Lecture Notes by Ken Marr
Chapter 11
(Silberberg 3ed)
Covalent Bonding: Valence Bond Theory and
Molecular Orbital Theory
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

1.
2.
Covalent Bonds
» Result from the overlap of valence shell atomic orbitals to share an electron pair s, p, or hybrid orbitals may be used to form covalent bonds e.g. Predict the Orbitals used for bonding in:
H
2,
HF, H
2
S, F
2

1.
2.
3.
Overlap of s orbitals
» H
2
Overlap of s and p orbitals
» HF
» H
2
S
Overlap of p orbitals
» F
2

Hybrid Orbitals
1.
2.
The use of only s and p orbitals does not explain bonding in most molecules!!!
e.g. BeCl
2
, CH
4
, H
2
O hybrid orbitals are used in these cases
Hybrid Orbitals are used to hold bonding and nonbonding electrons!
 s, p, and d orbitals may hybridize to form to form hybrid orbitals

Write Lewis structure for the molecule or ion, then...
1.
Determine number of electron pairs around the atom in question
2.
One orbital is needed for each electron pair sp hybridization provides 2 orbitals sp 2 hybridization provides 3 orbitals sp 3 hybridization provides.....?...........orbitals sp 3 d hybridization provides......?..........orbitals sp 3 d 2 hybridization provides....?.............orbitals

 Example of sp hybrid orbitals:
» BeCl
2


2
BF
3

1.
2.
3.
Examples of sp 3 hybrid orbitals
CH
4
, C
2
H
6
, H
2
O, NH
3
Example of sp 3 d hybrid orbitals
PCl
5
Example of sp 3 d 2 hybrid orbitals
SF
6

Bond Angle ~92 o

Mode of Orbital Overlap
Sigma vs. Pi Bonds
1.
Sigma Bonds ( sbond)
» Head to head overlap of s, p, or hybrid orbitals
» Responsible for the framework of a molecule
Single bond = one s bond

Mode of Orbital Overlap
Sigma vs. Pi Bonds
2.


Pi bonds ( p-
Bonds)
» Side to side overlap of p orbitals
» Restrict rotation
Double bond = one s bond + one p bond
Triple Bond = one s bond + two p bonds

Examples: Sigma vs. Pi Bonds
 Ethane
 Ethylene (ethene)
» Effect of pbonding on rotation about the sbond ?
 Acetylene (ethyne)
 Nitrogen
 Formaldehyde

Predict the hybrid orbitals used in the following




Nitrogen gas, N
2
Formaldehyde: H
2
CO
Carbon dioxide, CO
2
Carbon monoxide, CO

Sulfur dioxide, SO
2

2 o o
O S O
S = [Ne] 3s 2 3p x
2 3p y
1 3p z
1
This structure is...
» Favored by formal charge
» Requires ?? hybridization
Big Problems with this Structure..
» How many unhybridized p-orbitals are available for p bonding?
» How many p-orbitals are needed?

2
S = [Ne] 3s 2 3p x
2
•
3p
??? Hybridization y
1 3p z
1
•
•
Bond order?
Resonance?
O
S o o
O

Resonance: Delocalization of electrons


Shifting of p -bond electrons without breaking the s - bond
Although not favored by formal charge, B.O. = 1.5
O
O O
S o o
Resonance
S o o
O



 p -electron pair found in
molecular orbital formed from the overlap of porbitals
B.O. = 1.5
» same as measured B.O.
S – O bond length is intermediate between S – O and S = O bond lengths
O
S o o
O

Strengths and Weaknesses of
Valence Bond Theory



VB Theory  Molecules are groups of atoms connected by localized overlap of valence shell orbitals
VB , VSEPR and hybrid orbital theories work well together to explain the shapes of molecules
But……VB theory inadequately explains…
» Magnetic property of molecules
» Spectral properties of molecules
» Electron delocalization
» Conductivity of metals




The electrons in a molecule are found in Molecular
Orbitals of different energies and shapes
» Just as an atom’s electrons are located in atomic orbitals of different energies and shapes
MOs spread over the entire molecule
Major drawbacks of MO Theory
» Based on Quantum theory
» Calculations are based on solving very complex wave equations  major approximations are needed!
» Difficult to visualize




VB Theory incorrectly predicts that....
» O
2
» O
2 is diamagnetic with B.O. = 2 or....
is paramagnetic with B.O. = 1
MO Theory correctly predicts that....
» O
2 is paramagnetic with B.O. = 2
VB Theory requires resonance structures to explain bonding in certain molecules and ions
» MO Theory does not have this limitation




MO’s form when atomic orbitals overlap
Bonding MOs
» Result from constructive interference of overlapping electron waves
» Stabilize a molecule by concentrating electron density between nuclei
MO’s  more stable than AO’s  delocalize electron charge over a larger volume

Overlap of standing electron Waves
Constructive interference
Destructive interference

Fig. 11.13
(High e density)
(Low e density)

H
2 is more stable than the separate atoms

Antibonding MOs

Antibonding MOs
» Result from destructive interference of overlapping electron waves
» Reduce electron density between nuclei
–Destabilize a molecule
» Higher in energy than bonding MOs of the same type

Using MO Theory to Calculate Bond Order



VB definition of Bond Order....
» Number of electron pairs shared between 2 nuclei
MO Theory
B.O. = ½
(
No. Bonding e -
-
No. Antibonding e -
)
Meaning of B.O.
» B.O. > 0, then molecule more stable than separate atoms
» B.O. = 0, then zero probability of bond formation
» The greater the B.O., the stronger the bond

Why Do Some Molecules Exist and
Others Do Not?


