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 ?
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.
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