1. 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

2. Valence Bond Theory 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:
H2, HF, H2S, F2

4. Examples of s and p Orbitals involved in Bonding
Overlap of s orbitals H2
Overlap of s and p orbitals HF
H2S
Overlap of p orbitals F2

5. hybrid orbitals are used in these cases
The use of only s and p orbitals does not explain bonding in most molecules!!!
e.g. BeCl2, CH4 , H2O
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

6. How to Determine an Atom’s Hybridization
Write Lewis structure for the molecule or ion, then...
Determine number of electron pairs around the atom in question
One orbital is needed for each electron pair
sp hybridization provides 2 orbitals
sp2 hybridization provides 3 orbitals
sp3 hybridization provides.....? orbitals
sp3d hybridization provides......? orbitals
sp3d2 hybridization provides....? orbitals

8. Examples of Hybrid Orbitals
Example of sp hybrid orbitals:
BeCl2

13. Examples of Hybrid Orbitals
Example of sp2 hybrid orbitals
BF3

15. Hybrid Orbitals Examples of sp3 hybrid orbitals
CH4, C2H6, H2O, NH3
Example of sp3d hybrid orbitals
PCl5
Example of sp3d2 hybrid orbitals
SF6

21. Bond Angle ~92 o

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

23. Mode of Orbital Overlap Sigma vs. Pi Bonds
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

24. Examples: Sigma vs. Pi Bonds
Ethane
Ethylene (ethene)
Effect of p-bonding on rotation about the s-bond?
Acetylene (ethyne)
Nitrogen
Formaldehyde

29. Predict the hybrid orbitals used in the following
Nitrogen gas, N2
Formaldehyde: H2CO
Carbon dioxide, CO2
Carbon monoxide, CO
Sulfur dioxide, SO2

30. One option for SO2 S = [Ne] 3s2 3px2 3py1 3pz1 o o
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?

31. Another Option for SO2 S = [Ne] 3s2 3px2 3py1 3pz1 ??? Hybridization
Bond order?
Resonance?
o o

32. 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 o
Resonance

33. Molecular Orbital Theory
p-electron pair found in molecular orbital formed from the overlap of p-orbitals
B.O. = 1.5
same as measured B.O.
S – O bond length is intermediate between S – O and S = O bond lengths
o o

34. 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

35. Molecular Orbital Theory
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

36. Advantages of MO Theory
VB Theory incorrectly predicts that....
O2 is diamagnetic with B.O. = 2 or....
O2 is paramagnetic with B.O. = 1
MO Theory correctly predicts that....
O2 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

37. Formation of Molecular Orbitals
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

38. Overlap of standing electron Waves
Constructive interference
Destructive interference

39. (High e- density)
(Low e- density)
Fig

41. H2 is more stable than the separate atoms

42. 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

43. 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

44. Why Do Some Molecules Exist and Others Do Not?
Why do H2 and He21+ exist , but He2 does not? Recall…..Bonding results only if there is a net decrease in PE
Molecules with equal numbers of Bonding and antibonding electrons are unstable...Why?......
Antibonding MOs raise PE more than Bonding MOs lower PE

45. Use MO theory to predict if the following can form
Hydride ions: H2 1- and H2 2-
Li2 , Li2 1+ , Li2 2+ , Li2 1-
Be2 , Be2 1+ , Be2 2+ , Be2 1-

46. In He2, the antibonding electrons in s1s* cancel the PE lowering of s1s

49. Sigma vs Pi Molecular Orbitals
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 p- bonds?

51. No mixing of 2s and 2p orbitals Mixing of 2s and 2p orbitals
AO MO AO
MO Energy Levels for O2, F2 & Ne2
AO MO AO
MO Energy Levels for B2, C2 & N2

52. Explaining MO Energy Levels for Period 2 Elements
O2, F2 and Ne2
Paired electrons in 2p sublevel  Repulsions  2s and 2p different in Energy
No “mixing” occurs between 2s and 2p orbitals
Raises energy of s2s and s*2s MO
Energy of s2p < Energy p2p
B2, C2 and N2
Only unpaired electrons in 2p sublevel  2s and 2p are very close in energy
“Mixing” occurs between 2s and 2p orbitals
Lowers energy of s2s and s*2s MO
Energy of s2p > Energy p2p

54. Bonding in Diatomic Molecules of Period 2
Rules for filling of Molecular Orbitals
Apply the Rules for the filling of Atomic Orbitals (Aufbau principle)
Electrons 1st fill MOs of lowest energy
Only 2 electrons with opposite spin per MO
MOs of same energy (sublevel) half fill before electrons pair
Predict the bond order for each of the following molecules involving period 2 elements
Li2, Be2, B2, C2, N2, O2, F2, Ne2, NO

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

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

59. 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

61. Bonding in Solids
Why do metals conduct electricity and nonmetals do not?
Band Theory to the rescue!!

62. Band Theory
Energy Bands form 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

63. Energy Bands (MO Orbitals) for Na

64. Fig

65. Electrical Conductors
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

66. Fig

67. Nonconductors (Insulators)
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

68. Semiconductors
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

69. Doping of Semiconductors
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