Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-24T21:56:40.079Z Has data issue: false hasContentIssue false

Primary Photonic Processes in Energy Harvesting: Quantum Dynamical Analysis of Exciton Energy Transfer over Three-Dimensional Dendrimeric Geometries

Published online by Cambridge University Press:  22 June 2011

David L. Andrews
Affiliation:
School of Chemistry, University of East Anglia, Norwich NR4 7TJ, U.K.
Garth A. Jones
Affiliation:
School of Chemistry, University of East Anglia, Norwich NR4 7TJ, U.K.
Get access

Abstract

In molecular solar energy harvesting systems, quantum mechanical features may be apparent in the physical processes involved in the acquisition and migration of photon energy. With a sharply declining distance-dependence in transfer efficiency, the excitation energy generally takes a large number of steps en route to the site of its utilization; quantum features are rapidly dissipated in an essentially stochastic process. In the case of engineered dendrimeric polymers, each such step usually takes the form of an inward hop between chromophores in neighboring generation shells. A physically intuitive, structure-determined adjacency matrix formulation of the energy flow affords insights into the key harvesting and inward funneling processes. A numerical method based on this analytic approach has now been developed and is able to deliver results on significantly larger dendrimeric polymers, with the help of large multi-processor computers. Central to this study is the interpretation of key features such as the relevance of a spectroscopic gradient and the presence of traps or irregularities due to conformational changes and folding. With the objective of fine-tune the funneling process, this model now allows the incorporation of parameters derived from quantum chemical calculations, affording new insights into the detailed operation of the harvesting process in a variety of dendrimer systems.

Type
Research Article
Copyright
Copyright © Materials Research Society 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1] Andrews, D. L., Curutchet, C., and Scholes, G. D., “Resonance energy transfer: Beyond the Limits”, Laser Photonics Rev., 5, 114123 (2011) [doi: 10.1002/lpor.201000004].Google Scholar
[2] Beljonne, D., Curutchet, C., Scholes, G. D., and Silbey, R. J., “Beyond Förster resonance energy transfer in biological and nanoscale systems”, J. Phys. Chem. B, 113, 65836599 (2009) [doi: 10.1021/jp900708f].Google Scholar
[3] Cheng, Y. C. and Fleming, G. R., “Dynamics of light harvesting in photosynthesis”, Annu. Rev. Phys. Chem., 60, 241262 (2009) [doi: 10.1146/annurev.physchem.040808.090259].Google Scholar
[4] Andrews, D. L., Energy Harvesting Materials (World Scientific, New Jersey, 2005).Google Scholar
[5] Dykes, G. M., “Dendrimers: a review of their appeal and applications”, J. Chem. Technol. Biotechnol. 76, 903918 (2001) [doi: 10.1002/jctb.464] Google Scholar
[6] Adronov, A. and Fréchet, J. M. J., “Light-harvesting dendrimers,” Chem. Commun., 1701-1710 (2000) [doi:10.1039/b005993p].Google Scholar
[7] Archut, A. and Vögtle, G., “Functional cascade molecules,” Chem. Soc. Rev. 27, 233240 (1998) [doi:10.1039/a827233z].Google Scholar
[8] Minami, T., Tretiak, S., Chernyak, V., and Mukamel, S., “Frenkel-exciton Hamiltonian for dendrimeric nanostar,” J. Lumin. 87-89, 115118 (2000) [doi:10.1016/S0022-2313(99)00242-2].Google Scholar
[9] Balzani, V., Ceroni, P., Maestri, M., and Vincinelli, V., “Light-harvesting dendrimers,” Curr. Opinion. Chem. Biol. 7, 657665 (2003) [doi:10.1016/j.cbpa.2003.10.001].Google Scholar
