Semiempirical LCAO Methods for Molecules and Periodic Systems

1 Nonself-consistent Extended Hiickel—Tight-binding Method 

In this chapter we discuss the extension of LCAO semiempirical methods of molecular quantum chemistry to periodic systems and provide a comparison between semiempirical Hamiltonians for molecules and crystals. 

The approximate LCAO methods of quantum chemistry can be divided on empirical (semiquantitative) and semiempirical grounds. 

The empirical (semiquantitative) methods are based on a one-electron effective Hamiltonian and may be considered as partly intuitive extended Hiickel theory (EHT) for molecules [204] and its counterpart for periodic systems - the tight-binding (TB) approximation. As, in these methods, the effective Hamiltonian is postulated there is no necessity to make iterative (self-consistent) calculations. Some modifications of the EHT method introduce the self-consistent charge-configuration calculations of the effective Hamiltonian and are known as the method of Mulliken-Rudenberg [209]. 

The semiempirical methods are based on the simplification of the HF LCAO Hamiltonian and require the iterative (self-consistent) density matrix calculations complete and intermediate neglect of differential overlap (CNDO and INDO - approximations), neglect of diatomic differential overlap (NDDO) and others, using the neglect of differential overlap (NDO) approximation. 

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Semiempirical LCAO Methods for Molecules and Periodic Systems... 

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