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Chapter 11 Theories of Covalent Bonding. Theories of Covalent Bonding. 11.1 Valence Bond (VB) Theory and Orbital Hybridization. 11.2 The Mode of Orbital Overlap and the Types of Covalent Bonds. 11.3 Molecular Orbital (MO)Theory and Electron Delocalization.

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slide1

Chapter 11

Theories of Covalent Bonding

slide2

Theories of Covalent Bonding

11.1 Valence Bond (VB) Theory and Orbital Hybridization

11.2 The Mode of Orbital Overlap and the Types of

Covalent Bonds

11.3 Molecular Orbital (MO)Theory and Electron Delocalization

slide3

The Central Themes of VB Theory

Basic Principle

A covalent bond forms when the orbtials of two atoms overlap and are occupied by a pair of electrons that have the highest probability of being located between the nuclei.

Themes

A set of overlapping orbitals has a maximum of two electrons that must have opposite spins.

The greater the orbital overlap, the stronger (more stable) the bond.

The valence atomic orbitals in a molecule are different from those in isolated atoms.

slide4

Hydrogen, H2

Hydrogen fluoride, HF

Fluorine, F2

Atomic Orbital Overlap

Orbital overlap and spin pairing in diatomic molecules

slide5

Key Points

Types of Hybrid Orbitals

Hybrid Orbitals

The number of hybrid orbitals obtained equals the number of atomic orbitals mixed.

The type of hybrid orbitals obtained varies with the types of atomic orbitals mixed.

sp

sp2

sp3

sp3d

sp3d2

slide6

The sp hybrid orbitalsin gaseous BeCl2

atomic orbitals

hybrid orbitals

orbital box diagrams

slide7

The sp hybrid orbitalsin gaseous BeCl2 (continued)

orbital box diagrams with orbital contours

slide15

Step 1

Step 2

Step 3

Figure 10.1

Figure 10.12

Table 11.1

The conceptual steps from molecular formula to the hybrid orbitals used in bonding.

Molecular shape and e- group arrangement

Molecular formula

Lewis structure

Hybrid orbitals

slide16

PROBLEM:

Use partial orbital diagrams to describe mixing of atomic orbitals on the central atoms leads to hybrid orbitals in each of the following:

PLAN:

Use the Lewis structures to ascertain the arrangement of groups and shape of each molecule. Postulate the hybrid orbitals. Use partial orbital box diagrams to indicate the hybrid for the central atoms.

SAMPLE PROBLEM 11.1

Postulating Hybrid Orbitals in a Molecule

(a) Methanol, CH3OH

(b) Sulfur tetrafluoride, SF4

SOLUTION:

(a) CH3OH

The groups around C are arranged as a tetrahedron.

O also has a tetrahedral arrangement with 2 nonbonding e- pairs.

slide17

hybridized C atom

hybridized O atom

single C atom

single O atom

hybridized S atom

S atom

SAMPLE PROBLEM 11.1

Postulating Hybrid Orbitals in a Molecule

continued

(b) SF4 has a seesaw shape with 4 bonding and 1 nonbonding e- pairs.

slide18

Types of Covalent Bonds

Sigma () Bonds - Bonding that results from the end-to-end overlap is called a sigma bond. It has the highest electron density along the axis between the two nuclei. Single bonds are sigma bonds.

Pi () Bonds - Bonds that result from the side-to-side overlap of unhybridized p orbitals. The electron density is above and below the axis between the two nuclei.(This is why multiple bonds counted as one group of electrons in VSEPR theory)

The multiple part of multiple bonds are  bonds.In a double bond, there is one  and one  bond.

In a triple bond, there is one  and two  bonds.

slide19

both C are sp3 hybridized

s-sp3 overlaps to s bonds

sp3-sp3 overlap to form a s bond

relatively even distribution of electron density over all s bonds

The s bonds in ethane.

slide20

overlap in one position - s

p overlap - 

electron density

The s and p bonds in ethylene (C2H4)

slide21

overlap in one position - s

p overlap - 

The s and p bonds in acetylene (C2H2)

slide22

PROBLEM:

Describe the types of bonds and orbitals in acetone, (CH3)2CO.

PLAN:

Use the Lewis structures to ascertain the arrangement of groups and shape at each central atom. Postulate the hybrid orbitals taking note of the multiple bonds and their orbital overlaps.

sp3 hybridized

sp3 hybridized

sp2 hybridized

SAMPLE PROBLEM 11.2

Describing the Bonding in Molecules with

Multiple Bonds

SOLUTION:

bond

bonds

slide23

CIS

TRANS

Restricted rotation of p-bonded molecules

Rotation about the C-C bond can’t take place without breaking the  electron overlap.

slide24

The Central Themes of MO Theory

A molecule is viewed on a quantum mechanical level as a collection of nuclei surrounded by delocalized molecular orbitals.