[10] Ranasinghe, M. I., Varnavski, O. P., Pawlas, J., Hauck, S. I., Louie, J., Hartwig, J. F., and Goodson, T. III, “Femtosecond excitation energy transport in triarylamine dendrimers,” J. Am. Chem. Soc. 124, 65206521 (2002) [doi:10.1021/ja025505z].Google Scholar
[11] Katan, C., Terenziani, F., Mongin, O., Werts, M. H. V., Porres, L., Pons, T., Mertz, J., Tretiak, S., and Blanchard-Desce, M., “Effects of (multi)branching of dipolar chromophores on photophysical properties and two-photon absorption”, J. Phys. Chem. A, 109, 30243037 (2005) [doi: 10.1021/jp044193e].Google Scholar
[12] Burn, P. L., Lo, S. C., and Samuel, I. D. W., “The development of light-emitting dendrimers for displays”, Adv. Mater., 19, 16751688 (2007) [doi: 10.1002/adma.200601592].Google Scholar
[13] Paulo, P. M. R., Lopes, J. N. C., and Costa, S. M. B., “Molecular dynamics simulations of charged dendrimers: Low-to-intermediate half-generation PAMAMs”, J. Phys. Chem. B, 111, 1065110664 (2007) [doi: 10.1021/jp072211x].Google Scholar
[14] Badaeva, E., Harpham, M. R., Guda, R., Suzer, O., Ma, C. Q., Bauerle, P., Goodson, T., and Tretiak, S., “Excited-state structure of oligothiophene dendrimers: Computational and experimental study”, J. Phys. Chem. B, 114, 1580815817 (2010), [doi: 10.1021/jp109624d].Google Scholar
[15] Gao, J. K., Cui, Y. J., Yu, J. C., Lin, W. X., Wang, Z. Y., and Qian, G. D., “Enhancement of nonlinear optical activity in new six-branched dendritic dipolar chromophore”, J. Mater. Chem., 21, 31973203 (2011) [doi: 10.1039/c0jm03367g].Google Scholar
[16] Palma, J. L., Atas, E., Hardison, L., Marder, T. B., Collings, J. C., Beeby, A., Melinger, J. S., Krause, J. L., Kleiman, V. D., and Roitberg, A. E., “Electronic Spectra of the Nanostar Dendrimer: Theory and Experiment”, J. Phys. Chem. C, 114, 2070220712 (2010) [doi: 10.1021/jp1062918].Google Scholar
[17] Larsen, J., Puntoriero, F., Pascher, T., McClenaghan, N., Campagna, S., Åkesson, E., and Sundström, V., “Extending the light-harvesting properties of transition-metal dendrimers,” ChemPhysChem 8, 26432651 (2007) [doi:10.1002/cphc.200700539].Google Scholar
[18] Lor, M., De, R., Jordens, S., De Belder, G., Schweitzer, G., Cotlet, M., Hofkens, J., Weil, T., Herrmann, A., Müllen, K., Van Der Auweraer, M., and De Schryver, F. C., “Generation-dependent energy dissipation in rigid dendrimers studied by femtosecond to nanosecond time-resolved fluorescence spectroscopy,” J. Phys. Chem. A 106, 20832090 (2002) [doi:10.1021/jp012310p].Google Scholar
[19] Shortreed, M. R., Swallen, S. F., Shi, Z. Y., Tan, W. H., Xu, Z. F., Devadoss, C., Moore, J. S., and Kopelman, R., “Directed energy transfer funnels in dendrimeric antenna supermolecules,” J. Phys. Chem. B 101, 63186322 (1997) [doi:10.1021/jp9705986].Google Scholar
[20] Bar-Haim, A. and Klafter, J., “Dendrimers as light harvesting antennae,” J. Lumin. 76-77, 197200 (1998) [doi:10.1016/S0022-2313(97)00150-6].Google Scholar
[21] Bar-Haim, A. and Klafter, J., “Geometric versus energetic competition in light harvesting by dendrimers,” J. Phys. Chem. B 102, 16621664 (1998) [doi:10.1021/jp980174r].Google Scholar
[22] Swallen, S. F., Shi, Z.-Y., Tan, W., Xu, Z., Moore, J. S., and Kopelman, R., “Exciton localisation hierarchy and directed energy transfer in conjugated linear aromatic chains and dendrimeric supermolecules,” J. Lumin. 76-77, 193196 (1998) [doi:10.1016/S0022-2313(97)00149-X].Google Scholar
[23] van Patten, P. G., Shreve, A. P., Lindsey, J. S., and Donohoe, R. J., “Energy-transfer modeling for the rational design of multiporphyrin light-harvesting arrays,” J. Phys. Chem. B 102, 42094216 (1998) [doi:10.1021/jp972304m].Google Scholar
