The Pariser-Parr-Pople Crystal-Orbital Method

The Pariser-Parr-Pople Crystal-Orbital Method 

We saw in Chapter 1 that in the ab initio case the band structure of a linear chain can be obtained from the matrix equation (1.47) 

Here again denotes the 5th AO in the th cell, m is the number of orbitals, M the number of nuclei in the unit cell, Z the charge (in atomic units) of the ath nucleus, Fi the position vector of the electron and that 

The PPP CO method is derived by taking into account explicitly, as in the case of molecules, only the n electrons of the system. Putting S(A ) = 1, equation (3.1) reduces to the matrix eigenvalue equation 

Following the PPP method in the case of molecules, we introduce systematically the neglect of differential overlap and, taking into account only first-neighbor interactions, the elements of matrices F( ) in expression (3.2) take the forms  

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