[faraz.yashar]

Due to molecular orbital theory, we know the Lewis structure for dioygen is incorrect. Since we find that there are two antibonding pi orbitals with single electrons, we can deduce that oxygen is a biradical and instead of having a double bond it has a single bond accompanied by two free radical electrons.

So how can it be that if we have a single bond, the bond order of dioxygen is still two?  I understand it from the perspective of calculation (bond order = [#bonding-#antibonding]/2), but it makes no intuitive sense.  

Also, a double bond is defined by a pi and a sigma bond.  Which bonds in the MO diagram for dioxygen constitute these bonds?  Does the sigma bond come from the 2s orbitals or the 2pz orbitals?  Is there a pi bond that arises from the 2px and 2py orbitals?  How does one account for the antibonding electrons?

Thanks!

[tamim83]

Also, a double bond is defined by a pi and a sigma bond.  Which bonds in the MO diagram for dioxygen constitute these bonds?

Essentially you are asking which molecular orbitals are responsible for these bonds.  Lets say the bond forms along the z axis.  Then, the sigma bond will be formed from the overlap between the 2p_z orbitals.  The 2s orbitals will overlap to form sigma bonding and anti-bonding orbitals.  Since both these orbitals will be filled with electrons, they will sort of "cancel" one another out.   Both the 2p_x and 2p_y orbitals will overlap to form pi bonding and anti-bonding orbitals, 2 each.  The bonding orbitals will be completely filled, and as you have mentioned, each anti-bonding pi orbital will be half filled.  The half filled pi ant-bonding orbitals "cancel" one of the bonding orbitals, resulting in one pi bond.  So you do essentially end up with one sigma bond and one pi bond, which in valence bond theory would be a "double bond".  That is the reasoning behind the "bond order".  We are adding (and subtracting) atomic wavefunctions.  Anti-bonding electrons do not contribute to bonding since they don't allow for electrons to move between nuclei.  When they are occupied by electrons, they cancel bonding interactions. 

Quantum mechanics often goes against intuition, its not as cut and dry as valence bond theory or Lewis theory.  MO theory is pretty simple for a diatomic molecule like oxygen; we can nicely connect what it tells us to what we know from VBT and Lewis theory.  However, this does not happen with larger molecules, it gets much more complex.  But, MO theory is probably "closer to the truth" - the atomic world is a strange place. 

Hope this helps some.