A linear combination of atomic orbitals or LCAO is a superposition of atomic orbitals. In quantum mechanics, electron configurations of atoms are described as wave functions. In mathematical sense, these wave functions are the basis set of functions, the basis functions, of electrons of a given atom. In compounds, these orbital wave functions are modified, i.e. the electrons rearranged, according to the type of chemical bonding in which they participate. The term superposition can have several meanings: Quantum superposition Law of superposition in geology and archaeology Superposition principle for vector fields Superposition Calculus is used for equational first-order reasoning This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ... An atomic orbital is the description of the behavior of an electron in an atom according to quantum mechanics. ... Electron configuration is the arrangement of electrons in an atom, molecule or other body. ... A compound is an area of land that is surrounded by fences, walls, or barbed wire and is used for a particular purpose, especially an area containing buildings and where the entry and exit of people is controlled. ... In chemistry, a chemical bond is the force which holds together atoms in molecules or crystals. ...

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. Electron atomic and molecular orbitals In quantum chemistry, the molecular electronic states, i. ... Quantum chemistry is a branch of theoretical chemistry, which applies quantum mechanics to problems in chemistry. ... Jump to: navigation, search 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. ... Ugo Fano, 1912 - 2001 Ugo Fano, a leader in theoretical physics in the 20th century was born in Torino, Italy, in 1912 and passed away on February 13, 2001 in Chicago, Illinois, at the age of 88. ...

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. 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. ... Jump to: navigation, search In linear algebra, a basis is a minimum set of vectors that, when combined, can address every vector in a given space. ... 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). ... Jump to: navigation, search Properties The electron is a fundamental subatomic particle which carries a negative electric charge. ... A stylized representation of a lithium atom. ... Jump to: navigation, search Properties For alternative meanings see atom (disambiguation). ... Jump to: navigation, search A molecule is the smallest particle of a pure chemical substance that still retains its chemical composition and properties. ... Hydrogen-like atoms are atoms with one single electron. ... Slater-type orbitals are functions used as atomic orbitals in the linear combination of atomic orbitals molecular orbital method. ... Jump to: navigation, search Gaussian curves parameterised for statistics A Gaussian function (named after Carl Friedrich Gauss) is a function of the form: for some real constants a > 0, b, and c. ... In modern computational chemistry, quantum chemical calculations are typically performed within a finite set of basis functions. ... Jump to: navigation, search In mathematics, a coefficient is a multiplicative factor of a certain object such as a variable (for example, the coefficients of a polynomial), a basis vector, a basis function and so on. ... Computational chemistry is a branch of theoretical chemistry whose major goals are to create efficient mathematical approximations and computer programs that calculate the properties of molecules (such as total energy, dipole and quadrupole moment, vibrational frequencies, reactivity and other diverse spectroscopic quantitities and cross sections for collision of molecules with... Electron atomic and molecular orbitals In quantum chemistry, the molecular electronic states, i. ... Jump to: navigation, search Electron atomic and molecular orbitals A less formal description of the electrons in atoms can be found at Electron configuration. ... Koopmans theorem is an approximation in molecular orbital theory, such as density functional theory, or Hartree-Fock theory, in which the first ionization energy of a molecule is equal to the energy of the highest occupied molecular orbital (the HOMO), and the electron affinity is the negative of the energy...

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 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. ... In mathematics, the term irreducible is used in several ways. ...

Image File history File links Made in ChemDraw, shows the reducible representation of the bonding of water File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...

References

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