11-1

Chapter 11

Theories of Covalent Bonding

11-2

Theories of Covalent Bonding

11.1 Valence bond (VB) theory and orbital hybridization

11.2 The mode of orbital overlap and types of covalent bonds

11.3 Molecular orbital (MO) theory and electron delocalization

11-3

Figure 9.2

The three models of chemical bonding

11-4

Figure 9.11

Covalent bond formation in H2

11-5

Structure dictates shape

Shape dictates function

Key Principles

shape = conformation

Molecules can assume more than oneshape (conformation) in solution!

11-6

The Complementary Shapes of an Enzyme and Its Substrate

11-7

Valence-shell Electron-Pair Repulsion (VSEPR) Theory

A method to predict the shapes of molecules from their electronic structures (Lewis structures do not depictshape)

Basic principle: each group of valence electrons around a centralatom is located as far away as possible from the others in order to minimize repulsions

Both bonding and non-bonding valence electrons aroundthe central atom are considered.

AXmEn symbolism: A = central atom, X = surrounding atoms,E = non-bonding electrons (usually a lone pair)

11-8

Figure 8.12

A periodic table of partial ground-state electron configurations

11-9

Figure 10.12

The steps in determining a molecular shape

molecular formula

Lewis structure

electron-group arrangement

bond angles

molecular shape

(AXmEn)

Count all e- groups around the central atom A

Note lone pairs and double bonds

Count bonding and

non-bonding e- groups separately.

Step 1

Step 2

Step 3

Step 4

11-10

Figure 10.1

Steps to convert a molecular formula into a Lewis structure

molecular formula

atom placement

sum of

valence e-

remaining

valence e-

Lewis structure

Place the atom with the lowest EN in the center

Add A-group numbers

Draw single bonds and

subtract 2e- for each bond

Give each

atom 8e-

(2e- for H)

Step 1

Step 2

Step 3

Step 4

11-11

Figure 10.5

Electron-group repulsions and the five basic molecular shapes

Ideal bond angles are shown for each shape.

11-12

Figure 10.8

The three molecular shapes of the tetrahedral electron-group arrangement

Examples:

CH4, SiCl4,

SO42-, ClO4

-

Examples:NH3

PF3

ClO3

H3O+

Examples:

H2O

OF2

SCl2

11-13

Figure 10.10

The four molecular shapes of the trigonal bipyramidal electron-group arrangement

Examples:

SF4

XeO2F2

IF4+

IO2F2-

Examples:

ClF3

BrF3

Examples:

XeF2

I3-

IF2-

Examples:

PF5

AsF5

SOF4

11-14

VSEPR (Valence Shell Electron Pair RepulsionTheory)

Accounts for molecular shapes by assuming that electron groups tend to minimize their repulsions

Does not show how shapes can be explained fromthe interactions of atomic orbitals

11-15

The Central Themes of Valence Bond (VB) Theory

Basic Principle

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

Three Central 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 (hybridization).

11-16

Figure 11.1

Orbital overlap and spin pairing in

three diatomic molecules

hydrogen, H2

hydrogen fluoride, HF

fluorine, F2

11-17

Linus Pauling

Proposed that valence atomic orbitals in the molecule are different from those in the isolated atoms

Mixing of certain combinations of atomic orbitalsgenerates new atomic orbitals

Process of orbital mixing = hybridization; generateshybrid orbitals

11-18

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.

Key Points

sp sp2 sp3 sp3d sp3d2

Types of Hybrid Orbitals

11-19

Figure 11.2

The sp hybrid orbitals in gaseous BeCl2

atomic orbitals

hybrid orbitals

orbital box diagrams

VSEPR predicts a

linear shape

11-20

Figure 11.2

The sp hybrid orbitals in gaseous BeCl2 (continued)

