Previous examples of “pathological” bonding and the BH3 molecule illustrate 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. This

lecture then focuses on understanding 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 15

Chemical Reactivity: SOMO, HOMO, and LUMO

Synchronize when the speaker finishes saying

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Perspectives:

Molecule(Reality)

Computer(Approximate Schroedinger)

Chemist(Understand Bonds)

MissingBond ?

(e.g. 32nd of 33 occupied MOs)

Cf. Lecture 7 - Dunitz et al. (1981)

Experiment: Pathological Bonding

BentBonds ?

Would a Computer’s MOsProvide Understanding?

No! Far too complicated to answer “Why?”

But analysis in terms of pairwise bonding overlapof hybrid AOs provides

clear explanations.

Experiment: Pathological Bonding

MissingBond ?

BentBonds ?

BestOverlapPossiblefor 60°

C-C-C

Very PoorOverlap

>90°?

psp4.1sp1.4

Because sp4.1extendsto give best overlap

Why not p orbitals (90°)?

Rehybridizing to strengthen this

bond would weaken six others.

Three Views of BH3

2) Molecular Orbitals

1) Total Electron Density

3) Bonds from Hybrid AOs

(Nature)

(Computer)

(Student)

B

H

HH

ElectronCloud of

by "Spartan"

BH3

Total e-Density0.30 e/Å3

Mostly1s Core

of Boron

B

H

HH

BH3

Total e-Density0.15 e/Å3

BH3

Total e-Density (0.05 e/Å3)

Dimple

H atoms take e-densityfrom valence orbitals of B

BH+••H •

B•

BH3

Total e-Density0.02 e/Å3

BH3

Total e-Density0.002 e/Å3

van der Waalssurface

(definition)

BH3

Total e-Density0.002 e/Å3

ElectrostaticPotential

Energy of a+ probe onthe surface

low (-) high (+)

H

Computer PartitionsTotal e-Density

intoSymmetrical MOs

(à la Chladni)

BH3

8 low-energy AOs 8 low-energy MOs

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

3 H : 1s

AO “basis”

set

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

2s ••••

••

••

Radial Node

MOLECULAR ORBITALS

2px ••••

••

••

MOLECULAR ORBITALS

2py••

••

••

••

MOLECULAR ORBITALS

2pz

••••

••

••

MOLECULAR ORBITALS

3s

••••

••

••

MOLECULAR ORBITALS

3dx2-y2

••••

••

••

MOLECULAR ORBITALS

3dxy

••••

••

••

MOLECULAR ORBITALS

We PartitionTotal e-Density

intoAtom-Pair Bonds

(and anti-bonds)

& Lone Pairs(and vacant atomic orbitals)

(à la Lewis)

usually

When thisdoesn't work,and we must

use moresophisticatedorbitals, wesay there is

RESONANCE

2pz

••

••

••

•••••• ••BHHB

Same Total e-Density!

Same Total Energy!

BH

HB

For Many Purposes Localized Bond Orbitals are Not Bad

Boron Core

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

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

is our intermediate betweenH-like AOs and Computer MOs

When must we think more deeply?

When mixing of localized orbitals causes

Reactivityor

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 A

SOMO-SOMO(when they exist)

UMOs

many atoms"free radicals"

e.g. •H •Cl •CH3

not so common

ingly

molecule molecule

Which MOMixings Matter

forReactivity?

••

••

••

••

etc.

UMOs

••

••

••

etc.

UMOs

OMOsOMOs

••

••

B A

Nothing

Weak NetRepulsion

••

Negligible Mixing

because of Bad

E-match

molecule molecule

Which MOMixings Matter

forReactivity?

••

••

••

••

etc.

UMOs

••

••

••

etc.

UMOs

OMOsOMOs

B ABonding!

Unusually High

HOMOwith

Unusually Low

LUMO

••

molecule molecule

••

Negligible Mixing

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

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

High HOMO-Low LUMO

mixing constitutes

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:Compared to What?

••

*CH

CH

"usual"LUMO

"usual"HOMO

(or *CC )

(or CC )

I. Unmixed Valence-Shell AOs

III. Unusual AO Energy in MO

Sources of weirdness:

IV. Electrical Charge

II. Poor Overlap of AOs

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)

End of Lecture 15Oct. 18, 2008

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