The exciton—phonon interaction for triplet exciton bands of organic solids: An experimental and theoretical study

Very high resolution optical data on the temperature dependences of the Davydov component absorption profiles and polarization dependent one-phonon structures associated with the lowest triplet exciton band of anthracene are presented along with a theoretical framework for their interpretation. The interpretation of the one-particle exciton—phonon transitions involving both one-phonon creation and annihilation (cold and hot phonon transitions) is entirely consistent with the analysis of the T-dependent dephasing of the lowest zero-phonon Davydov transition in terms of two mechanisms: delocalized exciton—delocalized phonon scattering operative for the low frequency (< 30 cm^?) phonons which undergo no lattice distortion and: Raman like phonon scattering operative for the higher frequency phonons which do. It is the latter which leads to the identical T² linewidth dependences of the two Davydov components in the high T limit. The former scattering is dominant at the lowest temperatures. In addition, the, marked and polarization dependent mirror symmetry breakdown between the hot and cold one-particle transitions can be nicely understood in terms of interferences occurring between the Condon and phononic (from the dependence of the pure exciton transition dipoles on phonon coordinate displacement) contributions to the one-particle transition dipoles. It is argued that our findings for anthracene should prove useful for triplet exciton bands in other organic solids.     

Comment on the applicability of Urbach's rule to molecular crystals

The extent to which the absorption profile below the first exciton band can be predicted without recourse to resonance transfer and strong exciton—phonon coupling is evaluated for a crystal transition derived from a moderately intense free molecule transition. It is argued, on the basis of a simple model, that Urbach rule behavior can arise from the same class of weak exciton—phonon interactions that determine hot band absorption shapes.     

Some features of two-particle exciton-phonon excitations in molecular crystals

In this paper we present the results of a theoretical study of the optical absorption line shapes in the two-particle exciton-intramolecular phonon (IP) excitation regime in molecular crystals. The exciton-IP coupling was handled considering the exciton and the IP as a pair of interacting pseudo-particles and exploring the conditions for branching-off a two-particle bound state (TPBS) from the two-particle-continuum (TP), without invoking the exciton-IP decoupling approximation. We were able to handle both symmetry-allowed electronic transitions as well as symmetry-forbidden, vibronically-induced, electronic excitations. For symmetry-forbidden transitions we have provided a systemic derivation of Rashba's, Koster—Slater type formula where the local perturbation results from quadratic IP coupling. For the case of symmetry-allowed electronic transitions we derived a new approximate expression for the line shape, incorporating both linear and quadratic coupling terms and elucidating the conditions for a peaceful coexistence of TP and TPBS. Next, we have considered the exciton-IP system coupled to intermolecular lattice phonons (LP), taking into account the effects of bath diagonal “strong” coupling and of off-diagonal “weak” coupling. The diagonal exciton-LP coupling results in the appearance of side bands which should be viewed as three-particle resonances corresponding to an exciton + IP + LP. Off-diagonal exciton-LP coupling results in the relaxation of the exciton-IP TPBS to the TP continuum at finite temperatures. Finally, we have explored the effects of static structural disorder on the exciton-IP system, considering the effects of Anderson-type diagonal disorder. Configurational averaging was performed utilizing the coherent potential approximation, while the disorder field was represented in terms of a lorentzian distribution of the site excitation energies. Structural disorder drastically affects the TPBS, while the TP continuum is only slightly affected by disorder scattering.     

Some effects of structural disorder on the optical properties of organic molecular crystals

We investigate the effects of structural disorder on the absorption line shapes of the lowest exciton states in molecular crystals at zero temperature by the application of the average t-matrix approximation to a system characterized by a gaussian distribution of site excitation energies. The line shape exhibits asymmetric line broadening with the high energy portion being close to lorentzian, while the low energy edge is sharp. The energy dependence of the low energy tail is determined by the dimensionality of the exciton band structure.     

Absorption spectra of crystalline thiophthene

The near ultraviolet absorption spectra of crystalline thiophthene have been measured in polarised light at temperatures down to 4–6 K. The spectra show that only the Davydov component located at higher energies remains broad at low temperature. The nature of this broadening is discussed in terms of downward inter-band phonon scattering from the upper optical level by a librational phonon. A comparison of experimental data and theoretical calculations of energy levels and polarisation ratios based on the dipole—dipole approximation has been carried out, and the direction of polarisation of the π* ← π electronic transition which lies in the thiophthene molecular plane has been defined.     

