This year’s Nobel Prizes in Physics and Chemistry tie in nicely to the subjects of our course, including

today’s lecture. Examining the BH3 molecule illustrates how a chemist’s use of localized bonds, vacant

atomic orbitals, and unshared pairs to understand molecules compares with views based on the

molecule’s actual total electron density, and with computational molecular orbitals. The localized view is

then used to help understand reactivity in terms of the overlap of singly-occupied molecular orbitals

(SOMOs) and, more commonly, of an unusually high-energy highest occupied molecular orbital (HOMO)

with an unusually low-energy lowest unoccupied molecular orbital (LUMO). This generalizes the traditional

concepts of acid and base. Criteria for assessing reactivity are outlined and illustrated.

Chemistry 125: Lecture 15October 6, 2010

Chemical Reactivity: SOMO, HOMO, and LUMO

For copyright notice see final page of this file

Graphene’s unique MO structure gives it unique electrical and optical properties, stability, strength, and “resonance”.

Levitator by Martin Simon (UCLA)

Eppur sta fermo“and yet it stands still”

Graphene

Andre Geim’s Hand (1999)

Levitator by Martin Simon (UCLA)

“and yet it stands still”

Andre Geim’s Frog (1999)

http://nobelprize.org/nobel_prizes/chemistry/laureates/2010/

Three Views of BH3

2) Molecular Orbitals

1) Total Electron Density

3) Bonds from Hybrid AOs

(Nature)

(Computer)

(Chemist)Cf. Course Webpage

How BH3 Sees Itself:The Electron Cloud of

via "Spartan”STO 6-31G**

B

H

HH

B

H

HH

BH3

Total e-Density0.30 e/ao

3

Mostly1s Core

of Boron

BH3

Total e-Density0.15 e/ao

3

BH3

Total e-Density 0.05 e/ao

3

Dimple

H atoms take e-densityfrom valence orbitals of B

BH+••H •

B•

BH3

Total e-Density0.02 e/ao

3

BH3

Total e-Density0.002 e/ao

3

van der Waalssurface

(definition)

BH3

Total e-Density0.002 e/ao

3

HIGH(+ 55 kcal/mole)

LOW(-7.5 kcal/mole)

ElectrostaticPotentialEnergy of a+ probe onthe surface

H

low (-) high (+)

2) Molecular Orbitals

1) Total Electron Density

3) Bonds from Hybrid AOs

(Nature)

(Computer)

(Chemist)Cf. Course Webpage

Three Views of BH3

Computer PartitionsTotal e-Density

intoDelocalized MOs

.

(à la Chladni or Plum Pudding)

BH3

8 low-energy AOs 8 low-energy MOs

B : 1s , 2s , 2px , 2py , 2pz

3 H : 1s

“Minimal.. Basis Set”

of AOs

MOLECULAR ORBITALS

noccupied

BH3

8 electrons / 4 pairs

B : 5 electrons3 H : 3 1 electron

••••

••

••

OMOs

UMOs

LUMO

HOMO(s) •• ••

ccupied

ighest

owest

MOLECULAR ORBITALS

1s

••••

••

••

1s ••Boron Core

MOLECULAR ORBITALS

Cf. website

2s ••••

••

••

Radial Node

MOLECULAR ORBITALS

Cf. website

2px ••••

••

••

MOLECULAR ORBITALS

Cf. website

2py••

••

••

••

MOLECULAR ORBITALS

Cf. website

2pz

••••

••

••

MOLECULAR ORBITALS

Cf. website

3s

••••

••

••

MOLECULAR ORBITALS

Cf. website

3dx2-y2

••••

••

••

MOLECULAR ORBITALS

Cf. website

3dxy

••••

••

••

MOLECULAR ORBITALS

Cf. website

2) Molecular Orbitals

1) Total Electron Density

3) Bonds from Hybrid AOs

(Nature)

(Computer)

(Chemist)Cf. Course Webpage

Three Views of BH3

We Partitionthe same

Total e-Densityinto Atom-Pair Bonds

(and anti-bonds)

& Isolated AOs(lone pairs / vacant atomic orbitals)

(à la Lewis)

usually

When this

doesn't work,and we must

use moresophisticatedorbitals, wesay there is

RESONANCE

2pz

••

••

••

••

For Many Purposes Localized Bond Orbitals are Not Bad

Boron Core

And they are easier to think about; but beware of resonance.

••BH

H

B ••

H

B ••

Same Total Energyas computer!

HB

Same Totale-Density

also!

BH

HB

(and of properties of individual electrons)

The Localized Bond Orbital Picture(Pairwise Bond Orbitals and Isolated AOs)

is our intermediate betweenH-like AOs and Computer MOs

When must we think more deeply?

