Transport of excitation energy in a three-dimensional doped molecular crystal

We report here a theoretical formulation of the transport of excitation energy in a three-dimensional molecular crystal containing one impurity. The excitation is assumed to be localized in the jth site at time t, and the expression for the probability of finding the excitation at some other site j′ at a later time t′ is derived. The probability is given by the correlation function $ \left\langle {\hat P_j (t)\hat P_j (0)} \right\rangle $, where $ \left\langle {\hat P_m } \right\rangle $ represents the site projection operator, |m〉 〈m|. In our derivation we neglect the interaction among excitons of different bands, account for the presence of the impurity by adding a small perturbation term to the pure crystal Hamiltonian, and calculate the exciton solutions through first order. We consider a general impurity; that is, the trap depth is nonvanishing and may even be complex. The exciton–phonon interaction is taken to be linear in lattice displacement vectors; we assume that the short time behavior of $ \left\langle {\hat X} \right\rangle _{{\rm phonon}} $ gives the dominant contribution to the physical property X being studied and solve the dynamical problem by using a time-dependent effective potential consisting of fluctuations around the equilibrium average exciton–phonon interaction. Several limiting cases are briefly discussed.     

Transport of excitation energy in a doped molecular aggregate. III. numerical investigation of exciton hopping with various exciton-depleting processes

A brute-force numerical investigation has been carried out on the hopping of excitons in a three-dimensional molecular aggregate. Possibilities of vibronic decay, rapid chemical reactions of saturated species, radiative decay of overpopulated molecules, and cooperative chemical reactions involving saturated exciton populations on traps of two different types have been considered. Investigation have been performed with two types of initial distribution of excitons—facial and random—and for 10,000 or, sometimes, for 20,000 time steps each of duration 1ps. Several interesting observations have been made from this computer experiment: (1) The total number of occurrences of fast reactions depends upon the initial distribution of excitons. (2) It decreases if other exciton depleting processes are at work. (3) It also depends on the pattern of placement of traps. (4) The location of impurities also affects the rate of occurrence of these reactions. Thus, more reactions occur when the excitons are initially concentrated on one face and traps are suitably located on the path of flow of these excitons. A random initial distribution tends to equilibrate the excitons quickly over all the lattice points, thus giving rise to fewer reactions. (5) The number of reactions need not necessarily increase with the number of reaction centers; in fact, it decreases as more centers are added when the supply of excitons is severely limited. (6) A Complicated dynamics results when different types of additional processes, viz., enhanced fluorescence, radiative emissions, and cooperative chemical reactions are simultaneously allowed. The cooperative process has been clearly found to dominate. A first-order rate constant of about 10⁸ s-¹ has been calculated for the occurrence of the cooperative process. This rate is affected when other nonconserving processes are switched on. Observations (1), (4), and (5) are the most important conclusions of our work. They lie outside the scope of traditional models such as the random walk model, the diffusion model, and the lattice model for the migration of excitons in a molecular aggregate. © 1993 John Wiley & Sons, Inc.     

Transport of excitation energy at impurities distributed randomly in a three-dimensional crystal lattice

Using the continuous time random walks, the decay probability of an excitation at an impurity site is calculated numerically employing a general fractal distribution function in a three-dimensional disordered lattice. Results agree well with the previously calculated theoretical probabilities and also with experimental results.     

Polarization energy of a localized charge in a molecular crystal. IV. Effect of polarizability changes

The Fourier transform method and submolecule treatment described previously are used to derive an exact expression for the change ΔP in polarization energy of a localized charge when some of the surrounding molecules have polarizabilities different from those in the perfect crystal. The crystal structure is assumed unchanged. The method can be applied to vacancies, charged exciton complexes and X traps. It is illustrated by calculations of ΔP for isolated unrelaxed vacancies in anthracene. If the charge is not too near the vacancy, ? ΔP equals the charge-induced-dipole energy in an isotropic continuum having the average dielectric constant for anthracene.     

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.     

