Distorted Space and Multipoles in Electronic Structure Calculations

Sammanfattning: This thesis concerns methods for electronic structure calculations and some applications of the methods.The augmented planewave (APW) basis set and it’s relatives LAPW (linearised APW) and APW+lo (local orbitals) have been widely used for electronic structure calculations. Here a modification of the APW basis set based on a transformation of the basis functions from a curvilinear coordinate system. Applications to a few test systems show that the modified basis set may speed up electronic structure calculations of sparse systems.The local density approximation (LDA) is used in density functional theory. Although it is the simplest possible approximation possible for the unknown exchange-correlation energy functional, it has proven to give quite accurate results for a wide range of systems. LDA fails in systems where the non-local effects are important. By including non-local effects by adding an orbital dependent term to the energy functional, through for example the LDA+U method, the calculated properties of many materials are closer to experimental observations. In the thesis the most general formulation of the LDA+U method is presented and a new way of interpreting the results of a calculations by formulating the orbital dependent part of the energy functional in terms of multipole momentum tensors. Applications to some early actinide systems leads to a reformulations of Hund’s rules for polarisations associated with the spin and orbital magnetic moment and a suggestion for similar rules, Katt’s rules, valid in the strong spin orbit coupling regime.