Editing Molecular orbital (section)

==Overview==
A molecular orbital (MO) can be used to represent the regions in a [[molecule]] where an [[electron]] occupying that orbital is likely to be found. Molecular orbitals are approximate solutions to the [[Schrödinger equation]] for the electrons in the electric field of the molecule's [[atomic nuclei]]. However calculating the orbitals directly from this equation is far too intractable a problem. Instead they are obtained from the combination of atomic orbitals, which predict the location of an electron in an atom. A molecular orbital can specify the [[electron configuration]] of a molecule: the spatial distribution and energy of one (or one pair of) electron(s). Most commonly a MO is represented as a [[Linear combination of atomic orbitals molecular orbital method|linear combination of atomic orbitals]] (the LCAO-MO method), especially in qualitative or very approximate usage. They are invaluable in providing a simple model of bonding in molecules, understood through [[molecular orbital theory]].
Most present-day methods in [[computational chemistry]] begin by calculating the MOs of the system. A molecular orbital describes the behavior of one electron in the electric field generated by the nuclei and some average distribution of the other electrons. In the case of two electrons occupying the same orbital, the [[Pauli principle]] demands that they have opposite spin. Necessarily this is an approximation, and highly accurate descriptions of the molecular electronic wave function do not have orbitals (see [[configuration interaction]]).

Molecular orbitals are, in general, delocalized throughout the entire molecule. Moreover, if the molecule has symmetry elements, its nondegenerate molecular orbitals are either symmetric or antisymmetric with respect to any of these symmetries. In other words, the application of a symmetry operation '''S''' (e.g., a reflection, rotation, or inversion) to molecular orbital ψ results in the molecular orbital being unchanged or reversing its mathematical sign: '''S'''ψ = ±ψ. In planar molecules, for example, molecular orbitals are either symmetric ([[sigma bond|sigma]]) or antisymmetric ([[pi bond|pi]]) with respect to reflection in the molecular plane. If molecules with degenerate orbital energies are also considered, a more general statement that molecular orbitals form bases for the [[irreducible representation]]s of the molecule's [[symmetry group]] holds.<ref>{{Cite book|url=https://archive.org/details/isbn_9780471510949/page/102|title=Chemical applications of group theory|last=Cotton|first=F. Albert|date=1990|publisher=Wiley|isbn=0471510947|edition=3rd|location=New York|pages=[https://archive.org/details/isbn_9780471510949/page/102 102]|oclc=19975337|url-access=registration}}</ref> The symmetry properties of molecular orbitals means that delocalization is an inherent feature of molecular orbital theory and makes it fundamentally different from (and complementary to) [[valence bond theory]], in which bonds are viewed as localized electron pairs, with allowance for [[Resonance (chemistry)|resonance]] to account for delocalization.

In contrast to these symmetry-adapted ''canonical'' molecular orbitals, [[localized molecular orbitals]] can be formed by applying certain mathematical transformations to the canonical orbitals. The advantage of this approach is that the orbitals will correspond more closely to the "bonds" of a molecule as depicted by a Lewis structure. As a disadvantage, the energy levels of these localized orbitals no longer have physical meaning. (The discussion in the rest of this article will focus on canonical molecular orbitals. For further discussions on localized molecular orbitals, see: [[natural bond orbital]] and [[sigma-pi and equivalent-orbital models]].)