Transfer of excitation energy in a three-dimensional-doped molecular crystal. V. Self-consistency of the temporal processes involved in energy transfer in photosynthetic units

Numerical experiments were carried out to determine the timewise self-consistency of different physical processes involved in the energy transfer in green plant photosynthetic units. A 6 × 6 × 6 array of chlorophyll-a with cubic lattice constants a = b = c = 20 Å was chosen as a model of the thylakoid disc. Another model aggregate was obtained by substituting chlorophyll-b molecules for some of the chlorophyll-a molecules. In both models, a reaction center occupied a central site in the last xy plane. Two extreme arrangements were considered for the orientation of molecules. In one, the transition moments of all molecules were directed along the y-axis. The other had chlorophyll molecules randomly oriented. The four resulting model systems were used in our investigation on exciton generation, transport, decay by fluorescence, and trapping. All excitons were assumed to be generated by a 20 ms exposure to sunlight at high altitudes. The general trends noticed from these computations are as follows: The number of excitons generated is influenced by lattice disorders. Disorders also increase the time for the establishment of an equilibrium distribution. The decay of excitons by fluorescence is always a monotonic function of time. The energy transfer is adversely affected by a lower degree of orientation in the crystal: The trapping time increases with disorder. The number of trappings decreases with the onset of fluorescence of the host molecules and the trap. From these investigations, we also made three specific observations: (1) The efficiency of exciton utilization varies from 12% for a completely random arrangement of transition dipoles to 46% for a perfectly ordered arrangement. This agrees with the experimental efficiency, about 20%. (2) The number of excitons trapped varies from one to six. This tallies with the time scale of electron transfer along the Z-scheme that requires at least two excitons trapped in about 20 ms. Thus, the photon density and the exciton transfer rate are consistent with the rates of electron transfers. (3) The trapping rate also indicates that the thylakoid disc must resemble a considerably ordered system. © 1996 John Wiley & Sons, Inc.     

Role of diffusion in excitation energy transfer and migration

Effect of diffusion on excitation energy transfer and migration in a dye pair sodium fluorescein (donor) and Rhodamine-6G (acceptor) has been studied for different viscosities by both steady state and time domain fluorescence spectroscopic measurements. The donor-donor interaction appears to be weaker as compared to donor-acceptor interaction and thus favors direct Forster-type energy transfer. Interestingly, at low viscosity (water in this case) transfer appears to be controlled by material diffusion/energy migration. Further, acceptor dynamics reveals the fact that direct Forster transfer dominates in viscous media.     

Electronic energy trapping in a crystal due,to a dopant of higher excitation energy than the host

An excimer emitting crystal (9-cyanoanthracene) doped with a guest molecule (9-methoxyanthracene) having its first singlet level ca. 2000 cm^?1 above the host singlet exciton band exhibits efficient energy trapping as demonstrated by host sensitized, red-shifted emission and hetero-photodimerization. It is considered that the trapping is due to exciplex formation between host and guest molecules.     

Statistical treatment of exciton decay near the interface between a molecular crystal and a metal

A random-walk model is developed to describe transport and decay of Frenkel excitons in a molecular crystal near an absorbing contact taking into accou     

Negative polaron and triplet exciton diffusion in organometallic "molecular wires"

The dynamics of negative polaron and triplet exciton transport within a series of monodisperse platinum (Pt) acetylide oligomers is reported. The oligomers consist of Pt-acetylide repeats, [PtL(2)-C≡C-Ph-C≡C-](n) (where L = PBu(3) and Ph = 1,4-phenylene, n = 2, 3, 6, and 10), capped with naphthalene diimide (NDI) end groups. The Pt-acetylide segments are electro- and photoactive, and they serve as conduits for transport of electrons (negative polaron) and triplet excitons. The NDI end groups are relatively strong acceptors, serving as traps for the carriers. Negative polaron transport is studied by using pulse radiolysis/transient absorption at the Brookhaven National Laboratory Laser-Electron Accelerator Facility (LEAF). Electrons are rapidly attached to the oligomers, with some fraction initially residing upon the Pt-acetylide chains. The dynamics of transport are resolved by monitoring the spectral changes associated with transfer of electrons from the chain to the NDI end group. Triplet exciton transport is studied by femtosecond-picosecond transient absorption spectroscopy. Near-UV excitation leads to rapid production of triplet excitons localized on the Pt-acetylide chains. The excitons transport to the chain ends, where they are annihilated by charge separation with the NDI end group. The dynamics of triplet transport are resolved by transient absorption spectroscopy, taking advantage of the changes in spectra associated with decay of the triplet exciton and rise of the charge-separated state. The results indicate that negative polarons and excitons are transported rapidly, on average moving distances of ~3 nm in less than 200 ps. Analysis of the dynamics suggests diffusive transport by a site-to-site hopping mechanism with hopping times of ~27 ps for triplets and <10 ps for electrons.     

