Chem 5Chapter 12

Chemical Bonding II:Additional Aspects

Part 2

November 22, 2002

Summary of the Valence Bond Theory

• Hybridized orbitals are linear combinations of atomic orbitals of the central atom, matching the molecular geometry predicted by VSEPR.sp, sp2, sp3, sp3d, sp3d2

+ +

__H2C=CH2

Ethylene

• A σ bond results from an end-to-end overlap of two atomic or hybrid orbitals.

+

_

• A π bond results from a side-to-side overlap of two p orbitals. It is a single bond, with two electrons filling one π orbital.

In ethylene, the C=C double bond consists of a σ bond and a π bond.

In acetelyne, the C≡C triple bond consists of a σ bond and two π bonds.

Lewis structure of O2 O = O ::.. ..

Sometimes, valence bond theory does not work:

All electrons are paired.So O2 is expected to be diamagnetic.

O2 is paramagnetic.DemoParamagnetic: There are unpaired electrons.

Diamagnetic: No unpaired electrons. N2 is diamagnetic.

Robert S. Mulliken 1896 - 1986Born in Newburyport, Massachusetts, Mulliken was the son of an artist and a professor of organic chemistry at Massachusetts Institute of Technology. Heavily influenced by his father’s work, Mulliken developed an interest in chemistry as a boy, earning his B.S. at M.I.T. in 1917, and his Ph.D. at the University of Chicago in 1921.

Like Linus Pauling, Mulliken was exposed to the papers of G. N. Lewis and Irving Langmuir on chemical bonding during his Ph.D. period. He traveled extensively in Europe, meeting many prominent researchers. During a visit in 1925, he established a relationship with Friedrich Hund who helped him to advance the molecular orbital theory. This work formed the basis of the research that eventually earned him the Nobel Prize in Chemistry in 1966. However, it was overshadowed for some time by the valence-bond method advocated by Pauling.

Among the concepts introduced to chemists by Mulliken are molecular orbital, electron donor and acceptor, and electron affinity. He is credited with helping to provide a theoretical foundation for chemistry, which was primarily an empirical science at the time.

MOLECULAR ORBITAL THEORYBasic idea: Electron density between atoms gives a chemical bond

• Linear combinations of atomic orbitals (AO) result in molecular orbitals (MO).

• The number of MOs is equal to the number of AOs combined.

• When two MOs are formed from two AOs, constructive interference gives a bonding MO with a lower energy, and destructive interference gives an anti-bonding MO with a higher energy than the original AOs.

• For MOs formed with equal energy AOs, the more nodes, the higher the energy of the MO.

• Electrons fill MOs with the lowest energy first.

• Each orbital holds up to two electrons (Pauli exclusion principle)and obeys Hund’s rule, just like atomic orbitals.

MOs Formed from Linear Combination of Two 1s AOs

A B1sA + 1sB = MO1

A BElectron density builds up between the atoms

Constructive interference1sA – 1sB = MO2

AB

Electron densitylow in the middle

Destructive interference

1sA 1sB

The two MOs1sA – 1sB = MO2

+ -Node

σ anti-bonding orbital σ1s*

1sA + 1sB = MO1

+

σ bonding orbital σ1s

The Energy of the σ1s and σ1s* OrbitalsEnergy higher than the original orbitals

1s orbital in a free atom

A B

σ1s*1s orbital in a free atomE

σ1s

Energy lower than the original orbitals

The bonding in H2

E1s

σ1s*

1s

σ1s

H HH2

The electrons are placed in the σ1s.

The MO configuration of H2 is (σ1s)2.

E1s

σ1s*

1s

σ1s

H HH2

Two electrons in a bonding orbital results in a stable molecule.

He2

E1s

σ1s*

1s

Atomic configuration of He is 1s2

He He2 He

σ1s

One pair of electrons goes in σ1s

and the next pair in σ1s*

He2: (σ1s)2(σ1s*)2MO configuration

He

E1s

σ1s*He2 He

1s

σ1s

The bonding effect of the (σ1s)2 is cancelled by theantibonding effect of (σ1s*)2. The He2 is not stable.

The MO configurations, such as He2:(σ1s)2(σ1s*)2,tell us four things:

• Its shape, σ or π.

• The parent AOs.

• Its stability (bonding or antibonding): Antibonding is designated with an asterisk (*).

• The number of electrons.

BOND ORDERA measure of bond strength and molecular stability.

If # of bonding electrons > # of antibonding electronsthen the molecule is stable.

{ # of bonding electrons

# of antibondingelectrons–Bond order = 1/2 }

For He2 (σ1s)2(σ1s*)2 BOND ORDER = 0

A high bond order indicates high bond energy and short bond length.

Consider H2+,H2,He2

+,He2...

