即時熱輔助佔據密度泛函理論

Abstract

密度泛函理論，特別是Kohn--Sham(KS)密度泛函理論，因其高計算效率成為量子計算領域被廣泛應用的方法。然而，KS密度泛函理論假設了基態密度具有非交互作用純態勢可代表性，這甚至限制了精確的KS密度泛函理論處理多參考系統的能力。為了從根本擺脫此限制，熱輔助佔據密度泛函理論已被開發。模擬結果顯示，熱輔助佔據密度泛函理論在單參考系統表現類似KS密度泛函理論，在多參考系統則優於KS密度泛函理論。其中，熱輔助佔據密度泛函理論展現了藉由分數佔據軌域描述靜態關聯能的能力。 如同線性響應含時密度泛函理論和即時含時密度泛函理論，線性響應含時熱輔助佔據密度泛函理論已被提出並應用於獲取激發能。這篇論文將把熱輔助佔據密度泛函理論擴展為即時熱輔助佔據密度泛函理論，不做線性響應理論常見的微擾近似以求更廣的適用性。過去作品中未完好定義的Hartree交換關聯theta作用量泛函也會一併修正。我們應用模擬氫分子系統，並討論線性響應理論無法處理的高諧波產生。模擬結果顯示，適當θ的即時熱輔助佔據密度泛函理論在單參考系統表現類似即時含時密度泛函理論。在多參考系統，足夠大θ的即時熱輔助佔據密度泛函理論則修復了限制自旋表述與非限制自旋表述被破壞的對稱。

Density functional theory (DFT), specifically Kohn--Sham DFT (KS-DFT), is a widespread method in the field of quantum computation due to its high computational efficiency. However, KS-DFT assumes the ground-state density to be non-interacting pure-state (NI-PS) v_s-representable, which limits the ability of even exact KS-DFT to handle multi-reference systems. To relieve this limitation, thermally assisted-occupation DFT (TAO-DFT) has been developed. Simulation results suggest that TAO-DFT performs similarly to KS-DFT for single-reference systems, while outperforming KS-DFT for multi-reference systems. In particular, TAO-DFT is shown to describe static correlation through fractional orbital occupations. Similar to linear-response time-dependent DFT (LR-TD-DFT) and real-time time-dependent DFT (RT-TD-DFT), LR-TD-TAO-DFT has been proposed and utilized to extract excitation energies. In this thesis, we aim to extend TAO-DFT to real-time TAO-DFT. The often made small perturbation aprroximation in LR theory is dropped for universality. The ill-defined Hartree--exchange--correlation-theta (HXCθ) action functional in the previous work is also revised. Specifically, we apply RT-TAO-DFT to hydrogen molecules. The phenomenon of high harmonic generation (HHG), which falls outside the scope of LR theory, is simulated and discussed. Simulation results suggest that RT-TAO-DFT with suitable θ performs similar to RT-TD-DFT for single-reference systems. While for multi-reference systems, RT-TAO-DFT with sufficiently large θ fixes the symmetry-breaking issue between spin-restricted and spin-unrestricted formulations.