Investigation of molecular dimers inα-PTCDA byab initiomethods: Binding energies, gas-to-crystal shift, and self-trapped excitons

Abstract

Time-dependent density functional theory ͑TD-DFT͒, Hartree-Fock, second-order Møller-Plesset perturbation theory ͑MP2͒, and configuration interaction of singly excited states ͑CIS͒ are applied to crystalline PTCDA ͑3,4,9,10-perylene tetracarboxylic dianhydride͒. The systems investigated include single molecules in an optimized rectangular shape, and molecules and molecular dimers compatible with the experimental geometry in the crystalline ␣-phase. Total energy calculations for pairs of adjacent molecules result in a microscopic estimate for the intermolecular binding energy in the solid. The electronic transition energies are calculated with TD-DFT techniques and CIS. From a detailed comparison between the molecular excitations of a single molecule and different molecular dimers in the crystal, a large fraction of the gas-to-crystal shift can be assigned to the redshift of the HOMO-LUMO excitation energy induced by the neighboring molecules in the crystal. The molecular dimers are generalized to deformed molecules, resulting in model geometries for self-trapped excitons with long radiative lifetimes related to the small transition dipole moment associated to intermolecular charge transfer ͑CT͒ transitions. The part of the Stokes shift resulting from internal deformations is obtained from TD-DFT calculations, and the self-trapping along the intermolecular distance is determined from a combination of an MP2-based intermolecular van der Waals potential with CIS for the CT transitions. After a careful elimination of the energy offsets related to the applied methods and to the lack of the complete crystalline surroundings, the calculated transition energies for the deformed dimers can be used for assigning the long-living components of the photoluminescence spectra to pairs of oppositely charged molecules and to excimer states. For the crystalline ground state, we deduce a CT transition energy of 2.14 eV along the stacking direction, significantly below previous theoretical estimates.

Excitons in perylene tetracarboxdiimide crystals for optoelectronics

“…The first transition is a HOMO-LUMO one at 2.43 eV with an oscillator strength of 0.76. This compares well to other published results obtained with the same method [6,7]. Within the Born-Oppenheimer approximation, the nuclei are brought into a vibronic level of the excited molecule after absorption of light.…”

Crystallochromy of perylene pigments: Interference between Frenkel excitons and charge-transfer states

“…Previous optical studies of PTCDA have shown that Frenkel excitons and CT states mix only weakly, so that they result in quite different features in photoluminescence, 21,27,28 an interpretation corroborated by the small values of the transfer parameters t e and t h . PTCDA is one of the exceptional cases where information on the anisotropy of the optical response is available, 22,61 and in contrast to DIP, 32 the large angle between the transition dipoles of the two basis molecules yields oscillator strengths of similar size for both components of the dielectric tensor; compare Tables V and VI.…”

“…Therefore, PL bands arising from self-trapped CT states occur below recombination from the dispersion minimum of the lowest dispersion branch of the Frenkel exciton, E 00 F ͑k͒. 21,27,28 Moreover, weak transitions around 1.95 eV and 2.12 eV arising from E 00 CT and E 01 CT , respectively, allow the selective excitation of PL from CT states. 9,65 The value of E 00 CT = 1.95Ϯ 0.07 eV deduced from the Frenkel-CT model corresponds to an average CT transition energy of ͗E CT ͘ = E 00 CT + ͑S + + S − ͒ប = 2.12Ϯ 0.07 eV, in good agreement with an earlier estimate based on excimer PL arising from a selftrapped CT exciton modeled as a deformed dimer, indicating a value in the range ͗E CT ͘ = 2.14Ϯ 0.08 eV for the undeformed crystal.…”

“…[54][55][56] Moreover, the neutral molecular excitations in the crystal are redshifted by nearly 0.5 eV with respect to a monomer in weakly interacting surroundings 57 and with TD-DFT it can be investigated how different neighbors contribute to this effect. 28 For any microscopic investigation of a stacked dimer, the resulting transition energies will necessarily suffer from large energetic offsets with respect to a more complete description of the crystalline phase, so that approaches such as CIS, TD-HF, and TD-DFT can only generate raw data which will require further interpretation.…”

“…19 For PTCDA, on the other hand, Frenkel excitons and CT states result in independent photoluminescence ͑PL͒ features, 27 where the interpretation of PL from CT states requires the investigation of self-trapped CT excitons in deformed dimer geometries. 28 A model including only Frenkel excitons has allowed to quantify the anisotropic dielectric tensor, PL at low temperatures, and the dependence of electron-energyloss spectra on the momentum transfer. [20][21][22][29][30][31] Previous microscopic calculations of dielectric function and PL spectra raise the fundamental question under which conditions separate F and CT states or their mixing via electron or hole transfer determine the optical observables.…”