# Study of Barrier Heights and Magnetic Property Using Locally Scaled and Perdew-Zunger Self-Interaction Methods

#### Abstract

Kohn-Sham density functional theory is a widely used method to estimate the ground state total energies and densities of interacting correlated electronic structures of atoms, molecules, clusters, solids, and liquids. In theory, exact solutions for these properties can be obtained by solving self-consistent one-electron Schrodinger equations based on density functionals for the energy. The practical application of KS DFT require approximation to the exchange-correlation energy functional. Many density functional approximations (DFAs) have been developed with various degree of sophistication and complexity by the satisfaction of exact constraints. Depending on the complexity, these functionals include electron density, density gradients, density Laplacian, kinetic energy densities, Hartree-Fock exchange etc. Some examples of widely used non-empirical functionals are local density approximation (LDA), Perdew-Burke-Ernzerhof (PBE) generalized-gradient approximation (GGA), and strongly constrained and appropriately normalized (SCAN) meta-GGA. However, the remarkable success of the approximate density functional theory comes at a cost. There is an incomplete cancellation of the hartree and approximate exchange energies for one-electron densities, giving rise to a spurious interaction of an electron with itself. This is called the self-interaction error (SIE). Perdew-Zunger self-interaction correction (PZ SIC) makes an approximate density functional SIE free for all one-electron density. These DFAs can fail dramatically for cases such as systems with a stretched bond, transition state, where SIE is pronounced. Thus LDA, PBE and SCAN predict too low barrier height for a chemical reaction. We tested the Perdew and Zunger self-interaction correction (PZSIC) for the barrier heights of the representative test set BH76. The present work uses Fermi-Löwdin orbitals (FLOS) which are Fermi orbitals orthogonalized via Löwdin scheme. FLOs are localized orbitals through Fermi orbital descriptors (FODs) which are special positions to capture the electronic density of a system. The PZSIC implementation using FLOs, called FLOSIC, results in size-extensive implementation of the PZSIC. The PZSIC calculations provide more accurate results for stretched bond and anionic states but worsen properties where DFA performs well, this is known as the PZSIC paradox. The present thesis deals with development and assessments of methods to overcome the paradoxical behavior of PZSIC. We compare PZSIC against the new local scaling SIC (LSIC) with two different approaches. The first approach uses ratio of kinetic energy densities referred to as LSIC(z) hereafter. It showed impressive results by keeping the correct behavior PZSIC and improving it where PZSIC fails. LSIC(w), the second method that uses orbital and total densities as scaling factor. We compare the methods against orbital scaling SIC (OSIC). The comparison is done with an extensive test of reaction barrier heights of molecules and magnetic properties namely exchange coupling. Overall, the thesis presents application of new methods for self-interaction free density functional calculations for the study of barrier heights and magnetic exchange coupling.

#### Subject Area

Computational physics|Physics

#### Recommended Citation

Mishra, Prakash, "Study of Barrier Heights and Magnetic Property Using Locally Scaled and Perdew-Zunger Self-Interaction Methods" (2021). *ETD Collection for University of Texas, El Paso*. AAI28869600.

https://scholarworks.utep.edu/dissertations/AAI28869600