Abstract
The electronic coupling is an important factor for the electron transfer (ET) rate prediction. Based on the two-state model, the Generalized Mulliken-Hush (GMH) and Fragment Charge Difference (FCD) schemes have been useful approaches to calculate ET coupling from an excited state calculation. However, the ET problems are not always two-state in nature, i.e. the charge transfer (CT) state obtained is sometimes mixed with nearby local excited (LE) states in Configuration Interaction Singlets (CIS) method. Therefore, we develop a general multi-state approach for FCD without the need of manual assignment for the states and automate the process in generating the diabatic states. This scheme can be generalized for GMH as well. We test the new multi-state schemes for the performance in systems that have been studied using more than two states with FCD or GMH. We found that the multi-state approach yields much better charge-localized states and electronic couplings in these systems. Singlet fission is a process where a singlet exciton is split into a pair of triplet excitons. Since a high-energy photon is split into two lower-energy triplet excitons, it has the potential to increase the efficiency of solar cell. The reverse process, triplet-triplet annihilation (TTA) converts a high-energy exciton from two low-energy triplet excitations. It is also an important process that is capable of up-converting the photon energy. In the singlet fission process, the initial state is (S1S0) and final state is (T1T1). For TTA, the initial state is (T1T1) and final state is (S1S0). Computational method for singlet fission coupling is applicable to TTA. In the present work, we use Fragment Spin Difference (FSD) and direct coupling with natural transition orbitals (DC-NTO) methods to calculate the singlet fission/TTA coupling. Based on 4 orbitals model, we found that there exists a unique symmetry for coupling and it implies a different selection rule from that of electron transfer or energy transfer. Moreover, we found that the distance dependence with the electronic coupling is exponential decay and decay rate is larger than 2 angstrom^-1. It indicates that the singlet fission is the short range interaction. Moreover, we performed the singlet fission coupling and rate with the pentacene molecules and found that the theoretical rate would be approached to the experimental value (~100 fs), when the initial or final state is mixed with the CT component. Thus we conclude that the CT-mediated state plays an important role in singlet fission.