Exciton Band Structure Research Articles

Controlled Formation of the Two-Dimensional TTBC J-Aggregates in an Aqueous Solution

Strong experimental and theoretical evidence was provided on the controlled formation of the two-dimensional J-aggregates that were assembled in the herringbone morphology. The exciton-band structure formation of 1,1',3,3'-tetraethyl-5,5',6,6'-tetrachlorobenzimidazolocarbocyanine (TTBC) J-aggregates was investigated in ionic (NaOH) aqueous solution at room temperature. The control was achieved by changing the [TTBC] at a given [NaOH], or vice versa, and was monitored through the changes in the absorption, fluorescence excitation, and emission spectra. Specific attention was paid to expose the excited-state structure and dynamics through simulations of the excitonic properties, which included diagonal energetic disorder and phonon-assisted exciton relaxation. Aggregates were characterized by an asymmetrically split Davydov pair, an H-band (approximately 500 nm, 1300 cm(-1) wide, Lorentzian-like) and a J-band (approximately 590 nm, 235 cm(-1) wide, with a band shape typical of a one-dimensional J-aggregate), whose relative intensities showed a strong dependence on the [TTBC]/[NaOH]. The H-band is favored by high [TTBC] or high [NaOH]. An explanation of the control on the aggregate formation was given by correlating the changes in the absorption with the structural modifications and the subsequent changes in the dynamics, which were induced by variations in the dye and NaOH concentrations. The J-band shape/width was attributed to disorder and disorder-induced intraband phonon-assisted exciton relaxation. The intraband processes in both bands were estimated to occur in the same time scale (about a picosecond). It has been suggested that the wide energetic gap between the Davydov split bands (3000 cm(-1)) could get bridged by the excitonic states of the loosely coupled chains, in addition to the monomeric species at low [TTBC]. Phonon-assisted interband relaxation, through the band gap states and/or directly from the H- to the J-band, are suggested for accounting the difference between the bandwidths and shapes of the two bands. Energy transfer between the H-band and the monomeric species is suggested as crucial for tuning the relative strengths of the two bands.

Radiative Lifetime of Excitons in Carbon Nanotubes

We calculate the radiative lifetime and energy bandstructure of excitons in semiconducting carbon nanotubes within a tight-binding approach including the electron-hole correlations via the Bethe-Salpeter equation. In the limit of rapid interband thermalization, the radiative decay rate is maximized at intermediate temperatures and decreases at low temperature because the lowest-energy excitons are optically forbidden. The intrinsic phonons cannot scatter excitons between optically active and forbidden bands, so sample-dependent extrinsic effects that break the symmetries can play a central role. We calculate the diameter-dependent energy splittings between singlet and triplet excitons of different symmetries and the resulting dependence of radiative lifetime on temperature and tube diameter.

Band Structure and Local Dynamics of Excitons in Bacterial Light-harvesting Complexes Revealed by Spectrally Selective Spectroscopy

Hole-burned absorption and line-narrowed fluorescence spectra are studied at 5 K in wild type and mutant LH1 and LH2 antenna preparations from the photosynthetic purple bacterium Rhodobacter sphaeroides. Evidence was found in all samples, even in intact membranes, of the presence of a broad distribution of bacteriochlorophyll species that are unable to communicate energy between each other and to the exciton states of functional antenna complexes. The distribution maximum of these localized species determined by zero phonon hole action spectroscopy is at 783.5 nm in purified LH1 complexes and at 786.8 nm in B850-only mutant LH2 complexes. A well-resolved peak at 807 nm in LH1 complexes is assigned to the exciton band structure of functional core antenna complexes. Similar structure in LH2 complexes overlaps with the distribution of localized species. Off-diagonal (structural) disorder may be responsible for this exciton band structure. Our data also imply that pair-wise inter-chlorophyll couplings determine the resonance fluorescence lineshape of excitonic polarons.

