密度泛函架構下之高效率靜態關聯能修正方法之研究

Efficient treatments of static correlation in density functional framework

葉恕豪(Shu-Hao Yeh)

指導教授 ： 鄭原忠 ； 許昭萍

國立臺灣大學/理學院/化學研究所/博士(2022年)

https://doi.org/10.6342/NTU202202694

摘要

本論文之研究內容著重於，三種近期在密度泛函理論架構下，所開發出的靜 態關聯能誤差的修正方法。所謂靜態關聯能誤差為，源自於單一行列式波函數無 法同時處理能量簡併或近乎簡併之前緣分子軌域，而產生之系統性偏差；著名的 具體案例為在雙原子分子的解離過程中，其鍵結軌域與反鍵結軌域會逐步趨向 簡併。傳統上而言，人們會使用完全活性空間自洽場方法（complete active space self-consistent field, CASSCF） 來修正靜態關聯能誤差，但由於此方法計算複雜 度會隨目標系統大小陡然上升，應用於大型分子的計算將難以執行，或甚至無法 成功收斂。另一方面，科恩－沈密度泛函方法，雖能在保持較低計算量的同時， 模擬包含交換能與動態關聯能的大部分電子多體效應，但其並無法有效的處理靜 態關聯能。 為了解決靜態關聯能的計算問題，由密度泛函理論延伸出的，熱輔助佔據密 度泛函理論（thermally-assisted-occupation density functional theory, TAO-DFT） 與非整數自旋定域化軌道標度修正法（fractional-spin localized orbital scaling correction, FSLOSC） 相繼被提出。做為上述兩種方法的後繼研究，本論文前兩 章節之主題分別為，延伸自熱輔助佔據密度泛函理論的分子激發態計算方法，以 及將熱輔助佔據密度泛函理論中的靜態關聯能，重構回科恩－沈密度方法中的交 換關聯泛函中之關聯能修正方法；而在最後一章中，我們著重在研究結合非整 數自旋定域化軌道標度修正法與貝特－-沙彼得方程式（Bethe-Salpeter equation, BSE），並用於計算分子激發態位能曲線之計算。

關鍵字

計算化學 ； 全始計算 ； 電子結構 ； 密度泛函理論 ； 靜態關聯能

並列摘要

This dissertation is focused on the present development of treating static correlation error with density functional theories. Static correlation error is a systemic error arising from the single-determinant wavefunctions with nearly degenerate orbitals with different electron occupancy. A fundamental and important set of examples is the bond dissociation of molecules, where the occupied bonding orbital and unoccupied anti-bonding orbital gradually becomes degenerate. Conventionally, multi-reference methods such as complete active space self-consistent field (CASSCF) would be chosen to correct the error. However, the computation complexity scales steeply with the size of molecules, which would make simulations of large systems inefficient and sometimes inexecutable. Kohn-Sham (KS) density functional theory (DFT) , on the other hand, treats most of many-body effect arising from electron-electron interactions, exchange and dynamical correlation, except for the static correlation with a mild scaling. To resolve this issue, two methods in DFT framework, thermally-assisted-occupation density functional theory (TAO-DFT) and fractional-spin localized orbital scaling correction (FSLOSC), were developed independently. As a continuation of the developments of static correlation correction, we extended the TAO-DFT to simulate excited-state phenomena and further reformulated it include the static correlation correction into an exchange-correlation functional, which are covered in the first two chapters. In the third chapter, we combine the Bethe-Salpeter equation with FSLOSC method to calculate excitation energy and excited-state potential energy curves from a ground state corrected by FSLOSC.

並列關鍵字

computational chemistry ； electronic structure ； ab initio ； density functional theory ； static correlation

參考文獻

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