Chapter 11 Theories of Covalent Bonding - Mission...

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© 2009 Brooks/Cole - Cengage

Chapter 11 Theories of Covalent

Bonding

Atomic Orbitals Molecules

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Bonding and Molecular Structure

Questions —

• How are molecules held together?

• Why is O2 paramagnetic? And how is this property connected with bonding in the molecule?

• How can noble gases form molecules such as XeF2, XeF4, XeOF4, XeO3, etc…?

N2 with

triple

bond

Phosphorus

is a

tetrahedron

of P4 atoms.

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© 2009 Brooks/Cole - Cengage Hydrogen fluoride, HF.

11.1 Valence Bond (VB) Theory: The Orbital Overlap Model of Bonding

by Linus Pauling (1901-1994)

A covalent bond forms when the orbitals of two atoms overlap and a pair of electrons with opposite spins occupy the overlap region.

The Central Themes of VB Theory

The greater the orbital overlap, the stronger the

bond. Extent of orbital overlap depends on orbital shape & direction

Fluorine, F2.

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VB Theory and Orbital Hybridization The orbitals that form when bonding occurs are different

from the atomic orbitals in the isolated atoms. If no change occurred, we could not account for the molecular shapes

that are observed.

Atomic orbitals “mix” or hybridize when bonding occurs

to form hybrid orbitals. The spatial orientation of these hybrid orbitals correspond with

observed molecular shapes.

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Features of Hybrid Orbitals The number of hybrid orbitals formed equals the number

of atomic orbitals mixed.

The type of hybrid orbitals formed varies with the types of

atomic orbitals mixed.

The shape and orientation of a hybrid orbital maximizes

overlap with the other atom in the bond.

atomic

orbitals

hybrid

orbitals

One 2s and one 2p atomic orbital mix to form two sp hybrid orbitals.

Formation and orientation of sp hybrid orbitals and the bonding in BeCl2.

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Types of Hybridization

# bond shape hybrid # p left

2 linear sp 2

3 trigonal planar sp2 1

4 tetrahedral sp3 0

5 trigonal bipyramidal sp3d

6 octahedral sp3d2

The 5 types of orbital hybridization correspond to the 5

electron group arrangements in VSEPR theory. Available atomic orbitals mix to form a new set of HYBRID ORBITALS that will give the

maximum overlap in the correct geometry

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sp Hybridization Formation and orientation of sp hybrid orbitals and the

bonding in BeCl2.

One 2s and one 2p

atomic orbital mix

to form two sp

hybrid orbitals

The two sp orbitals are in

linear arrangement , 180°

apart.

Each half-filled sp orbital

overlaps with the half-

filled 2p orbital of a Cl

atom.

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sp2 Hybridization

Bonding in BF3

Bond

angle

120o

One 2s and two 2p

atomic orbitals mix to

form three sp2 hybrid

orbitals

Overlap of B and F orbitals to form BF3 - The three sp2 orbitals point to

the corners of an equilateral

triangle, their axes 120° apart.

- Each half-filled sp2 orbital

overlaps with the half-filled 2p

orbital of a F atom.

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The sp3 hybrid orbitals in CH4

sp3 Hybridization

One 2s and three 2p atomic

orbitals mix to form four sp3

hybrid orbitals

Overlap of C and H orbitals to form CH4 - The four sp3 orbitals point to the

corners of a tetrahedral shape, their

axes 109° apart.

- Each half-filled sp3 orbital overlaps

with the half-filled 1s orbital of a H

atom.

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The sp3 hybrid orbitals in NH3

The N lone pair

occupies an sp3

hybrid orbital,

giving a trigonal

pyramidal

shape.

The sp3 hybrid orbitals in H2O

The O lone pairs occupy two sp3

hybrid orbitals, giving a bent shape

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The sp3d hybrid orbitals in PCl5.

The formation of more than

four bonding orbitals requires

d orbital involvement in

hybridization. One 3s, three

3p, and one 3d atomic orbitals

mix to form five sp3d hybrid

orbitals

sp3d Hybridization

Overlap of P and Cl orbitals to form PCl5 - The five sp3d orbitals point to the

corners of a trigonal bipyramidal

shape, their axes 120° and 90° apart.

