Chapter 9 Bonding and Molecular Structure: Orbital ... · Jeffrey Mack California State University, Sacramento Chapter 9 Bonding and Molecular Structure: Orbital Hybridization and

Jeffrey Mack

California State University,

Sacramento

Chapter 9 Bonding and Molecular Structure: Orbital Hybridization and Molecular Orbitals

• Chapter 6 told us that the location of the valence

electrons in an atom is described by an orbital

model.

• It should seem reasonable that an orbital model

can also be used to describe electrons in

molecules.

• In this chapter, you will explore two common

approaches to rationalizing chemical bonding

based on orbitals:

• Valence Bond (VB) theory and Molecular Orbital

(MO) theory.

Orbitals & Theories of Chemical Bonding

Developed by Linus Pauling

• Premise: Bonding involves

valence electrons.

• Half-filled atomic orbitals on

bonding atoms overlap to

form bonds.

• Bonds are localized between

atoms (or as lone pairs).

• Leads to prediction of

molecular shape.

Linus Pauling, 1901-1994

Valence Bonding Theory

Developed by Robert S. Mullikan (1896-1986)

• Bonding electrons reside in Molecular Orbitals that

arise from the original atomic orbitals of the bonding

atoms.

• Bonding electrons are spread over the entire

molecule. (delocalized)

• Explains paramagnetism and electronic

spectroscopy in molecules.

1s

*1s

1s 1s

Molecular Orbital Theory

Overlap of two

s orbitals

A sigma bond is defined as a bond in which electron

density lies along the axis of the bond.

In H2 a sigma

() covalent

bond that arises

from the

overlap of two

half filled s

orbitals, one

from each

atom.

The Orbital Overlap Model of Bonding

Two s

orbitals

overlap

Overlap

of an s &

p orbital

Two p

orbitals

overlap

Sigma Bond Formation

The main points of the valence bond approach to

bonding are:

• Orbitals overlap to form a bond between two atoms.

• Overlapping orbitals hold two electrons of opposite

spin. Usually, one electron is supplied by each of

the two bonded atoms.

• The bonding electrons are localized with a higher

probability of being found within a region of space

between the bonding nuclei. Both electrons are

simultaneously associated with both nuclei.

Valence Bond Theory

Overlap: two orbitals existing in the same region of space

lp: lone pair of electrons (non-bonding)

bp: bonding pair of electrons (result of orbital overlap)

Central atom: the atom of concern in a molecule

hybridization: the linear combination of atomic orbitals

hybrid orbital: bonding orbitals that arise from the mixing of AO’s.

-bond: (sigma bond) overlap of orbitals along the bond axis

-bond: (pi bond) overlap of orbitals above and below the bond

axis.

single bond: one -bond

double bond: one -bond & one -bond

triple bond: one -bond & two -bonds

Valence Bond Terminology

When bonding occurs along a bond axis, it is

referred to as a “sigma” bond: ()

The electrons occupy space between the

nuclei.

X Y :

Sigma (σ) Bonding

When bonding occurs above and below a bond

axis, it is referred to as a “pi” bond: ()

The electrons occupy space above and below

the nuclei.

X Y

:

Pi (π) Bonding

Sigma () bonding: When bonding occurs along a

bond axis, it is referred to as a “sigma” bond.

Pi () bonding: When bonding occurs above and

below a bond axis, it is referred to as a “pi” bond.

A double bond is made up of a and a bond.

X Y :

:

Sigma (σ) Bonding & Pi (π) Bonding

The simple model of atomic orbital

overlap in H2, HF and F2 breaks

down for more complicated

molecules.

Consider methane: VSEPR theory

predicts bond angles of 109.5°.

These angles can’t be achieved with

the s, px, py & pz orbitals of the

central carbon atoms.

Hybridization of Atomic Orbitals

In order to attain the needed geometry, the atomic orbitals

(AO’s) mix or hybridize to form new valence bond orbitals.

2s

2p

carbon

consider carbon as a

central atom in a

molecule:

The valence orbitals

are the 2s & 2p’s

There are 4 valence

electrons:


This hybridization determines by the electron pair geometry

for the central atom.

carbon

The 4 valence electrons on carbon fill the orbitals by Hund’s

rule:

The new orbitals

are called

sp3 Valence

bond orbitals

Each half-filled orbital is capable of

forming a covalent bond.

2s

2p

carbon


Bonding in methane involves the overlap of the new sp3

hybrid orbitals in carbon with the 1s orbitals in hydrogen.

2s

2

p

sp3 hybrid valence

bond orbitals.

Carbon

H H H H

Each overlap contains two shared

electrons, one from each bonding nuclei.

Each overlap results in a –bond


Bonding in CH4

Since there are four sp3 hybrid orbitals, they must spread out to

form a tetrahedron about a central atom to minimize repulsion.

