Hamiltonian-Independent Generalization of the Fragment Excitation Difference Scheme

The fragment excitation difference (FED) scheme is a useful method for calculating the complete diabatic couplings of various energy transfer systems. The lack of a good definition for the transformation of the transition density matrix to the off-diagonal FED matrix elements limits FED to single-excitation methods. We have developed a generalized FED scheme called the θ-optimized FED (θ-FED) scheme which does not require transforming the transition density matrices. In θ-FED, two states of interest are linearly transformed by a mixing angle θ into two mixed states. The excitation difference of each mixed state is evaluated and optimized numerically to determine the mixing angle. This approach allows for finding diabatic states and the corresponding couplings for a general set of Hamiltonians.