Editing Molecular orbital (section)

===Gerade and ungerade symmetry===
For molecules that possess a center of inversion ([[centrosymmetry|centrosymmetric molecules]]) there are additional labels of symmetry that can be applied to molecular orbitals.
Centrosymmetric molecules include:
* [[Homonuclear molecule|Homonuclear]] diatomics, X<sub>2</sub>
* [[Octahedral molecular geometry|Octahedral]], EX<sub>6</sub>
* [[square planar molecular geometry|Square planar]], EX<sub>4</sub>.
Non-centrosymmetric molecules include:
* [[Heteronuclear molecule|Heteronuclear]] diatomics, XY
* [[Tetrahedral molecular geometry|Tetrahedral]], EX<sub>4</sub>.
If inversion through the center of symmetry in a molecule results in the same phases for the molecular orbital, then the MO is said to have gerade (g) symmetry, from the German word for even.
If inversion through the center of symmetry in a molecule results in a phase change for the molecular orbital, then the MO is said to have ungerade (u) symmetry, from the German word for odd.
For a bonding MO with σ-symmetry, the orbital is σ<sub>g</sub> (s'&nbsp;+&nbsp;s<nowiki>''</nowiki> is symmetric), while an antibonding MO with σ-symmetry the orbital is σ<sub>u</sub>, because inversion of s'&nbsp;–&nbsp;s<nowiki>''</nowiki> is antisymmetric.
For a bonding MO with π-symmetry the orbital is π<sub>u</sub> because inversion through the center of symmetry for would produce a sign change (the two p atomic orbitals are in phase with each other but the two lobes have opposite signs), while an antibonding MO with π-symmetry is π<sub>g</sub> because inversion through the center of symmetry for would not produce a sign change (the two p orbitals are antisymmetric by phase).<ref name = H&C />