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


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.


  1. [1]

    D. L. Andrews, C. Curutchet, and G. D. Scholes, “Resonance energy transfer: Beyond the Limits”, Laser Photonics Rev., 5, 114–123 (2011) [doi: 10.1002/lpor.201000004].

    CAS  Article  Google Scholar 

  2. [2]

    D. Beljonne, C. Curutchet, G. D. Scholes, and R. J. Silbey, “Beyond Förster resonance energy transfer in biological and nanoscale systems”, J. Phys. Chem. B, 113, 6583–6599 (2009) [doi: 10.1021/jp900708f].

  3. [3]

    Y. C. Cheng and G. R. Fleming, “Dynamics of light harvesting in photosynthesis”, Annu. Rev. Phys. Chem., 60, 241–262 (2009) [doi: 10.1146/annurev.physchem.040808.090259].

  4. [4]

    D. L. Andrews, Energy Harvesting Materials (World Scientific, New Jersey, 2005).

    Google Scholar 

  5. [5]

    G. M. Dykes, “Dendrimers: a review of their appeal and applications”, J. Chem. Technol. Biotechnol. 76, 903–918 (2001) [doi: 10.1002/jctb.464]

  6. [6]

    A. Adronov and J. M. J. Fréchet, “Light-harvesting dendrimers,” Chem. Commun., 1701–1710 (2000) [doi:10.1039/b005993p].

  7. [7]

    A. Archut and G. Vögtle, “Functional cascade molecules,” Chem. Soc. Rev. 27, 233–240 (1998) [doi:10.1039/a827233z].

  8. [8]

    T. Minami, S. Tretiak, V. Chernyak, and S. Mukamel, “Frenkel-exciton Hamiltonian for dendrimeric nanostar,” J. Lumin. 87–89, 115–118 (2000) [doi:10.1016/S0022–2313(99)00242–2].

  9. [9]

    V. Balzani, P. Ceroni, M. Maestri, and V. Vincinelli, “Light-harvesting dendrimers,” Curr. Opinion. Chem. Biol. 7, 657–665 (2003) [doi:10.1016/j.cbpa.2003.10.001].

  10. [10]

    M. I. Ranasinghe, O. P. Varnavski, J. Pawlas, S. I. Hauck, J. Louie, J. F. Hartwig, and T. Goodson III, “Femtosecond excitation energy transport in triarylamine dendrimers,” J. Am. Chem. Soc. 124, 6520–6521 (2002) [doi:10.1021/ja025505z].

  11. [11]

    C. Katan, F. Terenziani, O. Mongin, M. H. V. Werts, L. Porres, T. Pons, J. Mertz, S. Tretiak, and M. Blanchard-Desce, “Effects of (multi)branching of dipolar chromophores on photophysical properties and two-photon absorption”, J. Phys. Chem. A, 109, 3024–3037 (2005) [doi: 10.1021/jp044193e].

  12. [12]

    P. L. Burn, S. C. Lo, and I. D. W. Samuel, “The development of light-emitting dendrimers for displays”, Adv. Mater., 19, 1675–1688 (2007) [doi: 10.1002/adma.200601592].

  13. [13]

    P. M. R. Paulo, J. N. C. Lopes, and S. M. B. Costa, “Molecular dynamics simulations of charged dendrimers: Low-to-intermediate half-generation PAMAMs”, J. Phys. Chem. B, 111, 10651–10664 (2007) [doi: 10.1021/jp072211x].

  14. [14]

    E. Badaeva, M. R. Harpham, R. Guda, O. Suzer, C. Q. Ma, P. Bauerle, T. Goodson, and S. Tretiak, “Excited-state structure of oligothiophene dendrimers: Computational and experimental study”, J. Phys. Chem. B, 114, 15808–15817 (2010), [doi:10.1021/jp109624d].

  15. [15]

    J. K. Gao, Y. J. Cui, J. C. Yu, W. X. Lin, Z. Y. Wang, and G. D. Qian, “Enhancement of nonlinear optical activity in new six-branched dendritic dipolar chromophore”, J. Mater. Chem., 21, 3197–3203 (2011) [doi: 10.1039/c0jm03367g].

  16. [16]

    J. L. Palma, E. Atas, L. Hardison, T. B. Marder, J. C. Collings, A. Beeby, J. S. Melinger, J. L. Krause, V. D. Kleiman, and A. E. Roitberg, “Electronic Spectra of the Nanostar Dendrimer: Theory and Experiment”, J. Phys. Chem. C, 114, 20702–20712 (2010) [doi:10.1021/jp1062918].

  17. [17]

    J. Larsen, F. Puntoriero, T. Pascher, N. McClenaghan, S. Campagna, E. Åkesson, and V. Sundström, “Extending the light-harvesting properties of transition-metal dendrimers,” ChemPhysChem 8, 2643–2651 (2007) [doi:10.1002/cphc.200700539].