[24] Hahn, U., Gorka, M., Vögtle, F., Vicinelle, V., Ceroni, P., Maestri, M., and Balzani, V., “Light-harvesting dendrimers: efficient intra- and intermolecular energy-transfer processes in a species containing 65 chromophoric groups of four different types,” Angew. Chem. Int. Ed. 41, 35953598 (2002) [doi:10.1002/1521-3773(20021004)41:19<3595::AID-ANIE3595>3.0.CO;2-B].3.0.CO;2-B].>Google Scholar
[25] Tretiak, S., Chernyak, V., and Mukamel, S., “Localized electronic excitations in phenylacetylene dendrimers”, J. Phys. Chem. B, 102, 33103315 (1998) [doi:10.1021/jp980745f].Google Scholar
[26] Poliakov, E. Y., Chernyak, V., Tretiak, S., and Mukamel, S., “Exciton-scaling and optical excitations of self-similar phenylacetylene dendrimers”, J. Chem. Phys., 110, 81618175 (1999) [doi: 10.1063/1.478730].Google Scholar
[27] Avery, J. S., “Resonance energy transfer and spontaneous photon emission”, Proc. Phys. Soc., 88, 18 (1966) [doi: 10.1088/0370-1328/88/1/302].Google Scholar
[28] Gomberoff, L. and Power, E. A., “The resonance transfer of excitation”, Proc. Phys. Soc. 88, 281284 (1966) [doi: 10.1088/0370-1328/88/2/302].Google Scholar
[29] Craig, D. P. and Thirunamachandran, T., Molecular Quantum Electrodynamics. An Introduction to Radiation Molecule Interactions (Dover, New York, 1998), pp. 144149.Google Scholar
[30] Juzeliūnas, G. and Andrews, D. L., “Quantum electrodynamics of resonance energy transfer”, Adv. Chem. Phys. 112, 357410 (2000).Google Scholar
[31] Andrews, D. L. and Bradshaw, D. S.Virtual photons, dipole fields and energy transfer: a quantum electrodynamical approach”, Eur. J. Phys. 25, 845858 (2004) [doi: 10.1088/0143-0807/25/6/017].Google Scholar
[32] Salam, A., Molecular Quantum Electrodynamics. Long- Range Intermolecular Interactions (Wiley, New York, 2010), Chap. 4.Google Scholar
[33] Silbey, R., “Electronic energy transfer in molecular crystals”, Ann. Rev. Phys. Chem., 27, 203223 (1976).Google Scholar
[34] Scholes, G. D., Jordanides, X. J., and Fleming, G. R., “Adapting the Förster theory of energy transfer for modeling dynamics in aggregated molecular assemblies”, J. Phys. Chem. B, 105, 16401651 (2001) [doi: 10.1021/jp003571m].Google Scholar
[35] Jordanides, X. J., Scholes, G. D., and Fleming, G. R., “The mechanism of energy transfer in the bacterial photosynthetic reaction center”, J. Phys. Chem. B, 105, 16521669 (2001) [doi: 10.1021/jp003572e].Google Scholar
[36] Wong, K. F., Bagchi, B., and Rossky, P. J., “Distance and orientation dependence of excitation transfer rates in conjugated systems: Beyond the Förster theory”, J. Phys. Chem. A, 108, 57525763 (2004) [doi: 10.1021/jp03772].Google Scholar
[37] Jang, S., Cheng, Y.-C., Reichman, D. R., and Eaves, J. D., “Theory of coherent resonance energy transfer”, J. Chem. Phys., 129, 101104 (2008) [doi: 10.1063/1.2977974].Google Scholar
[38] Ishizaki, A. and Fleming, G. R., “Unified treatment of quantum coherent and incoherent hopping dynamics in electronic energy transfer: Reduced hierarchy equation approach”, J. Chem. Phys., 130, 234111 (2009) [doi: 10.1063/1.3155372].Google Scholar
[39] Ishizaki, A. and Fleming, G. R., “On the adequacy of the Redfield equation and related approaches to the study of quantum dynamics in electronic energy transfer”, J. Chem. Phys., 130, 234110 (2009) [doi: 10.1063/1.3155214].Google Scholar
[40] Poliakov, E. Y., Chernyak, V., Tretiak, S., and Mukamel, S., “Exciton-scaling and optical excitations of self-similar phenylacetylene dendrimers”, J. Chem. Phys., 110, 81618175 (1999) [doi: S0021-9606(99)51916-8].Google Scholar
[41] Yeow, E. K. L., Ghiggino, K. P., Reek, J. N. H., Crossley, M. J., Bosman, A. W., Schenning, A. P. H. J., and Meijer, E. W., “The dynamics of electronic energy transfer in novel multiporphyrin functionalized dendrimers: A time-resolved fluorescence anisotropy”, J. Phys. Chem. B, 104, 25962606 (2000) [doi: 10.1021/jp993116u].Google Scholar