orbital box diagrams with orbital contours

11-21

Figure 11.3

The sp2 hybrid orbitals in BF3

VSEPR predictsa trigonal planar

shape

11-22

Figure 11.4

The sp3 hybrid orbitals in CH4

VSEPR predicts a tetrahedral

shape

11-23

Figure 11.5

The sp3 hybrid orbitals in NH3

VSEPR predictsa trigonal

pyramidal shape

11-24

Figure 11.5

The sp3 hybrid orbitals in H2O

VSEPR predictsa bent (V) shape

11-25

Figure 11.6

The sp3d hybrid orbitals in PCl5

VSEPR predictsa trigonal bipyramidal

shape

11-26

Figure 11.7

The sp3d2 hybrid orbitals in SF6

VSEPR predicts anoctahedral shape

11-27

11-28

Figure 11.8

Conceptual steps from molecular formula to the hybrid orbitals used in bonding

molecular formula

Lewis structure

molecular shape

and e- group arrangement

hybrid orbitals

Figure 10.1

Step 1

Figure 10.12

Step 2 Step 3

Table 11.1

11-29

SAMPLE PROBLEM 11.1 Postulating Hybrid Orbitals in a Molecule

SOLUTION:

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

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

(a) methanol, CH3OH (b) sulfur tetrafluoride, SF4

(a) (a) CH3OH H

CH H

OH

The groups around C are arranged as a tetrahedron.

O has a tetrahedral arrangement

with two non-bonding e- pairs.

11-30

SFF

F

F

SAMPLE PROBLEM 11.1 (continued)

2p

2s

sp3 2p

2s

sp3

(b) SF4 has a seesaw shape with four bonding and one non-bonding e- pairs.

3p

3s

3d

S atomsp3d

3d

hybridized S atom

single C atom single O atom

hybridized O atomhybridized C atom

distortedtrigonal

bipyramidal

11-31

Figure 11.9

bonds in ethane, CH3-CH3

both carbons are sp3 hybridized s-sp3 overlaps to bonds

sp3-sp3 overlap to form a bond relatively even distribution of electron

density over all bonds

Covalent Bonds Between Carbon Atoms - Single Bonds

free rotation

~109.5o

11-32 Figure 11.10

and bonds in ethylene, C2H4

overlap in one position -

p overlap -

electron density

Covalent Bonds Between Carbon Atoms - Double Bonds

hindered rotation

~120o

11-33

Figure 11.11

and bonds in acetylene, C2H2

overlap in one position -

p overlap -

Covalent Bonds Between Carbon Atoms - Triple Bonds

hindered rotation

180o

11-34

Video: Hybridization

11-35

SAMPLE PROBLEM 11.2 Describing bonding in molecules with multiple bonds

SOLUTION:

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

PLAN: Use the Lewis structure to determine the arrangement of groups and the shape at each central atom. Postulate the hybrid orbitals, taking note of multiple bonds and their orbital overlaps.

H3C

C

CH3

O

sp3 hybridized

sp3 hybridized

CC

C

O

H

H

HHH

H

sp2 hybridized

bondsbond

CC

C

O

sp3

sp3

sp3

sp3

sp3

sp3

sp3

sp3

sp2 sp2

sp2

sp2

sp2sp2

H

HH

HH

H

11-36 Figure 11.12

Restricted rotation in -bonded molecules

cis trans

No spontaneous interconversion betweencis and trans forms (isomers) in solution at room temperature!

11-37

Limitations of VB Theory

Inadequately explains magnetic/spectral properties

Inadequately treats electron delocalization

VB theory assumes a localized bonding model

11-38

Molecular Orbital (MO) Theory

A delocalized bonding model

A quantum-mechanical treatment of moleculessimilar to that used for isolated atoms

Invokes the concept of molecular orbitals (MOs)(extension of atomic orbitals)

Exploits the wave-like properties of matter (electrons)

11-39

Central themes of molecular orbital (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).

11-40

Amplitudes of wave functions are added

Figure 11.13

An analogy between light waves and atomic wave functions

Amplitudes of wave functions are

subtracted

11-41

Figure 11.14

Contours and energies of the bonding and antibonding molecular orbitals in H2

11-42

Bonding MO: lower in energy than isolated atoms

Antibonding MO: higher in energy than isolated atoms

number of AOs combined = number of MOs produced

To form MOs, AOs must have similar energy and orientation

Sigma () and pi () bonds are denoted as before; a star (asterick)is used to denote antibonding MOs.

