長程修正的高階廣義密度梯度近似

Long-range corrected meta-generalized-gradient approximations

林佑昇(You-Sheng Lin)

指導教授 ： 蔡政達

國立臺灣大學/理學院/物理研究所/碩士(2012年)

https://doi.org/10.6342/NTU.2012.00693

摘要

Kohn–Sham 密度泛函理論已成為最廣泛應用的電子結構理論之一。但理論中
的重要部分，交換–相關能泛函仍未確知，並且需要近似。真實的交換–相關電洞
是完全非局域性的。加入了 Hartree-Fock (HF)交換能的混成密度泛函增加了模型中的非局域性。混成高階密度泛函已被證實可以表現得比混成廣義密度梯度近似還要好。長程修正的(LC)混成泛函只對於長程的電子–電子交互作用保留完整的 HF交換能，因而解決了一大部分的自我作用問題。
藉由將一個系統化地模擬 LC 混成密度泛函的方法應用到 M05 混成高階交換–相關泛函的形式，並加入經驗的原子–原子分散修正，吾人發表了一個新的 LC 高階廣義密度梯度近似，稱為 ωM05-D，可適用於熱化學、熱化學動力學以及非共價交互作用。測試顯示，對於大部分的應用，ωM05-D 之於 M05-2X 泛函，展現了可觀的改善。若和 LC 廣義密度梯度近似 ωB97X-D 比較，ωM05-D 展現了較小的自我作用誤差，與較佳的漸近特性。

關鍵字

密度泛函理論 ； 交換–相關 ； 高階廣義密度梯度近似 ； 分程的 ； 分散修正

並列摘要

Kohn–Sham density-functional theory (KS-DFT) has become one of the most popular electronic structure theories. However, its crucial ingredient, the exact exchange-correlation energy functional remains unknown and needs to be approximated. The exact exchange-correlation hole is fully nonlocal. Hybrid density functionals, which incorporate Hartree-Fock (HF) exchange, can help to include nonlocality. Hybrid meta density functionals have been shown capable of performing better than hybrid generalized gradient approximation (GGA). Long-range corrected (LC) hybrids retain full HF exchange only for long-range electron-electron interactions, and thereby resolve a significant part of the self-interaction problems.
By applying a general scheme for systematically modeling LC hybrid density functionals to the form of hybrid meta exchange-correlation functional M05, and including empirical atom-atom dispersion corrections, we present a new LC meta-GGA, called ωM05-D, for thermochemistry, thermochemical kinetics, and noncovalent interactions. Tests show that for most applications, ωM05-D exhibits noticeable improvement over the M05-2X functional. When compared to the LC-GGA, ωB97X-D, ωM05-D exhibits smaller self-interaction error (SIE) and better asymptotic behavior.

並列關鍵字

density-functional theory ； exchange-correlation ； meta-GGA ； range-separated ； dispersion correction

參考文獻

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