In 1931 E.Huckel investigated the conjugated linear polyenes like ethylene, 1-3-butadiene, and cyclic polyenes such as benzene and naphthalene. After that, his treatment was extended by C.Coulson, H.C.longuet-Higgins, and R. Hoffmann.
The predominantly planar molecule is a conjugated unsaturated hydrocarbon with alternate single and double bonds. In an n-carbon system, each carbon atom is Sp2 hybridized and has a 2pz orbital entered. Each pz orbital is perpendicular to the molecular plane and contains one Π-electron.
According to the LCAO-MO approximation, the molecular orbital was written as,
Here, ∅j = 2pz orbital centered on carbon atom j
∅s = Basis set
Overlap of n2pz atomic orbitals is formed nΠ molecular orbitals. H2, the basis function is the 1s atomic orbitals, while in HMO theory, the basis function is 2pz atomic orbitals.
Huckel gives the following assumptions for three kinds of integrals: coulomb integral, exchange (resonance) integral, and overlap integral. Are these secular equations,
- All overlap integrals are zero, which means Sij=0
- The energy of an electron in the 2pz orbital on the ith carbon atom symbol is α called the coulomb integral.
- Exchange integral Hij =Hji=0 the ith and jth orbitals are on adjacent carbon atoms is denoted as .
The Huckel secular equation is written as,
A dimensionless parameter x as x=(α -E)/β , is equation (3) registered as,
An n has real roots for expansions of this n×n determinant yields a polynomial equation; therefore, the conjugated polymer has n energy levels n Mos.
The energy of kth MO is,
Xk = kth root of the polynomial
α is the coulomb integral and β is the resonance integral, both negative.
xk = energy levels that value is positive are more neglected and more stable than the energy of an electron in a carbon 2pz orbital. This energy level is called BMO.
The same for ABMO is a negative value of xk.
Consider the following article’s application of the HMO theory of ethylene, 1,3-butadiene, and Benzene.
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