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Molecular Orbital Theory. Edward A. Mottel Department of Chemistry Rose-Hulman Institute of Technology. Bonding Theories. Ionic Model Skeleton Diagrams Lewis Dot Diagrams Formal Charge, Resonance Molecular Orbital Theory Extends atomic orbitals concepts to molecules. •. •. •. •. •.

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molecular orbital theory

Molecular Orbital Theory

Edward A. Mottel

Department of Chemistry

Rose-Hulman Institute of Technology

bonding theories
Bonding Theories
  • Ionic Model
  • Skeleton Diagrams
  • Lewis Dot Diagrams
    • Formal Charge, Resonance
  • Molecular Orbital Theory
    • Extends atomic orbitals concepts to molecules
bonding in diatomic molecules

A+

B

C

D

Ionic bonding

Covalent bonding

Bonding in Diatomic Molecules

Diatomic: molecule contains two atoms

large difference in

electronegativity

small difference in

electronegativity

Give an example of a compound with ionic bonding.

homodiatomic molecules

A

A

Homodiatomic Molecules

The best example of covalent bonding

involves homodiatomic molecules.

Contains two of the same type of atom.

e.g., H2, O2, F2, N2

Why are these molecules the best examples

of covalent bonding?

heterodiatomic molecules

positive end

negative end

Heterodiatomic Molecules

HF, BN and CO are heterodiatomic molecules.

Contain two different atoms.

H - F

These molecules are polar covalent.

What factors might help predict the positive

and negative ends of the molecule?

a little review
A Little Review

What is an orbital?

Give an example of an atomic orbital?

What is the name of the mathematical function

that determines the shape of an orbital?

What is the maximum number of electrons

that can be in one orbital?

molecular orbitals

1s atomic

orbital

1s atomic

orbital

Molecular Orbitals

When two atoms come close to each other,

what happens to the orbitals of each atom?

a bond forms

ssb molecular

orbital

sigma s bonding molecular orbital

molecular orbitals8
Molecular Orbitals

Orbital wave functions

can add & subtract to give

new wave functions and

corresponding

molecular orbitals (mo).

Atoms bond

together when

the wave functions

constructively overlap.

sigma bond s

nuclei

SIGMA BOND (s)

A bond between two atoms in which the electron

density of the molecular orbital is between the

two nuclei is called a sigma bond.

(ssb)2 molecular

orbital

molecular orbitals mo
Molecular Orbitals (mo)
  • Obey many of the same rules as atomic orbitals (ao).
  • two electrons per molecular orbital.
  • specific regions of space.
  • one molecular orbital formed for each atomic orbital used.
wave functions
Wave Functions

The amplitude (height) of each wavefunction

can either be positive or negative.

wavefunctions bonding antibonding orbitals
WavefunctionsBonding & Antibonding Orbitals

sb

Constructively interfere in certain regions of space.

s*

Destructively interfere in certain regions of space.

bonding antibonding orbitals

ssb

H

H

ss*

Bonding & Antibonding Orbitals

When a bonding

molecular orbital forms,

an antibonding

molecular orbital

also forms.

Bonds form where orbitals overlap and electrons are.

atomic and molecular orbitals

z

y

x

Atomic and Molecular Orbitals

Atomic orbitals include

3dz2

2py

1s

atomic and molecular orbitals15

y

x

px*

Atomic and Molecular Orbitals

Molecular orbitals include

z

ssb

sz*

atomic and molecular orbitals16
Atomic and Molecular Orbitals

This represents an orbital

atomic and molecular orbitals17

energy

Atomic and Molecular Orbitals

carbon: 1s2 2s2 2p2

An orbital can be empty

or can contain

1 or 2 electrons.

Orbitals

can have

different energies

molecular orbital diagrams
Molecular Orbital Diagrams
  • Examples
    • dihydrogen
    • dihelium
    • dihelium(I) ion
dihydrogen h 2

H

H

energy

H

H

Dihydrogen, H2

ss*

ssb

The branch lines indicate which

atomic orbitals are involved in

generating the molecular orbitals.

Two 1s1hydrogen orbitals

overlap to form assb

bonding molecular orbital

1s1 hydrogen orbital

of two hydrogen atoms

dihydrogen h 220

ss*

H

H

energy

Dihydrogen is diamagnetic

and contains onebond

(one pair of bonding electrons).

ssb

ao

mo

ao

(ssb)2

electronic configuration

of the hydrogen molecule.

