ••

• •

• •Oxide

O• •

••

••

O ••

• •

• •oxide

+ -

+ -+2 --

one

O ••• •

• •Peroxys

also for

HCNO(CNO in all six linear orders, plus ring)

Draw Lewis Dot Structures for:

H N C(in the order shown)

Start Lewis-Drill Problems:

Start Memorizing Functional Groups

DoubleMinimum

equilibrium

EQUILIBRIUM vs. RESONANCE

OH C N••

••• • +-

H C N O••

••

••

+ -all octets charge sepn

all octets still charge sepn poorer site for -

N position (relative to C O)

Ene

rgy

midwayleft

shift : to eliminate charge sepn.shift : to restore N octet

N closer to Cthan to O

N ~midwaybetween C and O

Geometric Implication?

but maybe in truth…

EQUILIBRIUM vs. RESONANCE

H C O••

••

••N+ -

SingleMinimum

resonance

OH C••

••• •N+-

single compromise

position for N

N position (relative to C O)

Ene

rgy

midwayleft

i.e. Notation too simplistic

Choice between

Resonance and Equilibrium

must be based onexperimental facts

(or a better theory)

that can distinguish singlefrom double minimum

Equilibrium vs. Resonance

A B A B

Two Real SpeciesOne Real SpeciesTwo “Reasonable”Structural Formulas

Failure of Simplistic Notation

Typically Unusually StableCompared to what?

Equilibrium vs. Resonance

H CO

O

HH C

O

O H••

••••

•• ••

••

••

••

••

••

H CO

O

H C

O

O

••••

•• •• ••

•••

•

Two Species

Two Species?

••

H C

O

O

H C

O

O

••••

•• ••

••

••

•••

•

One Nuclear Geometry!

•

•One Species!

(Evidence: Infrared Spectroscopy)

LORE

(Evidence: Electron Paramagnetic Resonance)

LORE: That which is learned; learning, scholarship, erudition.

Also, in recent use, applied to the body of traditional facts, anecdotes, or beliefs

relating to some particular subject (Oxford English Dictionary)

2. Structures in which all first-row atoms have filled octets are generally important; however, resulting formal charges and electronegativity differences can make appropriate nonoctet structures comparably important.

From a good Text

“empirical rules for assessing the relative importance of the resonance structures of molecules and ions.

1. Resonance structures involve no change in the positions of nuclei; only electron distribution is involved.

3. The more important structures are those involving a minimum of charge separation, particularly among atoms of comparable electronegativity. Structures with negative charges assigned to electronegative atoms may also be important.”

(our depiction of) ^

LORE

From Number of Valence Electronswe would like to predict:

Constitution (valence numbers for different atoms)

Reactivity

Charge Distribution

O2 O3

O•

• •• •

•

• •O ••

••••O

• ••

•

EquilateralTriangle

O•

• •• •

•O•

• •• •

• O•

• •• •

•O•

• •• •

•

OO

••

O• •

• •

OO O

OO

O+

DoubleBond

Open

Trivalent O is positive.

What is Ozone’s Structure?

OO

O

+

_

O O

O

Ring

OO

O

+

_

Open

A Problem in4 Dimensions!(3 distances + energy)

symmetrical single minimum?

Graph Helphttps://webspace.yale.edu/chem125/125/xray/DensityMaps/3din2d.htm

Be sure you can do the problems,but you don't have to hand them in.

(Click for an answer key)

US

GS

Energies from quantum calculations of Ivanic, Atchity, Ruedenberg 1997

Ring

Open

4-DimensionalStructure-

EnergyPlot

3 /Constrained by assuming symmetry

RR12 = R23

••••

Requires

e.g. R12, R23, Energy

Energy Contours

“Steepest-Descent” Path

Pass Between Valleys

O3

More Constrained4-Dimensional

Structure-Energy

Plot

Distance along Steepest-Descent Curve

Ene

rgy

(kca

l/m

ol)

Ring

Open

0

8

2 /

R12 ≠ R23

gives higher E

symmetrical"resonant”structure

Pass

Ozone

What of the charge distribution that

is “predicted” byLewis bookkeeping?

+ in middle

- on ends?

OO

O

+

_

OO

O

+

_

Open

symmetrical single minimum?

*) Energy of a proton on the “molecular surface”

Suface Potential* of Open Ozone (from Quantum-Mechanics)

HIGH(+ 25 kcal/mole)

(-16 kcal/mole)

LOW

+ in middle

- on ends?

YES!

From Number of Valence Electronswe would like to predict:

Constitution (valence numbers for different atoms)

Structure (distances & angles) (we’ll test this later)

Energy Content (we’ll test this later)

Reactivity (at least for H3N: BH3)

Charge Distribution (at least qualitatively for O3, H3N-BH3)

~

~

Lewis Dot Structure

Attempts to provide a “physical” basis for valence rules.

New: Reactivity from unshared pairs(both “hooks” from the same atom)

Convenient for electron bookkeeping(molecular charge; “formal” atomic charges;

qualitatively realistic, at least in the case of O3)

Stability and “Resonance”?

What’s so great about octets?How bad are sestets?

How bad are structures with formal charge separation?

How bad is “bad” charge separation?from 2007 Wiki: “I have a question when drawing

these structures. Is it more ‘important’ to try to fill the octet or to have lowest formal charge on

as many atoms, especially C, as possible? and WHY?”

Is it at all True?

Force Laws?

Are there e-pairsbetween nuclei and

unshared on some atoms?

In systems governed byinverse-square force laws

there can be no local minimum (or maximum)

of potential energy.

Earnshaw's Theorem(1839)

by p

erm

issi

on S

heff

ield

Uni

vers

ity

Samuel Earnshaw (1805-1888)

Visualizing Earnshaw - Coulomb's Electrostatics

“Lines of Force”MagneticElectrostatic

Faraday/Davy/Phillipsyoung

Michael Faraday

by p

erm

issi

on A

lfre

d B

ader

Col

lect

ion

Can show magnitude (as well as direction) of Force

2-D (Flatland)

force magnitude

line density

Circumferenceµ r2

Forceµ

line densityµ

1/r

Can show magnitude (as well as direction) of Force

3-Dimensions

Surfaceµ r2

Forceµ

line densityµ

1/r2

force magnitude

line density

In 3D such Diagrams Work only for Inverse Square Forces!

A positive particle has a local maximum or minimum of energy only at the location of

another charged particle, never in free space.

A positive particle has a local maximum or minimum of energy (peak or valley) only at the location of another charged particle,

never in free space.

In systems governed byinverse-square force laws

there can be no local minimum (or maximum)

of potential energy in free space.

Earnshaw's Theorem

(The only “stationary” points are saddle points.)

Levitator by Martin Simon (UCLA)

Eppur sta fermo“and yet it stands still”

End of Lecture 3Sept 3, 2010

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