Transferability of total energy expressions in the linear-combination-of-atomic-orbitals method

Abstract

In the linear-combination-of-atomic-orbitals method(LCAO) using localized atomic orbitals as basis, the size of the Hamiltonian matrix is relatively smaller than that for the plane wave basis. Thus, the LCAO method is applicable for complex solid state systems like supercells, defects, etc., In doing this, a good transferability of tight-binding parameters is important to describe precisely the physical properties of the complex systems. In this thesis, the LCAO approach based on model pseudopotentials as well as ab initio pseudopotentials is used to investigate the electronic structure for the diamond, simple cubic, body-centered cubic, and facecentered cubic structure in Si. The atomic orbitals and ionic potentials are expanded in Gaussian to do analytic calculations. The repulsive double-counting part in total energy is determined by substrating our calculated band energies from the first-principles pseudopotential calculations for the diamond structure of Si. To test the transerability of the repulsive energy to other structures and systems, several forms are examined in fitting. The structural energies for the sc, diamond, fcc, and bcc structures, the transverse optic phonon frequencies at the $\Gamma$-point in the Brillouine zone, the stable atomic geometries of Si2 and Si$_3$ clusters, and the pressure coefficient of the band gaps are studied. From the results, the best transferable form for the repulsive energy is found to be