The big picture

This course is not easy. Not only does it contain a large amount of information, its often abstract character and the fact that much of it has little relation with our everyday experience may be quite bewildering. This page is intended to help you see the structure in the theory of the chemical bond by listing the most essential points.

1. The stability and structure of a molecule depends on its energy. The structure is the arrangement of the nuclei that minimizes the energy. Changes (structural or electronic) that increase the energy reduce a molecule's stability. Quantum chemistry is therefore primarily concerned with the determination of the energy of a molecule and how this depends on the structure.
2. Because electrons are light particles, energies have to be determined using quantum mechanics. The quantum mechanical equation that gives us the energy is the Schrödinger equation.
3. Because nuclei are relatively massive, we can use the Born-Oppenheimer approximation. This means that we only need to solve the Schrödinger equation for the electrons. This gives us the electronic energy of a molecule. The total energy of a molecule is this electronic energy plus the Coulomb repulsion between the nuclei. The kinetic energy of the nuclei can be neglected.
4. Solving the Schrödinger equation for the electrons of a molecule gives us not only the electronic energy, but also the wave function of the electrons. This wave function is a function of the coordinates and spins of all electrons. The (absolute) square of the wave function is a probability distribution that tells you the probability of finding the electrons at definite positions and with definite spins.
5. The wave function of all electrons of a molecule is an extremely complicated function. To simplify dealing with such a wave function, we construct it out of functions that depend only on the coordinates and the spin of a single electron. These functions are called orbitals.
6. The wave function of all electrons of a molecule must change sign when two electrons are swapped. This is called the Pauli principle. The simplest way to construct a correct wave function from orbitals is making a so-called Slater determinant.
7. Very few things in quantum chemistry can be calculated exactly. In general one uses approximations. These can be quite accurate. If we approximate a wave function by a single Slater determinant, we are using Molecular Orbital theory. The orbitals in the Slater determinant are called molecular orbitals. There is an equation, called the Fock equation, that determines these molecular orbitals. It can be regarded as the one-electron analog of the Schrödinger equation. The equation also gives each molecular orbitals a so-called molecular orbitals energy. This energy is often interpreted as the energy of the electron in the molecular orbital.
8. Molecular orbitals are often still quite complicated functions. They can be made somewhat less complicated by writing them as linear combinations of atomic orbitals (LCAO approximation). The atomic orbitals are orbitals of the atoms from which a molecule is formed. They have well-defined shapes. We can use these shapes to group them into types (s, p, d, ...). These types are related to the groups of the periodic table. The atomic orbitals can also be grouped into shells (K, L, M, ..., or just 1, 2, 3, ...). These shells are related to the periods of the periodic table.
9. Molecular bonds can be identified with molecular orbitals. There are s bonds and p bonds. The difference depends on the shape of the corresponding molecular orbital, which depends in its turn on the type (i.e., shape) of the atomic orbitals from which the molecular is formed. A single bond is a s bond, a double bond is a s bond and a p bond, a triple bond is a s bond and two p bonds. A covalent bond has a molecular orbital to which atomic orbitals at different atoms contribute approximately equally. An ionic bond has atomic orbitals on different atoms contributing clearly different amounts. The angle between bonds is related to hybridization, which is the combination of atomic orbitals of different type on the same atom.