Exciton dynamics in molecular crystals from line shape analysis. Time response function of singlet excitons in crystal anthracene

From an accurate measure of the temperature dependence of the line shape function ω ?₂ (ω) information is obtained about the time behaviour of the response function of singlet excitons of small wavevector encompassed by the (0-0) band of the 4000 A Å transition in crystal anthracene. An apparatus to determine the reflection band profile with high accuracy needed to give correct ω ?₂ (ω) data is described. Although the data analysis is not without problems, there is strong evidence that the time behaviour of excitons in this transition is characterized by a stochastic collision time τ_c. The temperature dependence of τ_c is consistent with a model in which the intermolecular phonons are weakly coupled with the exciton created by either b or a polarized light. Phonon annihilation is predominant for the b-polarized transition but both phonon creation and annihilation are active for these polarized transition. The similar values of the exciton—phonon coupling function for both polarizations may indicate either the importance of higher multipole terms for that function or strong interband scattering. The relationships between τ_c and parameters from other experimental results on singlet excitons in crystal anthracene are considered. The results may allow for a better understanding of the mechanism of exciton—phonon coupling in crystals.     

Exciton dynamics in molecular crystals from line shape analysis. Spectral moment analysis of the origin region of the 4000 Å transition of crystal anthracene

A spectral moment analysis of the line shape function ω?₂(ω) in the region of the (0—0) band of the 4000 ŹB_2u ← ¹A_g transition in crystal anthracene at various temperatures is performed. The data are compared with the predictions of three coupling models, viz., weak exciton—photon with weak exciton—phonon coupling, strong exciton—photon with weak exciton—phonon coupling, weak exciton—photon with strong exciton—phonon coupling. The terms contributing to each spectral moment for each model are rendered explicit. The experimental data indicate that the exciton—intermolecular phonon coupling is primarily weak. The exciton interacts with optical phonons of about 90 cm^-1 frequency with a coupling strength of about 140 cm^-1 , a value near that predicted by a weak coupling model. The coupling strength is nearly the same irrespective of whether the exciton is created by b- or a-polarized light probably indicative of the importance of higher multipole contributions to the coupling although the existence of strong interband scattering could affect that suggestion. The coupling parameters g_op and g_ac are about 10^-1 and 10^-4 respectively.     

Exciton self-trapping in tetrafluoro-dimethyl-aminoacridine single crystals

The UV-visible optical spectra of 1,2,3,4-tetrafluoro-7-(N,N)dimethyl-amino-acridine single crystals are reported. The results are discussed on the basis of the molecular transitions and crystal packing in the framework of the theory of molecular excitons under a fluctuating potential field due to dynamic disorder. A strong local geometry distortion is demonstrated by applying the Urbach rule to the absorption tails, which is the amplitude of the local potential fluctuation being larger than the intermolecular transfer energy. The lineshape and linewidth of the emission band and its temperature dependence give further evidence of exciton self-trapping.     

Temperature dependence of the exciton—phonon coupling in the strong coupling limit: Results for solid nitrogen

High resolution (ΔE = 0.75 meV) absorption profiles of the vibronic bands in the range of the w¹Δ_u ← X¹Σ⁺_g and a¹II_g ← X¹Σ⁺_g exciton progressions at hv ≈ 8.9 eV in solid N₂ have been measured in the temperature range between 6 K and 30 K. These excitations are strongly localized so that the observed temperature dependence of the fine structure, consisting of a zero phonon line and a phonon side band, can be described very well in the model of strong exciton—phonon coupling at point defects. The experimental results for the w¹Δ_u transition are found to be consistent with the assumption of a Debye spectrum for the phonon density of states and we derive a value for the Debye temperature of θ = 78 K, which is in very good agreement with that derived from other measurements.     

Enhancement of coherent energy transport by disorder and temperature in light harvesting processes

We investigate the influence of static disorder and thermal excitations on excitonic energy transport in the light-harvesting apparatus of photosynthetic systems by solving the Schro?dinger equation and taking into account the coherent hoppings of excitons, the rates of exciton creation and annihilation in antennas and reaction centers, and the coupling to thermally excited phonons. The antennas and reaction centers are modeled, respectively, as the sources and drains which provide the channels for creation and annihilation of excitons. Phonon modes below a maximum frequency are coupled to the excitons that are continuously created in the antennas and depleted in the reaction centers, and the phonon population in these modes obeys the Bose-Einstein distribution at a given temperature. It is found that the energy transport is not only robust against the static disorder and the thermal noise, but it can also be enhanced by increasing the randomness and temperature in most parameter regimes. Relevance of our work to the highly efficient energy transport in photosynthetic systems is discussed.     

