熱輔助佔據密度泛函理論 (TAO-DFT) 中 B97 型密度泛函之發展與 TAO-DFT 的有限溫度延伸

Abstract

為了減少 Kohn–Sham 密度泛函理論（ KS-DFT）在強關聯體系中的定性誤差，本研究在熱輔助佔據密度泛函理論（ TAO-DFT）架構下，對 B97 型泛函（包含廣義梯度近似［ GGA］、全域雜化［ GH］及距離分段雜化［ RSH］泛函）進行最佳化，並加入基於 D4 模型的經驗色散修正。所得到的泛函分別命名為TAO-B97-D4、 TAO-B97X-D4 與 TAO-ωB97X-D4，其中用於得到系統無關的最佳虛溫 θ 的公式在本研究中重新擬合。此外，透過施加 θ = 0 的限制條件，亦在KS-DFT 架構下最佳化 B97 型 RSH 泛函，得到 KS-ωB97X-D4。為了處理線性響應近似下 TAO-DFT 中的虛假激發問題，本研究提出一種高效率方法，稱為 pTAO/TDA。為評估所發展泛函的效能，進行了廣泛的測試，包括非強關聯體系（如GMTKN55 與 EXTS 資料庫）與強關聯體系（如 iso-C40 資料庫與線型併苯）。測試集亦涵蓋部分具挑戰性的案例，例如對稱自由基陽離子的解離（如 H+ 2 與 He+ 2 ）、長距離分離分子中的電荷轉移激發（如 C2H4· · · C2F4 二聚體、 Ar· · · S3 二聚體與 S3· · · Ar 二聚體），以及 H2 與 N2 的解離。 KS-ωB97X-D4 在非強關聯體系下具有最佳表現；然而，若欲在非強關聯與強關聯體系之間皆達到更平衡的表現，則建議採用 TAO-ωB97X-D4。 本研究亦提出熱輔助佔據密度泛函理論（ TAO-DFT）的有限溫度延伸版本（ FT-TAO-DFT），以處理在高電子溫度 θel（例如 θel = 1000 K）下的強關聯體系。線型併苯之紅外光譜係由基於 FT-TAO-DFT 的全始算分子動力學（ FT-TAOAIMD）於 1000 K 下所得。對於接近室溫的模擬（ θel = 300 K）， FT-TAO-AIMD近似退化為基於 TAO-DFT 的全始算分子動力學（ TAO-AIMD），此時電子溫度效應被忽略（即 θel ≈ 0）。對於原子數目巨大的系統，可將 QM/MM 方法與 FT-TAO-DFT 結合，進行 FT-TAO-QM/MM 模擬。最後，為探討氬基質在實驗中對線型併苯紅外光譜所產生的低溫效應，本研究做了電子溫度 θel = 0 的FT-TAO-QM/MM 常模分析（ FT-TAO-QM/MM-NMA）。

To reduce qualitative errors in Kohn-Sham density functional theory (KS-DFT) for multi-reference systems, the B97-type functionals, including generalized-gradient approximation (GGA), global hybrid (GH) and range-separated hybrid (RSH) functionals, are optimized in thermally-assisted-occupation density functional theory (TAO-DFT), with the empirical dispersion correction based on the D4 model. The resulting functionals are denoted as TAO-B97-D4, TAO-B97X-D4 and TAO-ωB97X-D4, respectively, wherein the optimal system-independent fictitious temperatures θ are determined by the newly proposed analytical parametrization. By enforcing the constraint θ = 0, the B97-type RSH is also optimized in KS-DFT, yielding the resulting functional KS-ωB97X-D4. In addition, to address spurious excitations within linear-response time-dependent TAO-DFT, an efficient method, termed pTAO/TDA, is proposed. Extensive examinations, including those for single-reference systems (e.g., GMTKN55 and EXTS databases) and multi-reference systems (e.g., the iso-C40 database and linear n-acenes) are performed to benchmark the resulting functionals. The test set also includes some challenging cases, such as the dissociation of symmetric radical cations (e.g., H+ 2 and He+ 2 ), charge-transfer excitations in long-range separated molecules (e.g., C2H4· · · C2F4 dimer, Ar· · · S3 dimer, and S3· · · Ar dimer), and the dissociation of H2 and N2. For single-reference systems, KS-ωB97X-D4 achieves the best performance. However, to attain balanced performance across singlereference and multi-reference systems, TAO-ωB97X-D4 is recommended. Furthermore, the finite-temperature extension of TAO-DFT (FT-TAO-DFT) is proposed for multi-reference systems at a high electronic temperature θel (e.g., θel = 1000 K). The infrared (IR) spectra of linear n-acenes are obtained from FT-TAO-based ab initio molecular dynamics (FT-TAO-AIMD) at 1000 K. For simulations around room temperature (θel = 300 K), FT-TAO-AIMD approximately reduces to TAO-based AIMD (TAOAIMD), neglecting the electronic temperature effects (i.e., θel ≈ 0). For systems with a large number of atoms, a QM/MM scheme can be applied with FT-TAO-DFT, denoted as FT-TAO-QM/MM simulations. The low-temperature effects induced by the argon matrix on the IR spectra of n-acenes in experiment are studied, based on FT-TAO-QM/MM-based normal mode analysis (FT-TAO-QM/MM-NMA) with θel = 0.