Why do H
2 and He decrease in PE
2
1+ exist , but He
2 does not?
Recall…..Bonding results only if there is a net
Molecules with equal numbers of Bonding and antibonding electrons are unstable...Why?......
» Antibonding MOs raise PE more than
Bonding MOs lower PE

Use MO theory to predict if the following can form



Hydride ions: H
2
1and H
2
2-
Li
2
Be
2
, Li
2
1+ , Li
2
2 + , Li
2
1-
, Be
2
1+ , Be
2
2 + , Be
2
1-

In He
2
, the antibonding electrons in s
1s
* cancel the PE lowering of s
1s

 s
Molecular Orbitals form when.....
» s - atomic orbitals overlap
» p - atomic orbitals overlap head to head
 p
Molecular Orbitals form when.....

» p atomic orbitals overlap side to side
Why are s
bonds more stable than pbonds ?

No mixing of 2s and 2p orbitals
Mixing of 2s and 2p orbitals
AO MO AO
MO Energy Levels for O
2
, F
2
& Ne
2
AO MO AO
MO Energy Levels for B
2
, C
2
& N
2

Explaining MO Energy Levels for
Period 2 Elements
O
2
, F
2 and Ne
2
•
Paired electrons in 2p sublevel

Repulsions

2s and 2p different in Energy
• No “mixing” occurs between 2s and 2p orbitals
– Raises energy of s
– Energy of s
2p
2s and s *
2s
MO
< Energy p
2p
B
2
, C
2 and N
2
• Only unpaired electrons in 2p sublevel

2s and 2p are very close in energy
• “Mixing” occurs between 2s and 2p orbitals
– Lowers energy of s
– Energy of s
2p
2s and s *
2s
MO
> Energy p
2p



Bonding in Diatomic Molecules of
Period 2
Rules for filling of Molecular Orbitals
Apply the Rules for the filling of Atomic Orbitals (Aufbau principle)
1.
Electrons 1st fill MOs of lowest energy
2.
Only 2 electrons with opposite spin per MO
3.
MOs of same energy (sublevel) half fill before electrons pair
Predict the bond order for each of the following molecules involving period 2 elements
» Li
2
, Be
2
, B
2
, C
2
, N
2
, O
2
, F
2
, Ne
2
, NO

High Z effective of F results in lower energy or its AO’s

1.
Why are oxygen’s AO’s at lower a energy than nitrogen’s?
2.
Bond order?
3.
Para- or diamagnetic?

Delocalized Molecular Orbitals



MO Theory (unlike VB Theory) does not require resonance to explain the bonding in.....
» Carbonate ion, Nitrate ion, Formate ion, Acetate ion,
Benzene, etc.
MO Theory: Electron pairs can be shared by 3 or more atoms
.......Why?
» MOs can overlap 3 or more atoms
Delocalized Bonds form when an electron pair is shared by 3 or more atoms
» Offers stability in the same way that resonance offers stability

 Why do metals conduct electricity and nonmetals do not?
» Band Theory to the rescue!!

Band Theory
 Energy Bands f orm from the overlap of atomic orbitals of similar energy from all atoms in a solid
 Energy bands containing core (nonvalence) electrons are localized
» i.e. Do not extend far from each atom


Energy Bands containing valence electrons are delocalized
» I.e. extent continuously throughout the solid
Conduction band : Valence bands that are either partially filled or empty

Energy Bands (MO Orbitals) for Na

Fig. 12.37

 Have a conduction band that is partially filled
(e.g. Group IA & Transition Metals) ....
or.
...
 Have an empty conduction band that overlaps a filled valence band (i.e. Have a narrow band gap)
» e.g. Group IIA Metals

Fig. 12.38

 All valence electrons are used to form covalent bonds
 Have a large band gap between the filled valence band and the empty conduction band
 Some examples
» Glass, diamonds, rubber, most plastics

 Have a small band gap between the filled valence band and the empty conduction band
 Thermal Energy can promote electrons from filled valence band to empty conduction band
» e.g. Silicon

 p-type semiconductors
» Doped with a Group IIIA element
– Have one less electron than Si
 Causes positive holes in semi conductor
 Electricity flows through these positive holes
 n-type semiconductors
» Doped with a Group VA element
– Have one more electron than Si
 Causes negative holes in semiconductor
 Electricity flows through these negative holes