Transport of excitation energy in a three-dimensional doped molecular crystal. IV. Fourth-order propagation,exciton clothing,and exciton diffusion

The problem of excitons in interaction with phonons in a molecular crystal has been reinvestigated as a continuation of our earlier work. The exciton-phonon interaction has been taken to be linear in lattice displacements. The external medium, the phonon assembly, has been considered to be in thermal equilibrium. Following Simons, we have incorporated the effects of the medium on the exciton dynamics into a time-dependent effective potential that contains the equilibrium average exciton-phonon interaction as well as terms arising from the fluctuations in the medium's coordinates about their equilibrium values. A correlation function that represents the probability of exciton transfer has been given in the interaction picture. The time evolution of this correlation function has been determined by following Kubo's technique of cumulant expansion. The zeroth-, second-, and fourth-order contributions to the correlation function have been calculated in this way. The second- and fourth-order contributions have been diagrammatically represented. The second-order contribution has been explicitly calculated in different physical limits, namely, the slow exciton and the slow phonon limits at high and low temperatures and for very large and very small time. A few simple formulas for the transfer probability of a bare exciton in a molecular crystal of cubic symmetry have been derived from the Debye approximation for the dispersion of phonons. It has been specifically shown that the sum over phonon modes in the large time dynamics leads to a fully destructive interference in second order at a very low temperature and gives rise to a diffusive transport at a high enough temperature. A natural way of clothing the excitons has been considered and the clothed exciton has been represented diagrammatically. The dressing requires the correlation function to be redefined in terms of the clothed states and the clothed operators. The clothed exciton correlation function that represents the probability of transfer of excitons fully clothed by the phonons in thermal equilibrium turns out to be identical with the bare exciton correlation function. This attaches a novel interpretation to the correlation function which was originally defined by Simons. Transfer probabilities for a clothed exciton in a cubic crystal has been explicitly worked out for different physical limits under the Debye model of phonon dispersion. From these results a few expressions for the macroscopic diffusion coefficient of the clothed exciton have been obtained. A few critical comments have been incorporated. © 1996 John Wiley & Sons, Inc.     

Quantum master equation approach to the second hyperpolarizability of nanostar dendritic systems

We investigate the dynamic second hyperpolarizability (gamma) of nanostar dendritic systems using the quantum master equation approach. In the nanostar dendritic systems composed of three-state monomers, the multistep exciton states are obtained by the dipole-dipole interactions, and the directional energy transport, i.e., exciton migration, from the periphery to the core is predicted to occur by the relaxation between exciton states originating in the exciton-phonon coupling. The effects of the intermolcecular interaction and the exciton migration, i.e., exciton relaxation, on the gamma in the third-harmonic generation (THG) are examined in the three-photon off- and on- resonance regions using the two-exciton model. Furthermore, the method for analysis of spatial contributions of excitons to gamma is presented by partitioning the total gamma into the one- and two-exciton contributions. It turns out that the exciton relaxation between exciton states causes significant broadening of the spectra of gamma and their mutual overlap as well as the relative increase of two-exciton contributions in the nanostar dendritic system.     

Exciton-exciton interaction resulting from phonon-exciton coupling

It is shown using second quantization formalism and treating excitons as bosons that phonon-exciton coupling leads to exciton-exciton interaction. This interaction limits substantially the possibility of exciton condensation.

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Zusamenfassung Es wurde mit Hilfe des Formalismus der zweiten Quantisierung gezeigt, daß die Phonon-Exziton Kopplung zu einer Exziton-Exziton Wechselwirkung führt. Dabei wurden die Exzitonen als Bosonen behandelt. Diese Wechselwirkung begrenzt wesentlich die Möglichkeit einer Kondensation der Exzitonen.

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Resume En traitant les excitons comme bosons on a demontré par le formalisme de la deuxiéme quantisation que le couplage exciton-phonon conduit à l'interaction exciton-exciton. Cette interaction limite sensiblement la possibilité de la condensation des excitons.

     

Coherent third-order spectroscopic probes of molecular chirality

The third-order optical response of a system of coupled localized anharmonic vibrations is studied using a Green's function solution of the nonlinear exciton equations for bosonized excitons, which are treated as interacting quasiparticles. The explicit calculation of two-exciton states is avoided and the scattering of quasiparticles provides the mechanism of optical nonlinearities. To first-order in the optical wave vector we find several rotationally invariant tensor components for isotropic ensembles which are induced by chirality. The nonlocal nonlinear susceptibility tensor is calculated for infinitely large periodic structures in momentum space, where the problem size reduces to the exciton interaction radius. Applications are made to alpha and 3(10) helical infinite peptides.     

