COVALENT BONDING:ORBITALS

Chapter 9

Hybridization

The mixing of atomic orbitals to form special molecular orbitals for bonding.

The atoms are responding as needed to give the minimum energy for the molecule.

Molecular Geometry & Hybridization

Parent geometry determines the hybridization.

Molecular structure is the actual geometry.

Energy-level diagram showing the formation of four sp3

hybrid orbitals.

09_158

z

y

z

x

y

x

x

y

z

y

x

sp3

sp3

sp3

sp3

Hybridization

gives a tetrahedralarrangement

s

p y

p x

p z

x

y

z

z

y

x

y

z

x

y

z

z

x

One 2s and three 2p orbitals hybridize to form a new set of sp3 hybrid orbitals.

sp3 hybrid orbital

• 4 effective electron pairs.• tetrahedral geometry.• 109.5 o bond angle.

09_161

sp3

sp3

H1s

H1s H1s

H1s

C

sp3

sp3

The tetrahedral set of four sp3 orbitals of thecarbon atom share one electron each with the four hydrogen atoms to make a methane molecule.

09_162

sp3

sp3

H1s

H1s H

1s

lone pair

N

sp3

sp3

The nitrogen atom in ammonia is sp3 hybridized.

A sigma () bond centers along the internuclear axis.

A pi () bond occupies the space above and below the internuclear axis.

CCH H

HH

09_164

E

2p

2s p

Orbitals in an isolatedcarbon atom

sp2

Carbon orbitals in ethylene

Hybridization 2p

An orbital energy-level diagram for sp2 hybridization.

09_165

sp2 orbital

p orbital

sp2 orbital

sp2 orbital

In sp2 hybridization one p orbital remains unchangedand lies perpendicular to the plane of the hybrid.

09_166

C C

sp 2

sp 2

sp2

sp2

H1s

H1s

H1s

H1s sp2sp2

The shared electron pair of in ethylene occupiesthe region directly between the atoms to form a sigma () bond.

sp2 hybrid orbital

• three effective electron pairs.• trigonal planar geometry.• 120 o bond angle.

09_167

sigmabond

pi bondC C

p orbital p orbital

A carbon-carbon double bond consists of a bond and a bond. The bond is formed from unhybridized p orbitals in the space above and below the bond.

Pi and Sigma Bonds

bonds consist of an electron pair shared in the area centered between the atoms.

bonds occupy the space above and below a line joining the atoms.

Pi and Sigma Bonds

bonds allow rotation.

bonds do not allow rotation.

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(b)

H

C C

H

H

H

sp 2

sp 2

sp 2

sp 2

H1sH1s C C

2p

sp 2 sp 2

(a)

The orbitals used to form the bonds in ethylene.

09_169

z

s px yy

x

zz

y

gives a lineararrangement

x

y

z

Hybridization180°

xx x

y

z

Two sp orbitals are formed when one s and one p orbitalare hybridized. They are oriented at 180o to each other.

09_174

O C O

sigma bond(1 pair of electrons) pi bond

(1 pair ofelectrons)

pi bond(1 pair ofelectrons)

(a)

(b)

O C O

The hybrid orbitals in the CO2 molecule.

sp hybrid orbital

• two effective electron pairs.• linear geometry.• 180 o bond angle.

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(c)

NN

p

spsp

p

(a)

N

lone pair sigma bond lone pair

NN

(b)

sp sp sp sp

The nitrogen molecule forms a triple bond -- one and two bonds.

dsp3 hybrid orbitals

• five effective electron pairs.• trigonal bipyramidal geometry.• 90 o and 120 o bond angles.• hybrid orbitals are not all equivalent

as in the other types of hybridization.• Phosphorus pentachloride

d2sp3 hybrid orbitals

• six effective electron pairs.• octahedral geometry.• 90 o bond angles.• Sulfur hexafluoride.

09_179 Number ofEffective Pairs

Arrangementof Pairs

HybridizationRequired

2 Linear sp

180°

3 Trigonalplanar

sp2

120°

4 Tetrahedral

109.5°

5 Trigonalbipyramidal

dsp3

90°

120°

90°

90°

6 Octahedral d2sp3

sp3

The relationship of the number of effective pairs,their spatial arrangement, and the hybrid orbitals.

The Localized Electron Model

- Draw the Lewis structure(s)

- Determine the arrangement of electron pairs (VSEPR model).

- Specify the necessary hybrid orbitals.

Deficiencies of the LEM Model

• Does not adequately explain resonance.

• Does not work for odd-electron molecules and ions.

• Assumes that all electrons are localized about an atom.

