Linear Combination of Atomic Orbitals px, py and pz

In the previous post we have seen how two s atomic orbitals get overlapped and form one bonding and one antibonding molecular orbitals. In this post we will see how other atomic orbitals take part in the formation of molecular orbitals.

If atom A and atom B have three p orbitals p_x, p_y and p_z each, how can we decide which two orbitals will get overlapped? In LCAO, it is a rule that two atomic orbitals must have similar energies. That means p_x will overlap with p_x, similarly p_y with p_yand p_z with p_z.

Let’s see how p_x orbital gets overlapped with other p_x orbital. They can only meet head-on to overlap as they are parallel to the inter-nuclear axis. The bond formed by their head-on overlapping is called sigma bond. But there are two ways this can be done, either both overlapping lobes have similar sign or have opposite sings.

When both p_x orbitals have same signs they form sigma (σ) bonding molecular orbital. In this situation electron density is increased between the two nuclei. And if both p_x orbitals have opposite signs they form sigma star (σ^*) antibonding molecular orbital. Here electron density is decreased between the nuclei and node is formed. Node is a place where probability of finding electron is zero.

In the last post we have discussed about the symmetry of MO, either they are gerade or ungerade. Let’s examine σ and σ^*and try to find out which one is gerade or ungerade.

The signs of the lobes of σ MO remain the same on rotating it along the line joining the two nuclei and then about a line perpendicular to this line, which means it is gerade. But when we repeat similar procedure with σ* MO, the signs of the lobes change, which means it is ungerade.

Lets discuss the overlapping of p_y orbitals. They are perpendicular to the nuclear axis, that’s why they can overlap only in sidewise manner and the bond is called pi (π) bond. Here also two possibilities arise, either both lobes of overlapping orbitals have similar signs or one orbital get inverted at the time of overlapping resulting in oppositely signed lobes.

When both p_y  orbitals have similar signs they form π bonding MO and in the other case they form π^* antibonding MO. You can clearly see that in π MO electron density is increased above and below the inter-nuclear axis and node is formed at the inter-nuclear axis. While in π^* MO electron density is decreased everywhere and node is formed.

Let’s examine their symmetry. When we rotate π MO along the line joining the two nuclei and then about a line perpendicular to this line, the signs of the lobes change, which means it is ungerade. And when we repeat similar procedure with π ^* MO, the signs of both lobes changes in an identical manner that’s why it is gerade.

Next is p_z orbital. Two p_z orbital share the same axis so they can overlap sidewise and form pi (π) bond. They also form πbonding MO and in other case they form π^* antibonding MO.

What happens when two d orbitals get overlapped? They also make sidewise overlapping but the difference is that the bond formed is called the δ bond. When both orbitals have similar signs they form δ bonding MO and in other case they form δ ^*antibonding MO. If you try to find out their symmetry it becomes difficult because the sign on lobes changes four times on rotating them about the inter-nuclear axis.

I hope you have learned how two atomic orbitals combine to form molecular orbitals. But what is its significance? What information can we draw by this Molecular Orbital Theory? In the next post we will explore the applications of MOT.

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