Dihydrogen, H2

What advantage can

an orbital gain in forming

a molecular orbital from

an atomic orbital?

Why is dihydrogen

diamagnetic?

dihelium he 2

energy

atomic orbital

of one He atom

atomic orbital

of the other

He atom

Dihelium, He2

Two electrons occupy

the highest molecular orbital

forming a ss*

ss*

Each helium atom

has the electronic

configuration 1s2

(eachcontributes

2 electrons to the helium

molecular orbitals)

Two electrons occupy

the lowest molecular orbital

forming a ssb

ssb

dihelium he 222

ss*

energy

ssb

Dihelium, He2

Why doesn’t He2 exist

as a stable molecule?

The electronic configuration

of the dihelium molecule is

(ssb)2 (ss*)2

dihelium i ion he 2

He

He

He

energy

He+

Dihelium(I) Ion, He2+

ss*

ssb

How many valence electrons must be considered

in the dihelium(I) ion?

Complete the molecular orbital diagram using the available electrons.

dihelium i ion he 224

He

energy

He+

Dihelium(I) Ion, He2+

These represent

the atomic orbitals.

ss*

ssb

Shaded means

2 electrons

Lined

means 1

dihelium i ion he 225

He

energy

He+

Dihelium(I) Ion, He2+

ss*

ssb

Draw an outline of the molecular orbitals.

Fill-in the molecular orbitals,

shaded for 2 electrons, lined for 1.

dihelium i ion he 226

ss*

energy

ssb

Dihelium(I) Ion, He2+

What physical properties

are predicted for the

dihelium(I) ion?

(magnetic and bond order)

orbitals are wave functions
Orbitals Are Wave Functions
  • Wave functions contain mathematical terms that can have positive and negative values.
  • An s orbital value can either be less than zero or greater than zero.
  • The two lobes of a p orbital are separated by a node and have opposite signs.
orbitals are wave functions28
Orbitals Are Wave Functions

Different colors represent

opposite mathematical signs.

pi bond formation
Pi Bond Formation

y

A pi bond (p) occurs

when two lobes of each

atomic orbital overlap.

z

py- py Orbital Overlap

pi bond formation30

y

z

Pi Bond Formation

The molecular orbital

does not lie directly on

the internuclear axis.

y

y

z

Resulting Bonding

Molecular Orbital

py- py Orbital Overlap

p antibond formation
p Antibond Formation
  • What is the symbol of a p antibond?
  • How is a p antibond formed?
  • What does a p antibond look like?
pi antibond formation

y

z

Resulting Antibonding

Molecular Orbital

Pi Antibond Formation

y

z

py- py Antibond

Orbital Overlap

pi bonds

py*

pyb

Pi Bonds

py* bonding orbital

has four lobes and

holds a maximum

of two electrons.

pyb bonding orbital

has two lobes and

holds a maximum

of two electrons.

pi bonding involving p x orbitals

x

Pi Bonding Involving Px Orbitals

x

pxb

Resulting Bonding

Molecular Orbital

px- px Orbital Overlap

pi bonding involving p x orbitals35

x

x

Pi Bonding Involving Px Orbitals

px*

Resulting Antibonding

Molecular Orbital

px- px Antibonding

Orbital Overlap

pi bonding involving p orbitals

y

y

2p

x

z

Pi Bonding Involving p Orbitals

px-px overlap gives pxband px*

py-py overlap gives pyband py*

From the mo diagram,

how can you determine that

pxband pyb

are equally stable?

