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## Linear combination of atomic orbitals molecular orbital methodA ## Additional recommended knowledgeIt was introduced in 1929 by Sir John Lennard-Jones with the description of bonding in the diatomic molecules of the first main row of the periodic table, but had been used earlier by Pauling for H A mathematical description is or where (phi) is a molecular orbital represented as the sum of n atomic orbitals (chi), each multiplied by a corresponding coefficient . The coefficients are the weights of the contributions of the n atomic orbitals to the molecular orbital. The orbitals are thus 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. This quantitative approach is now known as the Hartree-Fock method. However, since the development of computational chemistry, the LCAO method often refers not to an actual optimization of the wave function but to a qualitative discussion which is very useful 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 approximately from comparing the energies of the atomic orbitals of the individual atoms (or molecular fragments) and applying some recipes known as level repulsion and the like. The graphs that are plotted to make this discussion clearer are called 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 C
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.
Quantitative theories are the Huckel method, the extended Huckel method and the Pariser–Parr–Pople method. ## References**^**Huheey, James.*Inorganic Chemistry:Principles of Structure and Reactivity***^**Friedrich Hund and Chemistry, Werner Kutzelnigg, on the occasion of Hund's 100th birthday, Angewandte Chemie, 35, 573 - 586, (1996)**^**Robert S. Mulliken's Nobel Lecture, Science, 157, no. 3785, 13 - 24, (1967)
Categories: Chemical bonding | Physical chemistry | Quantum chemistry |

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Linear_combination_of_atomic_orbitals_molecular_orbital_method". A list of authors is available in Wikipedia. |