Variation Method
Electronic coupling between excited states leads to changes in their energies and the formation of coupled states. The variation method is a simple approach that enables calculation of the energies and structures of coupled states in the basis of localized (uncoupled) states:
\(H_{\text{el}}c_{l}={\varepsilon}_{l}c_{l}\) (10)
where \(H_{\text{el}}\) is the Hamiltonian containing excitation energies of localized states (diagonal elements) and electronic couplings (off-diagonal elements), \({\varepsilon}_{l}\) are energies of coupled states and \(c_{l}\) are eigenvectors that show contributions of localized excitations to each coupled excited state.1-3 The variation method is based on Frenkel (or Frenkel-Davydov) exciton model.39 ,40
.
The excitation energies of uncoupled molecular fragments (diagonal elements of the Hamiltonian) are specified in the input file. The excitation energies can be obtained from quantum chemical computations or form experimental studies (see Refs. 6, 8 for review).
An example of the coupled states in the Fenna-Matthews-Olson complex2 is shown in Figure 4