1. Ch. 5: Advanced Theories of Bonding
Dr. Namphol Sinkaset
Chem 200: General Chemistry I

2. I. Chapter Outline Introduction Valence Bond Theory
Hybrid Atomic Orbitals
Multiple Bonds
Molecular Orbital Theory
Computational Chemistry

3. I. Introduction
We know covalent compounds share e- when they bond, but how do they do this?
VSEPR theory allows us to predict shapes, but what is the reason for these shapes?
We’d also like to be able to explain magnetic properties of covalent molecules, e.g. O2 vs. N2.

4. I. Introduction

5. I. Multiple Theories
Theories are simplified views of reality, so they have limitations.
Often, different theories are used to explain different aspects of the same system.
In this case, valence bond theory (VBT) explains why molecules have certain shapes whereas molecular orbital theory (MOT) explains magnetic properties of molecules.

6. II. Core Principles of VBT
VBT takes the idea of atomic orbitals (from quantum mechanics) and explains how they are used to form compounds.
The central idea of VBT: covalent bonds form when half-filled atomic orbitals of two atoms overlap and the overlap region, which is between the nuclei, is occupied by a pair of e-’s.

7. II. Interaction Calculation

8. II. Orbital Overlap The better the overlap, the stronger the bond.
Stronger bonds form when orbitals are oriented that allow overlap along the internuclear axis. Why?

9. II. Types of Orbital Overlap
Orbitals can overlap such that the overlap region lies on the internuclear axis.
This type of overlap creates a sigma (σ) bond.

10. II. Types of Orbital Overlap
Orbitals can also overlap such that the overlap region lies above and below the internuclear axis.
This type of overlap creates a pi (π) bond.
π bonds have a node along the internuclear axis.

11. II. Bonds in a Molecule
The first bond is always a σ bond, i.e. all single bonds are σ bonds.
Subsequent higher order bonds are π bonds.
In :N≡N:, there is one σ bond and two π bonds.

12. III. Simple VBT
Simple direct overlap of s, p, d, and f orbitals cannot account for the many shapes observed in molecules.
e.g. Since O is 1s22s22p4, we’d expect 2 H’s that are 1s1 to overlap with two half-filled p orbitals on O to make H2O.
However, this would be incorrect.

13. III. Simple VBT for H2O
Since the p orbitals are 90° apart, the bond angle is predicted to be 90°.
Experimentally, bond angle is measured as 104.5°.

14. III. Hybrid Atomic Orbitals
Linus Pauling proposed that valence atomic orbitals can be different than atomic orbitals in an isolated atom.
When atoms bond, new wavefunctions w/ different shapes form.
If atomic orbitals are mixed (via hybridization), new hybrid orbitals can be formed.
Linear combinations of atomic orbitals mathematically describe hybrid orbitals.

15. III. Atomic vs. Bonded O
An O atom isolated in space has a 2s and three 2p as its valence orbitals.
In H2O, these valence orbitals are mixed to form 4 degenerate orbitals that point to the corners of a tetrahedron.

16. III. Hybrid Atomic Orbitals
Important points about hybrid orbitals:
Hybrid orbitals don’t exist in isolated atoms, only in covalently-bonded atoms.
Hybrid orbitals have shapes/orientations that differ from atomic orbitals.
A set of hybrid orbitals are formed from a set of atomic orbitals; the # of hybrids is equal to the # of atomic orbitals used in their formation.
All hybrids in a set are equivalent in shape and energy.
The type of hybrids formed depends on it’s electron-pair geometry predicted by VSEPR.
Hybrid orbitals overlap to form σ bonds; unhybridized orbitals overlap to form π bonds.

17. III. Hybridization
In the next few slides, we go over the different hybridizations that a central atom undergoes to form covalent compounds.
Pay attention to the relationship between the type of hybridization and the resulting geometry of the molecule.

18. III. Formation of sp Hybrids

19. III. sp Hybridization
Be can undergo sp hybridization. To get the linear geometry, one s orbital is mixed with one p orbital.

20. III. Formation of sp2 Hybrids

21. III. sp2 Hybridization
B can undergo sp2 hybridization. To get the trigonal planar geometry, one s orbital is mixed with two p orbitals.

22. III. Formation of sp3 Hybrids

23. III. sp3 Hybridization
C commonly forms sp3 hybrids. To get the tetrahedral electron geometry, one s orbital is mixed with three p orbitals.

24. III. Bonding in Methane
In methane, carbon forms 4 sp3 hybrids which overlap with the s orbitals in hydrogen.

25. III. Bonding in Ethane
Bonding in ethane (C2H6) can be described as two C’s that are sp3 hybridized.

26. III. sp3d Hybridization
To get trigonal bipyramidal geometry, an s orbital, three p orbitals, and one d orbital are mixed.

27. III. Example of sp3d Compound

28. III. sp3d2 Hybridization
Octahedral geometry is obtained by mixing one s orbital, three p orbitals, and two d orbitals.

29. III. Example of sp3d2 Compound

30. III. Hybridize Only If Necessary
Hybridization was devised to explain experimental molecular geometries.
Sometimes, hybridization not necessary, e.g. H2O vs. H2S vs. H2Te.