Dispersion of electron–hole excitations in pentacene along (1 0 0)

The dispersion of the lowest lying singlet electron–hole excitation of pentacene along the reciprocal lattice vector (1 0 0) has been studied using electron energy-loss spectroscopy. This exciton shows a clear dispersion along the direction with a band width of about 100 meV. Moreover, the translational symmetry indicated by the exciton band structure does not agree with that reported from diffraction studies. This might be related to the interaction responsible for the dispersion which is of next nearest neighbor type only.

Chain Conformations and Photoluminescence of Poly(di-n-octylfluorene)

The diverse steady-state spectroscopic properties of poly(di-n-octylfluorene) are addressed from a molecular-level perspective. Modeling of representative oligomers support the experimental observation of at least three distinguishable classes of conformational isomers with differing chain torsion angles. One class appears to be populated by a single compact structural isomer, and this conforms to the so-called beta phase. A rigorous Franck-Condon analysis of the photoluminescence in conjunction with Frenkel-type exciton band structure calculations is performed. These results accurately reproduce all major spectral features of the photoabsorption and those of singlet exciton emission.

Characteristics of the two-dimensional infrared spectroscopy of helices from approximate simulations and analytic models

Abstract The characteristics of the two-dimensional infrared (2D-IR) rephasing, non-rephasing, absorptive and dispersive spectra of model helical polypeptides in the amide-I region are examined by simulation in the frequency domain, based on a vibrational exciton Hamiltonian matrix approach. Analytical models and solutions of the exciton band structure, the density of states, and the allowed IR transitions for the simplest cases are presented and compared with simulations. The through space and through bond vibrational anharmonic coupling energies between pair-wise amide units are evaluated by using ab initio density functional theory calculations on glycine di-, tri- and tetrapeptides, and by using the transition charge–transition charge interactions including charge-fluxes. A contour diagram at 5° interval of the nearest neighbor coupling energies for the right-handed helices in the region of −25° to −70° for both φ and ψ dihedral angles is provided. The static diagonal disorder is introduced into the Hamiltonian diagonal frequency through statistical models and is used to account for localizations of the excitations and the inhomogeneous broadening associated with the conformational fluctuations and local interactions with solvent. The role of the anharmonicity in constructing the 2D-IR spectra is described qualitatively, and the manifestations of the given anharmonicity in the 2D-IR spectra under various line broadening conditions are examined. The absorptive and dispersive 2D-IR spectra under several experimental polarization conditions have been examined, and spectral features for the 3 10 -and α-helices have been illustrated.

Intralayer and interlayer energy transfer from excitonic states into the Mn3d5shell in diluted magnetic semiconductor structures

We show that the Dexter-F\"orster-like radiationless resonance energy-transfer process from excitonic states into the Mn ${3d}^{5}$ shell in wide-gap (II,Mn)VI semiconductors is strongly enhanced if the total spin of the overall process is conserved. This requirement cannot be fulfilled in processes involving a bright exciton, i.e., other excitonic complexes or processes need to be involved. Of these we discuss dark excitons, donor-bound excitons ${D}^{0}X,$ negatively charged excitons ${X}^{\ensuremath{-}},$ and an Auger-like process. A careful analysis of the magnetic field and time dependence of the excitonic and Mn luminescence in the (Zn,Cd,Mn)Se samples under study gives evidence that the ${D}^{0}X$ complex plays a dominant role in the intralayer energy transfer. In asymmetric double quantum well (ADQW) structures consisting of a (Zn,Cd)Se well and a (Zn,Cd,Mn)Se well embedded in ZnSe barriers, there is a competition between the intralayer and interlayer energy-transfer processes from excitonic states into the Mn system. These interlayer processes take place between the Mn ions situated in the (Zn,Cd,Mn)Se well and spatially indirect excitons [where the hole is confined in the (Zn,Cd,Mn)Se and the electron confined in the (Zn,Cd)Se] as well as spatially direct excitons of the (Zn,Cd)Se well. The continuous magnetic-field tuning demonstrates convincingly the subtle interplay of excitonic band structure of the ADQW and spin effects in the energy-transfer processes. A spin-dependent energy transfer should be a general feature of rare-earth or transition-metal doped semiconductors such as II-VI or III-V semiconductors or even Er-doped Si or ${\mathrm{SiO}}_{2}.$

