Implementation and reassessment of the Perdew-Zunger self-interaction correction

Density functional theory (DFT) using semi-local functional approximations can describe many chemical properties to high accuracy, but in some cases large and even qualitative errors emerge. Some of these errors are ascribed to an unphysical interaction of each electron with itself, which is present as a result of the approximations made in the exchange-correlation functional. The Perdew-Zunger self-interaction correction (PZ-SIC) attempts to remove this spurious interaction from approximate functionals and does so for systems that include only a single electron. For many-electron systems, PZ-SIC had previously been found to result in an overcorrection in many cases. But, most previous applications of PZ-SIC restricted the orbitals to be real functions and did not take into account that orbitals are in general complex. The implications of the restriction to real orbitals were explored in detail in this thesis project and it was found that the effect on the total energy and on the structure of molecules can be large. Generally available electronic structure software could not be used for the calculations as this orbitaldensity dependent functional form is significantly different from common density functional approximations and a special optimization algorithm is needed. The electronic structure software Quantice was developed as part of this thesis project. It includes an efficient new algorithm for minimizing the energy of orbital-density dependent functionals, in particular PZ-SIC, as well as the option of using complex orbitals. The present reassessment of PZ-SIC including complex orbitals has extended and in some cases revised the results from previous studies. The total energy of atoms is found to be improved by PZ-SIC when applied to a suitable density gradient dependent functional. The overcorrection found in molecular properties is in many cases less severe when complex orbitals are used. The molecular structure of the CH3 radical, which had previously been found to become incorrect by the application of PZ-SIC, is shown here to be predicted correctly