- Linear combination of atomic orbitals molecular orbital method
A

**linear combination of atomic orbitals**or**LCAO**is aquantum superposition ofatomic orbitals and a technique for calculatingmolecular orbital s inquantum chemistry [*Huheey, James. "Inorganic Chemistry:Principles of Structure and Reactivity"*] . In quantum mechanics,electron configurations of atoms are described aswavefunctions . In mathematical sense, these wave functions are the basis set of functions, the basis functions, which describe the electrons of a given atom. Inchemical reactions , orbital wavefunctions are modified, i.e. theelectron cloud shape is changed, according to the type of atoms participating in the chemical bond.It 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 byLinus Pauling for H_{2}^{+}. [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)A mathematical description is

: $phi\_i\; =\; c\_1\; chi\_1\; +\; c\_2\; chi\_2\; +\; c\_3\; chi\_3\; +\; cdots\; +c\_n\; chi\_n$

or

: $phi\_i\; =\; sum\_\{r\}\; c\_\{ri\}\; chi\_r$

where $phi\_i$ (phi) is a

molecular orbital represented as thesum of natomic orbital s $chi\_r$ (chi), each multiplied by a corresponding coefficient $c\_r$. The coefficients are the weights of the contributions of the n atomic orbitals to the molecular orbital. TheHartree-Fock procedure is used to obtain the coefficients of the expansion from the Hartree-Fock procedure.The orbitals are thus expressed as

linear combination s ofbasis function s, and the basis functions are one-electron functions centered on nuclei of the componentatom s of themolecule . The atomic orbitals used are typically those ofhydrogen-like atom s since these are known analytically i.e.Slater-type orbital s but other choices are possible like Gaussian functions from standard basis sets.By minimizing the total

energy of the system, an appropriate set ofcoefficient s of the linear combinations is determined. This quantitative approach is now known as theHartree-Fock method. However, since the development ofcomputational 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 themolecular orbital s and their respective energies are deduced approximately from comparing the energies of theatomic orbital s of the individual atoms (or molecular fragments) and applying some recipes known aslevel repulsion and the like. 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 viaKoopmans' 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 C_{2v}symmetry. Then areducible representation of the bonding is determined demonstrated below forwater ::

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.

MO diagram s provide simple qualitative LCAO treatment.:

Quantitative theories are the

Huckel method , theextended Huckel method and thePariser–Parr–Pople method .**ee also***

Quantum chemistry computer programs

*Hartree-Fock

*Basis Set

*Tight binding **External links*** LCAO @ chemistry.umeche.maine.edu [

*http://chemistry.umeche.maine.edu/Modeling/lcao.html Link*]**References**

*Wikimedia Foundation.
2010.*

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