Exciton trapping by emitting two phonons at impurities in molecular crystals

2005

ABSTRACT:We investigate the exciton dynamics in a molecular crystal. The dynamics is based on the exciton Hamiltonian, the phonon Hamiltonian, and the exciton-phonon interaction linear in phonon coordinates. Using the interaction picture, expressions were previously obtained for the rate of coherent migration of the exciton clothed by phonons, and the rate of incoherent or hopping motion. In this work we derive an expression for the clothed exciton propagator, which permits an explicit calculation of the hopping rate. Thus, the rates of exciton generation, coherent transfer, and hopping are determined completely from theory. These velocity constants, along with the experimental fluorescence decay constants and reaction rate constants for the excited molecules, are used to write a generalized master equation that describes the rate of change of exciton population at each site. The master equation can be numerically solved by using a time step of the order of a few femtoseconds, while the excited-state reactions and exciton transfer occur in the picosecond scale. Exciton dynamics is numerically simulated for a simple model of thylakoid membrane in green plants. The model is based on the known characteristics of thylakoid architecture. The membrane is divided into 97 zones, each zone in the bulk containing 1,442 chlorophylls, one P700, and one P680. The latter two pigments are randomly placed in each zone, while keeping their distance between 55 and 60 Å. This accounts for the randomness in orientation. The disorder of the chlorophyll molecules within the domains of photosystems is neglected. Our findings are as follows. On average, about 6 million photons within the range of 655-681 nm pass through a membrane in 1 s. About 2.3% of incident photons are absorbed by the membrane chlorophyll molecules. For an excitation bandwidth of 70 -175 cm Ϫ1 , the coherent transfer rate between two adjacent molecules is 1.138 Ϯ 0.488 ps Ϫ1 . Because the Debye frequency is expected to be much smaller, the slow phonon limit applies. The exciton-phonon coupling constant that can be determined from the transition dipole-transition dipole interaction model leads to a hopping rate of 0.088 ps Ϫ1 at 300 K. A steady state is effectively achieved for each zone in the bulk in ϳ5 ns. After a period of 50 ns, P700 and P680 in average trap at the rate of 650 -702 and 629 -679 excitons per second, respectively. The average rate of charge separation and subsequent reactions of each excited photosystem varies as 592-639 per second for PSI and 630 -680 per second for PSII. These numbers lead to a reasonable estimate for the amount of glucose produced in each square meter of leaf area in a day.

Section: Introductionmentioning

confidence: 76%

“…Frenkel excitons are known to migrate in two ways 1–21. The first mechanism involves resonant energy transfer that is also involved in the formation of Frenkel excitons.…”

Section: Theorymentioning

confidence: 99%

Transport of excitation energy in a molecular aggregate. VIII. Numerical simulation of exciton processes in thylakoid membrane

Panda

2005

“…Very recently, Singh and Thilagam have considered the trapping of excitons by emitting two phonons at isotopic impurities for which the excitation energy is lower than that for the host molecule [25]. These authors have made use of composite exciton-phonon states (in the 0-0 phonon transition model) within the single phonon approximation [24].…”

Section: Discussionmentioning

confidence: 99%

“…Typical amplitudes (in one dimension) are shown in Figure 2. These modes determine the vibrational characteristics used in (25). The statistical function u / n approaches a constant value as the chain length increases [ Fig.…”

Section: Discussionmentioning

confidence: 99%

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

Priyadarshy

1987

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.

“…where T is the length of each time step. The interaction energies V h h , v h i , and V i h can be calculated from excitonic interaction and trap depth [15], quantities that can be computed by quantum chemical methods [ 161. Here, however, these parameters have been chosen realistically but quite arbitrarily: v h h = 31.36 cm-', v h i = 32.18 cm-', and V i h = 12.61 cm-'.…”

Section: A T a And Prabhumentioning

confidence: 99%

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

Prabhu

1993

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 lo8 s-' has been calculated for the occurrence of the cooperative process. This rate is affected when other nonconserving processes are switched on. Observations (l), (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. 0 1993 John Wiley & Sons, Inc.