Molecular Orbital Theory (MOT)

To describe the covalent bond formation and nature of electron sharing, two theories have been proposed : Valence Bond Theory (VBT) and Molecular Orbital Theory (MOT). In Valence Bond Theory, only the half filled orbitals of valence shell take part in bond formation and the remaining orbitals retain their identity. But MOT suggests the combination of all atomic orbitals having comparable energy and proper symmetry. MOT was developed by F.Hund and R.S. Mulliken in 1932. Main postulates of this theory are :

1. Atomic orbitals of comparable energy and proper symmetry combine together to form molecular orbitals.

2. The movement of electrons in a molecular orbital is influenced by all the nuclei of combining atoms. (Molecular orbital is polycentric in nature).

3. The number of molecular orbitals formed is equal to the number of combining atomic orbitals. When two atomic orbitals (AO's) combine together two molecular orbitals (MO's) are formed. One molecular orbital possess higher energy than correspoing atomic orbitals and is called antibonding MO (ABMO) and the other has lower energy and is called bonding MO(BMO).

4. In molecules electrons are present in molecular orbitals. The electron filling is in accordance with Pauli's exclusion principle, Aufbau principle and Hund's rule.

 The formation of molecular orbitals can be understood in terms of constructive or destructive interference of electron waves of combining atoms. In the fo rmation of BMO, the two electron waves of the bonding atoms reinforce each other while in the formation of ABMO, the electron waves cancel each other. The result is that in a bonding molecular orbital most of the electron density is located between the nuclei of bonded atoms and hence the repulsion between the nuclei is very small. The electron density between the nuclei hold them together and stabilizesthe system. But in ABMO there is very low electron density between the nuclei and hence the repulsion between them is high, which destabilizes the system.

Formation of Molecular Orbitals [Linear Combination of Atomic Orbitals -  LCAO Method]

Valence bond theory and Molecular orbital theory are the quantum mechanical theories of
chemical bonding. LCAO method (L inear Combination of Atomic Orbitals) is an effective approximation method to solve quantum mechanica1 problems (Schrodinger wave equation).

Let us consider the application of the LCAO method to H₂ molecule is formed from two H atoms A and B. Their atomic orbitals are designated as 'Ψ_A' and 'Ψ_B' respectively. Mathematically the fonnation of molecular orbitals is described by the linear combinations of 'Ψ_A'  and 'Ψ_B' as:

Ψ_MO  =    Ψ_A ± Ψ_B

Here Ψ_A + Ψ_B represents the bonding molecular orbitals while Ψ_A - Ψ_B represents the antibonding molecular orbital. ie, BM0 is formed by the addition of atomic orbitals while ABM0 results from subtraction of atomic orbitals.

The molecular orbitals formed by the combination of 1s orbitals are called sigma ( σ ) orbitals. σ orbitals are symmetric about the molecular axis. The BMO is designated as σ and ABMO is designated as σ* (sigma star). In case of p-orbitals, p_z orbitals combine to form σ molecular orbitals. The molecular orbitals of p_x and p_y are not symmetrical about the bond axis and they are termed as π (pi) MO's.

The bonding and antibonding MOs fonned by 1s, 2s and 2p orbitals are,

BMO   σ1s   σ2s   σP_z   π2P_x   π2P_y
 
ABMO   σ*ls   σ*2s   σ*P_z   π*2P_x  π*2P_y

The energy sequence of these molecular orbitals has been determined from spectroscopic data. The increasing order of energies of various molecular orbitals for O₂ and F₂ is given below.

σls  < σls  < σ2s  < σ*2s  < σ2P_z  < π2P_x = π2P_y < π*2P_x =  π*2P_y  < π*2P_z

But in the order of energies of molecular orbitals of molecules up to N₂, the energies of π2P_x and π2P_y are lower than 2pz. This change is due to the possibility of mixing of MO's of 2s and 2pz atomic orbitals. For these molecules the order is

σls  < σls  < σ2s  < σ*2s  < σ2P_z  < π2P_x = π2P_y < π*2P_x =  π*2P_y  < π*2P_z

Bond Order

Bond order is defined as the half of the difference between the number of electrons present in the bonding and the antibonding molecular orbitals.

ie, bond order = ½ [ N_b - N_a ]

Where N_b is the number of electrons in BMO and N_a is the number of electrons in ABMO.

Bond order is directly related to stability of molecule. IT the value of bond order is positive, the molecule is stable and if the value of bond order is negative or zero, the molecule is unstable, ie, it is not fanned [When the numberofbonding electrons is equal
to number of antibonding electrons no bond is formed].

The bond order is directly related to bond strength. This means that the higher the bond order, the larger is the bond dissociation energy of the molecule, ie the stronger is the bond.

The bond order of a molecule is inversely proportional to the bond length. i.e the higher the bond order, the smaller is the bond length.

The electronic configuration of a molecule helps to predict its magnetic character. If all the electrons in a molecule are paired, the substance is diamagnetic. If there are unpaired electrons in the molecular orbitals the molecule is para magnetic.

Bonding in certain homodiatomic molecules are discussed below:

i) Hydrogen molecule (H₂)

H₂ is formed by the combination of two hydrogen atoms. Each hydrogen atom has one electron in 1s orbital. The two electrons in H₂ molecule are present in cr 1 s molecular orbital. So electronic configuration of H₂ molecule is σ 1s².

In H₂ molecule, H atoms are bonded together by a single bond. Due to the absence of unpaired electron H₂ is diamagnetic in nature.

ii) Hydrogen molecule ion (H₂ ⁺)

This may be considered as the combination of a H atom and a H⁺ ion. H₂ ⁺ has only one electron, which occupies the σ1s orbital.

Its electronic configuration is σls¹

:. Bond order  =  ½ [N_b - N_a]
                            ½ [2-1] = ½

:.  H₂ ⁺ is stable and exists; it is paramagnetic in nature.

iii. Helium molecule (He2)

The electronic configuration of helium atom is 1s². Therefore in He₂ molecule, there would be 4 electrons. The electronic configuration of  He₂ is σls² , σ*ls²

Bond order of He₂ is½ [2 - 2] = 0
He₂ molecule is unstable and does not exist.