Self-trapping limited exciton diffusion in a monomeric perylene crystal as revealed by femtosecond transient absorption microscopy

Self-trapping and singlet-singlet annihilation of the free excitons in a monomeric (beta) perylene crystal were studied by using femtosecond transient absorption microscopy. The free exciton generated by the photo-excitation of the beta-perylene crystal relaxed to the self-trapped exciton with a rate constant of 7 x 10(10) s(-1). The singlet-singlet annihilation of the free exciton observed under the high excitation density conditions was competed with the self-trapping of the free exciton; we estimated the annihilation rate constant for the free exciton to be 1 x 10(-8) cm(3) s(-1) from the excitation density dependence of the free exciton decay. After self-trapping of the free exciton, no annihilation was observed in the 100 ps time range, suggesting that the diffusion coefficient was reduced drastically by self-trapping. The results show that the major factor limiting the exciton diffusion in the beta-perylene crystal is a relaxation of the free exciton to the self-trapped exciton, and not the lifetime of the exciton. Though the singlet-singlet annihilation rate constants and fluorescence lifetime of the beta-perylene crystal are similar to those of the anthracene crystal, the estimated exciton diffusion length (2 nm) in the beta-perylene crystal is much smaller than that (100 nm) in the anthracene crystal as a result of the exciton self-trapping.     

Study of exciton transport in luminescent molecular nanoclusters using energy traps

We used a squarylium dye SQ as a specific exciton trap for J aggregates of the amphiphilic cyanine dye amphi-PIC. The exciton transport parameters in amphi-PIC J aggregates were estimated using a modified Stern–Volmer equation. We found that SQ quenches 50% of the luminescence of amphi-PIC J aggregates for a ratio of 1 SQ molecule per 80 amphi-PIC molecules. Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 45, No. 1, pp. 50–53, January–February, 2009.     

Polarization energy of a localized charge in a molecular crystal. VI. Effect of excitons

The polarization energy of a localized charge carrier in a molecular crystal changes by ΔP near an exciton, viewed as a localized excited molecule of changed polarizability. Experimental polarizability changes in the first excited singlet state are used to calculate ΔP for various carrier and exciton positions in benzene, naphthalene, anthracene and tetracene. As the excited-state polarizability is larger, ΔP is normally negative, with minima ranging from ?12 meV in benzene to ?83 meV in tetracene. The change in charge-quadrupole energy ΔW_Q is estimated for naphthalene using a theoretical quadrupole moment for the first triplet state. At most sites |ΔW_Q| > |ΔP|, but the sign of ΔW_Q varies. The net exciton interaction with electrons in naphthalene varies from ?49 to +45 meV and with holes from ?106 to +29 meV. This behaviour is broadly complementary to that previously calculated for vacancies.     

Porphyrin boxes constructed by homochiral self-sorting assembly: optical separation, exciton coupling, and efficient excitation energy migration

meso-Pyridine-appended zinc(II) porphyrins Mn and their meso-meso-linked dimers Dn assemble spontaneously, in noncoordinating solvents such as CHCl3, into tetrameric porphyrin squares Sn and porphyrin boxes Bn, respectively. Interestingly, formation of Bn from Dn proceeds via homochiral self-sorting assembly, which has been verified by optical separations of B1 and B2. Optically pure enantiomers of B1 and B2 display strong Cotton effects in the CD spectra, which reflect the length of the pyridyl arm, thus providing evidence for the exciton coupling between the noncovalent neighboring porphyrin rings. Excitation energy migration processes within Bn have been investigated by steady-state and time-resolved spectroscopic methods in conjunction with polarization anisotropy measurements. Both the pump-power dependence on the femtosecond transient absorption and the transient absorption anisotropy decay profiles are directly associated with the excitation energy migration process within the Bn boxes, where the exciton-exciton annihilation time and the polarization anisotropy rise time are well described in terms of the F?rster-type incoherent energy hopping model by assuming a number of hopping sites of N = 4 and an exciton coherence length of L = 2. Consequently, the excitation energy hopping rates between the zinc(II) diporphyrin units have been estimated for B1 (48 ps)(-1), B2 (98 +/- 3 ps)(-1), and B3 (361 +/- 6 ps)(-1). Overall, the self-assembled porphyrin boxes Bn serve as a well-defined three-dimensional model for the light-harvesting complex.     

