Huckel Molecular Orbital Theory

Manisha Kanwar semester 1

1. Samrat Prithviraj Chauhan Government College Ajmer 2020-2021 Huckel Molecular Orbital Theory Submitted By Manisha Kanwar M.Sc. Chemistry Semester 1st Department of chemistry

2. Table of Content Introduction Postulates Ethylene Structure Electronic Density Secular Determinent Bond Order Energy of HMO Coefficient of HMO Reference

3. Introduction The huckel molecular orbital theory proposed by Erich huckel in 1936 is a very simple linear combination of atomic orbitals, method for the determination of energies of molecular orbitals of pi-electrons in pi-delocalised molecules. Such as ethylene, benzene, butadiene and pyridine. It is the theoretical basis for huckel’s rule foe the aromaticity of 4n+2 pi electrons cyclic, planar system. It was later extended to conjugated molecules. Such as pyrrole, furan that contain atoms other than carbon, known in this context as heteroatoms.

4. Postulates Huckel made the following postulates about the three kinds of integrals viz coulomb integral, exchange(resonance) integral and overlap integral, to simplify the secular equation. All overlap integrals are zero i.e. s ij =0. Coulomb integral hij, refers to the energy of an electron in the 2p z orbital on the ith carbon atom. Since we are dealing with carbon atoms only all such integrals are equal and are denoted by the symbol α . The exchange(resonance) integrals represent the energy of integration of two atomic orbitals for atom i and j not being direct bonded, H ij =H ji =0 unless the sth and jth orbitals are on adjacent carbon atom in which case they are designated as β .

5. Ethylene Structure The HMO may be written as form ψ=Σ Ci Φ j Ψ= C 1 Φ 1 = C 2 Φ 2 Φ 1 and Φ 2 are two atomic orbitals associated with c and c atoms Secular determinants are α -E β x 1 β α -E if α -E/ β= x then 1 x =0 Explanation of x determinant given an equation x²-1=0 x= ±1 if has two rates x=+1,-1

6. Energies of HMO are [E= α +xp β ] E 1 = α + β (corresponding to x= -1) energy of Bonding Molecular Orbital E 2 = α - β (corresponding to x=+1) energy of Antibonding Molecular Orbital Total energy E п =2( α + β )=2 α +2 β Since the energy of two electron in isolated carbon 2p orbitals is 2 α п Bond energy =(2 α +2 β )-2 α =2 β

7. Coefficients of HMO These are obtained after substituting the values of x in any one of the two secular equation are C 1 X+C 2 =0 C 1 +C 2 X=0 For x=-1 for bonding level C 1= C 2 x=+1 for antibonding level Since every molecular orbital is normalised the normalisation of the molecular orbital Ψ= C 1 Φ 1 +C 2 Φ 2 give rise to an equation C 1 ²+C 2 ²=1 where overlap integral is neglected C 1 ²+C 1 ²=1 2C 1 ²=1 C 1 =1/  2 and C 2 =1/  2 hence mo corresponds to the energy level Ψ 1 =1/  2  ( Φ 1 + Φ 2 ) Corresponds to the energy level E 1 = α + β Ψ 2 =1/  2 ( Φ 1 - Φ 2 ) Corresponds to the energy level E 2 = α - β

8. Electron density Since two п electron occupy the Molecular Orbital Ψ 1 in ground state to the п electron density is calculated for Ψ 1 Molecular Orbital. q i= Σ n j C² ij [total electron density on j th ] [C atom in occupied MO’s] q 1 =nxC² 11= 2x(1/  2) ²=1 (total electron density on first C-atom in Ψ 1 ) q 2 =nxC² 21= 2x(1/  2) ²=1 q=q 1 +q 2 =1+1=2(which is equal to the total number of п electron present in ethylene)

9. Bond order It is also calculated only for Bonding Molecular Orbitals that is Ψ 1. P k1 = Σ n i Ckj.Cij Partial BO between C1-C2 in Ψ 1 . Total BO is P 12 =2x1/2=1 which reveals that there is only 1 п-bond present between C 1 and C 2. Free valence It shows the reactivity of C-atom free valence at C-atom 1 and at C-atom 2 fi=N max -N j N j =total bond order between C 1 and C 2 f 1 =1.732-1=0.732 f 2 =1.732-1=0.732 [Both C-atom are same reactive]

10. Reference Quantum Chemistry by R.K.Prasad Advanced physical chemistry by Dr.J.N.Gurtu A.Gurtu

11. For Your Time and Attention Thank You