It follows then that an central atom that has a “tetrahedral”

EPG must have sp3 hybridization.

sp3 Hybridization

Water must also bond via sp3 hybrid valence bond

orbitals.

sp3 Hybridization

4 C atom orbitals

hybridize to form

four equivalent sp3

hybrid atomic

orbitals.

Bonding in a Tetrahedron Formation of Hybrid Atomic Orbitals

4 C atom orbitals hybridize to form four equivalent sp3 hybrid atomic orbitals.

Bonding in a Tetrahedron Formation of Hybrid Atomic Orbitals

Conclusion:

When the central atom in a molecule has

combination of 4 total sigma (single) bonds and

lone pairs, the hybridization at the central atom

is sp3.

sp3 Hybridization

In order to attain the needed geometry, the atomic orbitals

(AO’s) mix or hybridize to form new valence bond orbitals.

The 2s & two of the 2p orbitals mix:

The new hybrid

obitals all have the

same energy:

The new orbitals are called sp2 Valence bond orbitals

2p

sp2

there is one

p-orbital left

over

sp2 Hybridization

sp2 Hybridization

The remaining p-orbital is perpendicular to the three sp2

valence bond orbitals that spread out in a plane.

sp2 Hybridization

Bonding in BF3

The atomic orbitals on the

central B-atom can’t

accommodate 3 bonds!

sp2 Hybridization

The 1 s orbital and 2 p orbitals must

mix to form 3 new sp2 hybrid orbitals.

The 3 sp2 hybrid orbitals can now form sigma bonds

with each half-filled p-orbital on each fluorine atom.

This results in a “Trigonal Planar” molecular and

electron pair geometry.

Bonding in BF3

Bonding in an sp2 hybridized atom is shown below:

Each of the three sp2 orbitals can form a -bond with

another atom.

The left over p-orbital can form a -bond with another half-

filled p-orbital.

Two of the orbitals

overlap along the

bond axis:

“Sideways” overlap... results in a -bond!

“end on” overlap

sp2 Hybridization

Bonding in an sp2 hybridized atom is shown below:

Each of the three sp2 orbitals can form a -bond with

another atom.

The left over p-orbital can form a -bond with another half-

filled p-orbital.

Two of the orbitals

overlap along the

bond axis:

“Sideways” overlap... results in a -bond!

“end on” overlap

sp2 Hybridization

An example of sp2 hybridization is given by C2H4 (ethene)

The left over p-orbitals on each carbon overlap to form the -

bond (second half of the double bond).

Each sp2 orbital can form a -bond, two with each of the H’s

and one with the other carbon.

2s

2p

sp2 hybrid valence

bond orbitals.

2p

Carbon

C C

H H

H H

Trigonal planar EPG

at each carbon: sp2

hybridizaton!

sp2 Hybridization

An Example of sp2 Hybridization: C2H4

Multiple Bonding in C2H4

- Bonds in C2H4

The unused p orbital on each C atom contains an electron and this p orbital overlaps the p orbital on the neighboring atom to form the π bond.

-Bonding in C2H4

There is restricted rotation around C=C bond.

Consequences of Multiple Bonding

Restricted rotation around C=C bond.

Consequences of Multiple Bonding

Conclusion: When a central atom has a trigonal planar electronic

geometry (EPG), it is most likely to bond through sp2 hybridization.

Compounds containing double bonds ( + ) most often have have

sp2 hybridization.

Other Examples of Molecules with sp2: CH2O

The sp orbitals spread out to form a linear geometry (directed away

from one another) leaving the p orbitals perpendicular to the

molecular axis.

The sp orbitals can form -bonds or hold lone pairs. The two p-

orbitals can form the (2) -bonds in a triple bond.

An example of sp hybridization is given by C2H2 (acetylene)

2s

2p

sp hybrid valence bond

orbitals form.

2p

Carbon

sp Hybridization

Just as with sp2 hybridization, in sp hybridization, the left over

p-orbitals can form -bonds (in this case 2).

In acetylene (C2H2) there is a triple bond. (1 , 2 ’s)

sp Hybridization

and Bonding in C2H2

Other examples of molecules with sp hybridization are:

N2

:NN:

CN– (cyanide anion)

[:CN:]–

Conclusion: When a central atom has a linear electronic

geometry (EPG) with no lone pairs , it is most likely to bond

through sp hybridization.

Compounds containing triple bonds ( + 2) or adjacent

double bonds (CO2) have sp hybridization.

sp Hybridization

sp, sp2, & sp3 hybridization

Bonding in Glycine

Bonding in Glycine

Bonding in Glycine

Bonding in Glycine

Bonding in Glycine

For elements beyond the second period, we found several

examples where the central atom in a Lewis structure had

greater than 8 electrons in the valence shell.

