Distance and Orientation Dependence of Triplet–Triplet Energy Transfer Couplings Based on Nonorthogonal Multireference Wave Functions

Triplet-triplet energy transfer (TEnT) is of particular interest in various photochemical, photobiological, and energy science processes. It involves the exchange of spin and energy of electrons between two molecular fragments. Here, quasi-diabatic self-consistent field solutions were used to obtain the diabatic states involved in TEnT. The resonant Hartree-Fock approach was used to compute the nonorthogonal matrix elements for the two-state or four-state effective Hamiltonian and the overlap matrix. From the symmetric orthogonalized Hamiltonian, electronic coupling elements between the diabatic states in the TEnT process can be obtained. Two structural models, namely, naphthalene dimer and the 2,2'-bifluorene molecule, were employed to investigate the role of distance and orientation of the molecular fragments on the energy transfer process. It is observed that the inclusion of charge transfer states is critical to obtain the correct description of TEnT couplings. We discuss the effectiveness of the two-state model and four-state model in the successful evaluation of TEnT couplings. Spin density plots and biorthogonal orbitals were utilized to verify that the correct diabatic electronic structure of the TEnT states was determined.