New localized-orbital method for calculating the electronic structure of molecules and solids: Covalent semiconductors

A new minimal-basis method is developed for studying the electronic structure of molecules and solids. The method is based on optimization of the cancellation effects resulting from orthogonality conditions imposed on the localized orbitals. It is shown that, through the sequential construction of phase-dependent chemical orbitals, hybridization effects arising from interactions with higher-energy orbitals can be isolated and treated by perturbation theory. The present approach thus retains the attractive features of using a minimal basis set in the variational calculations and yet produces quantitatively accurate electronic structures. The method is especially suited for studying complex systems which are intractable using traditional tight-binding or other methods. Specific application is made to bulk covalent semiconductors (Si, Ge, and Se) to demonstrate the efficiency and accuracy of the method. For the semiconductors studied, the new method yields accurate results for both the valence- and the conduction-band states and reveals fundamental trends in their $p-d$ hybridization. Moreover, since the perturbative wave functions are in very good agreement with the exact wave functions, the calculations can be carried out self-consistently.