Molecular Orbital TheoryEdward A. Mottel

Department of Chemistry

Rose-Hulman Institute of Technology

A Little Review

What is an orbital?

What is the maximum number of electronsthat can be in one orbital?

What is the name of the mathematical functionthat determines the shape of an orbital?

Give an example of an atomic orbital?

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Molecular Orbitals

When two atoms come close to each other,

what happens to the orbitals of each atom?

a bond forms1s atomic

orbital1s atomic

orbitals

b molecularorbital

sigma s bonding molecular orbital

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Molecular Orbitals

Orbital wave functionscan add & subtract to givenew wave functions andcorrespondingmolecular orbitals (mo).

Atoms bondtogether when

the wave functionsconstructively overlap.

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SIGMA BOND ()

A bond between two atoms in which the electrondensity of the molecular orbital is between the

two nuclei is called a sigma bond.

(sb)2 molecular

orbital

nuclei

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Molecular Orbital Theory

Atomic orbitals can mix togetherto give a new set of molecular orbitals.

Similarities of atomic & molecular orbitals2 electrons max/orbital

occupy specific regions of space

One molecular orbital is formed for each atomic orbital used

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Orbitals Are Wave Functions

Wave functions contain mathematical termsthat can have positive and negative values.

An s orbital value can either beless than zero or greater than zero.

The two lobes of a p orbital are separated bya node and have opposite signs.

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Orbitals Are Wave Functions

Different colors representopposite mathematical signs.

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Sigma Bond Formation

z

pz- pz Orbital Overlap

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Sigma Bonds

z

pz- pz Orbital Overlap Resulting Molecular Orbital

(zb)

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Sigma Antibond Formation

z

pz- pz Orbital Overlap

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z

Sigma Antibond Formation

pz- pz Orbital Overlap

(z*)

Resulting AntibondingMolecular Orbital

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Sigma Bonds indicates themost probable

electron positionis on the

internuclearaxis

(zb)

(z*)

b indicates a bondingmolecular orbital

z indicates themolecular orbital involves

two pz atomic orbitals

* indicates an antibondingmolecular orbital

Electrons in this orbitalwill weaken the bondsbetween these atoms.

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Sigma Bonds

z

s indicates the molecular orbital involvesat least one s atomic orbital.

(sb)

(s*)

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Pi Bond Formation

z

y

py- py Orbital Overlap

A pi bond () occurswhen two lobes of eachatomic orbital overlap.

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Pi Bond Formation

z

y

z

y

py- py Orbital Overlap Resulting BondingMolecular Orbital

yThe molecular orbital

does not lie directly onthe internuclear axis.

Antibond Formation

What is the symbol of a antibond?

What does a antibond look like?

How is a antibond formed?

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Pi Antibond Formation

z

y

py- py Antibond Orbital Overlap

Resulting AntibondingMolecular Orbital

z

y

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Pi Bonds

yb

yb bonding orbital

has two lobes andholds a maximumof two electrons.

y*

y* bonding orbitalhas four lobes andholds a maximumof two electrons.

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Pi Bonding Involving Px Orbitals

xx

px- px Orbital OverlapResulting BondingMolecular Orbital

xb

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Pi Bonding Involving Px Orbitals

px- px AntibondingOrbital Overlap

Resulting AntibondingMolecular Orbital

xx x*

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Pi Bonding Involving p Orbitals

2ppx-px overlap gives x

b and x*

py-py overlap gives yb and y*

From the mo diagram,how can you determine that

xb and y

b

are equally stable?x

z

yy

Why are xb and y

b equally stable?

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Molecular Orbital DiagramsInvolving s and p Orbitals

ener

gy2s

1s

2p

overlap

direction

energy

The molecular orbitalsformed depend onthe atomic orbitals’

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Molecular Orbital DiagramsInvolving s and p Orbitals

2s

1s

2p

Bonding molecularorbitals

Antibonding molecularorbitals

Nonbonding molecularorbitals

Sigma bonds and antibonds

Pi bonds and antibonds

Identify the orbitalsthat represent the

following

Weak pz-s mo interaction Homonuclear examples:

O2, F2

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Diatomic Molecular Orbital DiagramStrong pz-s interaction

ener

gy

2s

1s

2pHomonuclearExamples:

Li2, B2, C2, N2

HeteronuclearExamples:

NO, BO, BO+,CO, CO+,CN, CN–

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Homonuclear Diatomic Molecules

Determine is the sequence of molecular orbitals based on the strong pz-s interaction diagram.

Determine the bond order and magnetic properties for homodiatomic molecules of the first nine elements.

Show the bond lengths are consistent with these diagrams.

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Orbital Sequence

ener

gy

2s

1s

2p

sn

sb

s*

x,yb

zb

x,y*z*

(sn) (s

b) (s*) (x,yb) (z

b) (x,y*) (z*)

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Complete the mo diagram for Li2, Be2, B2, C2 or N2

Dilithium (6 total e–) Bond Order and Magnetic Properties?

Diberyllium (8 total e–) Bond Order and Magnetic Properties?

Diboron (10 total e–) Bond Order and Magnetic Properties?

Dicarbon (12 total e–)Bond Order and Magnetic Properties?

Dinitrogen (14 total e–)

ener

gy

2s

1s

2p

sn

sb

s*

x,yb

zb

x,y*z*

Bond Order and Magnetic Properties?

First,fill in thevalence

electrons.

Then,fill in the

mo diagram

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Compare the bond order, bond length and magnetic properties of O2, O2

+ , O2

– and O2

2–

ener

gy

2s

1s

2p

sn

sb

s*

x,yb

x,y*z*

zb

O2O2+O2–O22–

1.207 Åproperties?1.123 Å

properties?1.26 Å

properties?1.49 Å

properties?

