Title: Semiempirical methods for excited states of nanomaterials
Description: Density functional theory (DFT) provides an affordable computational tool to understand electronic structure of various molecules and solids. However, the use of DFT is still challenging to investigate nanomaterials of intermediate size that are too small to assume translational symmetry and too large to be considered as molecules. This thesis focuses on developing cost-effective but accurate computational methods for nanomaterials and using the methods to rationalize and predict experimental behaviors. A notable difference of a nanomaterial from its bulk counterpart is that its properties are exceptionally sensitive to the dielectric environment, requiring a proper treatment of the surrounding dielectrics for an accurate understanding. The consequences of heterogeneous dielectric screening on transition metal dichalcogenides are studied by developing a new theory based on classical electrostatics, which closely reproduced the band gaps and optical gaps calculated by the ab initio GW approximation and the Bethe-Salpeter equation (BSE).

The relative insensitivity of the first optical transition energy observed by experiments was explained for the first time in terms of the cancellation effect of changes of the band gap and the exciton binding energy. The theory of heterogeneous dielectric environments is further developed to be used in an atomistic calculation of layered hybrid organic-inorganic lead halide perovskites via a tight-binding GW-BSE method. The binding energies of trions and biexcitons were also calculated using the stochastic variational method to give spectrum peak energies that show a good agreement with reported experimental measurements. Lastly, the tight-binding GW-BSE method is generalized into an atomistic, semiempirical approach to calculate the electronic structure and optical spectra of arbitrary nanomaterials, termed semiempirical GW (sGW) and BSE (sBSE).