應用超軟贗勢於非平衡態散射電子的密度泛函理論

Abstract

在密度泛函理論計算中，贗勢方法可以避免處理內層電子，增加第一原理的計算效率。在使用平面波基底的贗勢方法電子結構計算中，ultrasoft贗勢(USPP)優於Norm-conserving贗勢(NCPP)，這是因為USPP可使得價電子波函數在核心區域較為平滑，USPP能以較少的平面波基底數目達到和NCPP相同的計算精確度。因此我們在平面波基底的非平衡態密度泛函理論架構中引進USPP方法，在非平衡態密度泛函理計算程式架構下，利用USPP以Lippmann-Schwinger方程式解出奈米尺度接面系統散射電子的波函數。我們希望能減少使用平面波基底數目，降低電腦記憶體與計算量的需求，突破目前受限於電腦容量不足的計算瓶頸。我們比較NCPP與USPP兩種方法去計算分子元件的電流與電導，並觀察達計算收斂時所需的平面波基底數目。

In density functional theory(DFT),pseudopotentials can improve the efficiency of electronic-structure calculations because core electrons have been transformed away. Ultrasoft pseudopotentials (USPP) is even better than Norm conserving pseudopotentials(NCPP) in the efficiency of claculations. The reason for this is that wavefunctions of valence electrons calculated by USPP are smoother in the core regions than those calculated by NCPP. Compared with NCPP, fewer number of plane wave basis are required for USPP to reach the same accuracy. Thus, the implementation of USPP can significantly reduce plane waves basis. We, therefore, implement USPP in the framework of “DFT + Lippmann-Schwinger equation”, and apply it to obtain the wavefunctions of the scattering electrons self-consistently in atomic/molecular junctions. We calculate the current and conductance in molecular nanojunctions using wavefunctions calculated self-consistently in the framework of “DFT + Lippmann-Schwinger equation”. We investigate the efficiency of convergence in terms of the number of plane waves basis using USPP and NCPP, respectively.