When we care about individual electrons(ionization ; visible/uv absorption)

When mixing of localized orbitals causes

Reactivity ………….. or Resonance

Where are We?

MoleculesPlum-Pudding Molecules ("United Atom" Limit)

Understanding Bonds (Pairwise LCAO)"Energy-Match & Overlap"

Structure (and Dynamics) of XH3 MoleculesParsing Electron Density

Atoms3-Dimensional Reality (H-like Atoms)

HybridizationOrbitals for Many-Electron Atoms (Wrong!)Recovering from the Orbital Approximation

Recognizing Functional Groups

Payoff forOrganic

Chemistry!

ReactivitySOMOs, high HOMOs, and low LUMOs

Which MOMixings Matter

forReactivity?

••

••

••

••

etc.

••

••

••

etc.

UMOs

OMOsOMOs

B A

UMOs

Myr

iad

Pos

sibl

e P

airw

ise

Mix

ings

molecule molecule

Which MOMixings Matter

forReactivity?

••

••

••

••

etc.

••

••

••

etc.

UMOs

OMOsOMOs

••SOMO

SOMO••

B ASOMO-SOMO(when they exist)

UMOs

many atoms"free radicals"

e.g. •H •Cl •CH3

ingly

molecule molecule

(in order to survive must be kept from overlapping

not very common)

Which MOMixings Matter

forReactivity?

••

••

••

••

etc.

UMOs

••

••

••

etc.

UMOs

OMOsOMOs

••

••

B A

Nothing

4e-

Weak NetRepulsion

••

molecule molecule

(balances correlation atvan der Waals contact)

Negligible Mixing &

Stabilization because of Bad

E-match

Which MOMixings Matter

forReactivity?

••

••

••

••

etc.

UMOs

••

••

••

etc.

UMOs

OMOsOMOs

B ABonding!

Unusually High

HOMOwith

Unusually Low

LUMO

••

molecule molecule

••

Negligible Mixing &

Stabilization because of Bad

E-match

Which MOMixings Matter

forReactivity?

••

••

••

••

etc.

UMOs

••

••

••

etc.

UMOs

OMOsOMOs

B A••

Bonding!

Unusually High

HOMOwith

Unusually Low

LUMO

BASE

ACID

molecule molecule

or in common parlance

Most mixing of MOs affects neither overall energy nor

overall electron distribution for one (or more) of these reasons:

1) Electron occupancy 4 or 0

2) Poor energy match

3) Poor overlap BUT

Mixing of High HOMO

& Low LUMOconstitutes

Reactivity

Acid-Base TheoriesTHEORY ACID BASE

Lavoisier(1789)

OxidizedSubstance

Substance tobe Oxidized

Arrhenius(1887)

H+ Source OH- Source

Incr

easi

ng G

ener

ality

Brønsted/Lowry(1923)

H+ Donor H+ Acceptor

Lewis(1923)

e-Pair Acceptor"Electrophile"

e-Pair Donor"Nucleophile"

HOMO/LUMO(1960s)

unusually

High HOMOunusually

Low LUMO

••

sp3C 1sH

Unusual:

••

"usual"LUMO

"usual"HOMO

I. Unmixed Valence-Shell AOs

III. Unusual AO Energy in MO

Sources of weirdness:

IV. Electric Charge

II. Poor Overlap of AOs

Compared to What?*CH

CH

(or *CC )

(or CC )

I. Unmixed Valence-ShellAtomic Orbitals

••

*CH

CH

••

sp3C 1sH

BH3

low LUMO

••

CH3

high HOMO

••

NH3

high HOMO

"usual"LUMO

"usual"HOMO

••

OH2

high HOMO

••

OHhigh HOMO

(or *CC )

(or CC )

H+

low “LUMO”

(energies qualitative only)

(Also IV: Electrical Charge)

Acid-Base Reactions

H+ OH H-OH

H+ :NH3

H3B OH

H3B :NH3

H-NH3+

H3B-NH3+

Curved Arrows Designate e-Pair Shifts.

Start arrow at e-pair location in starting material.

End arrow at e-pair location in product.

(NOT atomic motion)H3B-OH

tetravalent N is +

tetravalent B is -

II. Poor-Overlap MOs

••

*C=O

C=O

•

•

pC

pO

••

*CH

CH

••

sp3C 1sH

••

*C=C

C=C

••

pC pC

high HOMO

low LUMO"usual"LUMO

"usual"HOMO

Bent

(energies qualitative only)

End of Lecture 15Oct. 6, 2010

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