1. Theories of Covalent Bonding
Chapter 11
Theories of Covalent Bonding

2. Theories of Covalent Bonding
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

3. The Central Themes of VB Theory
Basic Principle
A covalent bond forms when the orbtials of two atoms overlap and are occupied by a pair of electrons that have the highest probability of being located between the nuclei.
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.

4. Orbital overlap and spin pairing in diatomic molecules
Atomic Orbital Overlap
Orbital overlap and spin pairing in diatomic molecules
Hydrogen, H2
Hydrogen fluoride, HF
Fluorine, F2

5. Hybrid Orbitals Key Points
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.
Types of Hybrid Orbitals sp
sp2
sp3
sp3d
sp3d2

6. The sp hybrid orbitals in gaseous BeCl2
atomic orbitals
hybrid orbitals
orbital box diagrams

7. The sp hybrid orbitals in gaseous BeCl2 (continued)
orbital box diagrams with orbital contours

8. The sp2 hybrid orbitals in BF3

9. The sp3 hybrid orbitals in CH4

10. The sp3 hybrid orbitals in NH3

11. The sp3 hybrid orbitals in H2O

12. The sp3d hybrid orbitals in PCl5

13. The sp3d2 hybrid orbitals in SF6

15. Molecular shape and e- group arrangement
The conceptual steps from molecular formula to the hybrid orbitals used in bonding.
Figure 10.1
Step 1
Figure 10.12
Step 2
Step 3
Table 11.1
Molecular shape and e- group arrangement
Molecular formula
Lewis structure
Hybrid orbitals

16. SAMPLE PROBLEM 11.1
Postulating Hybrid Orbitals in a Molecule
PROBLEM:
Use partial orbital diagrams to describe mixing of atomic orbitals on the central atoms leads to hybrid orbitals in each of the following:
(a) Methanol, CH3OH
(b) Sulfur tetrafluoride, SF4
PLAN:
Use the Lewis structures to ascertain the arrangement of groups and shape of each molecule. Postulate the hybrid orbitals. Use partial orbital box diagrams to indicate the hybrid for the central atoms.
SOLUTION:
(a) CH3OH
The groups around C are arranged as a tetrahedron.
O also has a tetrahedral arrangement with 2 nonbonding e- pairs.

17. SAMPLE PROBLEM 11.1
Postulating Hybrid Orbitals in a Molecule
continued
single C atom
single O atom
hybridized C atom
hybridized O atom
(b) SF4 has a seesaw shape with 4 bonding and 1 nonbonding e- pairs.
S atom
hybridized S atom

18. Types of Covalent Bonds
Sigma () Bonds - Bonding that results from the end-to-end overlap is called a sigma bond. It has the highest electron density along the axis between the two nuclei. Single bonds are sigma bonds.
Pi () Bonds - Bonds that result from the side-to-side overlap of unhybridized p orbitals. The electron density is above and below the axis between the two nuclei. (This is why multiple bonds counted as one group of electrons in VSEPR theory)
The multiple part of multiple bonds are  bonds. In a double bond, there is one  and one  bond.
In a triple bond, there is one  and two  bonds.

19. relatively even distribution of electron density over all s bonds
The s bonds in ethane.
both C are sp3 hybridized
s-sp3 overlaps to s bonds
sp3-sp3 overlap to form a s bond
relatively even distribution of electron density over all s bonds

20. The s and p bonds in ethylene (C2H4)
overlap in one position - s
p overlap - 
electron density

21. The s and p bonds in acetylene (C2H2)
overlap in one position - s
p overlap - 

22. SAMPLE PROBLEM 11.2
Describing the Bonding in Molecules with
Multiple Bonds
PROBLEM:
Describe the types of bonds and orbitals in acetone, (CH3)2CO.
PLAN:
Use the Lewis structures to ascertain the arrangement of groups and shape at each central atom. Postulate the hybrid orbitals taking note of the multiple bonds and their orbital overlaps.
SOLUTION:
sp3 hybridized
sp2 hybridized
bond
bonds

23. Restricted rotation of p-bonded molecules
Rotation about the C-C bond can’t take place without breaking the  electron overlap.
CIS
TRANS

24. The Central Themes of 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).

25. An analogy between light waves and atomic wave functions.
Amplitudes of wave functions added
Amplitudes of wave functions subtracted.