We’ve seen that when four sp3 hybrid orbitals form, a central

atom can accommodate only up to 8 electrons in the valence

(bp & lp).

To place more electrons in the valence, we must bring the d–

orbitals into the “mix”.

At n = 3 l =

0…

1…

2…

s-orbitals

p-orbitals

d-orbitals

Valence Bond Theory (2): Expanded Valence

Phosphorous:valence electron configuration

of 3s23p3. (5 electrons)

Each of the five electrons forms a single bond

with a chlorine atom.

This means that central atom in the molecule needs 5 bonding

orbitals to achieve the trigonal bipyramidal electronic geometry.

This cannot happen with sp3

hybridization…

3s

3p

mix or

“hybridize” sp3 hybrid valence

bond orbitals.

Consider a Molecule Like PCl5

The only way to produce 5 half-filled orbitals on phosphorous

is by adding a fifth atomic orbital…

3s

3p

3d

mix the 3s, the

three 3p and one

3d

new sp3d hybrid valence

bond orbitals

Each of these half–filled sp3d orbitals can form a –bond with a

chlorine atom in PCl5.

3d


SF4 (sulfur tetrafluoride) ClF3 (chlorine trifluoride)

EPG: Trigonal Bipyramidal

MG: See Saw

EPG: Trigonal Bipyramidal

MG: T-shape

Additional example of sp3d hybrid molecules:

What about molecules with 12 electrons in the valence?

In order to achieve an expanded valence that can hold six electron

pairs (bp & lp) we need to form 6 new hybrid orbitals.

This requires the mixing of an s, three p’s and two d–atomic orbitals.

3s

3p

3d

mix the 3s, the

three 3p and two

3d’s

new sp3d2 hybrid valence

bond orbitals

3d


3s

3p

3d

mix the 3s, the

three 3p and two

3d’s

six new sp3d2 hybrid

valence bond orbitals

Each of these half–filled

sp3d2 orbitals can form a

–bond with a fluorine

atom.

3d

sulfur

sp3d2 Hybridization: SF6

SF6

Sulfur has a valence electron configuration of 3s23p4

(6 electrons).

Each of the six electrons forms a single bond with a

fluorine atom forming an octahedral MG and EPG.

The bonding can be described in terms of sp3d2

hybrid orbitals.

sp3d2 Hybridization: SF6

1. Start by drawing the Lewis structure (check formal charges)

2. Use VSEPR theory the electron group geometry about the central atom.

3. Relate the central atom electron group geometry to the corresponding hybridization.

4. Identify and label the orbital overlap in each bond.

5. Label the bonds with and bonds.

Predicting Hybridization

• Indicate the central atom hybridization for the

following.

XeF4

CH2O

BrF5

SF6

Br3

Hybridization Practice

BrF5 (bromine pentafluoride) XeF4 (xenon tetra fluoride)

Conclusion: Molecules with an octahedral EPG have sp3d2

hybridization at the central atom.

EPG: octahedral

MG: Square Pyramidal

EPG: octahedral

MG: Square Planar

Additional Examples of sp3d2

• Molecular Orbital Theory (MO) approaches

bonding between atoms from a different approach

than Valence Bond Theory.

• In Valence Bond theory, the atomic orbitals of a

bonding atom mix or hybridize to form localized

bonds that take on the EPG’s predicted by VSEPR

theory.

• In MO theory, the atomic orbitals are treated like

waves that constructively or destructively add to

form new Molecular Orbitals.

• The electrons of the molecule are distributed over

the entire molecule as a whole. (delocalized)


• Molecular Orbital Theory has several advantages

and differences over VESPR & VB theory:

• MO does a good job of predicting electron pair

spectra and paramagnetism, where VSEPR and the

VB theories don't.

• MO theory like VB theory, predicts the bond order of

molecules, however it does not need resonance

structures to describe molecules.

• The main drawback to our discussion of MO theory

is that we are limited to talking about diatomic

molecules (molecules that have only two atoms

bonded together), or the theory gets very complex.


MO Theory: Considered Hydrogen

When two wave functions (orbitals) on different atoms add

constructively they produce a new MO that promotes bonding

given by:

=

(1s)H(1) + (1s)H(2) H-H

when two waves add,

the amplitude increases: +

“constructive

interference”

atomic orbitals new Molecular Orbital

increased amplitude

MO Theory: Considered Hydrogen

When two wave functions (orbitals) on different atoms add

destructively they produce a new MO that decreases bonding

given by:

=

(1s)H(1) (1s)H(2) *H-H

when two waves subtract,

the amplitude decreases: +

“destructive

interference”

atomic orbitals new Molecular Orbital

no amplitude

(a node)

Consider hydrogen atoms combining to form H2.

The individual 1s atomic orbitals combine.

