Molecular orbital theory

MOT -Valence Bond Theory fails to answer certain questions like Why He₂ molecule does not exist and why O₂ is paramagnetic? Therefore in 1932 F. Hund and RS. Mullikan came up with theory known as Molecular Orbital Theory.

Some salient features of this theory are as follows

      ·       When two atomic orbitals overlap, they form two new orbitals called molecular orbitals .One of which is called bonding molecular orbital and other is called antibonding molecular orbital. These are formed by addition and subtraction of wave functions respectively.

      ·       Molecular orbitals are the energy states of a molecule in which the electrons of the molecule are filled.

      ·       Bonding molecular orbital has energy lower than the combining 'atomic orbitals while antibonding orbital has higher energy than the combining atomic orbitals.

      ·       Only those atomic orbitals can overlap to form molecular orbitals which have comparable energies and proper orientation.

     ·       Electrons present in the bonding molecular orbital contribute towards the stability of molecule while electrons present in antibonding molecular orbital contribute to the repulsions between the nuclei of the atoms.

      ·       The bonding molecular orbitals are denoted as σ, π, δetc., while antibonding molecular orbitals are denoted as σ*, π*, δ^* etc.

      ·       Electrons are filled in molecular orbitals according to ufbau principle and Pauli's exclusion principle

Linear Combination of Atomic Orbitals (LCAO)

     ·       According to wave mechanics the atomic orbitals can be expressed by wave function ‘Ψ’ which represent the amplitude of electron wave. Wave function is the result of solution of Schrodinger wave equation

     ·       Since we know that it cannot solved for any system containing more than one electron.

     ·       Molecular orbitals which are one electron function for molecules are difficult to obtain directly from the solution of Schrodinger wave equation

     ·       To overcome this problem an approximate method used is called LCAO

     ·       As per this method the formation of orbitals is because of Linear Combination (addition or subtraction) of atomic orbitals which combine to form molecule.

   Consider two atoms A and B which have atomic orbitals described by the wave functions Ψ_A and Ψ_B. If electron cloud of these two atoms overlap,

    then the wave function for the molecule can be obtained by a linear combination of the atomic orbitals Ψ_A and Ψ_B i.e. by subtraction or addition of wave functions of atomic orbitals

                                          Ψ_MO= Ψ_A + Ψ_B

                            The above equation forms two molecular orbitals

                      a). Bonding Molecular Orbitals

                      b). Non -bonding molecular orbitals            

b). Anti-Bonding Molecular Orbitals

 Bonding Molecular Orbitals

·   When addition of wave function takes place, the type of molecular orbitals formed are called Bonding Molecular orbitals and is represented by

                                         Ψ_MO = Ψ_A + Ψ_B.

·   They have lower energy than atomic orbitals involved.

·    It is similar to constructive interference occurring in phase because of which electron probability density increases resulting in formation of bonding orbital. Molecular orbital formed by addition of overlapping of two s orbitals

Anti-Bonding Molecular Orbitals

·     When molecular orbital is formed by subtraction of wave function, the type of molecular orbitals formed are called Antibonding Molecular Orbitals and is represented by

     Ψ_MO = Ψ_A - Ψ_B.

They have higher energy than atomic orbitals.

·       It is similar to destructive interference occurring out of phase resulting in formation of antibonding orbitals.

      ·       Molecular Orbital formed by subtraction of overlapping of two s-orbitals are shown in above figure. It is represented by σ* or π * called antibonding molecular orbital Antibonding.

      Distinction between Atomic and Molecular Orbitals-

s.no.	Atomic orbital	Molecular orbital
1	Atomic orbital is monocentric, i.e., electron cloud extends around the nucleus of a single atom	Molecular orbital is polycentric i.e. the electron Cloud extends around all the nuclei of bonded atoms in the molecule.
2	it is less stable.	It is more stable.
3	It has simple shape.	It has complex shape.
4	Atomic orbitals are designated as s, p, d, etc.	Molecular orbitals are designated as  (σ, π, δ   ,σ*, π*,δ*etc.

Energy Level Diagram of molecular orbital : 

◼ For diatomic homonuclear molecules such as Li2, Be2, B2, C2, N2 is (where the energy difference between 2 s and 2 p-orbitals is large and hence they cannot interact)

σ1s < σ∗1s < σ2s < σ∗2s < π2px=π2py<σ2pz <π∗2px= π∗2py <σ∗2pz

◼For homogeneous diatomic molecules such as O2, F2, Ne2, (where the difference in

energies between 2s and 2p-orbitals is small and hence they can interact)the energy

diagram is

σ1s < σ∗1s < σ2s < σ∗2s < σ2pz < π2px= π2py<π∗2px= π∗2py <σ∗2pz