Linear combination of atomic orbitals molecular orbital method
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In molecular physics, the linear combination of atomic orbitals molecular orbital method (usually called the LCAO MO method) 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.
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. By minimizing the energy, an appropriate set of coefficients of the linear combinations is determined.
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.
LCAOwater1.JPG
The irreducible representation as derived from the point group's operations
References
- Huheey, James. Inorganic Chemistry:Principles of Structure and
Reactivity