EXCITONS IN QUASI-ONE-DIMENSIONAL CRYSTALLINE PERYLENE DERIVATIVES: BAND STRUCTURE AND RELAXATION DYNAMICS

The exciton structure of crystalline MePTCDI (N-N'-dimethylperylene-3,4,9,10-dicarboximide) is modeled by a one-dimensional Hamiltonian, which includes the interactions between Frenkel excitons with several vibronic levels and charge-transfer excitons. Using appropriate fitting parameters, which are verified by quantum chemical calculations, this model can explain the main features of the low temperature absorption spectrum. Polarized absorption spectra show different polarization ratios for the various peaks. This polarization behavior is explained by the varying contribution of the charge-transfer transition dipole, which has a direction different from the Frenkel transition dipole. Our model for the exciton band structure is supported by transient emission measurements.

Charge-transfer exciton band structure in the fullerene crystal-model calculations

A three-dimensional analog of the Merrifield model of the coupling between Frenkel and charge-transfer (CT) excitons of the C60 fullerene crystal is presented. The model is based on the nearest-neighbor approximation for the off-diagonal interactions and is essentially nonempirical. The parameters are estimated from free-molecule data and from the results of theoretical calculations published by other authors. The band structure of CT excitons in C60 is calculated and discussed in the context of available experimental evidence. Residual ambiguities in the parametrization are removed by calculation of the electroabsorption spectrum and comparison with experiment, as described in the accompanying paper.

Polarized fluorescence in α-sexithienyl single crystal at 4.2 K

The polarized fluorescence spectra of the bc plane of α-sexithienyl (αT6) single crystal at T=4.2 K have been measured and analyzed. The spectra show a sharp component superimposed on a broad component. The origin of fluorescence at 18332 cm−1 with a rather narrow linewidth (FWHM=8 cm−1) is completely polarized along b. We assign it to a shallow X-trap 18 cm−1 below the bottom of the 1 1Bu exciton band. The 1 1Bu molecular electronic excited level splits in the crystal in four Davydov components (ag, bg, au, and bu) of which au and bu are dipole allowed. The calculated exciton band structure based on the Ewald sums, assuming the point dipole–dipole approximation, predicts two lowest degenerate Davydov components: an au b polarized component and a forbidden ag component. The fluorescence with the intrinsic sharp vibronic progressions is analyzed in terms of ground state totally symmetric modes which are in excellent agreement with Raman scattering data of the single crystal. Sharp c polarized false origins are identified at 18 167, 18 084, and 18 026 cm−1 and discussed either in terms of X-traps or Herzberg–Teller vibronic coupling with the second higher 2 1Bu molecular level polarized along the in plane short axis. A broad c polarized component is attributed to aggregates.

Energy Transfer and Relaxation Dynamics in Light-Harvesting Antenna Complexes of Photosynthetic Bacteria

The dissipative dynamics of excitons in the outer antenna system of photosynthetic bacteria is investigated using an equation of motion approach. The coupling to environmental degrees of freedom is treated employing Redfield relaxation theory. It is shown that within the secular approximation the concept of essential excitonic states provides a convenient means for reducing the number of coupled differential equations to be solved. Further we derive the appropriate quenching matrix that accounts for the flow of excitation energy between weakly interacting pigment pools. Numerical simulations are presented to emphasize the influence of the various relaxation and dephasing mechanisms as well as the excitonic band structure on the energy transfer.

Excitons in C60 studied by temperature-dependent optical second-harmonic generation.

