Both helices have a definite effect on the site energies without being dependent on protonation states. Exciton nature of the BChl a excitations in the FMO protein The close proximity of the BChl a molecules (∼10 Å) leads to electronic coupling between them that exceeds the electron-vibrational PRN1371 coupling in the FMO complex. Therefore, the system is usually described
by a superposition of the seven molecular BChl a states forming seven exciton states (Van Amerongen et al. 2000), and the electron-vibrational coupling is treated perturbationally. These excitonic interactions V ij between two chromophores i and j are dominated by the relative orientation of the transition dipole moments and the inverse cube of the distance between the BChl a molecules. The exciton levels have different cross sections and linewidths which together with a close Stattic order energy spacing results in a dense and complex spectrum. This can be seen in the low-temperature absorption spectra in which only three peaks out of seven are clearly visible. In order to describe the excitonic wavefunctions in the FMO protein, the following electronic Hamiltonian is used: $$ \hatH_0=\sum_j
E_j|j\rangle \langle j|+ \sum_j< i V_ij(|j\rangle\langle i|+|i\rangle\langle j|) $$ (1)in which E j represents the site energies of the uncoupled BChl a molecules and |j〉 the corresponding localized excitations. The exciton wavefunctions |α〉 are obtained by diagonalizing the Hamiltonian as $$ |\alpha\rangle=\sum_jC_\alpha(j)|j\rangle $$ (2)using the exciton expansion coefficients C α(i) which represent
the contribution of the individual BChl a molecules to an excitonic transition. The results of such calculations, as performed on the same system by a variety of research groups, are shown in the Tables 3, 4, and 5, where α runs vertically and i horizontally. Pearlstein used a point-monopole approach to describe the interaction between the individual BChl a molecules. The transition charge density is calculated for each molecule, represented by point charges at the position of individual atoms, and the interactions of all point charges with those of the Mannose-binding protein-associated serine protease other chromophore are considered. All the 21 BChl a of the see more trimeric FMO complex were included in the model, and the parameters for all the 21 degenerate and non-degenerate exciton transitions are displayed in the original article (Pearlstein 1992). It can be concluded that in each case only one or two of the BChl a pigments contribute significantly to the squared amplitude of the eigenvectors of the transitions. This means that none of the exciton states is delocalized over the complete subunit, let alone the trimer. Later this was verified by using a similar approach to model the absorption spectra (Gülen 1996).