11-43

Figure 11.15

Molecular orbital diagram for the H2 molecule

MOs are filledin the same sequenceas for AOs

(aufbau and exclusion

principles, Hund’s rule)

11-44

The MO bond order

[1/2 (no. of e- in bonding MOs) - (no. of e- in antibonding MOs)]

higher bond order = stronger bond

Has predictive power!

11-45 Figure 11.16

MO diagrams for He2+ and He2

En

erg

y

MO of He+

*1s

1s

AO of He+

1s

MO of He2

AO of He

1s

AO of He

1s

*1s

1s

En

erg

y

He2+ bond order = 1/2 He2 bond order = 0

AO of He

1s

can exist! cannot exist!

11-46

SAMPLE PROBLEM 11.3 Predicting species stability using MO diagrams

SOLUTION:

PROBLEM: Use MO diagrams to predict whether H2+ and H2

- can 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. Calculate the bond order.

1s1s

AO of HAO of H

1s1s

MO of HMO of H22++

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

HH22++ does exist! does exist!

MO of HMO of H22--

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

H2- does exist!

1s1s 1s1s

AO of HAO of H AO of HAO of H--

configuration is (1s)2(

1s)1

AO of HAO of H+

configuration is (1s)1

11-47

*2s

2s

2s2s

1s

*1s

1s

1s

Figure 11.17

1s

*1s

1s

1s

2s 2s

*2s

2s

Li2 bond order = 1 Be2 bond order = 0

Bonding in s-block homonuclear

diatomic moleculesEn

erg

y

Li2Be2

11-48

Bonding and antibonding MOs for coreelectrons cancel = no net contribution to bonding

Only MO diagrams showing MOs created bycombining valence-electron AOs are important.

11-49

Figure 11.18

Contours and energies of and MOs through combinations of 2p atomic orbitals

end-to-endoverlap

side-to-sideoverlap

11-50

Relative energies

2p < 2p < *2p < *2p

More effective end-to-end interactionrelative to side-to-side in bonding MOs

11-51

Figure 11.19

Relative MO energy levels for Period 2 homonuclear diatomic molecules

MO energy levels for O2, F2 and Ne2

MO energy levels for B2, C2 and N2

without 2s-2p mixing

with 2s-2p mixing

11-52

Figure 11.20

MO occupancy and molecular properties for B2 through Ne2

11-53

Figure 11.21

The paramagnetic properties of O2

Explained byMO diagram

11-54

SAMPLE PROBLEM 11.4 Using MO theory to explain bond properties

SOLUTION:

PROBLEM: As the following data show, removing an electron from N2 forms

an ion with a weaker, longer bond than in the parent molecule, 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 compare the results.

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

bond energy (kJ/mol)bond energy (kJ/mol)

bond length (pm)bond length (pm)

N2 N2+ O2 O2

+

945945

110110

498498841841 623623

112112121121112112

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

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

11-55

SAMPLE PROBLEM 11.4 (continued)

2s

2s

2p

2p

2p

2p

N2 N2+ O2 O2

+

bond orders

1/2(8-2) = 3 1/2(7-2) = 2.5 1/2(8-4) = 2 1/2(8-3) = 2.5

2s

2s

2p

2p

2p

2p

bonding e- lost

antibonding

e- lost

(weaker) (weaker)

11-56

En

erg

y

MO of HF

AO of H

1s

2px 2py

AO of F

2p

Figure 11.22

The MO diagram for HF

Heteronuclear DiatomicMolecules

lower in energythan 1s of H!

nonbonding MOs

11-57

In polar covalent compounds, bonding MOsare closer in energy to the AOs of the more

electronegative atom.

11-58

En

erg

yFigure 11.23

The MO diagram for NO

MO of NO

2s

AO of N

2p

*2s

2s

2sAO of O

2p

2p

2p

*2p

*2s

N O

0 0

N O

-1 +1

possible Lewis structures

bond order = 2.5

11-59

Figure 11.24

The lowest energy -bonding MOs in benzene and ozone

OO O

resonance hybrid