臺灣博碩士論文加值系統

由於一般的密度泛函近似,其長程行為多半遞減太快,為了修正半局域交換相 關泛函應用在有限大小系統的漸進行為,我們利用早期 Fermi Amaldi 的模型,作 為修正長程行為的基礎。Fermi Amaldi 模型不滿足尺度的一致性,因此我們將密 度侷限在原子附近,以解決此問題。基於現有的半局域交換相關泛函,加上具有 正確的漸進模式的交換位勢,並再考慮雙重計算的能量,我們提出 LFA (局限在 原子的 Fermi Amaldi) 方法。應用此漸進修正的方法在 Perdew-Burke-Ernzerhof 泛函,預測的最高被佔據態能量和雷德堡激發態能量具有顯著的改善。此外,我 們利用單位分解方法以降低計算成本,結果相當精確,和用數值積分的逼近結果 可以相差極小,由於計算效率的提昇,我們能將 LFA 應用在更多更大的系統。

Aiming to correct the asymptotic behavior of semilocal exchange-correlation (XC) functionals for finite system, we proposed a correction scheme, wherein an exchange energy density functional whose functional derivative has the exact −1/r asymptote can be added to any semilocal XC functional, as the double-counting energy can be easily discounted. Applying this asymptotic correction scheme to the Perdew-Burke-Ernzerhof functional, the predicted highest-occupied-molecular-orbital (HOMO) energies and Rydberg excitation energies of molecules are shown to be significantly improved. A computationally efficient method which is called the Resolution of the identity (RI) that has been implemented. This method can converge to the exact LFA faster than the numerical LFA method which evaluates LFA functional by performing numerical quadrature. With the great advancement in the efficiency, LFA is made practical for large system.

1 Introduction 8
2 Long-range correction of localized FA model 11
2.1 Fermi Amaldi model ........................... 11
2.2 Asymptotic Correction Scheme ..................... 14
2.3 Resolution-of-identity Approximation..................18
2.4 Results and Discussion.......................... 23
3 Summary and Conclusions 31
Bibliography 32
A Supplementary Material Part I 35
A.1 Sum rule for exchange correlation hole ................. 35
B Supplementary Material Part II 37
B.1 Size-consistency of LFA model...................... 37
B.2 Construction of atomic weight ...................... 39
C Supplementary Material Part III 40

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