1. Bonding & Molecular Structure:
Chemistry Lecture 26
Chapter 10:
Bonding & Molecular Structure:
Orbital Hybridization, Molecular Orbitals
Chapter Highlights
intro to VB & MO theory
orbital overlap
orbital hybridization
multiple bonding (p bonds)
bond order
MO theory

2. Two Approaches to Chemical Bonding
Chemistry Lecture 26
Two Approaches to Chemical Bonding
Valence Bond (VB) Theory: (Linus Pauling, 1954) assumes covalent bonding is due to overlap of atomic orbitals which create a region of shared electron density between the nuclei
Molecular Orbital (MO) Theory: (Robert Mulliken, 1966) assumes valence electrons are in molecular orbitals which extend over several atoms

3. Valence Bond Theory: Orbital Overlap
Chemistry Lecture 26
Valence Bond Theory: Orbital Overlap
Orbital overlap: If two H-atoms approach each other closely enough their 1s orbitals can partially occupy the same region of space….

4. VB Theory: Orbital Overlap
Chemistry Lecture 26
VB Theory: Orbital Overlap
HA:1sA
Overlap Region
HB:1sB
1sA
1sB
H-atoms
H2 molecule

5. Energy Profile of a Covalent Bond
Chemistry Lecture 23
Energy Profile of a Covalent Bond

6. Chemistry Lecture 26
Orbital Overlap
The valence bond orbital between two atoms is a region of high probability of finding the electron.
There is an optimum distance between the two nuclei, called the bond length: the distance of separation at which the total energy is minimized.
The imaginary line that passes through both nuclei is called the internuclear axis

7. Sigma (s) Bonds Sigma (s) bond:
Chemistry Lecture 26
Sigma (s) Bonds
Sigma (s) bond:
A bond in which the electron density is circularly symmetrical about the internuclear axis. The orbital overlap is along the internuclear axis.

8. What Orbitals Do We Use to Make the Tetrahedral Molecule CH4 ?
Chemistry Lecture 26
What Orbitals Do We Use to Make the Tetrahedral Molecule CH4 ?
C: [He]2s22p2
H: 1s1

9. Chemistry Lecture 26
Hybrid Orbitals
Hybridization: The process of mathematically mixing two or more atomic orbitals, on a single atom.
Hybrid orbital: The result of this blending of orbitals. The number of hybrid orbitals formed is always the same as the number of atomic orbitals used

10. CH4 has four equivalent C-H bonds
Chemistry Lecture 26
sp3 Hybridization
CH4 has four equivalent C-H bonds 1s 2s 2p
ground state
promoted state

11. Chemistry Lecture 26
sp3 Hybridization
sp3 hybrid orbitals: are formed from the mixing of one s-orbital and three p-orbitals. The arrangement of the four sp3 hybrid orbitals is tetrahedral, with a 109.5° angle between the hybrid orbitals
2sp3 1s

12. Chemistry Lecture 26
sp3 Hybridization

13. BF3 has three equivalent B-F bonds
Chemistry Lecture 26
sp2 Hybridization
BF3 has three equivalent B-F bonds 1s 2s 2p
ground state
promoted state

14. Chemistry Lecture 26
sp2 Hybridization
sp2 hybrid orbitals: are formed from the mixing of one s-orbital and two p-orbitals. The arrangement of the three sp2 hybrid orbitals is trigonal planar, with a 120° angle between the hybrid orbitals
2sp2 2p 1s

15. Chemistry-140 Lecture 26 November 8th, 1996
sp2 Hybridization

16. BeF2 has two equivalent Be-F bonds
Chemistry Lecture 26
sp Hybridization
BeF2 has two equivalent Be-F bonds 1s 2s 2p
ground state
promoted state

17. Chemistry Lecture 26
sp Hybridization
sp hybrid orbitals: are formed from the mixing of one s-orbital and one p-orbital. The arrangement of the two sp hybrid orbitals is linear, with a 180° angle between the hybrid orbitals
2sp 2p 1s

18. Chemistry Lecture 26
sp Hybridization

19. Chemistry Lecture 26

20. Bonding & Molecular Structure:
Chemistry Lecture 28
Chapter 10:
Bonding & Molecular Structure:
Orbital Hybridization, Molecular Orbitals
Chapter Highlights
intro to VB & MO theory
orbital overlap
orbital hybridization
multiple bonding (p bonds)
bond order
MO theory

21. BF3 has three equivalent B-F bonds
Chemistry Lecture 28
sp2 Hybridization
BF3 has three equivalent B-F bonds 1s 2s 2p
ground state
promoted state

