Exciton Band Structure Research Articles

Magnetic fine structure of triplet exciton bands in molecular crystals: 1,2,4,5-tetrachlorobenzene

The quantum mechanics of triplet excitons in molecular crystals is used to determine the effect of a finite excitation transfer interaction between interchange equivalent molecules on the exciton dispersion and density of states and on the zero field spectral density functions for intraband branch—branch transitions. Four cases of specific interest M > D,E; M ≈ D,E; M < D,E; and M ≈ 0 arise where M is the excitation transfer integral and D and E are the molecular magnetic fine structur parameters. Of these, only M > D,E and M ≈ 0 have been considered previously. The effects are illustrated for parameters of the 1,2,4,5-tetrachlorobenzene crystal.

Triplet exciton band structure of crystalline phenazine

The structure of the lowest triplet state of crystalline phenazine was studied by optical and magnetic resonance techniques. The exciton band was characterized by a large translationally equivalent splitting (17 ± 1 cm −1) which was determined from the resonance pair spectrum. The spin splittings were obtained using the optical detection of magnetic resonance of phosphorescent phenazine crystals at 1.5 K.

The decay of localized states into delocalized band states. Theory and preliminary experimental investigations using optically detected electron spin coherence

A technique for measuring the decay of localized excited triplet states into the delocalized band states of a solid utilizing the optical detection of electron spin coherence is described. Specifically, the use of optically detected electron spin locking for measuring kinetic phenomena in the presence of fluctuating triplet spin sublevel populations is presented and illustrated. In addition, preliminary experimental data is reported which yields the temperature dependence of the phonon assisted promotion of a localized isotopic site to an energy equal to that associated with the energies of the host exciton band. Finally, the data is analyzed in terms of a kinetic model which relates the localized state's rate of promotion and radiationless decay into the exciton band states to explicit features of the exciton and phonon band structure.

Exciton spectra of molecular crystals

ABSTRACT The present methods of investigation of the exciton band structures in molecular crystals, which are mainly based on the study of the interaction of excitons with isotopic impurities and intramolecular phonons, are considered. A review and an analysis of the wide range of papers on this problem are given. The results obtained so far on the exciton energy spectrum in benzene, naphthalene and anthracene are discussed.

Exciton band structure of crystalline anthracene

The density of states in the first exciton band of crystalline anthracene has been obtained at room, dry-ice-alcohol, and liquid nitrogen temperatures by applying a thermal modulation technique to observe the hot band-first exciton band optical transition (1-0 transition). The density of states function obtained has been interpreted in terms of the exciton band structure and the Davydov splitting. The K dependent selection rule for the 1-0 transition is discussed. The bandwidth of the first exciton band is 0.09 eV.

Probing the non-analytic properties of exciton band structures by reflection spectroscopy

A method of probing the exciton band structure about the centre of the Brillouin zone is developed. Oblique angle reflectance spectra at angles of incidence up to 80° for a (001) face of an anthracene crystal have been obtained for both an air-crystal and a silica-crystal interface. A method for transforming the reflectance data to optical constants is developed and used. From this method the direction of propagation of radiation k̂ at any frequency inside the crystal for any incident angle can be determined. For a model of an isotropic crystal consisting of anisotropic molecules, dipole-dipole theory for an arbitrary k̂ is developed, exciton band structures from this theory are calculated and theoretical spectra based on these calculated band structures are presented. The theoretical spectra are in very good agreement with the experimental data. Information about the exciton density of states is deduced from the results.

Planewise summation of point dipole-dipole interactions for some aromatic hydrocarbon crystals

Lattice sums of point dipole-dipole interactions have been evaluated by the method of planewise summation for wave vectors perpendicular to the (001) plane of aromatic hydrocarbon crystals. The interaction between a plane of dipoles and a single dipole located at the origin is called a plane sum. It is found that the magnitude of plane sums falls off very rapidly with perpendicular distance of the plane from the origin. The contribution from all plane sums not containing the origin is less than 10% of the total lattice sum for naphthalene, approximately 1% for anthracene and phenanthrene, and negligible in the cases of tetracene and pentacene. Some results for L axis dipoles on translationally inequivalent molecules are given below (units cm−1/Å2). I1L,2L(0) is the plane sum for the plane containing the origin, I1L,2L(1) is the nearest neighbor plane sum, and Ewald sum is the infinite crystal lattice sum. CrystalI1L,2L (0)I1L, 2L(1)Ewald sumNaphthalene3333−573219Anthracene2701−202661Tetracene4577−14575Pentacene463104631Phenanthrene424654255It is suggested that the existence of weakly coupled crystal planes simplifies the theoretical treatment of several exciton processes. A brief discussion is given for absorption and reflection spectra, exciton band structure and exciton-phonon coupling.

