1. Covalent Bonding: orbitals
Chapter 9
Covalent Bonding: orbitals

2. Topics Hybridization and the localized electron model
The molecular orbital model
Bonding in homonuclear diatomic molecules
Bonding in heteronuclear diatomic molecules
Combining the localized electron and molecular orbital models

3. 9.1 Hybridization and localized electron model
How do atoms share electrons between their valence shells?
The localized electron bonding model
A covalent bond is formed by the
pairing of two electrons with opposing
spins in the region of overlap of atomic
orbitals between two atoms
Overlap: the two orbitals share a
common region in space
This overlap region has high
electron charge density
The more extensive the overlap
between two orbitals, the stronger
is the bond between two atoms

4. According to the model:
For an atom to form a covalent bond it must have an unpaired electron
Number of bonds formed by an atom should be determined by its number of unpaired electrons

5. Sharing of two electrons between the two atoms.
How does Lewis theory explain the bonds in H2 and F2?
Sharing of two electrons between the two atoms.
Overlap Of
2 1s
2 2p H2
(1s1)
(1s1) F2
(1s22s22p5)
(1s22s22p5)
Localized electron model – bonds are formed by sharing of e- from overlapping atomic orbitals.

6. Hybridization of Atomic Orbitals
Based on ground-state electron configuration, carbon should have only two bonds
If a 2s electron is promoted to an empty 2p orbital, then four unpaired electrons can give rise to four bonds
These four orbitals become mixed, or hybridized to form bonds

7. Hybridization of Atomic Orbitals
Most of the electrons in a molecule remain in the same orbital locations that they occupied in the separated atoms
Bonding electrons are localized in the region of atomic orbital overlap

8. Hybridization ?
Two or more atomic orbitals are mixed to produce a new set of orbitals (blended orbitals)
Number of hybrid orbitals = number of atomic orbitals mixed

9. sp3 Hybridization Occurs most often for central atom only
The total number of hybrid orbitals is equal to the number of atomic orbitals combined

10. sp3 Hybridization
s and p orbitals of the valence electrons are blended.
one s orbital is combined with 3 p orbitals.
sp3 hybridization has tetrahedral geometry.

11. sp3 Hybridization
The carbon atom in methane (CH4) has bonds that are sp3 hybrids
Note that in this molecule carbon has all single bonds

12. In terms of energy 2p
Hybridization
sp3
Energy 2s

13. Methane building blocks
VSEPR

14. 3 sp Methane: Carbon 1s 2s 2px 2py 2pz sp3 sp3 sp3 sp3 Promote
Hybridize sp 3 x
109.5o z
Methane: Carbon

15. sp3 Orbital Hybridization in NH3
3 Equivalent half-filled orbitals are used to form bonds with 3H atoms. The 4th sp3 holds the lone pair 1s

16. Bonding in Ammonia Ammonia (NH3) is similar to CH4
except the lone pair of electrons occupies the 4th hybrid orbital
7N: 1s2 2s2 2p3

17. How about hybridization in H2O?
2 sp3 H 2p 2s 8O

18. sp2 Hybridization Consider BF3
The empty 2p orbital remains unhybridized
sp2 is comprised of one 2s orbital and two 2p orbitals to produce a set of three sp2 hybrid orbitals

19. Formation of sp2 Hybrid Orbitals

20. Hybrid orbitals and geometry
The geometric distribution of the three sp2 hybrid orbitals is within a plane, directed at 120o angles
This distribution gives a trigonal planar molecular geometry, as predicted by VSEPR

21. sp2 Hybridization scheme is useful in describing double covalent bonds, e.g. Ethylene
in CH2=CH2
Unhybridized orbital

22. 10.5

23. Nonhybridized p-orbitals

24. sp2 Hybridization scheme is useful in describing double covalent bonds, e.g. Ethylene

25. Sigma  and pi  bonds
Sigma bond is formed when two orbitals each with a single electron overlap
(Head-to-head overlap). Electron density is concentrated in the region directly between the two bonded atoms
Pi-bond is formed when two parallel p-orbitals overlap side-to-side
The orbital consists of two lopes one above the bond axis and the other below it.
Electron density is concentrated in the lopes
Electron density is zero along the line joining the two bonded atoms

26. H H C C H H

27. sp2 hybridization C2H4 Double bond acts as one pair. trigonal planar
Have to end up with three blended orbitals.
Use one s and two p orbitals to make sp2 orbitals.
Leaves one p orbital perpendicular.

