在最近幾年，利用擬粒子計算來描述材料上電子的激發態性質已獲得成功，例如能帶結構和吸收光譜。因為基於擬粒子的概念配合格林函數計算的近似，使得其理論計算得以執行應用。在理論上，包含電子與電子的斥力加上電子與原子核的屏蔽形成了擬粒子。在數學上，格林函數G具備描述擬粒子的特徵。搭配上具有屏蔽概念的自能Σ，激發態能量得以被定量的計算，我們稱之為動態屏蔽相互作用或者簡稱為GW近似法。此演算法由Hedin在1965年提出。在本研究中，我欲呈現GW擬粒子方法的兩個理論計算的應用。在第一個部分我們將分析的Mn3O4吸收光譜。基於所選取合適的團簇結構模型，我們計算得到的吸收光譜可以與實驗做很好的比較。因此，實驗上面的光譜特徵可以利用計算結果作分析。第二部分，GaN半導體的擬粒子能帶結構和激發光譜的計算結果。此結果對於利用GaN作為光觸媒的研究，是很重要的前置瞭解。In recently years, quasiparticle calculations have been used successfully to describe the electronic excited state properties of materials such as band structures and absorption spectra. A successful approximation for the determination of excited states is based on the quasiparticle concept and the Green function method. The Coulomb repulsion between electrons leads to depletion of negative charge around a given electron and the ensemble of this electron and its surrounding positive screening charge forms a quasiparticle. The mathematical description of quasiparticles is based on the Green function G, whose exact determination requires complete knowledge of the quasiparticle self-energy Σ. A determination of the self-energy Σ can only be approximated, and a working scheme for the quantitative calculation of excitation energies is the so-called dynamically screened interaction or the GW approximation (GWA). The GWA for the computation of quasiparticle energies was proposed by Hedin in 1965. In this study, I would like to show two applications using GW quasiparticle theory. In first part, we present the first analysis of three distinctive peaks appearing in absorption spectrum of Mn3O4 spinel. Based on a proper cluster model, we obtain the calculated spectrum which can be compared well with the experiments. Therefore, the assignments of the origin of the peaks on spectrum can be done. In the second part, the calculations of quasiparticle band structure and optical excitation spectrum of GaN wurtzite have been performed using first-principles methods. These results are the priority for theoretical analysis of photocatalytic reactions using GaN semiconductor.
