Linear combination of atomic orbitals molecular orbital method

A linear combination of atomic orbitals or LCAO is a superposition of atomic orbitals. The LCAO molecular orbital method or LCAO MO is a technique for calculating molecular orbitals in quantum chemistry. It was introduced in 1929 by Sir John Lennard-Jones and extended by Ugo Fano.

Related Topics:
Superposition - Atomic orbitals - Molecular orbital - Quantum chemistry - 1929 - Sir John Lennard-Jones - Ugo Fano

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The orbitals are expressed as linear combinations of basis functions, and the basis functions are one-electron functions centered on nuclei of the component atoms of the molecule. The atomic orbitals used are typically those of hydrogen-like atoms since these are known analytically (i.e. Slater-type orbitals) but other choices are possible like Gaussian functions from standard basis sets. By minimizing the total energy of the system, an appropriate set of coefficients of the linear combinations is determined. However, since the development of computational chemistry, the LCAO method often refers not to an actual optimization of the wave function but to a hand-waving discussion which is very usefull for predicting and rationalizing results obtained via more modern methods. In this case, the shape of the molecular orbitals and their respective energies are deduced approximatively from comparing the energies of the atomic orbitals of the individual atoms (or molecular fragments) and applying some recipes known as level repulsion and alike. The graphs that are plotted to make this discussion clearer are called correlation diagrams. The required atomic orbital energies can come from calculations or directly from experiment via Koopmans' theorem.

Related Topics:
Linear combination - Basis function - Basis - Function - Electron - Nuclei - Atom - Molecule - Hydrogen-like atom - Slater-type orbital - Gaussian function - Basis sets - Energy - Coefficient - Computational chemistry - Molecular orbital - Atomic orbital - Koopmans' theorem

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

This is done by using the symmetry of the molecules and orbitals involved in bonding. The first step in this process is assigning a point group to the molecule. A common example is water, which is of C2v symmetry. Then a reducible representation of the bonding is determined. Each operation in the point group is performed upon the molecule. The number of bonds that are unmoved is the character of that operation. This reducible representation is decomposed into the sum of irreducible representations. These irreducible representations correspond to the symmetry of the orbitals involved.

Related Topics:
Point group - Reducible representation

~ ~ ~ ~ ~ ~ ~ ~ ~ ~