藉由運用GW近似與BSE理論並結合不同基底(平面波 或 Wannier函數)展開的方式， 我們已經完成在鹼金屬鹵化物中考慮多體效應影響下的第一原理激發態計算。 新穎的第一原理Wannier 函數很適合用於瞭解強束縛Frenkel激子的傳播行為。 特別是用以解釋長久以來對於Frenkel 激子特性爭辯的問題。 儘管在鹼金屬滷化物中 ( 例如: 鋰化氟 ) 電子電洞對並不是藉由相同原子上的交互作用束縛在一起， 但是我們仍然可以鋰與氟原子Wannier 軌道所組成的”超級原子”的角度來理解這一類非常局域化的激子行為。 我們可以發現在將局域化的電子電洞對Wannier波函數相乘並做傅利葉轉換後很明顯的與角度有關。 而這個結果可以直接用於解釋非彈性x光散射實驗角度相依性的由來. 為了更進一步有效率的求得強交互作用系統中的線性響應函數, 我們將提出一個新的構想那就是”等效的雙粒子跳躍核心因子” . 這個等效的核心因子包含了所有激子如何移動的資訊而且也是造成局域化線性響應方程變寬的主要原因之一. 這個一般性的理論可以直接運用於描述強關聯系統裡局域化的激發態行為中 Using the combination of GW approximation and solving Bathe-Salpeter equation (BSE) in different bases (Plane-wave or Wannier bases), we perform ab inito excitation calculations for alkali halides with taking into account the many-body effects. A general new first-principles Wannier function method is proposed to explore the propagation of strongly bound Frenkel excitions. Specifically, long-standing debate of the Frenkel nature of the excitons can be explained well under this framework. Even the electron-hole pair in the alkali halides (such as LiF) is not bound through an on-site interaction its strongly localized excitonic character can be studied by the formation of a “super-atom” consisting of Wannier orbitals from both Li and F atoms. We find strongly angular dependence of the excitons by means of a direct product of the Fourier transform of the local particle-hole wave function. This result can straightforward explain the angular resolved inelastic x-ray scattering experiment. Furthermore, in order to solve response function of strongly interacting system within the linear response scheme more effectively, a new approach is proposed by formulating the “effective two-particle kinetic kernel” which contains all the mobility information of excitons. This general theoretical framework can be directly applied to the study of propagation of local excitations of strongly correlated systems.