Exciton Band Structure and Properties of a Real Linear Chain in a Molecular Crystal

An experimental study is presented that leads to the elucidation of the whole band structure for the triplet exciton state of 1,4-dibromonaphthalene. We show that the band states are essentially those of a linear chain characterized by nearest neighbor interactions along the c crystallographic axis. Although the crystal is topologically a three-dimensional network, for the practical purpose of energy transfer and trapping the crystal behaves as a set of linear chains. Heavy doping of DBN-h6 (host) with up to 18% DBN-d6 (guest) yielded the expected discrete spectra of a random linear array corresponding to a nearest neighbor interaction of 7.4± 0.1 cm−1 and total bandwidth of 29.6± 0.4 cm−1 for the zero-zero transition. A symmetric mode at 0+520 cm−1 was shown to have an exciton bandwidth of 15 cm−1, and an unsymmetric vibrational level at 0+250 cm−1 was shown to have a vanishing bandwidth in accordance with expectations from weak coupling theory. The quasiresonance interactions of host and guest were significant and were included in establishing the agreement between experiment and calculation. The total bandwidth is estimated to be 90± 20 cm−1. This type of doping has an effect on line shape even at very low concentration and even in undoped crystals the line shape is asymmetrical, perhaps due to impurities and imperfections that have small zero-order shifts from the band center. The intensity of transitions to the carbon-13 isotopic traps is shown to be distributed over the band states in the origin and is clearly visible in the narrow band nontotally symmetric vibrational state. The vibrational analysis of the crystal spectrum (electronic or vibrational states) is shown to be dependent on exciton effects even in the case where no Davydov splitting is observed. Spectra of DBN-h6 (guest, H) in DBN-d6 (host, D) were also studied and resonance multiplets were seen and identified in absorption and emission. We identified ··· DHD···, ··· DHHD···, ··· DHHHD···, and probably ··· DHDHD··· in the phosphorescence spectra at 2°K. We present a brief discussion of the effect of dimensionality on the dynamical features of energy transfer and trapping, and we show experimentally, that heavy doping (d6 in h6) enhances the phosphorescence of the crystal about 60-fold. In addition the existence at 2°K of a Boltzmann distribution over resonance multiplets leads us to propose a long-range trap-to-trap migration as part of the thermalizing process.

Application of the Coherent Potential Approximation to the Excited Electronic States of Substitutionally Disordered Molecular Crystals

In this paper we apply the coherent potential approximation for the calculation of the density of excited electronic states and of the optical properties of a variety of isotopically mixed molecular crystals where the pure crystal exciton band structure and density of state is determined by one, two, and three dimensional interactions. The crystal Hamiltonian is characterized by a random diagonal part and by a translationally invariant off diagonal part. Numerical results are provided for the following systems: (a) a one dimensional chain in the amalgamation limit, in the persistence case and in the separated bands limit; (b) the lowest triplet state of naphthalene in the separated bands case; (c) the lowest singlet state of naphthalene in the amalgamation limit, in the persistence case and in the separated bands limit. (d) The lowest singlet state of benzene in the persistence case and in the separated bands limit. These calculations demonstrated the general features of the density of states in substitutionally disordered crystals, such as the erosion of the Van Hove singularities in the band(s), and the nature of the intensity distribution such as number of Davydov components, their relative intensities, location, and widths. The predictions of the CPA for the moments of the density of states and for the optical properties concur with the predictions of the general moment expansion method for a configurationally averaged crystal. A general CPA scheme is provided to handle tertiary mixed crystals, which are of some experimental interest. To account for the concentration dependence of the optical properties of isotopically mixed benzene, we provide a semiquantitative extension of the CPA scheme, where the isotope effect on the environmental shift term is incorporated into the virtual crystal Hamiltonian resulting in concentration dependent diagonal terms in the crystal Hamiltonian.

