Time domain density functional theory

In the first part of this work, a brief overview over several strategies to combine such time domain transport simulations with first principles electronic structure theory is given. For the latter, we restrict ourselves to a discussion of time dependent density functional theory (TDDFT) only. This method is by far the most employed many body approach in this field and provides an excellent ratio of accuracy over computational cost, allowing for the treatment of realistic molecular devices. This digest builds on the earlier excellent survey by Koentopp and co-workers on a similar topic [13]. Admittedly and inevitably, the choice of the covered material is biased by the authors interests and background. 

As mentioned above, the results discussed below are obtained using Ab initio methods. Other methods used to study QDs are effective mass theory (EMT) and the pseudopotential techniques. EMT uses a particle-in-a-box model where the electron and hole masses are given by their bulk values. EMT is an intuitive description that explains general trends seen in experiments. The atomistic pseudopotential technique can be applied to large systems, but requires careful parameterization for each material. Ab initio approaches use minimal parameterization and are applicable to most materials. This makes them particularly useful for studying dopants, defects, ligands, core/shell systems and QD synthesis. The Hartree-Fock (HE) method and density functional theory (DFT) have been around for many decades, while time domain (TD) DFT and non-adiabatic molecular dynamics (NAMD) are more recent areas of research. Currently, ab initio TDDFT/NAMD is the only... 

This chapter is organized as follows. In section 1.1, we introduce our notation and present the details of the molecular and mesoscale simulations the expanded ensemble-density of states Monte Carlo method,and the evolution equation for the tensor order parameter [5]. The results of both approaches are presented and compared in section 1.2 for the cases of one or two nanoscopic colloids immersed in a confined liquid crystal. Here the emphasis is on the calculation of the effective interaction (i.e. potential of mean force) for the nanoparticles, and also in assessing the agreement between the defect structures found by the two approaches. In section 1.3 we apply the mesoscopic theory to a model LC-based sensor and analyze the domain coarsening process by monitoring the equal-time correlation function for the tensor order parameter, as a function of the concentration of adsorbed nanocolloids. We present our conclusions in Section 1.4. 

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