• Gives no direct information about bond energies.

Molecular Orbitals (MO)

Analagous to atomic orbitals for atoms, MOs are the quantum mechanical solutions to the organization of valence electrons in molecules. Electrons are considered to be delocalized over the entire molecule.

Types of MOs

bonding: lower in energy than the atomic orbitals from which it is composed.

antibonding: higher in energy than the atomic orbitals from which it is composed.

09_556

EMO2

1sA

H2HA HB

1sB

MO1

Energy diagram

(a)

Electron probability distribution

+ +

+ +(b)

The molecular orbital energy diagram for the H2 molecule and the MO1 and MO2 orbitals formed.MO1 = 1s and MO2 = 1s*.

Bond Order (BO)

Difference between the number of bonding electrons and number of antibonding electrons divided by two.

# bonding electrons # antibonding electronsBO =

2

Larger bond order means greater bond strength!

09_195

E

2p*

2p*

2p

2p

2s*

2s

B 2 C2 N 2 O2 F2

MagnetismPara–

magneticDia–

magneticDia–

magneticPara–

magneticDia–

magnetic

Bond order 1 2 3

2s

2s*

2p

2p

2p*

2p*

2 1

Observedbonddissociationenergy(kJ/mol) 290 620 942 495 154

Observed bondlength(pm) 159 131 110 121 143

The molecular orbital energy-level diagrams, bond orders,bond energies, and bond lengths for diatomic molecules.

In order to participate in MOs, atomic orbitals must overlap in space. (Therefore, only valence orbitals of atoms contribute significantly to MOs.)

09_187

Li

1s

2s

Li

1s

2s

The relative size of the lithium 1s and 2s orbitals.The 1s orbital can be considered to be localized and do not participate in bonding.

09_189

(a)

(b) (c) (d)

B B

The boron molecule will form one and two bonds.

09_190

2py 2py

2px 2px

Antibonding

Bonding

2p

*2p

Antibonding

Bonding

*2p

2p

(b)

(a)

The two p orbitals that overlap head on make two molecular orbitals -- one bonding and one antibonding.The two p orbitals that lie parallel overlap to produce two molecular orbitals, one bonding and one antibonding.

Paramagnetism

- unpaired electrons

- attracted to induced magnetic field

- much stronger than diamagnetism

- B2 & O2

09_195

E

2p*

2p*

2p

2p

2s*

2s

B 2 C2 N 2 O2 F2

MagnetismPara–

magneticDia–

magneticDia–

magneticPara–

magneticDia–

magnetic

Bond order 1 2 3

2s

2s*

2p

2p

2p*

2p*

2 1

Observedbonddissociationenergy(kJ/mol) 290 620 942 495 154

Observed bondlength(pm) 159 131 110 121 143

The molecular orbital energy-level diagrams, bond orders,bond energies, and bond lengths for diatomic molecules.

Diamagnetism

- paired electrons

- repelled from induced magnetic field

- much weaker than paramagnetism

- C2 , N2 , & F2 .

09_193

Glass tubing

Sample tube

Electromagnet

Balance

Apparatus used to measure the paramagnetismof a sample. A paramagnetic sample will appearheavier when the electromagnet is turned on.

09_198

E

1s

HFmolecule

Hatom

Fatom

2p

*

A partial molecular orbital energy-level diagramfor the HF molecule. Bond order is 1 -- a single bond.

09_199

H nucleus F nucleus

The electron probability distribution in the bondingmolecular orbital of the HF molecule.

Pi and Sigma Bonds

bonds in a molecule are described as being localized.

bonds are considered to be delocalized over the entire molecule.

NO2 Molecule

Draw the Lewis Structure, determine the parent geometry, the actual geometry, and the approximate bond angle.

Draw the Lewis Structure, draw themolecular orbital energy-level diagram, determine the bond order, and the type ofmagnetism for the NO+ ion.

NO+ ION

09_202

H H

H

sp2

C C

C

CC

C

sp2

H1s

H

H H

The bonding system in the benzene molecule.

09_203

H H

H

H

H H

H H

H H

(a) (b)

H

H

The molecular orbital system in benzene. Theelectrons in the orbitals are delocalized over thering of carbon atoms.

Outcomes of MO Model

1. As bond order increases, bond energy increases and bond length decreases.

2. Bond order is not absolutely associated with a particular bond energy.

3. N2 has a triple bond, and a correspondingly high bond energy.

4. O2 is paramagnetic. This is predicted by the MO model, not by the LE model, which predicts diamagnetism.

Combining LE and MO Models

bonds can be described as being localized.

bonding must be treated as being delocalized.