[42] Nakano, M., Kishi, R., Nakagawa, N., Nitta, T., and Yamaguchi, K., “Quantum master equation approach to the second hyperpolarizability of nanostar dendritic systems”, J. Phys. Chem. B, 109, 76317636 (2005) [doi: 10.1021/jp044599r].Google Scholar
[43] Zhu, H., May, V., and Röder, B., “Mixed quantum classical simulations of electronic excitation energy transfer: The pheophorbide- a DAB dendrimer P4 in solution”, Chem. Phys., 351, 117128 (2008) [doi: 10.1016/j.chemphys.2008.04.009].Google Scholar
[44] Megow, J., Röder, B., Kulesza, A., Bonačić-Koutecký, V., and May, V., “A mixed quantum–classical description of excitation energy transfer in supramolecular complexes: Förster theory and beyond”, ChemPhysChem, 12, 645656 (2011) [DOI: 10.1002/cphc.201000857].Google Scholar
[45] Fernandez-Alberti, S., Kleiman, V. D., Tretiak, S., and Roitberg, A. E., “Nonadiabatic molecular dynamics simulations of the energy transfer between building blocks in a phenylene ethynylene dendrimer”, J. Phys. Chem. A, 113, 75357542 (2009) [doi: 10.1021/jp900904q].Google Scholar
[46] Andrews, D. L., Li, S. P., Rodrìguez, J., and Slota, J., “Development of the energy flow in light-harvesting dendrimers”, J. Chem. Phys., 127, 134902 (2007) [doi: 10.1063/1.2785175].Google Scholar
[47] Andrews, D. L. and Li, S. P., “Energy flow in dendrimers: An adjacency matrix representation”, Chem. Phys. Lett., 433, 239243 (2006) [doi: 10.1016/j.cplett.2006.11.049].Google Scholar
[48] Andrews, D. L., Rodrìguez, J., Bradshaw, D. S., and Wells, S. C., “Alternative resonance energy transfer mechanisms in polymer light harvesting”, Mater. Res. Soc. Symp. Proc., 1120, 1120M03-05 (2009).Google Scholar
[49] Acocella, A., Jones, G. A., and Zerbetto, F., “Mono- and bichromatic electron dynamics: LiH, a test case”, J. Phys. Chem. A, 110, 51645172 (2006) [doiI: 10.1021/jp060195i].Google Scholar
[50] Jones, G. A., Acocella, A., and Zerbetto, F., “Nonlinear optical properties of C60 with explicit time-dependent electron dynamics”, Theor. Chem. Acc., 118, 99106 (2007) [doi: 10.1007/s00214-007-0251-4].Google Scholar
[51] Acocella, A., Jones, G. A., and Zerbetto, F., “What is adenine doing in photolyase?”, J. Phys. Chem. B, 114, 41014106 (2010) [doi: 10.1021/jp101093z].Google Scholar
[52] Jones, G. A., Acocella, A., and Zerbetto, F., “On-the-fly, electric-field-driven, coupled electron-nuclear dynamics”, J. Phys. Chem. A, 112, 96509656 (2008) [doi: 10.1021/jp805360v].Google Scholar
[53] Graves, J. S. and Allen, R. E., “Response of GaAs to fast intense laser pulses”, Phys. Rev. B, 58, 1362713633 (1998) [doi: S0163-18299801843-8].Google Scholar
[54] Castro, A., Marques, M. A. L., and Rubio, A., “Propagators for the time-dependent Kohn – Sham equations”, J. Chem. Phys., 121, 34253433 (2004) [doi: 10.1063/1.1774980].Google Scholar
[55] Ashkenazi, G., Kosloff, R., and Ratner, M. A., “Photoexcited electron transfer: Short-time dynamics and turnover control by dephasing, relaxation, and mixing”, J. Am. Chem. Soc., 121, 33863395 (1999) [10.1021/ja981998p].Google Scholar
[56] Engel, G. S., Calhoun, T. R., Read EL, E. L., Ahn, T. K., Mancal, T., Cheng, Y.-C., Blankenship, R. E., and Fleming, G. R., “Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems”, Nature, 446, 782786 (2007) [doi: 10.1038/nature05678].Google Scholar
[57] Lee, H., Cheng, Y-. C., and Fleming, G. R., “Coherence dynamics in photosynthesis: Protein protection of excitonic coherence’, Science, 316, 14621465 (2007) [doi: 10.1126/science.1142188] Google Scholar
[58] Collini, E., Wong, C. Y., Wilk, K. E., Curmi, P. M. G., Brumer, P., and Scholes, G. D., “Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature”, Nature, 463, 664669 (2010) [doi: 10.1038/nature08811].Google Scholar