When they add, a lower energy -bonding MO forms.

When they subtract, a higher energy *-antibonding MO forms


• Bonding and antibonding sigma MO’s are formed from 1s orbitals on adjacent atoms.


Molecular orbitals result when atomic orbitals on bonding

atoms constructively and destructively combine:

When they add, lower energy bonding Molecular Orbitals

(MO’s) form, when they subtract, higher energy anti-bonding

MO’s form.

Anti-bonding orbitals are designated by an asterisk (*) called a

star.

1s 1s

1ss

*

1ssE

nerg

y

Molecular Orbital Diagrams

Once again we consider the simplest

molecule, H2.

When two hydrogen atoms combine the

1s orbitals on each can add or subtract

to form a 1s bonding or *1s

anti-bonding orbital.

Each H-atom has one 1s electron that can contribute to the

MO bonding and anti-bonding MO’s.

Just as in the electron configurations of atoms, the electron fill

from the lowest energy MO first (Aufbau principle) only

pairing when forced to (Hund’s rule). Each MO can only hold

two electrons of opposite spin (Pauli principle)

1s

*1s

1s 1s

H-atom H-atom

Molecular Orbital Diagrams

• Electrons in bonding molecular orbitals add

stability.

• Electrons in anti-bonding molecular orbitals

reduce stability.

# of Bonding electrons - # antibonding electronsBO

2=

Bond Order in Molecular Orbital

Bond Order = 1 (single bond)

MO electron configuration of:

One also sees that the molecule (H2) is diamagnetic

(no unpaired electrons)

2

1s( )s

1s

*1s

1s 1s

2 electrons in a bonding MO

0 electrons in an anti-bonding MO

2 01

2

-= =

H-atom H-atom

# of Bonding electrons - # antibonding electronsBO

2=

Bond Order: The Bonding in H2 is described by…

What happens to a H2 molecule

if one of the electrons is excited

to the anti-bonding orbital?

1s

*1s

ground state H2

2 0Original BO 1

2

-= =

1s

*1s

excited state H2

1 1New BO 0

2

-= =

The molecule falls

apart!

Photodissociation

1s 1s

1s 1s

H-atom H-atom

Excited States

1s

*1s

He: 1s2

2 2BO 0

2

-= =

Molecular Orbital theory

predicts that the molecule

is unstable!

1s 1s

electrons in AO’s

fill the MO’s

Why Doesn’t He2 Exist?

Sigma Bonding from p-Orbitals

Sideways overlap of atomic 2p orbitals that lie in the same

direction in space give bonding and antibonding MOs.

Molecular Orbitals from Atomic p-Orbitals

The three 2p orbitals on each side combine to form

six new Molecular Orbitals that can accommodate up

to 12 electrons.

2p 2p

2pp

*

2pp

2ps

*

2ps

This configuration is seen for B, C and N only…

2p

*

2

The two and the

two are degenerate.p

The MO Correlation Diagram for the 2p Atomic Orbitals

The three 2p orbitals on each side combine to form

six new Molecular Orbitals that can accommodate up

to 12 electrons.

2ps

2p 2p

2pp

*

2pp

*

2ps

This configuration is seen for O and F only…

The MO Correlation Diagram for the 2p Atomic Orbitals

The overall MO diagram for the 1s, 2s and 2p orbitals:

1s MO’s

2p MO’s

2s MO’s

*1s

1s

Since the 1s and 2s MO’s are full, they do not contribute any

net bonding Any net bonding will be determined by the 2p

MO’s.

Each O–atom has four 2p

electrons:

The electrons fill the MO’s fill by the Aufbau principle and Hund’s

rule.

2p 2p

2pp

*

2pp

*

2ps

O - atom O - atom

2ps

Bonding in O2

Since the 1s and 2s MO’s are full, they do not contribute any

net bonding Any net bonding will be determined by the 2p

MO’s.

Each O–atom has four 2p

electrons:

The electrons fill the MO’s fill by the Aufbau principle and Hund’s

rule

2p 2p

2pp

*

2pp

*

2ps

O - atom O - atom

2ps

Bonding in O2

2p 2p

2pp

*

2pp

*

2ps

O - atom O - atom

6 2BO 2

2

-= =

This agrees with the Lewis dot structure: O=O

double bond

However, VB theory did not

tell us that the molecule is

paramagnetic!

2ps

Bonding in O2

The Paramagnetism of O2

(a) Making liquid O2. (b) Liquid O2 is a light blue color.

(c) Paramagnetic liquid O2 clings to a magnet. (d) Diamagnetic liquid N2 is not attracted to a

magnet.

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Chapter 9 Bonding and Molecular Structure: Orbital ... · Jeffrey Mack California State University, Sacramento Chapter 9 Bonding and Molecular Structure: Orbital Hybridization and