Date of Degree
Neepa T. Maitra
dynamics; memory; step; time dependent density functional theory
Time-dependent density functional theory (TDDFT) is a method of choice for calculations of excitation spectra and response properties in materials science and quantum chemistry. The many-body problem is mapped into a set of one-body Schrödinger equations, called the Kohn-Sham (KS) equations. In principle, the one-body potential can be chosen such that the density of the interacting system is exactly reproduced by the KS system. However, one component of the one-body potential has to be approximated and is typically "adiabatic". Though in linear response regime adiabatic approximations give quite good spectra, it is important to explore their performances in non-equilibrium dynamics.
In this thesis, I will present the results of the explorations on non-equilibrium dynamics in TDDFT. For the first study, a decomposition of exact exchange-correlation potential into kinetic and interaction components is derived. We compare the components with that of "adiabatic" counterparts in non-perturbative dynamics and find that the interaction component is less poorly approximated adiabatically than the kinetic component. A salient feature is that step structures generically appear, of relevance in the second study. We prove that the step structures only appear in the non-linear response regime. We find an exact condition which is typically violated by the approximations in use today. Spuriously time-dependent spectra in TDDFT can be explained and we find that the more the condition is violated the worse the dynamics is. In last, we envision that orbital functionals are able to incorporate the memory effects and compensate the deficiencies of the "adiabatic" approximations.
Luo, Kai, "Exploring Non-Equilibrium Dynamics in Time Dependent Density Functional Theory" (2015). CUNY Academic Works.