Exciton migration dynamics in a dendritic molecule: quantum master equation approach using ab initio molecular orbital configuration interaction method

We investigate the exciton migration dynamics in a dendritic molecular model composed of pi-conjugation linear-leg units (acetylenes and diacetylene) and a benzene ring (branching point) using the quantum master equation approach with the ab initio molecular orbital (MO) configuration interaction (CI) method. The efficient migration of exciton from short-length linear legs (acetylenes) to long-length linear leg (diacetylene) via a benzene ring is observed. As predicted in previous studies, the exciton (electron and hole) distributions are relatively well localized in each generation segmented by the meta-branching point (meta-substituted benzene ring) though the electron and hole distributions are delocalized and are somewhat spatially different from each other within each generation. It is found that the excitons localized in the generation composed of short linear legs occupy in higher-lying exciton states, while those in the generation composed of long linear legs do in lower-lying ones. These features suggest the decoupling of pi-conjugation at the meta-branching point. On the other hand, the relaxation effect between exciton states is found to be caused by the exciton-phonon coupling, in which the existence of common configurations (electron-hole pairs) in CI wave functions between adjacent exciton states (having primary distributions on short and long linear-leg regions, respectively) is important for the relaxation between their exciton states. This feature indicates the importance of partial penetration of pi-conjugation through the meta-substituted benzene ring in excited states for such exciton migration.     

An adiabatic local model for the internal structure of charge-transfer excitons: Dimers and trimers

In charge-transfer crystals, the exciton-phonon interaction significantly influences the internal structure of charge-transfer excitons (CTEs). The formation of CTE dimers and trimers is considered in an adiabatic non-centrosymmetric model which includes phonon dispersion. Changes of lattice frequencies near the CTE are analysed.     

Temperature dependence of ESR lineshapes of triplet excitons in molecular pairs

The ESR lineshape of triplet excitons moving between two differently oriented molecules of a pair is calculated. Our model hamiltonian contains the electronic interaction matrix element for the coherent exciton transport, the Zeeman energy of the triplet spin in an external magnetic field, the fine structure of the differently oriented molecules, the phonons in the crystal which are described as a heat bath, and the microscopic interaction between excitons and phonons. For the naphthalene pair the lineshapes are discussed with respect to the temperature and a parameter characterizing the strength of the interaction between excitons and photons.     

Resonant coupling of bound excitons with LO phonons in ZnO: excitonic polaron states and Fano interference

We report on a photoluminescence observation of robust excitonic polarons due to resonant coupling of exciton and longitudinal optical (LO) phonon as well as Fano-type interference in high quality ZnO crystal. At low enough temperatures, resonant coupling of excitons and LO phonons leads to not only traditional Stokes lines (SLs) but also up to second-order anti-Stokes lines (ASLs) besides the zero-phonon line (ZPL). The SLs and ASLs are found to be not mirror symmetric with respect to the ZPL, strongly suggesting that they are from different coupling states of exciton and phonons. Besides these spectral features showing the quasiparticle properties of exciton-phonon coupling system, the first-order SL is found to exhibit characteristic Fano lineshape, caused by quantum interference between the LO components of excitonic polarons and the continuous phonon bath. These findings lead to a new insight into fundamental effects of exciton-phonon interactions.     

A model calculation on the transport of excitation energy in a molecular crystal

We report a model calculation of the transport of a local (site) excitation in a doped molecular crystal containing one impurity. We do not consider the impurity as a direct trap for electronic excitations (zero trap depth) but assume that exciton-phonon interaction is exclusively given by the coupling of excitons with the vibrational displacement of the impurity. The dynamical problem is solved by using a time-dependent effective potential consisting of equilibrium average exciton-phonon interaction and fluctuations around this average. Two correlation functions are computed using the slow phonon limit and assuming that the temperature of the system is 300 K. Transmission of the excitation energy over a distance of eight spacings takes place, electronically, within a few picoseconds. With the exciton-phonon interaction switched on, calculated correlation functions diminish very rapidly with increasing time, indicating that an irreversible transfer of excitonic energy to the thermal bath takes place. Thus transmission of the excitation energy over such a distance (and without a high rate of trapping) is not an efficient process.     

Composite exciton-phonon states in molecular crystals

It is known that the diagonalization of the exciton-phonon Hamiltonian gives rise to the composite exciton-phonon energy states. Within the single phonon approximation, two different diagonalized Hamiltonians are obtained for 0–0 and 0–1 phonon transitions in pure molecular crystals. The resulting secular equations are solved, and analytical expressions for the energy eigenvalues corresponding to the two transitions are derived. The thermal broadening due to the composite exciton-phonon states interaction is also calculated at low temperatures, and the results agree with experiments.     

Triplet excitons in molecular pairs: Analytical investigation of electron spin resonance

For triplet excitons in pairs of differently oriented molecules ESR lineshape is investigated analytically using a microscopic model. The model hamilton takes into account the coherent tranfer of the exciton between the two molecules, the Zeeman and fine-structure energy and the interaction with phonons. The analytical expression for the line positions and linewidths are evaluated using values characteristic for triplet excitons in naphthalene pairs.     

Calculation of the exciton green's function of a molecular crystal from a two-site dynamical coherent potential approximation

A new two-site dynamical coherent potential approximation for exciton-phonon interaction models corresponding to a homomorphic partition of the hamiltonian is described. The renormalization of both the site energy and the exciton bandwidth is accomplished in contrast to single-site CPA models.     