The crystal and molecular structure of trimethyltin(IV) chloride, a chlorine-bridged, linear polymer

The crystal and molecular structure of trimethyltin(IV) chloride has been determined by the heavy-atom technique, and refined to a final R value of 0.041 for 1375 independent reflections (2θ < 53°; Mo-K_a radiation I > 2σ(I)) recorded at 138 ± 2 K on a Nonius CAD-4 counter diffractometer. The crystals are monoclinic with space group I2/c; a 12.541(8), b 9.618(11), c 11.015(11) Å, β 92.62(7)°, Z = 8, D_calcd 1.994 g cm⁻³. The needle crystals are composed of polymeric chains of chlorine atoms bridging non-planar trimethyltin(IV) units at unequal (2.430(2) and 3.269(2) Å) distances. The zig-zag chains are bent at chlorine (angle Sn---Cl Sn 150.30(9)°), but nearly linear at tin (angle Cl---Sn Cl 176.85(6)°) to describe a distorted trigonal bipyramidal geometry at tin with the trimethyltin groups eclipsed. The interchain d(Sn Cl) distances are greater than 4.1 Å. The angles carbon—tin—carbon (mean 117.1(3)°) are larger than tetrahedral, while the angles carbon—tin—chlorine (mean 99.9(2) Å) are smaller, in accord with isovalent hybridization principles, but more severely distorted than in the gas-phase, monomeric structure. The tin—chlorine distance of 2.430(2) Å is also longer than in the gas phase monomer, and the intermolecular contact of 3.269 Å is shorter than in other organotin chloride bridged systems (sum of Van der Waals radii 3.85 Å).     

Toward a molecular scale interpretation of excitation energy transfer in solvated bichromophoric systems

This paper presents a quantum-mechanical study of the intramolecular excitation energy transfer (EET) coupling in naphthalene-bridge-naphthalene systems in gas phase and in solution. ZINDO and TDDFT response schemes are compared using both an exact and an approximate solution. The approximate solution based on a perturbative approach uses the single chromophore properties to reconstruct the real system coupling thus neglecting possible through-bond effects which conversely are accounted for in the exact solution. The comparison of the results of the two approaches with the experiments allows a detailed analysis of the relative importance of through-bond and through-space effects as well as a more complete understanding of the modifications in the EET coupling with the size of the system, the chromophore-chromophore distance, and solvation.     

Towards a molecular scale interpretation of excitation energy transfer in solvated bichromophoric systems. II. The through-bond contribution

In this paper we present a quantum-mechanical investigation on the mechanisms which promote intramolecular EET coupling. This investigation is done by using a new computational strategy in which we combine a configuration-interaction and a linear response approach. The combined use of these two methods allows a direct identification and a quantification of both "direct" (coulomb and exchange) and through-bond (superexchange and charge-transfer) contributions. In addition, solvent effects are introduced using the polarizable continuum model. The method is applied to a family of naphthalene-bridge-naphthalene and naphthalene-bridge-anthracene systems, and the results obtained are compared with experiments. The results found suggest that the through-bond charge-transfer effects are not significant when the EET goes through permitted excitations on distant chromophores (see DN4 and DN6) while they become as important as (or even more important than) the covalent terms for EETs involving weakly allowed excitations (see A6N). By contrast, the presence of a very short bridge (in DN2) allows a very efficient delocalization of the excitation energy which is also largely modified by the presence of a solvent.     

Electrical properties and defect chemistry of TiO2 single crystal. IV. Prolonged oxidation kinetics and chemical diffusion

Measurements of both electrical conductivity and thermoelectric power were used to monitor the equilibration kinetics of undoped single-crystal TiO(2) during prolonged oxidation at 1123 and 1323 K and p(O(2)) = 75 kPa. Two kinetics regimes were revealed: kinetics regime I (rapid kinetics), which is rate-controlled by the transport of oxygen vacancies, and kinetics regime II (slow kinetics), which is rate-controlled by the transport of titanium vacancies. The incorporation of titanium vacancies allows undoped p-type TiO(2) to be processed in a controlled manner. The kinetics data were used to determine the chemical diffusion coefficient (D(chem)) associated with the transport of titanium vacancies, which is equal to D(chem) = 8.9 x 10(-14) m(2) s(-1) and D(chem) = 9.3 x 10(-15) m(2) s(-1) at 1323 and 1123 K, respectively.