Molecular Orbitals in Diatomic Molecules.

Not all atomic orbitals overlap to make molecular orbital, There are some of necessary conditions to follow by the atomic orbitals to overlap. If these conditions are not satisfied, overlap of atomic orbital is not possible, These main conditions for formation of molecular orbitals are:
Approximately the same energy: Each atomic orbital is associated with some energy, if two overlapping atomic orbitals have different energies like one is from 1s and other is from 2s atomic orbitals, there is huge energy difference. In this case overlap si not possible. They need to have same energy, like 1s orbital of one atom overlaps with 1s orbital of other atom as they have same energy.
Matching Symmetry: Symmetry as discussed in previous video also known as gerade or ungerade is also important as the sign of overlapping atomic orbital is very important in formation of bonding or anti bonding orbitals. If two atomic orbitals have same sign they will form bonding orbital and if they have different signs of wave function of atomic orbital, they will form anti bonding molecular orbitals.
Positive overlap to form bonding orbital: As discussed in previous point that two positive signed wave function of atomic orbitals overlap to give bonding molecular orbital. It is necessary to have bonding conditions, as this stabilises the resulting molecule by decreasing the overall energy while anti bonding condition increases the energy and destabilises the resulting molecule, so we need bonding situation and not antibonding situation.
Molecular orbital digram is a plot of atomic orbitals and molecular orbitals with respect to energy, Energy is plotted vertical. Please note that the orbital higher in energy are less stable while lower in energy are more stable.

If we see the atomic orbitals indicated in red colour, we can say that the increasing order of energy is from 1s to 2s to 2p and so on, similarly the decreasing order of stability if from 1s to 2s to 2p and so on. So as energy increases stability decreases.

When two 1s orbitals overlap, as the s orbitals are spherical axial overlap takes place and sigma bond forms. In this case two molecular orbitals one is bonding and one anti bonding molecular orbitals are formed, it can be seen from the diagram that the bonding orbitals are at lower level than the atomic orbital, you can see the blue line is at lower level than the red line. So energy of sigma 1s orbital decreases increasing the stability of this molecular orbital while incase of antibonding molecular orbital every increases making this molecular orbital unstable.

Similar situation is seen in overlap of 2s atomic orbitals, they form sigma 2s bonding molecular orbital and sigma star 2s anti bonding molecular orbital.

Incase of 2p atomic orbital three lobes of atomic orbitals are in three different directions, we consider z direction as the overlap direction so 2pz overlap is along the axis and thus it forms sigma bond while other two 2px and 2py are lateral to the axis of overlap so they form pi bonds. The energy of sigma 2pz is at lowest along these molecular orbital while the energy of anti bonding sigma star 2pz is highest. The energy of pi orbitals are in between these two molecular orbitals. The energy of pi 2px and pi 2py is same and can be represented on the same line.
The distribution of electrons in the molecular orbitals is on the basis of Aufbau principle. Aufbau principle states that orbitals of lesser energy levels will be occupied by electrons first.
𝛔(1s) 𝛔*(1s) 𝛔(2s) 𝛔*(2s) 𝛔(2pz) 𝝅(2px) = 𝝅(2py) 𝝅*(2px) = 𝝅*(2py) 𝛔*(2pz)
Electron density: Bonding and antibonding molecular orbitals show different patterns of electron distribution. In general, it may be stated that:
(a) Bonding orbitals are responsible for an increase in electron density between the nuclei.
(b) Antibonding orbitals reduce electron density between the nuclei and have nodes.
(c) The inner shells are so highly attracted by the nucleus that they suffer contraction and become almost spherical in shape instead of oval. Their overlap is very insignificant and they are, therefore, ignored in drawing up the electron configuration of the molecules.
Bond Order: is the number of covalent bonds formed in a molecule. It is given by one half of the difference between the number of electrons in bonding orbitals and those in antibonding orbitals.
\text{Bond order}=\frac { \left( N_{ bonding }-N_{ antibonding } \right) }{ 2 }
If Nbonding Nantibonding the molecule is more stable.

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