Introduction to Molecular Orbital Theory
________________________________________
1. Introduction
Modern chemistry has depended upon the use of models of increasing comlexity. Atoms can be represented as spheres connected by cyclinders or sticks. In order to understand the mechanism of many reactions, Lewis Theory, developed by Robinson and Ingold, can provide a succesful answer.
Lewis Theory uses curly arrows to denote electron migration during a chemical reaction and has led to a greater understanding of the factors controlling chemical reactions.
Pauling with others, developed Resonance Theory, which provided the rationale to an all-embracing orbital theory. The use of "canonical forms" and "resonance hybrids", alonng with extensive use of curvy arrows has provided the fundamental background to modern organic theory, but for eg. Diels-Alder and pericyclic reactions, the curly arrow format is not very clear and in some instances the reactions are described as no-machanism reactions. Woodward and Hoffmann showed that by examining the interaction of the frontier molecular orbitals (ie. the Highest Occupied, HOMO and Lowest Unoccupied, LUMO) both the regio- and stereospecificity could be accountred for.
Woodward and Hoffmann work was assimilated into general organic reaction theory.
2. Atomic and Molecular Orbitals
By sharing electron, molecules can form bonds, and it is possible to regard the sharing of two electrons by two atoms as constituting a chemical bond. Atoms can share one, two or three electrons (forming single, double and triple bonds).
A hydrogen atom consists of a nucleus (a proton) and an electron. It is not possible to accurately determine the position of the electron, but it is possible to calculate the probability of findng the electron at any point around the nucleus. With a hydrogen atom the probability distribution is spherical around the nucleus and it is possible to draw a spherical boundary surface, inside which there is a 95% possibility of finding the electron. The electron has a fixed energy and a fixed spatial distribution called an orbital. In the helium atom there are two electrons associated with the helium nucleus. The electrons have the same spatial distribution and energy (ie. they occupy the same orbital), but they differ in their spin (Pauli exlusion principle). In general: electrons in atomic nuclei occupy orbitals of fixed energy and spatial distribution, and each orbital only contains a maximum of two electrons with anti-parallel spins.
In physics, periodic phenomena are associated with a "wave equation", and in atomic theory the relevant equation is called the "Schrödinger Equation". The wave equation predicts discrete solutions in one dimension for a particle confined to a box with infinite walls,The solutions can be shown as in the figure below:



1 - 4 represent solutions of increasing energy. In three dimensions, the equation determines the energy and defines the spatial distribution of each electron. Solutions of the wave equations in three-dimensions allows calculation of the "shape" of each orbital. The first five solutions of the wave equation for an electron associated with a proton can be shown in the figure below:




In the hydrogen atom, the 1s atomic orbital has the lowest energy, while the remainder (2s, 2px, 2py and 2pz) are of equal energy (ie.degenerate), but for all other atoms, the 2s atomic orbital is of lower enegry than the 2px, 2py and 2pz orbitals, which are degenerate.
In atoms, electrons occupy atomic orbitals, but in molecules they occupy similar molecular orbitals which surround the molecule. The simplest molecule is hydrogen, which can be considered to be made up of two seperate protons and electrons. There are two molecular orbitals for hydrogen, the lower energy orbital has its greater electron density between the two nuclei. This is the bonding molecular orbital - and is of lower energy than the two 1s atomic orbitals of hydrogen atoms making this orbital more stable than two seperated atomic hydrogen orbitals. The upper molecular orbital has a node in the electronic wave function and the electron density is low between the two positively charged nuclei. The energy of the upper orbital is greater than that of the 1s atomic orbital, and such an orbital is called an antibonding molecular orbital.
Normally, the two electrons in hydrogen occupy the bonding molecular orbital, with anti-parallel spins. If molecular hydrogen is irradiated by ultra-violet (UV) light, the molecule may absorb the energy, and promote one electron into its antibonding orbital , and the atoms will seperate. The energy levels in a hydrogen molecule can be represented in a diagram - showing how the two 1s atomic orbitals combine to form two molecular orbitals, one bonding and one antibonding This is shown below - by clicking upon either the  or * molecular orbital in the diagram - it will show graphically in a window to the right: