本論文使用CASTEP（Cambridge Serial Total Energy Package）工具進行計算，並針對硼酸鹽晶體中的LBO、CBO、CLBO晶體進行無陽離子的虛擬晶體計算結果做討論，並對其DOS(Density of state)以及orbital density做詳細的觀察與比較，我們發現電子的局域化程度不同而引導出框架有效體積的概念 。 由比較框架有效體積發現，在某一區間的軌域密度值，其框架有效體積大小趨勢會與能隙大小趨勢呈反比，可用來解釋LBO、CBO、CLBO晶體中的能隙大小趨勢。 我們對其他硼酸鹽系列之晶體做框架有效體積的探討(MBO、MBBF、MBOF)，發現都存在框架有效體積大小趨勢與能隙大小趨勢呈反比的軌域密度值範圍，加強了以框架有效體積大小趨勢來解釋能隙大小趨勢的可行性與說服力。 In this paper, we use CASTEP（Cambridge Serial Total Energy Package）to calculate cation removed borate nonlinear optical crystals (no-L_LBO、no-C_CBO、no-CL_CLBO). DOS (Density of state) and the orbital density are observed in detail, we found difference in the degrees of electron localization, and therefore propose an method effective volume in crystal. By comparing effective volume in crystal, within certain range of orbital density coress-bonding effective is inverse for band gap, it can be used to explain band gap trend of LBO、CBO、CLBO. We apply effctive volume method to other borate crystals (MBO、MBBF、MBOF), we can also find orbital density range which the effective volume is inverse proportional to band gap, this further strencth the feasibility and convincing power of the idea of using effctive volume of framwork to predict band gap trend.
