Development And Applications Of Time-Dependent Density Functional Theory For Open Systems

This thesis is devoted to the research on the real-time electronic dynamics for open systems. With the development of the study on microscopic systems, the real-time electronic dynamics becomes an important research topic. Time-dependent density functional theory for open systems (TDDFT-OS) method has been employed to characterize the real-time electronic dynamics due to its ex-cellent balance between the accuracy and efficiency. In this method, the whole system is divided into two parts:the system and its environment. In general, the size of the system part is quite limited compared to its surrounding environment. In the TDDFT-OS method, the influence of the environment to the system is con-sidered by the environment spectral function. In this way, the real-time evolution equation for the open system is obtained. This thesis is organized as follows:Chapter1is the introduction of the background and development of TDDFT-OS method. The TDDFT method has been widely used in simulating the elec-tronic dynamics of microscopic systems. Then, Zheng and Chen et al. develop the time-dependent holographic electron density theorem which is the theoretic foundation of TDDFT for open system. The main difficulty for TDDFT-OS is the exact treatment of the dissipative term. In this chapter, the non-equilibrium Green’s function treatment of the dissipative term is introduced. Combined with the adiabatic wide band limit, the self-closed evolution equations for open sys-tem can be deduced. However, this method neglects the energy dependence of environment spectral function and simplifies the memory effect of system Green’s function, which will lead to certain simulation errors. To solve this problem, the TDDFT-HEOM method is proposed.In Chapter2, the theoretic derivation of TDDFT-HEOM method is present-ed. The development of HEOM method is firstly introduced. It is emphasized that HEOM method has the natural advantage to be combined with TDDFT be-cause it terminates automatically at the second level for noninteracting electronic systems. In order to simplify the numerical calculation, either the wide-band limit or the spectral decomposition method can be adopted to convert,-the integration over, energy to summation. Due to the drawback of the wide-band limit that it neglects the energy dependence of the spectral function, the Lorentzian spectral decomposition method is actually employed in this thesis.In Chapter3, the TDDFT-HEOM method is applied to the electronic dy-namics of two types of model systems, the quasi-1D atomic chain and the2D graphene surface. For the quasi-1D case, the solution of the one-dimensional envi-ronment spectrum function is firstly derived. Then the current response to bias is obtained. Note that TDDFT-OS method is usually restricted to one-dimensional systems. In the remaining part of this chapter, the application of TDDFT-HEOM method is extended to2D graphene surface electronic dynamics, by virtue of the reciprocal-space sampling method for the2D environment spectral function.For practical application of TDDFT, a boundary condition should be imposed explicitly or implicitly. Besides the open boundary condition adopted in TDDFT-HEOM for open system, isolated boundary condition and periodic boundary con-dition are also used in TDDFT simulations for isolated and periodic systems. In Chapter4, the effects from these boundary conditions on the system electron-ic dynamics are investigated. The importance of the open boundary condition is highlighted for the investigation on the local perturbation system This at the same time verifies the accuracy of TDDFT-HEOM method for open systems.