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. In quantum chemistry, molecular orbitals are the statistical states electrons can have within molecules. ... Quantum chemistry is the application of quantum mechanics to problems in chemistry. ... 1929 was a common year starting on Tuesday (link will take you to calendar). ... John Edward Lennard-Jones (October 27, 1894 - November 1, 1954) was a mathematician who held a chair of theoretical physics at Bristol University, and then a chair of theoretical science at Cambridge University. ...

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. In mathematics, linear combinations are a concept central to linear algebra and related fields of mathematics. ... In functional analysis and its applications, a function space can be viewed as a vector space of infinite dimension whose basis vectors are functions not vectors. ... In mathematics, a subset B of a vector space V is said to be a basis of V if it satisfies one of the four equivalent conditions: B is both a set of linearly independent vectors and a generating set of V. B is a minimal generating set of V... In mathematics, a function is a relation, such that each element of a set (the domain) is associated with a unique element of another (possibly the same) set (the codomain, not to be confused with the range). ... Properties The electron (sometimes called negatron; commonly represented as e−) is a subatomic particle. ... The nucleus (atomic nucleus) is the center of an atom. ... Properties For alternative meanings see atom (disambiguation). ... In science, a molecule is the smallest particle of a pure chemical substance that still retains its chemical composition and properties. ... Energy is a fundamental quantity that every physical system possesses; it allows us to predict how much work the system could be made to do, or how much heat it can exchange. ... In mathematics, a coefficient is a multiplicative factor that belongs to a certain object such as a variable (for example, the coefficients of a polynomial), a basis vector, a basis function and so on. ...

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. In crystallography, a crystallographic point group or crystal class is a set of symmetry operations that leave a point fixed, like rotations or reflections, which leave the crystal unchanged. ...

References

• Huheey, James. Inorganic Chemistry:Principles of Structure and

Reactivity