You Zhi-Qiang, Hsu Chao-Ping, Fleming Graham R
Institute of Chemistry, Academia Sinica, 128 Academia Road Section 2, Nankang, Taipei 115, Taiwan.
J Chem Phys. 2006 Jan 28;124(4):044506. doi: 10.1063/1.2155433.
Triplet-triplet (TT) energy transfer requires two molecular fragments to exchange electrons that carry different spin and energy. In this paper, we analyze and report values of the electronic coupling strengths for TT energy transfer. Two different methods were proposed and tested: (1) Directly calculating the off-diagonal Hamiltonian matrix element. This direct coupling scheme was generalized from the one used for electron transfer coupling, where two spin-localized unrestricted Hartree-Fock wave functions are used as the zero-order reactant and product states, and the off-diagonal Hamiltonian matrix elements are calculated directly. (2) From energy gaps derived from configuration-interaction-singles (CIS) scheme. Both methods yielded very similar results for the systems tested. For TT coupling between a pair of face-to-face ethylene molecules, the exponential attenuation factor is 2.59 A(-1)(CIS6-311+G(**)), which is about twice as large as typical values for electron transfer. With a series of fully stacked polyene pairs, we found that the TT coupling magnitudes and attenuation rates are very similar irrespective of their molecular size. If the polyenes were partially stacked, TT couplings were much reduced, and they decay more rapidly with distance than those of full-stacked systems. Our results showed that the TT coupling arises mainly from the region of close contact between the donor and acceptor frontier orbitals, and the exponential decay of the coupling with separation depends on the details of the molecular contacts. With our calculated results, nanosecond or picosecond time scales for TT energy-transfer rates are possible.
三重态-三重态（TT）能量转移要求两个分子片段交换携带不同自旋和能量的电子。在本文中，我们分析并报告了TT能量转移的电子耦合强度值。提出并测试了两种不同的方法：（1）直接计算非对角哈密顿矩阵元。这种直接耦合方案是从用于电子转移耦合的方案推广而来的，其中两个自旋定域的无限制哈特里-福克波函数被用作零阶反应物和产物态，并直接计算非对角哈密顿矩阵元。（2）从组态相互作用单重态（CIS）方案导出的能隙计算。对于所测试的体系，两种方法得到的结果非常相似。对于一对面对面的乙烯分子之间的TT耦合，指数衰减因子为2.59 Å⁻¹（CIS6-311+G(**)），约为电子转移典型值的两倍。对于一系列完全堆叠的多烯对，我们发现TT耦合强度和衰减率与它们的分子大小无关，非常相似。如果多烯是部分堆叠的，TT耦合会大大降低，并且它们随距离的衰减比完全堆叠体系更快。我们的结果表明，TT耦合主要源于供体和受体前沿轨道紧密接触的区域，并且耦合随间距的指数衰减取决于分子接触的细节。根据我们的计算结果，TT能量转移速率有可能在纳秒或皮秒时间尺度。
