Molecular Orbital Theory
The quantum mechanical treatment of electrons in molecules yields molecular orbitals (MO), which are mathematical descriptions of regions of high electron charge density in a molecule. This is similar to the quantum mechanical treatment of electrons in atoms which yields atomic orbitals.
Bonding and Antibonding Orbitals
Let's look at the formation of a hydrogen molecule from two hydrogen atoms. As the atoms approach each other to form the molecule, their 1s atomic orbitals overlap. Two molecular orbitals result.
One molecular orbital is obtained by adding the two 1s atomic orbitals. This gives a molecular orbital with a region of high electron density between the the two nuclei. Molecular orbitals that are concentrated in regions between nuclei are called bonding orbitals. The bonding orbital just described is denoted, s1s. The s denotes a molecular orbital which has a cylindrical shape about the bond axis.
The other molecular orbital is obtained by subtracting the 1s atomic orbital on one atom from the 1s atomic orbital on the other atom. This gives a molecular orbital with electron density in the region between the two nuclei of almost zero. Molecular orbitals that are concentrated in regions other than between two nuclei are called antibonding orbitals. The antibonding orbital in the hydrogen molecule is denoted s*1s. We would read this as sigma star 1s. The asterisk tells us that it is an antibonding orbital.
Three ideas that we used in writing the electron configurations of atoms carry over to the assignment of electrons to molecular orbitals.
Electrons seek the lowest energy molecular orbital available to them.
The maximum number of electrons that can be present in a molecular orbital is two.
Electrons enter molecular orbitals of identical energies singly before they pair up.
Formation of Molecular Orbitals From 2p Atomic Orbitals
There are two ways in which 2p atomic orbitals can interact to form molecular orbitals. One pair of 2p orbitals can overlap along their axis to give one bonding and one antibonding s orbital. The other two pairs of 2p orbitals overlap sideways (see figure below) to give two bonding and two antibonding p orbitals.
Bond Order
The term bond order is simply another way of saying the number of bonds between two atoms. In molecular orbital theory, bond order is defined as one-half the difference between the number of electrons in bonding orbitals and the number of electrons in antibonding orbitals. Bond order does not have to be a whole number, values such as 1/2, and 3/2 are possible.
Relative Energies of 2s and 2p atomic orbitals and Molecular Orbitals They Form
The diagram below shows the relative energies of the 2s and 2p orbitals and the s and p molecular orbitals they form. The arrows show the occupation of molecular orbitals by the valence electrons of O2. The electron configuration can also be written as KK( s2s)2(s*2s)2(p2p)4(s2s2p)2(p*2p)2. Note that KK represents ( s2s1s)2(s*1s)2. There are eight bonding electrons and four antibonding electrons. The bond order is
bond order = 1/2(8 - 4) = 2
Notice from the diagram that the electron configuration for O2 shows two unpaired electrons, this means that O2 is paramagnetic.