22. Chemistry Lecture 28
sp2 Hybridization
sp2 hybrid orbitals: are formed from the mixing of one s-orbital and two p-orbitals. The arrangement of the three sp2 hybrid orbitals is trigonal planar, with a 120° angle between the hybrid orbitals
2sp2 2p 1s

23. Chemistry-140 Lecture 26 November 8th, 1996
sp2 Hybridization

24. BeF2 has two equivalent Be-F bonds
Chemistry Lecture 28
sp Hybridization
BeF2 has two equivalent Be-F bonds 1s 2s 2p
ground state
promoted state

25. Chemistry Lecture 28
sp Hybridization
sp hybrid orbitals: are formed from the mixing of one s-orbital and one p-orbital. The arrangement of the two sp hybrid orbitals is linear, with a 180° angle between the hybrid orbitals
2sp 2p 1s

26. Chemistry Lecture 28
sp Hybridization

27. Chemistry Lecture 28

28. Chemistry Lecture 28

29. Sigma (s) Bonds Sigma (s) bond:
Chemistry Lecture 28
Sigma (s) Bonds
Sigma (s) bond:
A bond in which the electron density is circularly symmetrical about the internuclear axis. The orbital overlap is along the internuclear axis.

30. Multiple Bonds In almost all cases, single bonds are s-bonds
Chemistry Lecture 28
Multiple Bonds
In almost all cases, single bonds are s-bonds
BUT: To explain double and triple bonds we need another kind of bond.
C2H2 acetylene
C2H4 ethylene

31. Chemistry Lecture 28
p-Orbital Overlap
p-bonds: those in which the electron density is above and below the internuclear axis. The internuclear axis is a region of zero electron density.

32. Ethylene (sp2 hybridization)
Chemistry Lecture 28
Ethylene (sp2 hybridization)
10 of 12 valence electrons are used to form the C-H (four) and C-C (one) s-bonds. The extra p-orbitals are perpendicular to the plane of the molecule and contain a single electron 1s 2s 2p
ground state
promoted state 1s
2sp2 2p
sp2 hybridization

33. Ethylene (sp2 hybridization)
Chemistry Lecture 28
Ethylene (sp2 hybridization)

34. Ethylene (sp2 hybridization)
Chemistry Lecture 28
Ethylene (sp2 hybridization)

35. Ethylene (sp2 hybridization)
Chemistry Lecture 28
Ethylene (sp2 hybridization)
H(1s)
C(sp2)
C(p)
s-bonds
p-bond

36. Acetylene (sp hybridization)
Chemistry Lecture 28
Acetylene (sp hybridization)
6 of 10 valence electrons are used to form the C-H (two) and C-C (one) s-bonds. The TWO extra p-orbitals are perpendicular to the axis of the molecule and contain a single electron each 1s 2s 2p
ground state
promoted state 1s
2sp 2p
sp hybridization

37. Acetylene (sp hybridization)
Chemistry Lecture 28
Acetylene (sp hybridization)

38. Acetylene (sp hybridization)
Chemistry Lecture 28
Acetylene (sp hybridization)

39. Consequences of Multiple Bonding
Chemistry Lecture 28
Consequences of Multiple Bonding
Free rotation occurs around
the axis of a single s-bond Cl H C
This cannot occur for a multiple p-bond system and isomers may result
cis
trans

40. Bond Order and Hybridization in Resonance Structures
Chemistry Lecture 28
Bond Order and Hybridization in Resonance Structures
TWO p-electrons over THREE atoms. O-O bond order is 1.5!!
O-O distance & energy an average of a single & a double bond

41. Identifying Orbital Hybridization Schemes
Chemistry Lecture 28
Identifying Orbital Hybridization Schemes
Question
Complete this Lewis structure and assign hybridization schemes to all the non-hydrogen atoms. How many electrons are there in p-orbitals in this compound?

42. Identifying Orbital Hybridization Schemes
Chemistry Lecture 28
Identifying Orbital Hybridization Schemes
sp3
sp2
Answer
Since there is only ONE p-bond, the number of electrons in p-bonds is TWO!