31. III. Sample Problem
Identify the type of hybridization expected in the central atom of the following molecules.
SF4
XeF4
PCl3
ClO3-
BrF3

32. III. Higher Order Bond Formation
Recall that higher order bonds are formed from overlap of normal atomic orbitals.
Hybridizations that don’t use all atomic orbitals leave the possibility of forming π bonds.

33. III. Bonding in Ethene
Higher order bonds still count as one electron region, so the C’s are sp2 hybridized.

34. III. C Hybridization in Ethene
We see that there would be a p orbital that is singly filled for each C.
With the correct orientation, a π bond can form.

35. III. Bonding Scheme in Ethene
σ: H(1s) – C(sp2)
σ: C(sp2) – C(sp2)
π: C(2p) – C(2p)

36. III. Triple Bonds
It should make sense that atoms that are sp hybridized lead to triple bonds.

37. III. Bonding Scheme in H-C≡C-H
σ: H(1s) – C(sp)
σ: C(sp) – C(sp)
π: C(2p) – C(2p)

38. III. Sample Problem
Identify the bonding schemes in the two diagrams.

39. III. The Resonance Problem
The resonance seen above doesn’t affect the assignment of hybridization.
However, neither structure describes the e-’s in π bonds well.
The π e-’s aren’t in one position, but are delocalized.

40. IV. Another Problem
Lewis theory predicts O2 has a double bond with two lone pairs on each O.
However, it’s paramagnetic!

41. IV. O2 Has Unpaired Electrons
O2 is not magnetic, but it is attracted to magnetic fields (paramagnetic).
Experiments show that O2 has two unpaired electrons; however, Lewis theory doesn’t predict this at all.
We turn to molecular orbital theory.

42. IV. Core Principles of MOT
VBT treats e-’s as being in atomic orbitals which a big simplification.
The main difference from VBT: e-’s belong to the entire molecule, and they exist in molecular orbitals.
Quantum mechanics is applied to a molecule instead of individual atoms to get new orbitals that belong to the molecule.

43. IV. Formation of MO’s
Applying quantum mechanics to molecules requires applying trial wavefunctions.
The most common trial functions involve taking weighted linear combinations of atomic orbitals.
i.e. mathematically adding/subtracting atomic orbitals (atomic wavefunctions) to form MO’s (molecular wavefunctions).

44. IV. Linear Combinations
When two atomic wavefunctions are subtracted from one another, you get an antibonding MO.
Antibonding MO’s have a region of zero e- density between nuclei (called a node).
When two atomic wavefunctions are added together, you get a bonding MO.
Bonding MO’s have a region of high e- density between nuclei, thus lowering PE.

45. IV. Creating Wavefunctions
Remember that atomic orbitals are 3D waves.
Like other waves, they can be combined into new waves.

46. IV. Destructive vs. Constructive

47. IV. Filling MO’s
Rules for filling MO’s are the same as for filling AO’s.
Aufbau principle
Pauli exclusion principle
Hund’s rule
A molecular orbital diagram shows the relative energy and number of e-’s in each MO, as well as the AO’s that formed them.

48. IV. MO Diagram for H2
Electron configuration: (σ1s)2

49. IV. Bond Order
In MOT, bond order is something that is calculated. A bond order greater than 0 indicates increased stability for atoms when bonded.
B.O. = ½ [(e-’s in bonding MOs) – (e-’s in antibonding MOs)]

50. IV. Why Doesn’t He2 Exist?
Electron configuration: (σ1s)2 (σ*1s)2

51. V. Homonuclear Diatomics
In general, only valence orbitals interact to form MO’s.
s orbital interactions are easy – create a bonding and a nonbonding MO as seen in H2.
How do p orbitals interact to form MO’s?

52. V. MO’s From p Orbitals
py and pz create two sets of degenerate orbitals.

53. V. Homonuclear MO Diagrams
MO diagrams of p-block elements will have MO’s formed from s and p orbitals.
For O2, F2, and Ne2 (theoretical), the order of the MO’s is as expected.
For Li2 to N2, the energy level of the p orbitals is low enough to allow orbital mixing (specifically s-p mixing) with the s orbitals; this changes the order of the MO’s.

54. V. The Effect of s-p Mixing

55. V. Sample Problem
Construct molecular orbital diagrams for N2 and O2. Additionally, determine whether or not these molecules are diamagnetic or paramagnetic, calculate their bond orders, and write the valence e- molecular orbital configuration.

56. V. Comparison of Theories
Valence Bond Theory
Molecular Orbital Theory
Bonds are localized between one pair of atoms.
Electrons are delocalized over entire molecule.
Bonds formed from overlap of atomic and hybrid orbitals.
Atomic orbitals are combined to form molecular orbitals.
Forms sigma or pi bonds.
Creates bonding and antibonding interactions.
Predicts molecular shape based on regions of e- density.
Predicts arrangement of electrons in molecules.
Requires multiple structures to describe resonance.
Accounts for resonance through molecular orbitals.

57. VI. Computational Chem
Application of MOT to larger molecules requires computational effort.
Computational chemistry is a whole branch of chemistry.
We look at results for two larger molecules, CH4 and O3.

58. VI. CH4: VBT vs. MOT

59. VI. CH4 Bonding MO #2

60. VI. Resonance in O3, VBT

61. VI. Resonance in O3, MOT