Atomic wave functions are summed to obtain molecular wave functions.

If wave functions reinforce each other, a bonding MO is formed (region of high electron density exists between the nuclei).

If wave functions cancel each other, an antibonding MO (*) is formed (a node of zero electron density occurs between the nuclei).

slide25

Amplitudes of wave functions added

Amplitudes of wave functions subtracted.

An analogy between light waves and atomic wave functions.

slide28

s*1s

Energy

1s

1s

1s

1s

s1s

AO of He

AO of He+

AO of He

AO of He

MO diagram for He2+ and He2

s*1s

Energy

s1s

MO of He+

MO of He2

He2 bond order = 0

He2+ bond order = 1/2(exists)

slide29

PROBLEM:

Use MO diagrams to predict whether H2+ and H2- exist. Determine their bond orders and electron configurations.

PLAN:

Use H2 as a model and accommodate the number of electrons in bonding and antibonding orbitals. Find the bond order.

s

s

1s

1s

1s

1s

AO of H-

AO of H

AO of H

AO of H

s

s

SAMPLE PROBLEM 11.3

Predicting Species Stability Using MO Diagrams

SOLUTION:

bond order = 1/2(1-0) = 1/2

bond order = 1/2(2-1) = 1/2

H2+ does exist

H2- does exist

configuration is (s1s)2(s2s)1

MO of H2-

MO of H2+

configuration is (s1s)1

slide30

s*2s

s*2s

2s

2s

2s

2s

s2s

s2s

s*1s

s*1s

1s

1s

1s

1s

s1s

s1s

Bonding in s-block homonuclear diatomic molecules.

Be2

Li2

Energy

Li2 bond order = 1(is observed)

Be2 bond order = 0(not observed)

slide32

Relative MO energy levels for Period 2 homonuclear

diatomic molecules.

without 2s-2p mixing

with 2s-2p mixing

MO energy levels for O2, F2, and Ne2

MO energy levels for B2, C2, and N2

slide34

PROBLEM:

As the following data show, removing an electron from N2 forms an ion with a weaker, longer bond than in the parent molecules, whereas the ion formed from O2 has a stronger, shorter bond:

PLAN:

Find the number of valence electrons for each species, draw the MO diagrams, calculate bond orders, and then compare the results.

N2

N2+

O2

O2+

Bond energy (kJ/mol)

945

841

498

623

Bond length (pm)

110

112

121

112

SAMPLE PROBLEM 11.4

Using MO Theory to Explain Bond Properties

Explain these facts with diagrams that show the sequence and occupancy of MOs.

SOLUTION:

N2 has 10 valence electrons, so N2+ has 9.

O2 has 12 valence electrons, so O2+ has 11.

slide35

2p

2p

2p

2p

s2s

s2s

SAMPLE PROBLEM 11.4

Using MO Theory to Explain Bond Properties

continued

N2

N2+

O2

O2+

2p

antibonding e- lost

bonding e- lost

2p

2p

2p

s2s

s2s

bond orders

1/2(8-2)=3

1/2(7-2)=2.5

1/2(8-4)=2

1/2(8-3)=2.5

slide37

s

1s

2px

2py

2p

s

AO of H

AO of F

The MO diagram for HF

Energy

MO of HF

slide38

s*s

*p

2p

2p

sp

p

s*s

2s

2s

AO of N

AO of O

ss

The MO diagram for NO

Energy

possible Lewis structures

MO of NO

slide40

Figure 10.1

The steps in converting a molecular formula into a Lewis structure.

Place atom with lowest EN in center

Molecular formula

Step 1

Atom placement

Add A-group numbers

Step 2

Sum of valence e-

Draw single bonds. Subtract 2e- for each bond.

Step 3

Give each atom 8e-

(2e- for H)

Remaining valence e-

Step 4

Lewis structure

slide41

Figure 10.12

The steps in determining a molecular shape.

See Figure 10.1

Molecular formula

Step 1

Lewis structure

Count all e- groups around central atom (A)

Step 2

Electron-group arrangement

Note lone pairs and double bonds

Step 3

Count bonding and nonbonding e- groups separately.

Bond angles

Step 4

Molecular shape (AXmEn)