28. In terms of energy 2p 2p
Hybridization
sp2
Energy 2s

29. sp Hybridization H-Be-H 1s2 2s2 4Be
The geometric distribution of the two sp hybrid orbitals is linear , directed at 180o angles
This distribution gives a linear molecular geometry
H-Be-H
1s2 2s2
4Be

30. In terms of energy 2p 2p sp
Hybridization
Energy 2s

31. This hybridization scheme is useful
in describing triple covalent bonds
in acetylene HC CH
Hybridization in
Unhybridized orbitals

33. Carbon–Carbon Triple Bonds

34. Hybridization in molecules containing multiple bonds
The extra electron pairs in double or triple bonds have no effect upon the geometry of molecules
Extra electron pairs in multiple bonds are not located in hybrid orbitals
Geometry of a molecule is fixed by the electron pairs in hybrid orbitals around the central atom
All unshared electron pairs
Electron pairs forming single bonds
One (only one) electron pair in a multiple bond

35. CO2 O C O
C can make two s and two p
O can make one s and one p

36. dsp3/sp3d Hybridization
This hybridization allows for expanded valence shell compounds – typical for group 5A elements, e.g., 15P
A 3s electron can be promoted to a 3d subshell, which gives rise to a set of five sp3d hybrid orbitals
Central atoms without d-orbitals, N, O, F, do not form expanded octet

37. Phosphorus Pentachloride
PCl5 P Cl Cl Cl Cl Cl P Cl Cl P Cl Cl Cl Cl
VSEPR

38. 3 sp d Trigonal Bipyrimidal Phosphorus Pentachloride: Phosphorus 2 3s
sp3d sp3d sp3d sp3d sp3d
Neon 2 3s
3px
3py
3pz
dxz dyz dxy dx2-y2 dz2
Hybridized
90o
Promoted
sp d 3
120o
Trigonal Bipyrimidal
120o
Phosphorus Pentachloride: Phosphorus

39. d 2sp3/sp3d2 hybridization
This hybridization allows for expanded valence shell compounds – typically group 6A elements, e.g., S
A 3s and a 3p electron can be promoted to the 3d subshell, which gives rise to a set of six sp3d2 hybrid
orbitals

40. Predicting Hybridization Schemes
In hybridization schemes, one hybrid orbital is produced for every simple atomic orbital involved
Write a plausible Lewis structure for the molecule or ion
Use the VSEPR method to predict the
electron-group geometry of the central atom
Count # of e-pairs around the atom
Multiple bond is counted as one pair
Choose the hybrid set having same
number of orbitals

41. Success of the localized electron model
Overlap of atomic orbitals explained the stability of covalent bond
Hybridization was used to explain the molecular geometry predicted by the localized electron model
When lewis structure was in adequate, the concept of resonance was introduced to explain the observed properties

42. Weakness of the localized electron model
It incorrectly assumed that electrons are localized and so the concept of resonance was added
Inability to predict the magnetic properties of molecules like O2 (molecules containing unpaired electrons)
No direct information about bond energies

43. 9.2 Molecular Orbital Theory
Molecular orbitals (MOs) are mathematical equations that describe the regions in a molecule where there is a high probability of finding electrons
Atomic orbitals of atoms are combined to give a new set of molecular orbitals characteristic of the molecule as a whole
The number of atomic orbitals combined equals the number of molecular orbitals formed.
(Two s-orbitals Two molecular orbitals)