Absorption,fluorescence and stimulated fluorescence by polaritons in thin anthracene crystals. A re-interpretation of spectroscopic properties of anthracene

The transmission, absorption (excitation spectra) and fluorescence spectra of thin (? 47 nm) free mounted anthracene flakes have been measured. True absorption in b polarization in the region of the lowest exciton state occurs as a result of scattering by phonons. It has a minimum near the transverse exciton frequency and a maximum near the longitudinal exciton frequency, in agreement with expected polariton behaviour. Thickness dependent polariton states have finite absorption and fluorescence transition probabilities (due to crystal inhomogeneities) and are observed below the transverse exciton frequency. These polariton states represent the energy reservoir for excitation energy in the bulk of the crystal. A surface-induced exciton state is the origin of the sharp line fluorescence from pure crystals and accounts for the high efficiency of stimulated fluorescence at low temperatures. Stimulated fluorescence can also be observed from the polariton modes when excitation occurs in these modes. Resonance interactions between polariton modes and impurity levels represent an important pathway for fluorescence quenching in crystalline anthracene.     

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.     

Interpretation of the optical dephasing time and lineshape function in the S0 → T1 exciton transitions of 1,4-dibromonaphthalene

The lineshape function for the S₀ → T₁ absorption in 1,4-dibromonaphthalene (DBN) is analyzed in terms of exchange theory. It is shown that the dominant optical dephasing mechanism for the electric dipole transition to the k = 0 state in the band results from the absorption and emission of a low energy optic phonon. This process dephases the optical absorption because of frequency differences of the phonon in the ground and excited state. In addition, it is shown how to extract the energy of the phonon responsible for dephasing, the phonon absorption rate, and the lifetime in the phonon promoted state from the data. The analysis of the data for DBN shows that very little dephasing of the optical transition occurs before ≈ 15 K but from 15 K to ≈ 40 K the singlet-triplet transitions to site I (20192 cm^?1) and site II (20245 cm^?1) are dephased by absorption and emission of an ≈ 38 cm^?1 and 45 cm^?1 phonon respectively. The phonon absorption rates by the k = 0 state in the exciton band are similar for both sites being 5 × 10⁶ s^?1 and 3 × 10⁵ s^?1 at 4 K and 7 × 10¹¹ s^?1 and 4 × 10¹¹ s^?1 at 30 K for site I and II respectively. Finally, the lifetimes in the phonon promoted state for sites I and II are 0.23 and 0.28 ps over the range 15–40 K.     

Thermal broadening of the J-band in disordered linear molecular aggregates: a theoretical study

We theoretically study the temperature dependence of the J-band width in disordered linear molecular aggregates, caused by dephasing of the exciton states due to scattering on vibrations of the host matrix. In particular, we consider inelastic one- and two-phonon scatterings between different exciton states (energy-relaxation-induced dephasing), as well as the elastic two-phonon scattering of the excitons (pure dephasing). The exciton states follow from numerical diagonalization of a Frenkel exciton Hamiltonian with diagonal disorder; the scattering rates between them are obtained using the Fermi golden rule. A Debye-type model for the one- and two-phonon spectral densities is used in the calculations. We find that, owing to the disorder, the dephasing rates of the individual exciton states are distributed over a wide range of values. We also demonstrate that the dominant channel of two-phonon scattering is not the elastic one, as is often tacitly assumed, but rather comes from a similar two-phonon inelastic scattering process. In order to study the temperature dependence of the J-band width, we simulate the absorption spectrum, accounting for the dephasing-induced broadening of the exciton states. We find a power-law (T(p)) temperature scaling of the effective homogeneous width, with an exponent p that depends on the shape of the spectral density of the host vibrations. In particular, for a Debye model of vibrations, we find p approximately 4, which is in good agreement with the experimental data on J aggregates of pseudoisocyanine [I. Renge and U. P. Wild, J. Phys. Chem. A, 101, 7977 (1997)].     