  18. [18]

    M. Lor, R. De, S. Jordens, G. De Belder, G. Schweitzer, M. Cotlet, J. Hofkens, T. Weil, A. Herrmann, K. Müllen, M. Van Der Auweraer, and F. C. De Schryver, “Generation-dependent energy dissipation in rigid dendrimers studied by femtosecond to nanosecond time-resolved fluorescence spectroscopy,” J. Phys. Chem. A 106, 2083–2090 (2002) [doi:10.1021/jp012310p].

  19. [19]

    M. R. Shortreed, S. F. Swallen, Z. Y. Shi, W. H. Tan, Z. F. Xu, C. Devadoss, J. S. Moore, and R. Kopelman, “Directed energy transfer funnels in dendrimeric antenna supermolecules,” J. Phys. Chem. B 101, 6318–6322 (1997) [doi:10.1021/jp9705986].

  20. [20]

    A. Bar-Haim and J. Klafter, “Dendrimers as light harvesting antennae,” J. Lumin. 76–77, 197–200 (1998) [doi:10.1016/S0022–2313(97)00150–6].

  21. [21]

    A. Bar-Haim and J. Klafter, “Geometric versus energetic competition in light harvesting by dendrimers,” J. Phys. Chem. B 102, 1662–1664 (1998) [doi:10.1021/jp980174r].

  22. [22]

    S. F. Swallen, Z.-Y. Shi, W. Tan, Z. Xu, J. S. Moore, and R. Kopelman, “Exciton localisation hierarchy and directed energy transfer in conjugated linear aromatic chains and dendrimeric supermolecules,” J. Lumin. 76–77, 193–196 (1998) [doi:10.1016/S0022–2313(97)00149–X].

  23. [23]

    P. G. van Patten, A. P. Shreve, J. S. Lindsey, and R. J. Donohoe, “Energy-transfer modeling for the rational design of multiporphyrin light-harvesting arrays,” J. Phys. Chem. B 102, 4209–4216 (1998) [doi:10.1021/jp972304m].

  24. [24]

    U. Hahn, M. Gorka, F. Vögtle, V. Vicinelle, P. Ceroni, M. Maestri, and V. Balzani, “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, 3595–3598 (2002) [doi:10.1002/1521-3773(20021004)41:193.0.CO;2-B].

  25. [25]

    S. Tretiak, V. Chernyak, and S. Mukamel, “Localized electronic excitations in phenylacetylene dendrimers”, J. Phys. Chem. B, 102, 3310–3315 (1998) [doi:10.1021/jp980745f].

  26. [26]

    E. Y. Poliakov, V. Chernyak, S. Tretiak, and S. Mukamel, “Exciton-scaling and optical excitations of self-similar phenylacetylene dendrimers”, J. Chem. Phys., 110, 8161–8175 (1999) [doi: 10.1063/1.478730].

  27. [27]

    J. S. Avery, “Resonance energy transfer and spontaneous photon emission”, Proc. Phys. Soc, 88, 1–8 (1966) [doi: 10.1088/0370-1328/88/1/302].

  28. [28]

    L. Gomberoff and E. A. Power, “The resonance transfer of excitation”, Proc. Phys. Soc. 88, 281–284 (1966) [doi: 10.1088/0370-1328/88/2/302].

  29. [29]

    D. P. Craig and T. Thirunamachandran, Molecular Quantum Electrodynamics. An Introduction to Radiation Molecule Interactions (Dover, New York, 1998), pp. 144–149.

  30. [30]

    G. Juzeliūnas and D. L. Andrews, “Quantum electrodynamics of resonance energy transfer”, Adv. Chem. Phys. 112, 357–410 (2000).

    Google Scholar 

  31. [31]

    D. L. Andrews and D. S. Bradshaw “Virtual photons, dipole fields and energy transfer: a quantum electrodynamical approach”, Eur. J. Phys. 25, 845–858 (2004) [doi:10.1088/0143-0807/25/6/017].

  32. [32]

    A. Salam, Molecular Quantum Electrodynamics. Long- Range Intermolecular Interactions (Wiley, New York, 2010), Chap. 4.

  33. [33]

    R. Silbey, “Electronic energy transfer in molecular crystals”, Ann. Rev. Phys. Chem., 27, 203–223 (1976).

    CAS  Article  Google Scholar 

  34. [34]

    G. D. Scholes, X. J. Jordanides, and G. R. Fleming, “Adapting the Förster theory of energy transfer for modeling dynamics in aggregated molecular assemblies”, J. Phys. Chem. B, 105, 1640–1651 (2001) [doi: 10.1021/jp003571m].