44. Molecular orbitals
Two atomic orbitals combine to form a bonding molecular orbital and an anti-bonding MO*.
Electrons in bonding MO’s stabilize a molecule
Electrons in anti-bonding MO’s destabilize a molecule
For the orbitals to combine, they must be of comparable energies. e.g., 1s(H) with 2s(Li) is not allowed
The molecular orbitals are arranged in order of increasing energy.
The electronic structure of a molecule is derived by feeding electrons to the molecular orbitals according to same rule applied for atomic orbitals

45. Electrons go into the lowest energy molecular orbital available
Molecular orbitals
Each molecular orbital can hold a maximum of two electrons with opposite spins
Electrons go into the lowest energy molecular orbital available
Hund’s rule is obeyed
Molecular orbital model will be applied only to the diatomic molecules of the elements of the first two periods of the Periodic Table

46. Formation of molecular orbitals by combination of 1s orbitals
The hydrogen molecule
Bonding MO1 = enhanced region of electron density
Electron density is concentrated away from
internuclear region
Electron density is concentrated between nuclei
Destructive interference
Constructive interference HB HA
Antibonding MO2 = region of diminished electron density

47. Energy level diagram in hydrogen (H2).
Bonding molecular orbital has lower energy and greater stability than the atomic orbitals from which it was formed.
antibonding molecular orbital has higher energy and lower stability than the atomic orbitals from which it was formed.

48. The Molecular Orbital Model
We use labels to indicate shapes, and whether the MO’s are bonding or antibonding.
MO1 = s1s
MO2 = s1s* (* indicates antibonding)
We can write them the same way as atomic orbitals
H2 = s1s2

49. Bond order Bond Order =1/2 (bonding e – antibonding e)
(number of bonds)
Higher bond order = stronger bond

50. Bond order for H2

51. Bond order for He2+ and He2
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

52. 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-
configuration is (s1s)1 1s
AO of H 1s
AO of H +
configuration is (s1s)2(s1s)1
MO of H2-
MO of H2+

53. ( ) - bond order = 1 2 Number of electrons in bonding MOs
Number of electrons in antibonding MOs ( - )
bond order 1

54. 9.3 Bonding in homonuclear diatomic molcules
For atomic orbitals to participate in molecular orbitals, they must overlap in space
Thus only valence orbitals of atoms contribute significantly to the molecular orbitals of the molecule
Inner orbitals are too small to overlap and thus their electrons are assumed to be localized and not participate in bonding

55. Only outer orbitals bond
The 1s orbital is much smaller
than the 2s orbital
When only the 2s orbitals
are involved in bonding
Don’t use the s1s or s1s*
for Li2
Li2 = (s2s)2
In order to participate in
bonds the orbitals must
overlap in space.

56. Bonding in s-block homonuclear diatomic molecules.
s*2s
s2s
s*2s
s2s 2s 2s 2s
Bonding in s-block homonuclear diatomic molecules.
Be2
Li2
Energy
Be2 bond order = 0
Li2 bond order = 1

57. Possible interactions between two equivalent p orbitals and the corresponding molecular orbitals- + -
Head-to-head overlap
+: High e- density +
-: Low e- density
Side-to-side overlap

58. Molecular Orbital (MO) Configurations
The number of molecular orbitals (MOs) formed is always equal to the number of atomic orbitals combined.
The more stable the bonding MO, the less stable the corresponding antibonding MO.
The filling of MOs proceeds from low to high energies.
Each MO can accommodate up to two electrons.
Use Hund’s rule when adding electrons to MOs of the same energy.
The number of electrons in the MOs is equal to the sum of all the electrons on the bonding atoms.

59. Expected Energy Diagram
s2p*
p2p*
p2p* 2p 2p
p2p
p2p
s2p
Energy
s2s* 2s 2s
s2s

60. B2 2p 2p
Energy 2s 2s

61. B2
(s2s)2(s2s*)2 (s2p)2
Bond order = (4-2) / 2
Should be stable.

62. Magnetism Magnetism has to do with electrons.
Paramagnetism: substance is attracted by a magnet.
associated with unpaired electrons.
Diamagnetism: substance is repelled by a magnet.
associated with paired electrons.
Experimentally, B2 was found to be paramagnetic
However, Orbital diagram shows that it is diamagnetic?

