熱輔助佔據密度泛函理論中自旋對稱性之恢復

Abstract

科恩—沈呂九密度泛函理論（KS-DFT）在常見的交換關聯泛函下，對多參考系統可能算得錯誤的自旋密度及其相關性質。氫分子的解離是典型的例子；在其自旋極化解中，可違背現實，出現自旋對稱性破缺，導致 KS-DFT 在同一交換關聯泛函下的自旋極化解與自旋非極化解不一致。近期數值結果表明，藉適當的虛擬溫度，熱輔助佔據密度泛函理論（TAO-DFT）能解決這個問題。本文基於 TAO-DFT 構建了一套線性響應理論，證明在足夠的虛擬溫度下，TAO-DFT 必能消除多參考系統中的自旋對稱性破缺；並以 TAO-DFT 計算不同虛擬溫度下 H2、N2、He2 及 Ne2 的解離及扭曲的乙烯分子，作為例證。

For multireference systems, Kohn-Sham density functional theory (KS-DFT) with conventional exchange-correlation (xc) functionals can yield erroneous spin densities and related properties. A typical example is the dissociation of H2, where unphysical spin-symmetry breaking can arise in the spin-polarized solutions, resulting in distinct spin-polarized and spin-unpolarized solutions derived from the same xc functional in KS-DFT. Recently, thermally-assisted-occupation density functional theory (TAO-DFT) has been shown numerically to resolve this problem when an appropriate fictitious temperature is chosen. In this thesis, a linear response theory based on TAO-DFT is constructed to prove that TAO-DFT with a sufficiently high fictitious temperature can always eliminate the spin-symmetry breaking in multireference systems. As an illustration, TAO-DFT calculations with various fictitious temperatures are performed for the dissociation of H2, N2, He2, and Ne2, along with twisted ethylene.