# Molecular Orbital Diagram for dioxygen

In the MO diagram for $O_{2}$ : Shouldn't there be 3 different $3\sigma_{g}$ Bonding MO's as each p orbital can form a $\sigma_{g}$ Bonding MO along its respective axes?

In which case the $3\sigma_{g}$ has 6 electrons rather than 2.

• Do you know what the definition of a $\sigma$ orbital is? Also, a single orbital can never have 6 electrons in it. It can only have a maximum of 2. – bon Dec 5 '15 at 10:00
• Yes I think its an orbital which has no nodal planes as its rotated about its inter-nuclear axis. Its invariant under cylindrical rotation about the nucleus. I understand that an orbital can never have more than 2 electrons, but doesn't the p orbital along the x axis form a different $\sigma_{g}$ bonding MO in comparison the p orbital along the y and z axes? – J.Gudal Dec 5 '15 at 10:05
• Look at the orbitals formed by overlap of two $p_x$ orbitals (taking z as the internuclear axis, by convention) and tell me whether they have $\sigma$ symmetry. – bon Dec 5 '15 at 10:08
• No they don't. Oh right thanks I get it now, it makes sense. – J.Gudal Dec 5 '15 at 10:10
• Feel free to answer your own question so that it can be of use to future users. – bon Dec 5 '15 at 10:13

Thanks to bon in the comments I understand that since the z-axis is taken by convention as the inter-nuclear axis, the $p_x$ and $p_y$ orbitals are unable to form molecular orbitals that are invariant under cylindrical rotation about the z axis. Consequently there is only one $3\sigma_g$ and one $3\sigma_u$ orbital formed from $p_z$ orbitals.