Excitonic Properties of Perylene Diimide Based Dyes

The paper is devoted to the comprehensive study of the electronic properties of eight molecules in the framework of the density functional theory (DFT) implemented in the ABINIT code. The first stage of calculations is based on the semi-local variant of the DFT approach, which involves the use of a generalized gradient functional for exchange-correlation energy (GGA). Optimization of the structure of molecules is performed within the framework of DFT-GGA theory. At the second stage, the electronic structure of the molecules in the ground state was calculated. The third stage was to determine the role of the static electron-hole interaction in the formation of the electron energy spectrum. The Green's function necessary for its realization was based on the eigenvalues and wave functions found at the previous stage within the DFT-GGA formalism. The Green's function method allows to obtain the energy of quasiparticle excitations including the static electron-hole interaction, which is not taken into account in the DFT-GGA approach. Quasiparticle energies are obtained in the first order perturbation of the Green's function, that is, in the GW approximation. The fourth step of our study was to clarify the role of the dynamic interaction of an electron and a hole in the formation of optical constants taking into account exciton effects. It was implemented using the Bethe-Salpeter equation (BSE), whose parameters were based on the solutions obtained in the previous stages. It was found that the smallest value of E_g found in the GGA approximation belongs to the PR 178 molecule, and in the GW approximation it is acquired by the PB 32 molecule. The BSE formalism leads to the smallest value of E_g for the PR 178 molecule. The largest value of E_g in the GGA approach belongs to the PR 179 molecule, in the GW formalism – to the molecule PR 190, and in the BSE theory – to the PB 31 molecule. It was found that in the GGA approach the band gap E_g lies in the energy range of 0.52 ≤ E_g ≤ 1.47 eV, in the GW approximation, 6.08 ≤ E_g ≤ 7.92 eV, and in the BSE formalism, 0.08 ≤ E_g ≤ 1.35 eV.