Dioxygen

What are the advantages and disadvantagesof this description of dioxygen?

OO ••

••• •

•• ••• •

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Compare the physical properties predicted for Dioxygen by the Lewis Dot Diagram and MO Theory

Bond Order Magnetic Properties

Lewis DotStructure

MolecularOrbitalTheory

2 ? (diamagnetic)

2paramagnetic

2 unpaired electrons

OO ••

••• •

•• ••• •

Liquid dioxygen will cling to the pole of a magnet.

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Compare the physical properties for the Dioxygenyl(I) Ion, Dioxygen, Superoxide Ion and

Peroxide Ion

BondLength

BondOrder

O2+

O2

O2–

O22–

1.123 Å

1.207

1.26

1.49

2.5

2

1.5

1

MagneticProperties

paramagnetic (1)

paramagnetic (2)

paramagnetic (1)

diamagnetic

Oxygen-Oxygen Bonds

Which oxygen-oxygen bond is easier to break?

OO

••• •

••

• • HOH O

• • • •

• • • •

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Difluorine (18 total e–)Bond Order and Magnetic Properties?

Dineon (20 total e–)

ener

gy

2s

1s

2p

sn

sb

s*

x,yb

x,y*z*

zb

Bond Order and Magnetic Properties?

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Homodiatomic MoleculesElectronic Configuration

H2

He2

Li2

Be2

B2 (sn)4 (s

b)2 (s*)2 (xb)1 (y

b)1

(sn)4 (s

b)2 (s*)2

(sn)4 (s

b)2

(sb)2 (s*)2

(sb)2

bondlength

(Å)

magneticproperties

0.74

2.67

1.59

diamagnetic

diamagnetic

paramagnetic

bondorder

1

0

1

0

1

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Homodiatomic Molecules

C2

N2

O2

F2

Ne2

bondlength (Å)

magneticproperties

1.31

1.207

diamagnetic

diamagnetic

paramagnetic

bondorder

2

3

2

1

0

diamagnetic1.10

1.42

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Skeleton Diagram FailuresCarbon Monoxide

C O C Oor

How would the hybridization of theatoms in carbon monoxide be described?

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energ

y

COC O

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Carbon Monoxide

Sigma orbital overlaps of CO.

+

- + -+

+

+ + + +

+

- + - +

-

+ + - -

-

- + + -

-

- + + -

-

- + + -

+

- + - +

Is the HOMO of carbon monoxidebonding, nonbonding or antibonding?

CO 1.1282 Å

CO+ 1.1151 Å

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energ

y

COC O

Where oncarbon monoxide

is theHOMO located?

Species containingthree or more atoms

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Beryllium Hydride

Draw the orbital overlaps of BeH2.

Rank the orbitals in terms of energy.

++ +

++ - -

-+ +

-+ + -

Draw a molecular orbital diagram of BeH2.

(draw the nodes in each diagram)

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energ

y

BeH2Be 2 H

Sigma () bonds form

orbitals are conserved

two bonds are formed

all e- are paired

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Draw the molecular orbital diagram forthe nitrate ion.

What is the hybridization of nitrogen?

How many atomic orbitals are there?

How many p- orbitals are there?

How are the energies of the p- orbitalsgoing to split?

How many nonbonding orbitals are expected?

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Nitrate Ion

N••••

• •• •O

O ••••

•• ••

O

••

••••

••

N••••

• •• •O

O ••••

••••

O

••

••••

••

N••••

• •• •O

O ••••

••

O ••••

••••••

The double bond is delocalized overthe three nitrogen-oxygen bonds.

Bond order = 1.33

+ + +

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Nitrate Ion

The nitrogen-oxygen bond length is intermediate between N-O and N=O.

typical N-O bond length: 1.40 Å

typical N=O bond length: 1.21 Å

-

NOO

O1.22 Å

What is thehybridizationof nitrogen?

How do the orbitals of the atomsin nitrate overlap?

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Nitrate Ion

Top down view(xz plane)

The nitrogen atomin nitrate ion

is sp2 hybridizedand overlaps a

pz orbital oneach oxygen.

three N - Osigma bonds

N••••

• •• •O

O ••••

•• ••

O

••

••••

••

+

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Nitrate Ion

Top down view(xz plane)

If you don’tbelieve in

hybridization.

three N - Osigma bonds

N••••

• •• •O

O ••••

•• ••

O

••

••••

••

+

How doesthe doublebond form?

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Nitrate Ion

Edge on view

N••••

• •• •O

O ••••

•• ••

O

••

••••

••

pi overlap involvesthe nitrogen py orbitalwith all three oxygen

py orbitals toform one pi bond

the oxygen orbitalswith single electrons

change from oneoxygen atom to another

+y

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Nitrate Ion

Edge on view

one N - O pi bonddelocalized over

three oxygen atomsthis hybridizationrequires that the

nitrate ion isplanar

What would the py-orbitalslook like if all four atoms

in this ion were not planar?

y

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Nitrate Ion

Edge on view

one N - O pi bonddelocalized over

three oxygen atomsifnitrate ion

wasn’tplanar

What would the py-orbitalslook like if all four atoms

in this ion were not planar?

y

energ

y

3 ON NO3-

Sigma Bonding PatternsNitrogen s, px and py orbitals overlap with oxygen.

energ

y

3 ON NO3-

How are the energies of the p- orbitalsgoing to split?

energ

y

3 ON NO3-

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energ

y

COC O

energ

y

O O ON