Studies of Self-interaction Corrections in Density Functional Theory

Abstract: The self-interaction error (SIE) in density functional theory (DFT) appears from the fact that the residual self-interaction in the Coulomb part and that in the exchange part do not cancel each other exactly. This error is responsible for the unphysical orbital energies of DFT and the failure to reproduce the potential energy curves of several physical processes.The present thesis addresses several methods to solve the problem of SIE in DFT. A new algorithm is presented which is based on the Perdew-Zunger (PZ) energy correction and which includes the self-interaction correction (SIC) self-consistently (SC SIC PZ).When applied to the study of hydrogen abstraction reactions, for which conventional DFT can not describe the processes properly, SC PZ SIC DFT produces reasonable potential energy curves along the reaction coordinate and reasonable transition barriers.A semi-empirical SIC method is designed to correct the orbital energies. It is found that a potential coupling term is generally nonzero for all available approximate functionals. This coupling term also contributes to the self-interaction error. In this scheme, the potential coupling term is multiplied by an empirical parameter , introduced to indicate the strength of the potential coupling, and used to correct the PZ SIC DFT. Through a fitting scheme, we find that a unique can be used for C, N, O core orbitals in different molecules. Therefore this method is now used to correct the core orbital energies and relevant properties. This method is both efficient and accurate in predicting core ionization energies.A new approach has been designed to solve the problem of SIE. A functional is constructed based on electron-electron interactions, Coulomb and exchange-correlation parts, which are free of SIE. A post-SCF procedure for this method has been implemented. The orbital energies thus obtained are of higher quality than in conventional DFT. For a molecular system, the orbital energy of the highest occupied molecular orbital (HOMO) is comparable to the experimental first ionization potential energy.