- Each half-filled sp3d orbital overlaps

with the half-filled 3p orbital of a Cl

atom.

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The sp3d2 hybrid orbitals in SF6

sp3d2 Hybridization

The formation of more than

four bonding orbitals requires

d orbital involvement in

hybridization. One 3s, three

3p, and two 3d atomic orbitals

mix to form six sp3d2 hybrid

orbitals

Overlap of S and F orbitals to form SF6 - The six sp3d2 orbitals point to the

corners of a square pyramidal

shape, their axes 90° apart.

- Each half-filled sp3d2 orbital

overlaps with the half-filled 2p

orbital of an F atom.

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Table 11.1 Composition and Orientation of Hybrid Orbitals.

From molecular formula

to hybrid orbitals

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Bonding in Glycine

O

C

O H

H

H

NH

Hsp

3

sp3

sp3

sp2

••

••

••C

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Problems

Use Valence Bond (VB) Theory to describe

the bonding in H3O+, CH3NH2, and SF4.

Strategy: Write the Lewis dot structure for

the molecule. The electron group geometry

around each central atom determines the

hybrid orbital set for that atom.

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11.2 Modes of Orbital Overlap &

the Types of Covalent Bonds

A sigma (σ) bond is formed by end-to-end overlap of orbitals.

A pi (p) bond is formed by sideways overlap of orbitals.

All single bonds are σ bonds.

A double bond consists of one σ bond and

one p bond. A triple bond consists of one σ

bond and two p bonds

A p bond is weaker than a σ bond because

sideways overlap is less effective than end-to-

end overlap.

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The s bonds in ethane (C2H6)

both C are sp3

hybridized

s bond formed by s-sp3

overlap

End-to-end sp3-sp3 overlap to

form a s bond

A σ bond is cylindrically

symmetrical, with its

highest electron density

along the bond axis.

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

There is relatively even

distribution of electron

density over all s bonds.

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The s and p bonds in ethylene (C2H4)

A p bond has two

regions of electron

density.

unhybridized 2p orbitals

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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Each C is sp hybridized and has

two unhybridized p orbitals.

The s and p bonds in acetylene (C2H2) Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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Electron density and bond order in

ethane, ethylene, and acetylene

A double bond is less than twice as strong as a single bond,

because a p bond is weaker than a σ bond.

However, in terms of bond order, a single bond has BO = 1, a

double bond has BO = 2, and a triple bond has BO = 3.

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Problem

Use VB Theory and Orbital Hybridization

to describe the bonding in acetone,

CH3COCH3, and acetonitrile, CH3CN.

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Orbital Overlap & Molecular Rotation

There is restricted rotation around C=C bond.

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Consequence of Multiple Bonds

cis-1,2-Dichloroethylene

polar molecule, bp 60 0C

trans-1,2-Dichloroethylene

non-polar molecule, bp 47.5 0C

The two isomers of 1,2-dichloroethylene (C2H4 Cl2) are

different molecules


Limitation of VB Theory: The Paramagnetic Properties of O2

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11.3 Molecular Orbital (MO) Theory

& Electron Delocalization The combination of orbitals to form bonds is viewed as the

combination of wave functions.

Atomic wave functions (AOs) combine to form molecular

wave functions (MOs).

# of AOs combined always equals # of MOs formed.

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Key Distinctions between VB & MO Theories

Valence Bond (VB) Theory and Orbital Hybridization

- closely related to Lewis’s idea of bonding and lone pairs of localized electrons on a particular atom.

- used for qualitative, visual picture of molecular structure,

particularly for polyatomic molecules and all molecules in

ground (lowest energy) states.

Molecular Orbital (MO) Theory

- ‘spread out’ or delocalized electrons in MOs. - used for quantitative picture of bonding, especially for

molecules in excited states.

- used in explaining magnetic and spectral properties

(e.g., the colors of compounds).

- the only theory that can describe accurately the bonding

in molecules such as O2 and NO.