σ1s*

σ1s

Magnetism

Bond order

Bond energy (kJ/mol)

Bond length (pm)

H2+

Para-

½

225

106

He2+

Para-

½

251

108

He2

__

0

—

—

H2

Dia-

1

436

74

E

First row diatomic molecules and ions

E

1s

σ1s*

1s

σ1s

2s

σ2s*

2s

σ2sFill the MO’s withelectrons, two in each MO from thelowest energy level

Li2

Now look at second period homonuclear diatomic molecules

Electron configuration for Li2

E

1s

σ1s

1s

2s

σ2s

σ2s*

(σ1s)2(σ1s*)2(σ2s)2

2s

Bond Order = (4 - 2)/2 =1

A stable single bond.σ1s

*

The σ1s and σ1s* orbitals cancel.

We can omit the inner shell.

Be2DIBERYLLIUM

Be Be2 Be

σ2s*

E2s 2s

σ2s

Fill the orbitals

Electron configuration for Be2 is (σ2s)2(σ2s*)2.

E2s

σ2s*

Be Be2 Be

2s

Bond Order =(2 - 2)/2 =0

No bondσ2s

How about B2?because the Boron atoms have 2p electrons.

We need to use 2p orbitals to form MOs

Two 2px AOs σ2px & σ*2px MOs

-- ++

_ - --+

σ2px

- -++ -+

σ*2px

Bonding

Anti-bonding

Two 2pz AOs π2pz & π*2pz MOs

+

-

+

-+

-π2pz

+

π*2pz

+

-+

-_

Bonding

Anti-bonding

+- -

+

-

+π2py

+

- +-+

_

Two 2py AOs π2py & π*2py MOs

π*2pyAnti-bonding

Bonding

E

2sσ2s*

2s

σ2s

2p 2pσ2p

π2p

σ2p*ENERGY LEVEL DIAGRAM

The π do not split as much because of weaker overlap.

π2p*

The π2px and π2py are degenerate

We have not considered interactions between s and p orbitals, which pushes the σ2pup and σ∗2s down.

MODIFIED ENERGY LEVEL DIAGRAM

E

2s

σ2s*

2s

σ2s

2p

σ2p*

2pσ2p

π2p*Notice that the σ2p and π2phave switched !

π2p

The Order of π2p and σ2p Changes for O, F and Ne

σ2p is more stable because the larger Zeffcompensates for the repulsion by σ2s and σ*2s.

2s

σ2s*

2s

σ2s

2pσ2p

π2p2p

B2 C2 N2σ2p*

σ2p

π2p

π2p*

Being away from the axis, π2p is more stable than σ2p , which isrepelled by σ2s and σ*2s.

Li2 O2 F2

E σ2p*π2p*

2p 2p

σ2s*

2s 2s

σ2s

Electron configuration for B2

E

2s

σ2s*

2s

σ2s

2p

σ2p*

2pσ2p

π2p* B is [He] 2s22p1

π2p Fill electrons from 2s, 2p into σ2s , σ2s* and π2p

Electron configuration for B2:

2s

σ2s*

2s

σ2s

2p

σ2p*

2pσ2p

π2p

π2p*

(σ2s)2(σ2s*)2(π2p)2

Abbreviated configuration

Complete configuration

(σ1s)2(σ1s*)2(σ2s)2(σ2s*)2(π2p)2

Bond order = (4 - 2)/2 =1

Use HUND’s RULEUnpaired electrons

Paramagnetic!

E

σ2p*π2p*σ2p

π2p

σ2s*σ2s

Magnetism

Bond order

Bond E. (kJ/mol)

Bond length(pm)

B2

Para-

1

290

159

C2

Dia-

2

620

131

N2

Dia-

3

942

110

O2

Para-

2

495

121

F2

Dia-

1

154

143

E

NOTE SWITCH OF LABELS

Second row diatomic molecules

OXYGEN

σ2p*π2p*π2p

σ2p

σ2s*σ2s

E

O O Expected to be diamagnetic

Lewis Structure

It was a triumph of MO theory to explain the paramagnetism of O2!

Consistent with the DEMO!

Bond Order = (6-2)/2 =2

PARAMAGNETIC

OXYGENO O

This excited state of O2 is diamagnetic,whereas the ground state of O2 is paramagnetic.

This MO configuration has all electrons paired, but is higher in energy according to Hund’s rule.

What does the Lewis structure correspond to in a MO conf.?

σ2p*π2p*π2p

σ2p

σ2s*σ2s

E

Demo: Chemiluminascence of Singlet Oxygen

Such diamagnetic O2 in the excited state can be generated in the following chemical reaction, and emits light to return to the paramagnetic ground state.

Cl2(aq) + H2O2 (aq) + 2OH- → O2*(g) + 2Cl- (aq) + 2H2OExcited state

O2*(g) → O2(g) + hν