Why are pxband pybequally stable?

molecular orbital diagrams involving s and p orbitals

2p

energy

2s

1s

Molecular Orbital DiagramsInvolving s and p Orbitals

The molecular orbitals

formed depend on

the atomic orbitals’

overlap

direction

energy

molecular orbital diagrams involving s and p orbitals38

2p

2s

1s

Molecular Orbital DiagramsInvolving s and p Orbitals

Identify the orbitals

that represent the

following

Nonbonding molecular

orbitals

Antibonding molecular

orbitals

Pi bonds and antibonds

Bonding molecular

orbitals

Sigma bonds and antibonds

Weak pz-s mo interaction

Homonuclear examples:

O2, F2

diatomic molecular orbital diagram strong p z s interaction

2p

energy

2s

1s

Diatomic Molecular Orbital DiagramStrong pz-s interaction

Homonuclear

Examples:

Li2, B2, C2, N2

Heteronuclear

Examples:

NO, BO, BO+,

CO, CO+,

CN, CN–

homonuclear diatomic molecules
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.
slide41

2p

energy

2s

1s

Orbital Sequence

(ssn)

(ssb)

(ss*)

(px,yb)

(szb)

(px,y*)

(sz*)

sz*

px,y*

szb

px,yb

ss*

ssb

ssn

slide42

Dinitrogen (14 total e–)

Diboron (10 total e–)

Dicarbon (12 total e–)

Diberyllium (8 total e–)

Dilithium (6 total e–)

sz*

px,y*

energy

2p

szb

px,yb

ss*

ssb

2s

ssn

1s

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

Bond Order and Magnetic Properties?

Bond Order and Magnetic Properties?

Bond Order and Magnetic Properties?

Bond Order and Magnetic Properties?

Bond Order and Magnetic Properties?

First,

fill in the

valence

electrons.

Then,

fill in the

mo diagram

slide43

sz*

px,y*

energy

2p

px,yb

szb

ss*

1.123 Å

1.207 Å

1.26 Å

1.49 Å

2s

properties?

properties?

properties?

properties?

ssb

ssn

1s

Compare the bond order, bond length and magnetic properties of O2, O2+, O2–and O22–

O2

O2–

O2+

O22–

dioxygen

O

O

Dioxygen

What are the advantages and disadvantages

of this description of dioxygen?

compare the physical properties predicted for dioxygen by the lewis dot diagram and mo theory

O

O

Lewis Dot

Structure

Molecular

paramagnetic

Orbital

2 unpaired electrons

Theory

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

Bond Order

Magnetic Properties

2

? (diamagnetic)

2

Liquid dioxygen will cling to the pole of a magnet.

compare the physical properties for the dioxygenyl i ion dioxygen superoxide ion and peroxide ion

Magnetic

Bond

Properties

Order

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

Bond

Length

O2+

paramagnetic (1)

1.123 Å

2.5

O2

paramagnetic (2)

1.207

2

O2–

paramagnetic (1)

1.26

1.5

O22–

diamagnetic

1.49

1

oxygen oxygen bonds

H

O

H

O

O

O

Oxygen-Oxygen Bonds

Which oxygen-oxygen bond is easier to break?

slide48

Difluorine (18 total e–)

Dineon (20 total e–)

sz*

px,y*

energy

2p

px,yb

szb

ss*

2s

ssb

ssn

1s

Bond Order and Magnetic Properties?

Bond Order and Magnetic Properties?

homodiatomic molecules49

1

diamagnetic

0

1

diamagnetic

0

1

paramagnetic

Homodiatomic Molecules

bond

length

(Å)

magnetic

properties

bond

order

Electronic Configuration

H2

(ssb)2

0.74

He2

(ssb)2 (ss*)2

Li2

(s1sn)4 (ssb)2

2.67

Be2

(s1sn)4 (ssb)2 (ss*)2

B2

(s1sn)4 (ssb)2 (ss*)2 (pxb)1 (pyb)1

1.59

homodiatomic molecules50
Homodiatomic Molecules

Electronic Configuration

(s1sn)4(ssb)2(ss*)2(px,yb)4

C2

N2

(s1sn)4 (ssb)2 (ss*)2 (px,yb)4 (szb)2

O2

(s1sn)4 (ssb)2 (ss*)2 (px,yb)4 (szb)2 (px*)1 (py*)1

F2

(s1sn)4 (ssb)2 (ss*)2 (px,yb)4 (szb)2 (px,y*)4

Ne2

(s1sn)4 (ssb)2 (ss*)2 (px,yb)4 (szb)2 (px,y*)4 (sz*)2

homodiatomic molecules51

2

3

2

1

0

Homodiatomic Molecules

bond

length (Å)

bond

order

magnetic

properties

C2

1.31

diamagnetic

N2

1.10

diamagnetic

O2

1.207

paramagnetic

F2

1.42

diamagnetic

Ne2