43. Bonding & Molecular Structure:
Chemistry Lecture 29
Chapter 10:
Bonding & Molecular Structure:
Orbital Hybridization, Molecular Orbitals
Chapter Highlights
intro to VB & MO theory
orbital overlap
orbital hybridization
multiple bonding (p bonds)
bond order
MO theory

44. O O = An Introduction to Molecular Orbitals
Chemistry Lecture 29
An Introduction to Molecular Orbitals
Molecular Orbitals: Valence electrons are in molecular orbitals, MO’s extending over the whole molecule.
Emphasizes the uniqueness of each molecule rather than being the sum of its atoms (VB theory)
Why Bother!!!
O2 is paramagnetic!! That's a good reason!!
O O =

45. Molecular Orbitals From Atomic Orbitals
Chemistry Lecture 29
Molecular Orbitals From Atomic Orbitals
TWO atomic orbitals HA(1s) and HB(1s) combine mathematically (a linear combination) to produce TWO molecular orbitals H2 (s1s) and H2(s1s*).
s1s = Bonding MO
s1s* = Antibonding MO

46. Molecular Orbitals From Atomic Orbitals
Chemistry Lecture 29
Molecular Orbitals From Atomic Orbitals
Bonding MO (s1s): From addition of the two atomic orbitals. Leads to an increased probability that the electrons are found in this region. Electrons and orbital are concentrated between the nuclei.
Antibonding MO (s1s*): From subtraction of the two atomic orbitals. Leads to a reduced probability that the electrons are found in this region. Without significant electron density between the nuclei, they are repelled.

47. Molecular Orbital Description of H2
Chemistry Lecture 29
Molecular Orbital Description of H2
HA(1s)
HB(1s)
sigma*
antibonding MO
with node
sigma
bonding MO

48. A Molecular Orbital Diagram for H2
Chemistry Lecture 29
A Molecular Orbital Diagram for H2

49. Some Basic Principles of MO Theory
Chemistry Lecture 29
Some Basic Principles of MO Theory
A first principle: The number of molecular orbitals (MO) produced is always equal to the number of atomic orbitals (AO) used in the combination.
A second principle: Bonding MO’s are always lower in energy and antibonding MO’s higher in energy than their parent AO’s.
A third principle: Electrons are assigned to MO’s with successively higher energies; obeying the Pauli exclusion principle and Hund’s rule.

50. Bond order = 1/2 [(number of electrons in bonding MO’s)
Chemistry Lecture 29
Bond Order in MO Theory
Recall: Bond order was defined as the number of bonding electron pairs linking two atoms.
In MO Theory:
Bond order = 1/2 [(number of electrons in bonding MO’s)
- (number of electrons in antibonding MO’s)]

51. Bond Order From an MO Diagram
Chemistry Lecture 29
Bond Order From an MO Diagram
H2: (s1s)2 (s1s*)
Bond order for H2 = 1
He2: (s1s)2 (s1s*)2
Bond order for He2 = 0

52. A Molecular Orbital Diagram for Li2
Chemistry Lecture 29
A Molecular Orbital Diagram for Li2

53. Formation of s(2p) and s(2p)* MO’s
Chemistry Lecture 29
Formation of s(2p) and s(2p)* MO’s

54. Formation of p(2p) and p(2p)* MO’s
Chemistry Lecture 29
Formation of p(2p) and p(2p)* MO’s

55. MO’s Derived From the 2p Orbitals
Chemistry Lecture 29
MO’s Derived From the 2p Orbitals

56. MO Diagram for First Row Diatomics X2
Chemistry Lecture 29
MO Diagram for First Row Diatomics X2

57. (Lowest Unoccupied MO)
Chemistry Lecture 29
MO Diagram for N2
(Highest Occupied MO)
HOMO
(Lowest Unoccupied MO)
LUMO

58. N2:(s1s)2(s1s*)2(s2s)2(s2s*)2(p2p)4(s2p)2(p2p*)(s2p*)
Chemistry Lecture 29
Electron Configuration and
Bond Order for the N2 Molecule
N2:(s1s)2(s1s*)2(s2s)2(s2s*)2(p2p)4(s2p)2(p2p*)(s2p*)
N2:[core](s2s)2(s2s*)2(p2p)4(s2p)2
Bond order for N2 = 1/2 (8 - 2) = 3

59. Chemistry Lecture 29
MO Diagram for O2

60. O2:(s1s)2(s1s*)2(s2s)2(s2s*)2(p2p)4(s2p)2(p2p*)2(s2p*)
Chemistry Lecture 29
Electron Configuration and
Bond Order for the O2 Molecule
O2:(s1s)2(s1s*)2(s2s)2(s2s*)2(p2p)4(s2p)2(p2p*)2(s2p*)
O2:[core](s2s)2(s2s*)2(p2p)4(s2p)2(p2p*)2
Bond order for O2 = 1/2 (8 - 4) = 2
MO Theory predicts that O2
has TWO unpaired electrons
and is therefore PARAMAGNETIC!!

61. Textbook Questions From Chapter # 10
Chemistry Lecture 29
Textbook Questions From Chapter # 10
Review concepts: 1, 2, 3, 4, 5
Hybrid orbitals: 16, 18, 20, 24
Molecular orbital theory: 30, 34
General questions: 36, 40, 43, 45, 53
Conceptual questions: 61