63. Magnetism
The energies of of the p2p and the s2p are reversed by p and s interacting
The s2s and the s2s* are no longer equally spaced.
Here’s what it looks like.

64. Correct energy diagram
s2p*
p2p*
p2p* 2p
s2p 2p
p2p
p2p
s2s* 2s 2s
s2s

65. B2
s2p*
p2p* 2p 2p
s2p
p2p
s2s* 2s 2s
s2s

66. MO energy level digrams for diatomic molecules of B2 through F2
Note that for O2 and F2 2p orbital is lower in energy than 2p orbitals
MO energy level digrams for diatomic molecules of B2 through F2

67. Patterns As bond order increases, bond energy increases.
As bond order increases, bond length decreases.
Direct correlation of bond order to bond energy is not always there
O2 is known to be paramagnetic.

68. SAMPLE PROBLEM
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.

69. SAMPLE PROBLEM
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

70. 9.4 Bonding in heteronuclear
diatomic molecules
Will deal with molecules of atoms adjacent to each other in the Periodic Table
Simple type has them in the same energy level, so can use the orbital diagrams used for homonuclear molecules already known to us
Slight energy differences. NO

71. 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
Bond order=
Experimentally NO is
paramagnetic
MO of NO

72. Nitric oxide, NO
# valence e- =
5(N) + 6(O) = 11 2p 2p 2s 2s

73. Two non-bonding orbitals are the lone pairs on F
The MO diagram for HF s
Two non-bonding orbitals
are the lone pairs on F
seen in The Lewis structure
for HF
AO of H 1s s
Energy
Note the H1S
is less stable
than the F2P 2p
MO of HF
AO of F

74. 2p Partial molecular orbital energy-level diagram for HF 1s
Other valence electrons of F are
assumed to be localized s
F binds its valence
electrons more
tightly than H
Energy 1s
Note the H1S
is less stable
(has more energy) than the F2P 2p
Since both electrons are lowered in
energy, HF molecule is more stable
Than individual atoms. This is the
Driving force for bond formation
AO of H
MO of HF
AO of F

75. Partial molecular orbital energy-level diagram for HF
The  molecular orbital containing the bonding electron pair shows greater electron probability close to F
Thus, F atom will have a slight excess of –ve charge, i.e., electron sharing is not equal
Consequently, MO diagrams accounts for bond polarity

76. The MO Energy-level diagram for both the NO+ and CN- ions
# valence e in NO+ = 10
Same order as homonuclear atoms

77. 9.5 Combining the localized electron and molecular orbital models
sp orbitals are called the Localized electron model
s and p Molecular orbital model
Localized is good for geometry, doesn’t deal well with resonance.
seeing s bonds as localized works well
It is the p bonds in the resonance structures that can move.
 molecular orbital can be considered to be spread over the entire molecule rather than being concentrated between the two atoms
Electrons occupying the  molecular orbital belong to the whole molecule; they are described as Delocalized

78. The resonance structures for O3 and NO3-
The two extra electrons in the double bond are found in the
delocalized -orbital associated with the whole molecule
Also, there are 3 -bonds localized between S and O atoms
Thus bond distances are the same

79. Bonding in Benzene
The structure of benzene, C6H6, discovered by Michael Faraday in 1825, was not figured out until 1865 by F. A. Kekulé
Kekulé discovered that benzene has a cyclic structure and he proposed that a hydrogen atom was attached to each carbon atom and that alternating single and double bonds joined the carbon atoms together

80. Benzene
This kind of structure gives rise to two important resonance hybrids and leads to the idea that all three double bonds are delocalized across all six carbon atoms

81. Benzene
A better description of bonding in benzene results when a combination of the two models is used for interpretation
Six p-orbitals can be used to -molecular orbitals
The electrons in the resulting -molecular orbitals are delocalized above and below the plane of the ring.
Thus, C-C bonds are equivalent as obtained from experiment

82. p delocalized bonding
C6H6 H H

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

84. Delocalized molecular orbitals are not confined between two adjacent bonding atoms, but actually extend over three or more atoms.