Semiempirical LCAO Methods in Cyclic-cluster Model

2 Semiempirical LCAO Methods in Cyclic-cluster Model 

In cyclic-cluster calculations we return to the molecular level without the loss of the symmetry, replacing a whole crystal by one supercell (multiple of the primitive unit cell), applying to it PBC and embedding a cyclic cluster in the Madelung field of the surrounding crystal. Instead of the system of coupled LCAO equations (4.57) for different wavevectors in the BZ we have one equation to be solved in each iteration as in the case of molecules. 

In EHT for crystals the one-electron Hamiltonian and overlap integrals matrix elements (6.4) and (6.5) depend on wavevector k and are the sums over a direct lattice. The order M of the corresponding matrices H and S is equal to the number of AOs in the primitive unit ceb. 

In the CCM the superceb is introduced so that the order of the matrices in the secular equation (6.4) is equal to L x M, where L is defined in (6.51) and means the number of primitive cebs in a superceb. The calculation is made only for fc = 0 so that instead of (6.4) we obtain the molecular-type seqular equation 

The cycUc cluster can be chosen in the form of the Wigner-Seitz unit cell (shown by the dotted Une in Fig. 6.1 with the center at boron atom 1). A connection of the interaction range to this ceUs atoms was discussed in [301]. 

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