以全初始方法研究激發態能量轉移

Ab Initio Study on Excitation Energy Transfer

游志強(Zhi-Qiang You)

指導教授 ： 許昭萍 ； 游靜惠

國立清華大學/理學院/化學系/博士(2012年)

https://doi.org/10.6843/NTHU.2012.00225

摘要

激發態能量轉移是電子激發能從一個予體經由非輻射轉移到一個收體的過程。能量轉移的電子耦合值是決定能量轉移速率一個很重要的參數。在微擾理論第一階近似下，能量轉移耦合值可近似為偶極矩–偶極矩作用（Förster theory）以及電子交換積分（Dexter theory）。這兩項近似經常使用於理論研究及實驗結果闡述中。然而，此耦合值近似只有在予受體間長距離下才合理。

為此，我們發展了 fragment spin difference (FSD) 及 fragment excitation difference (FED)。這兩個方法都用本徵態計算，可以用來計算激發態能量轉移的完整耦合值，不限於長距離與對稱性，並且可以使用於分子間與分子內能量轉移的問題。在一系列的共軛分子系統測試下，我們證實了 FSD 及 FED 方法能夠提供可信賴的能量轉移耦合值。

我們使用 FSD 研究光合作用集光系統中的光保護機制。主要是三重態的葉綠素分子以奈米速率轉移三重態激發能量至鄰近的類胡蘿蔔分子上。我們正確地估計了三重態能量轉移中的電子耦合值，並用以估計此三重態轉移速率。我們的結果證實了該三重態能量轉移的確是在奈米範圍內。我們也使用 FED 方法計算了光合作用反應中心葉綠素 special pair 的能量轉移耦合值。我們的結果顯示了耦合值中的短距離效應為主要貢獻。因此 FSD 及 FED 方法能夠合理地估計激發態能量轉移耦合值，可以應用於一般大型非對稱的分子系統。我們預期 FED 及 FSD 在研究激發態能量轉移上是相當有用的方法。

關鍵字

激發態能量轉移

並列摘要

Excitation energy transfer (EET) refers to the nonradiative transfer of an electronic excitation from a donor molecule to an acceptor molecule (or fragment). The electronic coupling is one of the important factors in describing the transition rate. The electronic coupling for EET has been dissected with a perturbation theory, which gives rise to a dipole–dipole interaction (Förster theory) and an electron exchange integral (Dexter coupling) between electronic transitions of donor and acceptor and they are valid only for donor/acceptor separated at a large distance.

To calculate the electronic coupling, we have developed the fragment-spin difference (FSD) and fragment-excitation difference (FED) schemes for triplet and singlet energy transfer, respectively. As eigenstate-based methods, FSD and FED allow us to extract the coupling from the full electronic Hamiltonian. The EET coupling obtained is not subject to a long-distance condition. The FSD and FED schemes are generally applicable to both intermolecular and intramolecular EET, regardless of their symmetry.

The FSD scheme can be used to study triplet excitation energy transfer (TET). Numerical benchmark for the FSD were performed in two series of π-conjugation model systems. The FSD coupling exhibits weak dependence on molecular size and shows an exponential dependence on the intermolecular distance. The FSD results were also compared with those obtained from the conventional exchange integral, and we found that FSD yields more consistent results.

The FSD was used to study TET in the light-harvesting complexes of purple bacteria and dinoflagellates. For all light-harvesting complexes studied, there exist nanosecond TET from the chlorophylls to the carotenoids. The result supports a direct triplet quenching mechanism for the photoprotection function of carotenoids. The TET rates are similar for a broad range of carotenoid triplet state energy, which implies a general and robust TET quenching role for carotenoids in photosynthesis The result is also consistent with the weak dependence of TET kinetics on the type or the number of π-conjugation lengths in the carotenoids and exhibits the robustness of carotenoids in photosynthesis systems.

The FED scheme can be used to study singlet excitation energy transfer (SET). For a pair of stacked naphthalenes, the short-range coupling was found with similar value and distance dependence as TET coupling. The FED was employed to calculated SET coupling in special pairs of the reaction centers of purple bacteria. We found that the short-range coupling represents the dominant contribution to the total SET coupling.

We have developed the FED and FSD schemes to calculate excitation energy transfer coupling. We found them useful for a large number of systems. The coupling values obtained are mostly consistent with those calculated with other methods, with FED and FSD results being more reliable, as judged by their distance dependent behavior. FED and FSD are useful in offering physical insights in applications. With their general applicability, we expect them to be useful in the future.

並列關鍵字

Excitation energy transfer

參考文獻

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