Exciton Superexchange, Resonance Pairs, and Complete Exciton Band Structure of B12u Naphthalene

A method for the determination of complete exciton band structures in molecular crystals is given. Pairwise exciton interactions are derived from resonance-pair data using an exciton “superexchange” approach. Koster and Slater's impurity cluster formulation is found to be applicable to nontrivial interchange symmetry systems, within the “restricted Frenkel–Davydov” theory. The derivation starts from the recent general formulation for isotopically mixed crystals of arbitrary concentrations. The resonance pair states are given by the second-order self-energy of the mixed crystal Green's function. General symmetry arguments and moment sum rules have been worked out for resonance pairs. It is demonstrated for naphthalene-h8 resonance pairs in naphthalene-d8 that superexchange corrections are not only inevitable for the B12u pair states but that they can also be utilized to assign experimental pairwise interactions to definite crystal directions, i.e., specific pairs. The naphthalene first singlet excited state 0–0 vibronic exciton band is successfully described by the “restricted Frenkel–Davydov” dispersion relation: ε(k±) = ∑ e Meexp(ik·Re ± ∑ i Miexp(ik·Ri), where e = a, b, c, (a + c) and i = 12(a + b), [12(a + b) + c]. Three sets of M's that are consistent with all resonance-pair and monomer mixed crystal data are tabulated. The only one consistent with a multipole expansion gives for the Me's and Mi's, respectively, − 0.6, − 3.9, − 3.7, 6.1, and 18.0, 2.0 cm−1. This point multipole expansion is safely limited to nonnearest-neighbor interactions and truncated beyond transition octopoles (Q31c = 7 and Q33c = 72 Å3). The translational shift is − 4.5 ± 4 cm−1, and the hot-band density-of-states function has been independently reproduced from the mixed crystal data, indicating that exciton–phonon coupling is small. The results are compared with ab initio calculations and new criteria for theoretical computations are suggested.

Local Excitons and Exciton Band Structure in Naphthalene

AbstractPositions of the electron levels of the local exciton energy in a naphthalene crystal doped with thionaphthene, indole, and benzofurane are calculated. The guest molecule is assumed to change the excitation energy of one host molecule nearest to the impurity. Also it is considered that the main contribution to the exciton dispersion law comes from the matrix elements of resonance interaction between nearest naphthalene molecules which are in inequivalent positions in the ab plane of the crystal. Good agreement between the theoretical and experimental values favours the validity of the chosen local centre model and exciton dispersion law employed.

Calculation of the Exciton Band Structure of the 3800- and 2500-Å Singlet Transitions of Crystalline Anthracene

The exciton band structure of the 3800- and 2500-Å transitions of anthracene has been calculated in the dipole approximation. It is found that the branches of both transitions are flat for wave vectors k normal to the (001) plane. In other directions considered the exciton energy exhibits dispersion. The calculations also reveal that for all the directions considered the lowest energy of the 2500-Å exciton band is not a k = 0 state.

Frenkel Exciton Superexchange, Pair Interactions, and Dispersion Relation:B2u1Naphthalene Crystal

Guest-host-guest exciton exchange (superexchange) is appreciable in the $^{1}B_{2\mathrm{u}}$ state of a ${\mathrm{C}}_{10}$${\mathrm{H}}_{8}$-${\mathrm{C}}_{10}$${\mathrm{D}}_{8}$ mixed crystal. The experimental resonance pair fine structure in this system has been satisfactorily fitted, resulting in three sets of six pairwise exciton interactions, consistent with all known experimental data. A point multipole expansion, limited to nonoverlapping charge distributions and truncated after the transition-octupole-transition-octupole term, is only consistent with one set, whose values are presented. Using these values, the exciton band structure is completely determined within the restricted Frenkel limit.

Information on the Exciton Band Structure of the 1B2u State of Crystalline Naphthalene from the Variation of Energy Denominators Method

Perturbation shifts of guest levels in isotopic mixed crystals of naphthalene have been determined. These data verify that the density function for exciton states is almost symmetric over the entire exciton band of the first singlet state. This result agrees with the entire band structure as observed in band-to-band transitions and disagrees with the band structure calculated from the octopole model for the inter-molecular interaction. The transition energies of guest levels also disagree with a model for the exciton splitting involving configuration interaction with charge transfer states. A possible source of the exciton splitting is suggested, and the available data for evaluating theoretical descriptions are outlined.

