Editing Molecular orbital (section)

===Homonuclear diatomics===
Homonuclear diatomic MOs contain equal contributions from each atomic orbital in the basis set. This is shown in the homonuclear diatomic MO diagrams for H<sub>2</sub>, He<sub>2</sub>, and Li<sub>2</sub>, all of which containing symmetric orbitals.<ref name = H&C />

====H<sub>2</sub>====
[[File:H2OrbitalsAnimation.gif|thumb|right|300px|Electron [[wavefunction]]s for the [[atomic orbital|1s orbital]] of a lone hydrogen atom (left and right) and the corresponding bonding (bottom) and antibonding (top) molecular orbitals of the H<sub>2</sub> molecule. The [[real part]] of the wavefunction is the blue curve, and the [[imaginary part]] is the red curve. The red dots mark the locations of the nuclei. The electron wavefunction oscillates according to the [[Schrödinger wave equation]], and orbitals are its [[standing wave]]s. The standing wave frequency is proportional to the orbital's kinetic energy. (This plot is a one-dimensional slice through the three-dimensional system.)]]
As a simple MO example, consider the electrons in a [[hydrogen]] molecule, H<sub>2</sub> (see [[MO diagram#Diatomic MO diagrams|molecular orbital diagram]]), with the two atoms labelled H' and H". The lowest-energy atomic orbitals, 1s' and 1s", do not transform according to the symmetries of the molecule. However, the following symmetry adapted atomic orbitals do:

{| class="wikitable"
|-
!1s'&nbsp;–&nbsp;1s"
|Antisymmetric combination: negated by reflection, unchanged by other operations
|-
!1s'&nbsp;+&nbsp;1s"
|Symmetric combination: unchanged by all symmetry operations
|}

The symmetric combination (called a bonding orbital) is lower in energy than the basis orbitals, and the antisymmetric combination (called an [[antibonding]] orbital) is higher. Because the H<sub>2</sub> molecule has two electrons, they can both go in the bonding orbital, making the system lower in energy (hence more stable) than two free hydrogen atoms. This is called a [[covalent bond]]. The [[bond order]] is equal to the number of bonding electrons minus the number of antibonding electrons, divided by 2. In this example, there are 2 electrons in the bonding orbital and none in the antibonding orbital; the bond order is 1, and there is a single bond between the two hydrogen atoms.{{cn|date=June 2022}}

====He<sub>2</sub>====
On the other hand, consider the hypothetical molecule of He<sub>2</sub> with the atoms labeled He' and He". As with H<sub>2</sub>, the lowest energy atomic orbitals are the 1s' and 1s", and do not transform according to the symmetries of the molecule, while the symmetry adapted atomic orbitals do. The symmetric combination—the bonding orbital—is lower in energy than the basis orbitals, and the antisymmetric combination—the antibonding orbital—is higher. Unlike H<sub>2</sub>, with two valence electrons, He<sub>2</sub> has four in its neutral ground state. Two electrons fill the lower-energy bonding orbital, σ<sub>g</sub>(1s), while the remaining two fill the higher-energy antibonding orbital, σ<sub>u</sub>*(1s). Thus, the resulting electron density around the molecule does not support the formation of a bond between the two atoms; without a stable bond holding the atoms together, the molecule would not be expected to exist. Another way of looking at it is that there are two bonding electrons and two antibonding electrons; therefore, the bond order is 0 and no bond exists (the molecule has one bound state supported by the Van der Waals potential).{{citation needed|date=January 2014}}

====Li<sub>2</sub>====
[[Dilithium]] Li<sub>2</sub> is formed from the overlap of the 1s and 2s atomic orbitals (the basis set) of two Li atoms. Each Li atom contributes three electrons for bonding interactions, and the six electrons fill the three MOs of lowest energy, σ<sub>g</sub>(1s), σ<sub>u</sub>*(1s), and σ<sub>g</sub>(2s). Using the equation for bond order, it is found that dilithium has a bond order of one, a single bond.<ref>{{Cite journal |last=König |first=Burkhard |date=1995-02-21 |title=Chemical Bonding. VonM. J. Winter. 90 S., ISBN 0-19-855694-2. – Organometallics 1. Complexes with Transition Metal-Carbon σ-Bonds. VonM. Bochmann. 91 S., ISBN 0-19-855751-5. – Organometallics 2. Complexes with Transition Metal-Carbon π-Bonds. VonM. Bochmann. 89 S., ISBN 0-19-855813-9. – Bifunctional Compounds. VonR. S. Ward. 90 S., ISBN 0-19-855808-2. – Alle aus der Reihe: Oxford Chemistry Primers, Oxford University Press, Oxford, 1994, Broschur, je 4.99 £ |url=https://onlinelibrary.wiley.com/doi/10.1002/ange.19951070434 |journal=Angewandte Chemie |language=de |volume=107 |issue=4 |pages=540 |doi=10.1002/ange.19951070434}}</ref>

====Noble gases====
Considering a hypothetical molecule of He<sub>2</sub>, since the basis set of atomic orbitals is the same as in the case of H<sub>2</sub>, we find that both the bonding and antibonding orbitals are filled, so there is no energy advantage to the pair. HeH would have a slight energy advantage, but not as much as H<sub>2</sub> + 2 He, so the molecule is very unstable and exists only briefly before decomposing into hydrogen and helium. In general, we find that atoms such as He that have full energy shells rarely bond with other atoms. Except for short-lived [[Van der Waals bonding|Van der Waals complexes]], there are very few [[noble gas compound]]s known.{{cn|date=June 2022}}