Electron configurations for molecules

 
____ 1sσ*
 
 
____ 1sE 1s _____
HH
 _____1 
 H2 
The energy of one of the molecular orbitals formed on overlap of atomic orbitals is higher than that of the atomic orbitals, and the energy of the other molecular orbital is lower.
The molecular orbital with higher electron density between the nuclei is of lower energy because these electrons are attracted to both nuclei.

The lower energy molecular orbital (1sσ in this case) is more stable than the atomic orbitals on separated atoms and is referred to as a bonding orbital.
Electrons in bonding molecular orbitals stabilize the molecule.

The higher energy orbital (1sσ* in this case) is referred to as an antibonding orbital.
Electrons in antibonding molecular orbitals destabilize the molecule.
Each pair of atomic orbitals overlap to give a bonding and an antibonding molecular orbital. The electron density in regions between the nuclei is higher in bonding than in antibonding orbitals.

The number of electrons occupying valence molecular orbitals for a particular species equals the number of valence electrons for that species.

In the most stable electron configuration the electrons are in orbitals of lowest energy.
No more than two electrons can occupy a molecular orbital.  The two electrons must have opposite spin.
Molecular orbitals of equal energy are all occupied singly before a second electron enters any of them.