Queen Mary, University of London

An Introduction to Molecular Orbital Theory



1.   Introduction

      What should you know already ?
      Localized and Non-Localized Approaches to Bonding

2.   Exact Solutions to the Schrödinger Equation ?

      All we have to do is solve the Schrödinger Equation
      Hamiltonian for the Hydrogen Molecule

3.   The Way Forward - Assumptions and Approximations

      Simplification 1 (Born - Oppenheimer Approximation)
      Simplification 2 (Orbital Approximation)
      Simplification 3 (LCAO Approximation)

4.   LCAO and the Variational Principle

      The Variational Principle
      Procedure for Implementing the Principle
      Overlap of Two Atomic Orbitals
      Summary of Terminology
      The Secular Equations and Secular Determinant
         Case 1 : Overlap of Two Identical Orbitals
         Case 2 : Overlap of Two Dissimilar Orbitals
      What are the Molecular Orbital Wavefunctions ?

5.   Partial Charges and Bond Orders

      Partial Charges
      Bond Orders

6.   Hückel Theory

      Basic Assumptions
      A Closer Look at the Secular Determinant
      Linear Conjugated Hydrocarbons
      Cyclic Conjugated Hydrocarbons

7.   Symmetry and Hybridisation

      Bonding in HX Molecules



   Appendix 1 : Minimization of the Expression for the Orbital Energy

   Appendix 2 : Determinants and Simultaneous Equations

   Appendix 3 : Normalisation of MOs and Electron Density Distribution

Authorship : This material was prepared by Dr Roger Nix, whilst working at Queen Mary, University of London.

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