The Simple Hiickel Method - Theory

This can be abbreviated to the seductively simple-looking form 

Equation 4.36 says that an operator (H) acting on a function (i]/) equals a constant (E) times the function ( H hat of psi equals E psi ). Such an equation 

The eigenvalue formulation of the Schrodinger equation is the starting point for our derivation of the Hiickel method. We will apply Eq. 4.36 to molecules, so in this context H and i// are the molecular Hamiltonian and wavefunction, respectively. 

The integration variable dv indicates integration with respect to spatial coordinates (x, v. r in a Cartesian coordinate system), and integration over all of space is implied, since that is the domain of an electron in a molecule, and thus the domain of the variables of the function ij/. One might wonder why not simply use E = Ihj/hjr. the problems with this function are that it goes to infinity as ij/ approaches zero, and it is not well-behaved with regard to finding a minimum by differentiation. 

Next we approximate the molecular wavefunction i/t as a linear combination of atomic orbitals (LCAO). The molecular orbital (MO) concept as a tool in interpreting electronic spectra was formalized by Mulliken23 starting in 1932 and building on earlier (1926) work by Hund24 [31] (recall that Mulliken coined the word 

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