Impurities in a homogeneous electron gas

Graduation date: 2005Immersion energies for an impurity in a homogeneous electron gas with a uniform\ud positive background charge density have been calculated numerically using\ud density functional theory. The numerical aspects of this problem are very demanding\ud and have not been properly discussed in previous work. The numerical\ud problems are related to approximations of infinity and continuity, and they have\ud been corrected using physics based on the Friedel sum rule and Friedel oscillations.\ud The numerical precision is tested extensively. Immersion energies are obtained for\ud non-spin-polarized systems, and are compared with published data. Numerical\ud results, such as phase shifts, density of states, dielectric constants, and compressibilities, are obtained and compared with analytical theories. Immersion energies\ud for excited systems are obtained by varying the number of electrons in the bound\ud states of an impurity. The model is extended to spin-polarized systems and is\ud tested in detail for a carbon impurity. The spin-coupling with an external magnetic\ud field is considered mainly for a hydrogen impurity. These new results show\ud very interesting behavior at low densities