Influence of Higher Excited Singlet States on Ultrafast Exciton Motion in Pigment-Protein Complexes

Abstract— Numerical simulations of the ultrafast exciton motion in photosynthetic antenna complexes are used to reproduce measured data of optical pump-probe experiments. Emphasis is put on a chlorophyll aL/chlorophyll b dimer of the light-harvesting complex of the photosystem II of higher plants (LHC-II). To account for intramolecular excited-state absorption the standard exciton theory is extended to the inclusion of a second higher excited singlet state per chlorophyll molecule. The density matrix theory is applied to describe the dissipative dynamics of excitons. Different mechanisms for energy relaxation and dephasing including pure dephasing processes are discussed. As a result, a further refinement of earlier calculations on the one-color pump-probe spectra at the LHC-II can be presented. In particular, the presence of non-Markovian effects with respect to the exciton-vibrational interaction in the LHC-II, discovered previously in the two-color pump-probe spectrum, is demonstrated here for the one-color pump-probe case.     

Influence of the fine-structure interaction and of the g-tensor anisotropy on the ESR lineshape of triplet excitons in molecular crystals with two molecules in the unit cell

Recently a set of equations has been derived describing the influence of the quasi-incoherent exciton motion on the ESR lineshape of triplet excitons in molecular crystals with two molecules per unit cell. Starting from these equations in the case of rapid exciton motion analytic expressions for the positions and widths of the ESR lines are calculated by second order perturbation theory taking into account the different orientations of the fine-structure interaction tensors and of the g-tensors at the two inequivalent molecules in the unit cell. Explicit expressions of the angular dependence of these quantities for rotation of the magnetic high-field around the a^?, b^?, c^?-axes of crystals of the anthracene type are given. Finally contact to experimental results is made.     

Exciton-phonon self-trapping: A continuous transition

An exciton-phonon system of a linear aggregate is investigated in the intermediate-coupling regime. For sufficiently large intermolecular coupling. the variational approach predicts a discontinuous transition from a mobile exciton at weak exciton-phonon coupling to an immobile exciton at strong coupling. Fully converged numerical calculations exhibit strong deviations from the variational approach at intermediate exciton-phonon coupling strength and do not show a discontinuous transition. In the strong-coupling regime, results from the variational approach (which are closely related to the small polaron theory) deviate considerably from numerically converged calculations and an appropriate perturbation approximation.     

Optical Absorption and Photo-Luminescence Spectra of Molecular van der Waals Systems: Frenkel Exciton Resonance Effects

Applying the principle of conservation of energy, the photo-absorption-luminescence (p-a-l) cycle of resonant Frenkel excitons in aggregates is explained in terms of the p-a-l cycles of isolated molecules. The method employed to measure the Stokes shift of Frenkel Exciton Resonance (FER) systems, derived from our model, is found to differ significantly from that employed currently. Our postulate, that the aggregate v-e transition energy, in the frame of reference of a resonant exciton, decreases as function of the localisation length of the exciton, is demonstrated by the excellent agreement of the model with existing data. This has allowed the determination of the localisation length of resonant excitons from readily available spectra. As the localisation length is a good indicator of the order of a system, this result will be useful in molecular self-assembly (MSA) research. Results from the model suggest that Frenkel exciton resonance is vibrationally modulated, and the collective exciton eigenstate of a resonant Frenkel exciton can couple the v-e manifolds of 2N molecules together via the electronic resonance interaction, even in the absence of direct intermolecular vibrational coupling. In essence, we demonstrate that the photo-physics of an exciton that is resonant over many molecules is fundamentally determined by the photo-physics of the isolated molecule just as one would expect.     

The Exciton Model for Molecular Materials: Past,Present and Future?

In assemblies of identical molecules or chromophores, electronic excitations can be described as excitons, bound electron-hole pairs that can move from site to site as a pair in a coherent manner. The understanding of excitons is crucial when trying to engineer favorable photophysical properties through structuring organic molecular matter. In recent decades, limitations of the concept of an exciton have become clear. The exciton can hybridize with phonon and photons. To clarify these issues, the exciton is discussed within the broader context of the gauge properties of the electromagnetic force.     

Interaction of excitons with charge carriers in organic solids: charged excitonic complexes

The coupled states of molecular excitons with charge carriers are considered. In centrosymmetric crystals the attraction of excitons to charge carriers arises mainly from the increase of molecular polarizability on electronic excitation, so that the exciton energy decreases in the electric field of the charge. In noncentrosymmetric crystals, the main contribution to the energy of exciton-charge interaction comes from the change of the static dipole moment of the molecule on excitation. Some physical consequences and possible experimental observations of the above-mentioned coupled states are discussed.     

Comparative reinvestigation of the interaction of phonons with Wannier and Frenkel excitons in crystalline solids

The interaction of lattice vibrations with excitons in inorganic and organic semiconductors/insulators is reinvestigated. These results expose the comparative nature of exciton—phonon interaction in the two types of solids and produce two new coupling functions useful for Frenkel exciton—phonon interaction.