The electric-dipole-forbidden $^{1}$${\mathit{T}}_{1\mathit{g}}$ excitonic state of solid ${\mathrm{C}}_{60}$ at \ensuremath{\Elzxh}\ensuremath{\omega}=1.81 eV can be probed with a second-harmonic generation (SHG) experiment. We show that the SHG line shape depends strongly on the degree of rotational order. We observe a splitting into two peaks below the rotational ordering phase-transition temperature of 260 K. The origin of this splitting is discussed in terms of a possible Jahn-Teller effect, a possible Davydov splitting due to the four molecules per unit cell in the low-temperature phase, and a mixing of the nearly degenerate $^{1}$${\mathit{T}}_{1\mathit{g}}$ and $^{1}$${\mathit{G}}_{\mathit{g}}$ free molecule states because of the lower symmetry in the solid. The exciton band structure is calculated with a charge-transfer-mediated propagation mechanism as suggested by Lof et al. and with one-electron (-hole) transfer integrals determined from band-structure calculations. Comparison with our experimental SHG data leads to a reasonable agreement and shows that a mixing of $^{1}\mathrm{\ensuremath{\Gamma}}_{1\mathit{g}}$ and $^{1}$${\mathit{G}}_{\mathit{g}}$ states may explain the splitting at low temperature.

Exciton band structures in 2D aggregates of cyanine dyes

Herring‐bone structures (see figure, where the rectangles are the dye molecules and the arrows indicate the oscillation of the transition dipoles) can be classified on the basis of the angle of mutual orientation of the two molecules per unit cell. Those with small angles showing nearly resonant fluorescence emission from the most redshifted transition (J‐aggregates). magnified image

Organic molecular crystals: formation of excimers

For pyrene and α-perylene crystals the formation of excimers is investigated taking into account the sandwich-like arrangement of the molecules in the unit cell. The excitonic band structure consists of broad and narrow bands, which couple in a weak and strong manner, respectively, to the phonons. The antisymmetric states are identified as excimers.

Transport of dipolar excitons in disordered systems

We study the interaction of dipolar excitons in a disordered lattice with a classically fluctuating bath to elucidate the effects of dephasing on phenomena connected with Anderson localization. We find general agreement with recent approximate analytical theory — the existence of incipient localization for dipolar excitons for a sufficiently disordered lattice and for states beyond a quasi-mobility edge. An interesting interplay with the band structure of dipolar excitons leads to some unusual results in the weakly disordered case.

Two-dimensional model of charge transfer excitons in polyacene crystals

A two-dimensional analog of the Merrifield model of the coupling between Frenkel and charge transfer (CT) excitations of a molecular crystal is proposed and applied for the calculation of the band structure of the CT excitons in the crystals of linear polyacenes. The solutions are compared with those obtained within the previously used linear model and the limitations of the latter are discussed. Some possible applications of the new approach for the interpretation of experimental data are suggested.

Band structure of charge transfer excitons in crystalline tetracene

The band structure of low energy CT excitons in tetracene is calculated within the linear crystal model. The results show that, due to the inequivalence of two sublattices, the eigenstates are generally non-degenerate and have a substantial permanent dipole moment. This suggests that the mechanism of electro-absorption may be different in centrosymmetric and non-centrosymmetric polyacene crystals.

Optical spectra of molecular crystals: The effect of exciton band structure on spectra and linewidths

We discuss the spectrum (linewidths and positions) of the first triplet state of the molecular crystals anthracene, napthalene, and phenazine. These crystals have similar exciton bandwidths, but varying amounts of anisotropy in the intermolecular interactions. We analyze the linewidths at zero temperature using isotopic scattering as the broadening mechanism, and the temperature dependence using one and two phonon scattering processes as the broadening mechanism.

Band structure of charge transfer excitons in anthracene

The model applied previously for the interpretation of the electro-absorption spectra of anthracene is used to calculate the band structure of low energy charge transfer excitons for the b direction of that crystal. Possible consequences of the obtained band structure for the interpretation of electro-absorption spectra are discussed. The effect of the coupling between the CT and the Frenkel excitons on the properties of the latter is also addressed.

Theory of Inelastic Low‐Energy Electron Scattering with Generation of Surface and Bulk Excitons in Molecular Crystals

AbstractThe inelastic scattering of electrons on the surface of a semi‐infinite crystal with creation of surface and bulk molecular excitons is considered. Analytical expressions are obtained for the cross‐section of inelastic scattered electrons. The angular and energy dependences of cross‐section are investigated. A strong peak of the electron scattering is noted to be due to definite value of the wave vector of bulk exciton. The possibility to investigate the exciton band structure is discussed.