How do you determine how many electrons occupy the anti bonding orbitals?

For molecular orbital theory: How do you determine how many electrons occupy the anti bonding orbitals? Also, why does hydrogen gas have no anti bonding orbitals- if each atom's electrons form a molecular orbital, then their energy is reduced so where does the extra energy go ?

• Hydrogen has antibonding orbitals - just that it is unfilled.
– t.c
Oct 7, 2014 at 19:55
• Why are they unfilled? Wouldnt the conservation of energy require an antibonding orbital and a molecular orbital to be both filled up? Oct 7, 2014 at 20:00
• Forming a bond makes the molecule more stable. So the "extra energy" is released to the system. That's the definition of an energetically favorable reaction ($\ce{H + H -> H2}$). Oct 8, 2014 at 1:05
• Not necessarily @LDC3. The bond may just be weakened. Oct 8, 2014 at 4:50
• @Dissenter OK, I'll clarify. If you promote an electron into an anti-bonding orbital, the bond weakens and may undergo a reaction. If the molecule obtains an electron which must go into the anti-bonding orbital, the bond will likely break, resulting in a radical.
– LDC3
Oct 8, 2014 at 4:53

This is the MO diagram for Hydrogen. As you can see, for hydrogen atom, there is only 1 electron in the 1s orbital. Two hydrogens could come together to form a sigma bond, resulting in lowered energy. This doesn't mean that there is no sigma antiorbital, but rather due to the fact that hydrogen only contributes one electron each leading to a sum of two electrons, there are not enough electrons to fill the antiorbital, hence it is unfilled.

Now, imagine if it was helium instead. Helium has two 1s electrons, therefore, if two He atoms form a bond, 4 electrons has to be placed into the molecular orbitals. Since every orbital can hold a maximum of 2 electrons, two electrons would be in the sigma orbital, and the other two would be in the sigma antiorbital. An orbital and antiorbital would effectively cancel out, therefore, you see Helium exist in the monoatomic state.

• So each molecule can have up to only one molecular orbital/antiorbital? Oct 7, 2014 at 20:24
• It depends. For diatomic molecules, yes. For anything other than those, the electron distribution may not be that simple. For example acetylene chemgapedia.de/vsengine/media/vsc/en/ch/2/oc/stoffklassen/…
– t.c
Oct 7, 2014 at 20:28
• @user58953 For every bonding orbital, there's an antibonding orbital. As you can see in the lower diagram, there are four bonding orbitals and four antibonding orbitals. Oct 7, 2014 at 21:53
• Note that these MO diagrams only work for simple diatomics. More complicated diatomics or molecules will require symmetry and energy and overlap considerations. Oct 7, 2014 at 21:57
• You have tried to implement @Dissenter's comment, but how you wrote it it is wrong. MO Theory can be and is applied to any molecule - you just cannot put it in a two dimensional diagram anymore. Also note, that hybridisation is only a mathematical tool, hence hybrid orbitals are not a necessity to form any bonds. Oct 8, 2014 at 3:01

It is many years since I did bonding theory, more than I care to remember. In the 1s orbtal there is only one electron and the volume occupied fills a large region of space. The anti bonding orbital may be very small. In the 2s orbital with 2 electrons the region of space exhibited by the bonding orbital is so large that the nodal plane of the anti bonding orbital lies within the domain of space occupied by the bonding orbital. See T W G Solomons, Fundamentals of Organic Chemistry, 1982. The illustration of the molecular orbitals in this way gives an insight into the relative size and reinforcement of orbitals in a way line diagrams do not. I hope this is helpful. Chris