原子序1到4的原子基態和氫原子高階諧波產生的計算

Calculation of the Ground State of Atom Z=1-4 and High-Order Harmonic Generation for Hydrogen Atom

范力文(Li-Wen Fan)

指導教授 ： 江進福

國立交通大學/理學院/物理研究所/碩士(2014年)

https://doi.org/10.6842/NCTU.2014.01043

摘要

最近數十年隨著密度泛函理論(density functional theory)和電腦的發展，藉由數值方法達成原子系統相關性質的準確計算逐漸可行。本研究目標在於對原子系統基態的Kohn-Sham計算以及研究透過Krieger-Li-Iafrate(KLI)程序近似最佳等效位能(optimized effective potential)對自我交互作用修正後的準確性。在基態計算的基礎上，模擬在強場下的原子系統是另一個目標。廣義擬值譜法(generalized pseudo-spectral method)是對於數值解Kohn-Sham方程獲得Kohn-Sham軌域以及數值解Poisson方程獲得Hartree位能的有效方法。對於時變計算，以分離運算子法(split operator method)處理時間算子。在結果的部分，我們先從原子序1到4以不同的交換相關泛函的Kohn-Sham計算獲得總能和其分量，再與前人的結果比較以驗證我們的計算可靠。再進一步，我們用KLI程序近似最佳等效位能並執行只有交換泛函的計算，結果顯示總能和游離能在自我交互作用修正後的準確性。最後，我們模擬在雷射場的氫原子並獲得高階諧波產生頻譜。

關鍵字

擬值譜法 ； 微分矩陣 ； 分離運算子法 ； 時變薛丁格方程式 ； 高階諧波產生 ； 密度泛函理論 ； 最佳等效位能

並列摘要

The accurate calculation about properties of many-electron atomic system may be performed by numerical method in recent few decades due to the development of density functional theory and computer. The aim of the present research was to perform Kohn-Sham (KS) calculations in ground state of atomic system and investigate the accuracy of the KS calculations with optimized effective potential (OEP) approximated by Krieger-Li-Iafrate (KLI) procedure to correct the self-interaction. Based on the calculation of ground state, simulating dynamics of atomic system in intense field is the other aim. Generalized pseudo-spectral (GPS) was the useful method to numerically solve KS equation to find KS orbitals and Poisson’s equation to find Hartree potential. For time-dependent calculations, spilt operator method was used to deal with the time operators. In the results section, we first obtained the total energies and their components from the KS calculations for atoms Z=1-4 with various exchange-correlation functionals and compared them with other works to make sure our calculation is reliable. Next, we performed the KS calculations with exchange-only functional and OEP approximated by KLI procedure, and we displayed the accuracy of total energies and ionization energies without self-interaction. Finally, we simulated the dynamics of a hydrogen atom in the laser field and obtained the high-order harmonic generation (HHG) spectra.

並列關鍵字

pseudo-spectral method ； differential matrix ； split operator method ； time-dependent Schrodinger equation ； high-order harmonic generation ； density functional theory ； optimized effective potential ； Krieger-Li-Iafrate approximation

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