位移技術應用在多參考態微擾理論的關鍵評核

Abstract

為了描述激發態與開殼層系統，多參考態微擾理論 (multireference perturbation theory) 是精確的電子相關 (electron-correlation) 方法中為最受信賴且計算上較可實行的。然而，多參考態微擾理論卻存在著一個嚴重的問題，稱之為入侵態 (intruder states) 問題。入侵態會使得系統的位能面不連續且導致沒有物理意義的結果。多參考態微擾理論配合位移技術 (shift techniques) 的使用可以很有效地移除入侵態。儘管如此，用多參考態微擾理論來研究系統的化學性質會隨著位移技術所使用的參數而劇烈地改變。我們因此著手進行各種可運用的位移技術研究，即實數位移 (real shift)、虛數位移 (imaginary shift) 與入侵態規避技術 (intruder state avoidance technique)，並找出其適當的位移參數值。本論文藉由不同的多參考態微擾理論的方法結合各種位移技術，研究了15種雙原子分子中的65條低能量電子態 (low-lying electronic states) 之位能曲線。我們用不同的位移值來極限測試這些位能曲線及其光譜常數 (spectroscopic constants) 並與實驗值作比較。最後，運用統計分析來決定每一種位移技術的優化的位移參數值。研究結果顯示當使用優化的位移參數值，不僅可以有效地移除入侵態，還可以減少研究系統在光譜常數上的誤差。

For describing excited states and open-shell systems, multireference perturbation theory (MRPT) is the most reliable and computationally feasible among accurate electron-correlation methods. However, the MRPT methods are subject to a serious problem, known as the intruder state problem. The intruder states shall cause discontinuities in the potential energy surface of a system leading to non-physical results. The use of shift techniques in the MRPT may efficiently eliminate intruder states. Nevertheless, the chemical properties of the system studied using MRPT can change strongly depending on the parameter employed in the shift techniques. We therefore undertook an investigation for available shift techniques (e.g., real shift, imaginary shift, and intruder state avoidance techniques) to find appropriate values of these shift parameters. In this Thesis, 65 potential energy curves of low-lying electronic states of 15 diatomic molecules were studied using different MRPT methods combined with various shift techniques. The potential energy curves and their spectroscopic constants were critically evaluated for various values of the shift parameter, and compared with experiment. Finally, we used statistical analysis to determine the optimal value of the shift parameter in each shift technique. The research results show that the shift techniques can efficiently eliminate the intruder states and at same time they also reduce the error in spectroscopic parameters of the studied system when an optimal value of shift parameter is used.