Temperature-dependent relaxation of excitons in tubular molecular aggregates: Fluorescence decay and stokes shift

We report temperature-dependent steady-state and time-resolved fluorescence studies to probe the exciton dynamics in double-wall tubular J-aggregates formed by self-assembly of the dye 3,3'-bis(3-sulfopropyl)-5,5',6,6'-tetrachloro-1,1'-dioctylbenzimidacarbocyanine. We focus on the lowest energy fluorescence band, originating from the inner cylindrical wall. At low temperatures, the experiments reveal a nonexponential decay of the fluorescence, with a typical time scale that depends on the emission wavelength. At these temperatures we also find a dynamic Stokes shift of the fluorescence spectrum and its nonmonotonic dependence on temperature under steady-state conditions. All these data indicate that below about 20 K the excitons in the lowest fluorescence band do not reach thermal equilibrium before emission occurs, while above about 60 K thermalization on this time scale is complete. By comparing the two lowest fluorescence bands, we also find indications for fast energy transfer from the outer to the inner wall. We show that the Frenkel exciton model with diagonal disorder, which previously has been proposed to explain the absorption and linear dichroism spectra of these aggregates, yields a quantitative explanation to the observed dynamics. To this end, we extend the model to account for weak phonon-induced scattering of the localized exciton states; the spectral dynamics are then described by solving a Pauli master equation for the exciton populations.     

One-dimensional J-aggregates: Dependence of the properties of the exciton band on the model of the intermolecular coupling

The spectral properties of one-dimensional thiacarbocyanine dye aggregates were simulated by the combination of exciton interaction with a diagonal energetic disorder. Contrary to previous models incorporating disorder, the exciton interaction was calculated using the transition densities obtained form PPP-wave functions and interactions between all molecules were considered. The effects of the aggregate size, non-nearest neighbor interactions, diagonal disorder and to some extent exciton phonon coupling on the spectral position of the maxima, the FWHM of the spectra and the superradiance are investigated for H- and J-aggregates at 298 and 20 K. At 298 K the experimental properties of H-aggregates and J-aggregates of 3,3^′-disulfopropyl-5,5^′-dichloro-carbocyanine with 1 molecule per unit cell are compared to the simulations.     

Laser studies of vibrational energy transfer and relaxation of CO trapped in solid neon and argon

The infrared emission of CO trapped in solid Ne and Ar is observed at low temperature. The first vibrational level of ¹²C¹⁶O is excited by a Q-switched frequency doubled CO₂ laser. The emission spectrum consists of several lines arising from upper vibrational levels of ¹²C¹⁶O and also of ¹³C¹⁶O and ¹²C¹⁸O which are present in natural abundance. An interpretation is proposed which is based on the assumption that long range dipole—dipole interaction is the main physical process involved in these experiments. Resonance energy transfer produces an energy migration among ¹²C¹⁶O molecules without any change in vibrational populations. Phonon assisted energy transfer takes place between vibrational levels of the various isotopic species present in the solution. In order to satisfy the resonance condition a phonon is emitted or absorbed whose energy compensates for the energy mismatch between the transitions in each interacting molecule due to isotopic effect and or vibrational anharmonicity. The range of this process is greatly extended by energy migration. At the low phonon bath temperature phonon emission is much more probable than phonon absorption. So a strong excitation of upper vibrational levels with in some cases population inversions is observed.Molecular impurities act as efficient quenching centers even at very low concentration. When highly purified samples are used, the fluorescence decay time is found to be 20.6 ms in Ne and 14.5 ms in Ar and does not significantly depend upon concentration and temperature. It is concluded that radiationless relaxation is unimportant.     

Exciton-phonon coupling and disorder in the excited states of CdSe colloidal quantum dots

We study the origin of the spectral line shape in colloidal CdSe nanocrystal quantum dots. The three-pulse photon echo peak shift (3PEPS) data reveal a temperature-independent fast decay, obscuring the quantification of the homogeneous linewidth. The optical gap and Stokes shift are found to have an anomalous behavior with temperature, which is size, capping group, and surrounding polymer matrix independent. Using these results and combining them with simulations, we discuss the role of exciton-phonon coupling, static inhomogeneity, exciton fine structure, and exciton state disorder in the linewidth of the nanocrystal. In particular, our analysis shows that the disorder due to surface imperfections and finite temperature effects, as well as the relaxation within the fine structure, can have significant impact on the steady-state absorption spectrum, 3PEPS data, and dephasing processes.