Predicting the electronic structure of extended organic molecules constitutes an important fundamental task of modern chemistry. Studies of electronic excitations, charge-transfer, energy-transfer, and isomerization of conjugated systems form the basis for our understanding of the photophysics and photochemistry of complex molecules1-3 as well as organic nanostructures and supramolecular assemblies.4,5 Photosynthesis and other photochemical biological processes that constitute the basis of life on Earth involve assemblies of conjugated chromophores such as porphyrins, chlorophylls, and carotenoids.6-8 Apart from the fundamental interest, these studies are also closely connected to numerous important technological applications.9 Conjugated polymers are primary candidates for new organic optical materials with large nonlinear polarizabilities.10-19 Potential applications include electroluminescence, light emitting diodes, ultrafast switches, photodetectors, biosensors, and optical limiting materials.20-27 Optical spectroscopy which allows chemists and physicists to probe the dynamics of vibrations and electronic excitations of molecules and solids is a powerful tool for the study of molecular electronic structure. The theoretical techniques used for describing spectra of isolated small molecules are usually quite different from those of molecular crystals, and many intermediate size systems, such as clusters and polymers, are not readily described by the methods developed for either of these limiting cases.28

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Density Matrix Analysis and Simulation of Electronic Excitations in Conjugated and Aggregated Molecules

Perylenetetracarboxylic acid dianhydride (PTCDA) stacks face-to-face in crystals and multiple quantum wells (MQWs). Excitations of PTCDA stacks are mixed molecular (Frenkel) and charge-transfer (CT) states coupled to a molecular vibration. Eclipsed stacks and molecular conjugation imply strong Frenkel–CT mixing in absorption and electroabsorption, with k=0 at the top of the exciton band, and negligible mixing at k=π for emission from the bottom. The exciton–phonon-CT dimer developed for k=0 processes is a nonadiabatic approximation for narrow CT bands. Quantitative dimer spectra are obtained in the vibronic basis of displaced harmonic oscillators for excited PTCDA and radical ions. We present a joint analysis of absorption and emission in PTCDA stacks and MQWs using parameters from solution, molecular calculations, and related conjugated systems. Polarized single-crystal absorption decisively relates the entire 2–3 eV system to molecular π–π* transitions, while electroabsorption with field along the stack implicates adjacent ions in the stack. The simple structure and extensive PTCDA spectra make possible detailed modelling of mixed Frenkel–CT vibronics that were far less accessible in previous organic molecular crystals. Since the coupled mode is closely related to polyenes and conjugated polymers, PTCDA provides a bridge between molecular insulators and extended systems capable of charge transport.

Vibronic structure of PTCDA stacks: the exciton–phonon-charge-transfer dimer

The neutral excitations in poly(p-phenylenevinylene) are studied in conjunction with the vibronic structure of the lowest optical transitions. Combining the configuration interaction of Wannier-localized electron–hole pairs with an empirical description of electron–phonon coupling, we obtain the potential energy surfaces of monoexcited states and the Condon electron–vibrational spectra in absorption and emission. The S1→S0 luminescence band shape is found compatible with self-localization of S1 within about 10 monomers, driven exclusively by electron–phonon coupling. The singlet and triplet polaron–excitons are exchange–split by about 1 eV and differ substantially in terms of average electron–hole separation.

Polaron–excitons and electron–vibrational band shapes in conjugated polymers

Theoretical and computational studies of excitons in conjugated polymers

Spin-dependent electron–hole (e–h) recombination in poly(p-phenylenevinylene) chains is modeled by the dissipative dynamics of the multilevel electronic system coupled to the phonon bath. The underlying Hamiltonian incorporates the Coulomb and exchange interactions of spin-singlet and spin-triplet monoexcitations in Wannier-orbital basis and their coupling to the prominent Franck–Condon active modes. In agreement with experiment, we obtain that the ratio of singlet versus triplet exciton formation rates is strongly conjugation-length dependent and increasing on going from the model dimer to the extended chain. The result is rationalized in terms of a cascade interconversion mechanism across the electronic levels. In parallel to the direct formation of spin-dependent excitons, e–h capture is found to generate long-lived charge-transfer states, whose further phonon-mediated relaxation to the bottom of the density of states is hindered by the near e–h symmetry of conjugated hydrocarbons. Being nearly spin independent, such states most likely form an intersystem crossing pre-equilibrium, from which the singlet e–h binding channel is about ten times faster than the triplet one.

Dissipative dynamics of spin-dependent electron–hole capture in conjugated polymers

The crossover from band to correlated states in half-filled quantum cell models is studied in a molecular-exciton framework based on a chain of dimers. Crystal states with one or several excited dimers yield analytical excitation energies to first order in interdimer Coulomb interactions V(p,p') for excitonic chains or interdimer electron transfer ${\mathit{t}}_{\mathrm{\ensuremath{-}}}$=t(1-\ensuremath{\delta}) for Hubbard chains. Molecular-exciton analysis of excitations and transition moments rationalizes exact numerical solutions of oligomers with arbitrary intradimer correlations U, ${\mathit{V}}_{1}$, and electron transfer ${\mathit{t}}_{+}$=t(1+\ensuremath{\delta}), including the number, positions, and transition moments of low-lying excitations. Short correlation lengths of infinite chains with large alternation \ensuremath{\delta}\ensuremath{\ge}0.6 lead to converged crystal states for oligomers containing N=4--7 dimers. The present approach provides a detailed picture of excited-state crossovers with increasing U, ${\mathit{V}}_{1}$, and V(p,p'). Quite generally, the lowest singlet excitation ${\mathit{S}}_{1}$ is one-photon allowed (1B) on the band side of the spin-charge crossover and two-photon allowed (2A) on the correlated side. Intermediate correlations and large \ensuremath{\delta} reveal different crossovers in Hubbard chains, where 1B involves charge transfer between dimers, and excitonic chains, where 1B has an excited dimer.We also obtain two-photon transition moments M and extend vanishing M(2A) in the band limit up to U=2${\mathit{t}}_{+}$, the \ensuremath{\delta}\ensuremath{\sim}1 crossover of Hubbard chains. We find finite M(2A) on the correlated side, however, where 2A contains two triplet dimers in either alternating Hubbard or excitonic chains. Their different spin-charge crossovers appear as an abrupt and continuous increase, respectively, of two-photon intensity on going from the correlated to the band side. The greater delocalization (\ensuremath{\delta}\ensuremath{\sim}0.07--0.33) realized in conjugate polymers is consistent with excitonic chains. The potential V(p,p') in the Pariser-Parr-Pople model for conjugated hydrocarbons distinguishes strongly fluorescent polymers with ${\mathit{S}}_{1}$=1B from others with ${\mathit{S}}_{1}$=2A. We also relate our results at large \ensuremath{\delta} to other approximations for nonlinear optical spectra of conjugated polymers.

GW Hayden

Papers

Molecular-exciton approach to spin-charge crossovers in dimerized hubbard and excitonic chains