First principles methods for electronic structure calculations of solids

Sammanfattning: A straightforward gradient expansion of the exchange energy of a perturbed electron gas is performed. Studied perturbations range from very weak to those that produce, e.g., a silicon-like band structure with a band gap. The expansions involve density gradients up to fourth degree and we include all terms originating in linear- and second-order response theory. The expansion reproduces exactly calculated exchange energies with an accuracy of the order of a few mRy per electron for metallic systems. For systems with a band-gap the accuracy is reduced by an order of magnitude. We have developed a T-matrix formalism for performing ab initio calculations on real systems with strong short-range correlations. The method is applied to Ni and we obtain a satellite structure below the Fermi level as well as a reduced exchange splitting. We also found a new satellite structure above the Fermi level, which can be ascribed to particle-particle scattering. The onsite screened interaction within the random phase approximation is calculated for Ni. It is found that the value of the statically screened interaction in the 3d orbital is 2.2. eV which is significantly smaller than the values obtained from the constrained LDA method (3.7-5.4 eV). We analyze the possible origins of the difference and reconcile the discrepancy by taking into account the energy dependence of the screened interaction. A basis-free method for calculating the bandstructures of periodic systems is developed. The many-center problem is divided into one-center problems by employing a projection function. The full solution is then obtained by summing over the one-center solutions, ensuring the correct Bloch symmetry. Due to the division into one-center problems, the method is expected to scale as ~N to N^2 where N is the number of atoms in the unit cell. The feasibility of the method is demonstrated by calculating the free-electron and Cu bandstructures.