Contents
1 The Electronic Structure Determination . . . . . . . . . . . . . . . . . . . . . .
1
1.1 Variation Method (Molecular Orbital Linear Combination
of Atomic Orbitals, MO-LCAO) . . . . . . . . . . . . . . . . . . . . . . . .
2
1.2 A Matrix Formulation of MO Calculations . . . . . . . . . . . . . . . . .
3
1.3 The Hückel Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.3.1 The Case of the Allyl Anion (MO-LCAO
by p Orbitals) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.4 The Extended Hückel Procedure . . . . . . . . . . . . . . . . . . . . . . . .
6
1.5 Group Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5.1 Rules for the Elements Which Constitute a Group . . . . . 12
1.5.2 Group Multiplication Tables . . . . . . . . . . . . . . . . . . . . . 12
1.5.3 Representation of Symmetry Operations by Matrices . . . 13
1.6 Irreducible Representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.6.1 Character Table of groups . . . . . . . . . . . . . . . . . . . . . . . 17
1.6.2 Factoring the Total Representations into Irreducible
Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.6.3 Relation Between Molecular Wave Functions
and Irreducible Representations . . . . . . . . . . . . . . . . . . . 20
1.6.4 Obtaining Molecular Orbitals with a Given
Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2 Symmetry Orbitals for Different Bis and Polyatomic Molecules . . . . 25
2.1 Homonuclear Diatomic Molecules A-A of the Periodic
Table First Row . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2 Water Molecule, as Example of Triatomic Molecule . . . . . . . . . . 29
2.3 Ammonia Molecule, as Example of Tetratomic Molecule . . . . . . 33
2.4 Methane Molecule, as Example of Pentatomic Molecule . . . . . . . 36
2.5 Considerations About the Models of Chemical Bond in Use
Before the Adoption of the Symmetry Molecular Orbital
Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
xi
1 The Electronic Structure Determination . . . . . . . . . . . . . . . . . . . . . .
1
1.1 Variation Method (Molecular Orbital Linear Combination
of Atomic Orbitals, MO-LCAO) . . . . . . . . . . . . . . . . . . . . . . . .
2
1.2 A Matrix Formulation of MO Calculations . . . . . . . . . . . . . . . . .
3
1.3 The Hückel Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.3.1 The Case of the Allyl Anion (MO-LCAO
by p Orbitals) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.4 The Extended Hückel Procedure . . . . . . . . . . . . . . . . . . . . . . . .
6
1.5 Group Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5.1 Rules for the Elements Which Constitute a Group . . . . . 12
1.5.2 Group Multiplication Tables . . . . . . . . . . . . . . . . . . . . . 12
1.5.3 Representation of Symmetry Operations by Matrices . . . 13
1.6 Irreducible Representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.6.1 Character Table of groups . . . . . . . . . . . . . . . . . . . . . . . 17
1.6.2 Factoring the Total Representations into Irreducible
Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.6.3 Relation Between Molecular Wave Functions
and Irreducible Representations . . . . . . . . . . . . . . . . . . . 20
1.6.4 Obtaining Molecular Orbitals with a Given
Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2 Symmetry Orbitals for Different Bis and Polyatomic Molecules . . . . 25
2.1 Homonuclear Diatomic Molecules A-A of the Periodic
Table First Row . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2 Water Molecule, as Example of Triatomic Molecule . . . . . . . . . . 29
2.3 Ammonia Molecule, as Example of Tetratomic Molecule . . . . . . 33
2.4 Methane Molecule, as Example of Pentatomic Molecule . . . . . . . 36
2.5 Considerations About the Models of Chemical Bond in Use
Before the Adoption of the Symmetry Molecular Orbital
Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
xi