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