Das Fluoreszenzspektrum von Anthracen-Kristallen

The fluorescence spectrum of extremely purified and good anthracene crystals has been re­measured. It is compared with the exciton band structure as calculated by Davydov and Sheka. The origin of the intrinsic fluorescence is at 25 097 cm-1. This is the lower edge of the exciton band with k ≠ 0. Therefore this 0.0-transition is forbidden. The allowed 0.0.transition of the lower Davydov component of the exciton band is observed at 25 298 cm-1 with very low intensity. This is the position of the very short living state k = Q (Q=photon wave vector) in the exciton band. Further observations concerning the structure and temperature dependent width of emission lines, the nature of exciton-phonon and exciton-vibron coupling and the large band width in absorption are also in good agreement with the calculated band structure. The polarization ratio of the strongest vibronic transitions is 7.5 ± 1 good agreement with the oriented gas model. The spectral region near the forbidden 0.0-transition is completely 6-polarized. Effects of defects in the spectrum (series of lines due to impurities and X-traps, continuous back­ground) were widely eliminated. They are discussed here only as far as necessary for a better understanding of the unperturbed crystal spectrum. In an appendix a list of 154 fluorescence lines is given.

Exciton Band Structures in Polypeptides

The singlet and triplet states of π-electrons in peptide group are first determined such that the ASMO-SCF-CI calculation including all the possible configurations can reproduce the observed wavelength of optical absorption maximum. It is shown that the doubly-excited configurations make a non-negligible contribution to the electronic states. Next, in terms of the Frenkel-Peierls method, the singlet and triplet exciton bands for both the H-bonded and the main polypeptide-chains in the two β-structures and in the α-helix are calculated to the second-order perturbation. It is shown that the exciton band structures are dependent only on the sorts of peptide-chains but non on the conformations, and that the interaction between bands does not exert any important effect on the structures.

Band structure limits for anthracene triplet excitons from magnetic resonance

A general expression for NMR relaxation relates the anthracene triplet exciton band-structure to magnetic resonance data. Limiting ranges for the exciton band breadth, B ex , are thereby specified: 1.6 × 10 9 sec -1 < < B ex < 9 × 10 9 sec -1 or B ex > 1.7 × 10 11 sec -1.

Effects of pressure and temperature on exciton absorption and band structure of layer crystals: Molybdenum disulphide

The effect of pressures of up to 60 kbars on the exciton series in the spectral region of 2 eV in molybdenum disulphide has been investigated at room and liquid nitrogen temperatures, using a diamond anvil device. An electronic band model, suggested by the crystallography of the layered material and the optical spectra of the various polytypes, is made the basis for the discussion of the experimental results. An indirect energy gap of 0.25 eV determines the electrical properties of the intrinsic material, but transitions from a lower, spin-orbit split valence band produce the exciton series and fundamental absorption edge. It is shown that under these circumstances the pressure coefficient of an exciton peak can be separated into two parts; the pressure coefficient of the direct gap and the pressure dependence of the exciton binding energy which is a result of changes in the free carrier density that are necessarily related to the pressure variation of the indirect gap.

Polarization Investigations of Localized Exciton States of Doped Benzene Crystals

AbstractThe absorption spectra of localized exciton states of benzene crystals doped with heterocyclic compounds are studied at T = 4.2 °K using polarized light. When the localized level approaches the exciton A‐band edge, the intensity of the localized absorption is shown to increase anomalously in the a‐component and to decrease in the c‐component of the absorption spectrum. Simultaneously the A‐band is partly depolarized and shifts towards the violet side. The experimental results obtained favour certain conclusions about the exciton band structure and the exciton effective mass and are qualitatively interpreted on the basis of current theories of localized states.

Exciton Band Structures in Homopolynucleotides

Singlet exciton band structures in single stranded homogeneous polynucleotides have been determined within the framework of Frenkel exciton model without or with interband configuration mixing. Intermonomer interactions are taken into account to a distance of the order of 20A using the best available π-electron molecular orbitals obtained by us in the previous study. Configuration mixing between lowest nine exciton bands is taken into account explicitly. Mixing process seems to be very important to determine reliable band widths, especially in poly A. Obtained band widths are 0.64 eV in poly A, 0.34 eV in poly U, 0.55 eV in poly G and 0.26 eV in poly C respectively without configuration mixing and 0.25 eV in poly A, 0.34 eV in poly U, 0.49 eV in poly G and 0.23 eV in poly C respectively with configuration mixing. In poly A and poly U the absorption maximum corresponding to the lowest excitation slightly shifts to the short wave length side from that of monomer. On the contrary, appreciable red shifts can ...