26. Contours and energies of the bonding and antibonding molecular orbitals (MOs) in H2.

27. The MO diagram for H2

28. MO diagram for He2+ and He2 He2+ bond order = 1/2 (exists)
Energy
s*1s
s1s
s*1s
AO of He 1s
AO of He+ 1s
AO of He 1s
AO of He 1s
Energy
s1s
MO of He+
MO of He2
He2 bond order = 0
He2+ bond order = 1/2 (exists)

29. SAMPLE PROBLEM 11.3
Predicting Species Stability Using MO Diagrams
PROBLEM:
Use MO diagrams to predict whether H2+ and H2- 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. Find the bond order.
SOLUTION:
bond order = 1/2(1-0) = 1/2
bond order = 1/2(2-1) = 1/2 s s s s
H2+ does exist
H2- does exist 1s
AO of H
AO of H- 1s
AO of H 1s
AO of H
configuration is (s1s)2(s2s)1
MO of H2-
MO of H2+
configuration is (s1s)1

30. Be2 Li2 Bonding in s-block homonuclear diatomic molecules. Energy s*2s
Li2 bond order = 1 (is observed)
Be2 bond order = 0 (not observed)

31. Contours and energies of s and p MOs through combinations of 2p atomic orbitals

32. Relative MO energy levels for Period 2 homonuclear diatomic molecules.
without 2s-2p mixing
with 2s-2p mixing
MO energy levels for O2, F2, and Ne2
MO energy levels for B2, C2, and N2

33. MO occupancy and molecular properties for B2 through Ne2

34. SAMPLE PROBLEM 11.4
Using MO Theory to Explain Bond Properties
PROBLEM:
As the following data show, removing an electron from N2 forms an ion with a weaker, longer bond than in the parent molecules, whereas the ion formed from O2 has a stronger, shorter bond:
Bond energy (kJ/mol)
Bond length (pm) N2
N2+ O2
O2+
945
110
498
841
623
112
121
Explain these facts with diagrams that show the sequence and occupancy of MOs.
PLAN:
Find the number of valence electrons for each species, draw the MO diagrams, calculate bond orders, and then compare the results.
SOLUTION:
N2 has 10 valence electrons, so N2+ has 9.
O2 has 12 valence electrons, so O2+ has 11.

35. SAMPLE PROBLEM 11.4
Using MO Theory to Explain Bond Properties
continued N2
N2+ O2
O2+
2p
s2s
s2s
2p
2p
2p
2p
antibonding e- lost
bonding e- lost
2p
2p
2p
s2s
s2s
bond orders
1/2(8-2)=3
1/2(7-2)=2.5
1/2(8-4)=2
1/2(8-3)=2.5

36. The lowest energy p-bonding MOs in benzene and ozone.

37. The MO diagram for HF AO of H Energy AO of F MO of HF s 1s s 2p 2px
2py
MO of HF

38. possible Lewis structures
sp
*p
s*s
The MO diagram for NO 2s
AO of N 2p 2s
AO of O 2p
Energy
possible Lewis structures
s*s
ss
MO of NO

39. End of Chapter 11

40. The steps in converting a molecular formula into a Lewis structure.
Figure 10.1
The steps in converting a molecular formula into a Lewis structure.
Place atom with lowest EN in center
Molecular formula
Step 1
Atom placement
Add A-group numbers
Step 2
Sum of valence e-
Draw single bonds. Subtract 2e- for each bond.
Step 3
Give each atom 8e-
(2e- for H)
Remaining valence e-
Step 4
Lewis structure

41. The steps in determining a molecular shape.
Figure 10.12
The steps in determining a molecular shape.
See Figure 10.1
Molecular formula
Step 1
Lewis structure
Count all e- groups around central atom (A)
Step 2
Electron-group arrangement
Note lone pairs and double bonds
Step 3
Count bonding and nonbonding e- groups separately.
Bond angles
Step 4
Molecular shape (AXmEn)