Editing Molecular orbital theory (section)

==Linear combination of atomic orbitals (LCAO) method==
In the [[LCAO]] method, each molecule has a set of [[molecular orbital]]s. It is assumed that the molecular orbital [[wave function]] ''ψ<sub>j</sub>'' can be written as a simple weighted sum of the ''n'' constituent [[atomic orbital]]s ''χ<sub>i</sub>'', according to the following equation:<ref>{{cite book |author=Licker, Mark J. |title=McGraw-Hill Concise Encyclopedia of Chemistry |location=New York |publisher=McGraw-Hill |year=2004 |isbn=978-0-07-143953-4}}</ref>

<math display="block"> \psi_j = \sum_{i=1}^{n} c_{ij} \chi_i.</math>

One may determine ''c<sub>ij</sub>'' coefficients numerically by substituting this equation into the [[Schrödinger equation]] and applying the [[variational principle]]. The variational principle is a mathematical technique used in quantum mechanics to build up the coefficients of each atomic orbital basis. A larger coefficient means that the orbital basis is composed more of that particular contributing atomic orbital – hence, the molecular orbital is best characterized by that type. This method of quantifying orbital contribution as a [[linear combination of atomic orbitals]] is used in [[computational chemistry]]. An additional [[unitary transformation]] can be applied on the system to accelerate the convergence in some computational schemes. Molecular orbital theory was seen as a competitor to [[valence bond theory]] in the 1930s, before it was realized that the two methods are closely related and that when extended they become equivalent.

Molecular orbital theory is used to interpret [[ultraviolet–visible spectroscopy]] (UV–VIS). Changes to the electronic structure of molecules can be seen by the absorbance of light at specific wavelengths. Assignments can be made to these signals indicated by the transition of electrons moving from one orbital at a lower energy to a higher energy orbital. The molecular orbital diagram for the final state describes the electronic nature of the molecule in an excited state.

There are three main requirements for atomic orbital combinations to be suitable as approximate molecular orbitals.

# The atomic orbital combination must have the correct symmetry, which means that it must belong to the correct [[irreducible representation]] of the [[molecular symmetry|molecular symmetry group]]. Using [[linear combination of atomic orbitals|symmetry adapted linear combinations]], or SALCs, molecular orbitals of the correct symmetry can be formed.
# Atomic orbitals must also overlap within space. They cannot combine to form molecular orbitals if they are too far away from one another.
# Atomic orbitals must be at similar energy levels to combine as molecular orbitals. Because if the energy difference is great, when the molecular orbitals form, the change in energy becomes small. Consequently, there is not enough reduction in energy of electrons to make significant bonding.<ref>{{cite book |last1=Miessler |first1=Gary L. |title=Inorganic Chemistry |last2=Fischer |first2=Paul J. |last3=Tarr |first3=Donald A. |date=2013-04-08 |publisher=Pearson Education |isbn=978-0-321-91779-9 |language=en |url=https://books.google.com/books?id=VSktAAAAQBAJ}}</ref>