Advances in One-Electron Self-Interaction-Correction Methods for Accurate and Efficient Self-Interaction-Free Density Functional Calculations
Density functional theory (DFT) is a widely used computational method for studying electronic structures of atoms, molecules, and solids. It provides an exact theory for obtaining ground state energy from the ground state density. However, since the exact exchange-correlation functional remains unknown, approximate exchange-correlation functionals called approximate density approximations (DFAs) are used. The foundation of many DFAs is the local spin density approximation (LSDA). It serves as the starting point for constructing various DFAs. However, DFAs are prone to self-interaction errors (SIE) due to the improper cancellation of the approximate exchange energy and the Coulomb energy. This issue impacts the accuracy of the results obtained with DFAs. One way to address this issue is using one-electron self-interaction correction (SIC) methods. A well-known example of the one-electron SIC methods is the Perdew and Zunger SIC (PZSIC). The one-electron SIC schemes require localized orbitals to avoid the size-extensivity problem, and one choice of such orbitals is the Fermi Löwdin orbitals (FLOs). The Fermi Löwdin orbital SIC (FLOSIC) code is an implementation of various SIC schemes using FLOs, allowing researchers to utilize SIC methods. This dissertation provides an overview of DFT and SIC methods, development of new SIC schemes, and evaluates the performance of these methods using standard benchmarks datasets and different applications. This thesis introduces simplification of FLOSIC scheme to expedite SIC calculations by performing SIC calculations on a select set of orbitals. This approach, which we called vSOSIC, provides comparable performance to PZSIC that applies SIC to all orbitals for a wide range of properties. We conducted a study on the effect of SIE in the spin-state gaps of four octahedral Fe(II) complexes. The removal of self-interaction was found to be crucial for obtaining accurate spin-state gaps as regular DFA calculations perform poorly in this context. The locally scaled SIC method (LSIC) demonstrated good performance, exhibiting a mean absolute error comparable to CCSD(T) when compared to diffusion Monte-Carlo (DMC) data. Accurately describing spin-state gaps through efficient computations is valuable for modelling novel devices in technology, such as molecular switches. Furthermore, the initial LSIC calculations were perturbatively on top of optimal PZSIC calculations. Subsequently, the full self-consistency of the LSIC method was developed, and it was demonstrated that LSIC’s good performance is maintained in the full self-consistency method. This confirms that the LSIC method exhibits comparable accuracy to higher-level density functionals.
Computational chemistry|Computational physics|Physical chemistry
Gonzalez, Selim Sabag Romero, "Advances in One-Electron Self-Interaction-Correction Methods for Accurate and Efficient Self-Interaction-Free Density Functional Calculations" (2023). ETD Collection for University of Texas, El Paso. AAI30635051.