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Central Themes of MO Theory

Addition of AOs forms a bonding MO, which has a region of high electron density between the nuclei.

Subtraction of AOs forms an antibonding MO, which has a node, or region of zero electron density, between the

nuclei.

Bonding MO and Anti-bonding MO have different

shapes and energies

The bonding MO is

lower in energy and

the antibonding MO

is higher in energy

than the AOs that

combined to form

them.

Contours and energies of H2 bonding s and antibonding s* MOs


Molecular Orbital Diagrams An MO diagram, just like an atomic orbital diagram, shows

the relative energy and number of electrons in each MO.

The MO diagram also shows the AOs from which each MO

is formed.

1. # of MO’s = # of atomic orbitals used.

2. Bonding MO is lower in energy than its parent atomic

orbitals. Antibonding MO is higher.

3. Atomic orbitals combine to form MOs most effectively

when the atomic orbitals are of similar energy.


Filling MOs with Electrons 1. Electrons assigned to MO’s of increasing energy

2. An MO can hold a maximum of 2 electrons with

opposite spins

3. Orbitals of equal energy are half-filled, with spins

parallel, before any of them are filled


Dihelium (He2) Molecule (s1s)

2 (s*1s)2

BO = ½(2-2) = 0

Bond order = 1/2 [# e- in bonding MOs

- # e- in antibonding MOs]

Bond Order

Hydrogen (H2) Molecule: (s1s)

2 (s*1s)0

BO = ½(2-0) = 1


Learning Check

What is the electron configuration of the H2+

ion in MO terms. Compare the bond order of

this ion with He2+ and H2

-. Do you expect H2+

to exist?

Strategy: Fill the number of valence

electrons in the MO diagram or write

electron configuration in MO terms. Then

calculate Bond Order.


Bonding in s-block homonuclear diatomic molecules

Li2

Li2 bond order = 1

Be2

Be2 bond order = 0

Homomuclear Diatomic Molecules

of Period 2 Elements


Shapes and energies of s and p MOs

from combinations of 2p atomic orbitals


Relative MO energy levels for Period 2

homonuclear diatomic molecules

MO energy levels

for O2, F2, and Ne2

without 2s-2p

mixing

MO energy levels

for B2, C2, and N2

with 2s-2p

mixing

Note the

change in

energy of s2p

and p2p MOs

with s-p mixing

s-p mixing

occurs

when s &

p-orbitals

are close in

energy (< ½

filled 2p, or

< 12

valence

electrons)


MO occupancy

and molecular

properties for

B2 through Ne2.

The MO

theory fully

explains the

paramagnetic

properties of

O2.

Note the change in order of

energy of s2p and p2p MOs on

going from N2 to O2.


Learning Check

The cation O2+ and N2

+ are important

components of Earth’s upper atmosphere.

Write electron configurations in MO terms

for these ions. Predict their bond orders and

magnetic behavoirs.

Strategy: Count the number of valence

electrons and place them in the MO

diagrams.


The MO diagram

for HF.

- No p MOs. The s MO

between 1s of H and 2p

of F. As F is much higher

in EN than H, it holds

electrons tighter

resulting the bonding MO

is closer F 2p orbitals.

- The 2 lone pairs

electrons belong to F and

do not form bonds. They

are in nonbonding

MOs.

Electron Configurations for

Heteronuclear Diatomic Molecules


The MO diagram for NO.

- Total 11 valence electrons:

s-p mixing and electron

configuration:

(s2s)2(s2s*)

2(p2p)4(s2p)

2(p2p*)1

- B.O. = 2.5, consistent with

2 resonance structures

- the single electron is

closer to N than to O

Electron Configurations for

Heteronuclear Diatomic Molecules


Problems

Write electron configurations in MO terms and

calculate bond order for CO, and ClF.


Fig. 9-22, p. 431

Molecular Orbitals in Ozone, O3, molecule

Polyatomic Molecules:

Resonance and MO Theory

The p

electrons

delocalize

through-

out the

molecule


Fig. 9-24, p. 432

Molecular Orbitals in Benzene, C6H6, molecule

Chapter 11 Theories of Covalent Bonding - Mission...

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