短長程修正的混成密度泛函帶改善色散修正

Short- and Long-Range Corrected Hybrid Density Functionals with Improved Dispersion Corrections

王志維(Chih-Wei Wang)

指導教授 ： 蔡政達

國立臺灣大學/理學院/物理學研究所/碩士(2016年)

https://doi.org/10.6342/NTU201603151

摘要

為了改善長程修正(LC)的混成密度泛函在核電子游離與核電子激發的表現，本研究藉由加一個餘補誤差函數至原本作為分程函數的誤差函數上以調整Hartree-Fock交換能中的分程函數。此混成觀點被應用於LSDA、PBE、B97三種密度泛函近似之上，並加入改善的經驗原子-原子色散修正D3以減少非共價作用誤差。我們透過ωB97訓練集最佳化泛函參數。所得之泛函：SLC-LDA-D3、SLC-PBE-D3、SLC-B97-D3，通稱短長程修正的(SLC)混成密度泛函，與PBE、LC-ωPBE、ωB97、ωB97X、ωB97X-D、ωB97X-D3在廣泛的測試集比較，包含核電子游離、核電子激發、S66集、AE113、IP131、EA131、FG131、雙同原子陽離子解離、價激發與Rydberg激發、長程電荷轉移激發。SLC泛函在核電子游離與核電子激發比起其他泛函準確很多，並在其他應用和LC泛函的表現相近。

關鍵字

密度泛函理論 ； 交換相關 ； 分程的 ； 色散修正 ； 核電子游離 ； 核電子激發

並列摘要

In order to improve the performance of long-range corrected (LC) hybrid density functionals in core ionizations and core excitations, we adjust the range separation function for Hartree-Fock exchange by adding a complementary error function to the original error function. This hybrid scheme is applied to various density functional approximations including LSDA, PBE, and B97. The D3 empirical atom-atom dispersion corrections is also applied in order to correct non-covalent interactions. We optimize the functional parameters via the ωB97 training set. The resulting functionals, SLC-LDA-D3, SLC-PBE-D3, and SLC-B97-D3, are compared with PBE, LC-ωPBE, ωB97, ωB97X, ωB97X-D, and ωB97X-D3 on a wide range of test sets, including core ionizations, core excitations, S66 Set, AE113, IP131, EA131, and FG131 database, homonuclear diatomic cation dissociations, valence and Rydberg excitations, and long-range charge-transfer excitations. The SLC functionals are much more accurate in core ionizations and core excitations than other functionals, and perform similarly to the LC functionals in other applications.

並列關鍵字

density functional theory ； exchange-correlation ； range-separated ； dispersion correction ； core ionization ； core excitation

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