  35. [35]

    X. J. Jordanides, G. D. Scholes, and G. R. Fleming, “The mechanism of energy transfer in the bacterial photosynthetic reaction center”, J. Phys. Chem. B, 105, 1652–1669 (2001) [doi: 10.1021/jp003572e].

  36. [36]

    K. F. Wong, B. Bagchi, and P. J. Rossky, “Distance and orientation dependence of excitation transfer rates in conjugated systems: Beyond the Förster theory”, J. Phys. Chem. A, 108, 5752–5763 (2004) [doi: 10.1021/jp03772].

  37. [37]

    S. Jang, Y.-C. Cheng, D. R. Reichman, and J. D. Eaves, “Theory of coherent resonance energy transfer”, J. Chem. Phys., 129, 101104 (2008) [doi: 10.1063/1.2977974].

  38. [38]

    A. Ishizaki and G. R. Fleming, “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].

  39. [39]

    A. Ishizaki and G. R. Fleming, “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].

  40. [40]

    E. Y. Poliakov, V. Chernyak, S. Tretiak, and S. Mukamel, “Exciton-scaling and optical excitations of self-similar phenylacetylene dendrimers”, J. Chem. Phys., 110, 8161–8175 (1999) [doi: S0021-9606(99)51916-8].

  41. [41]

    E. K. L. Yeow, K. P. Ghiggino, J. N. H. Reek, M. J. Crossley, A. W. Bosman, A. P. H. J. Schenning, and E. W. Meijer, “The dynamics of electronic energy transfer in novel multiporphyrin functionalized dendrimers: A time-resolved fluorescence anisotropy”, J. Phys. Chem. B, 104, 2596–2606 (2000) [doi: 10.1021/jp993116u].

  42. [42]

    M. Nakano, R. Kishi, N. Nakagawa, T. Nitta, and K. Yamaguchi, “Quantum master equation approach to the second hyperpolarizability of nanostar dendritic systems”, J. Phys. Chem. B, 109, 7631–7636 (2005) [doi: 10.1021/jp044599r].

  43. [43]

    H. Zhu, V. May, and B. Röder, “Mixed quantum classical simulations of electronic excitation energy transfer: The pheophorbide-a DAB dendrimer P4 in solution”, Chem. Phys., 351, 117–128 (2008) [doi: 10.1016/j.chemphys.2008.04.009].

  44. [44]

    J. Megow, B. Röder, A. Kulesza, V. Bonacic-Koutecký, and V. May, “A mixed quantum-classical description of excitation energy transfer in supramolecular complexes: Förster theory and beyond”, ChemPhysChem, 12, 645–656 (2011) [DOI:10.1002/cphc.201000857].

  45. [45]

    S. Fernandez-Alberti, V. D. Kleiman, S. Tretiak, and A. E. Roitberg, “Nonadiabatic molecular dynamics simulations of the energy transfer between building blocks in a phenylene ethynylene dendrimer”, J. Phys. Chem. A, 113, 7535–7542 (2009) [doi:10.1021/jp900904q].

  46. [46]

    D. L. Andrews, S. P. Li, J. Rodrìguez, and J. Slota, “Development of the energy flow in light-harvesting dendrimers”, J. Chem. Phys., 127, 134902 (2007) [doi: 10.1063/1.2785175].

  47. [47]

    D. L. Andrews and S. P. Li, “Energy flow in dendrimers: An adjacency matrix representation”, Chem. Phys. Lett., 433, 239–243 (2006) [doi: 10.1016/j.cplett2006.11.049].

  48. [48]

    D. L. Andrews, J. Rodrìguez, D. S. Bradshaw, and S. C. Wells, “Alternative resonance energy transfer mechanisms in polymer light harvesting”, Mater. Res. Soc. Symp. Proc., 1120, 1120-M03-05 (2009).

  49. [49]

    A. Acocella, G. A. Jones, and F. Zerbetto, “Mono- and bichromatic electron dynamics: LiH, a test case”, J. Phys. Chem. A, 110, 5164–5172 (2006) [doiI : 10.1021/jp060195i].

  50. [50]

    G. A. Jones, A. Acocella, and F. Zerbetto, “Nonlinear optical properties of C60 with explicit time-dependent electron dynamics”, Theor. Chem. Acc., 118, 99–106 (2007) [doi :10.1007/s00214-007-0251-4].

  51. [51]

    A. Acocella, G. A. Jones, and F. Zerbetto, “What is adenine doing in photolyase?”, J. Phys. Chem. B, 114, 4101–4106 (2010) [doi : 10.1021/jp101093z].

  52. [52]

    G. A. Jones, A. Acocella, and F. Zerbetto, “On-the-fly, electric-field-driven, coupled electron-nuclear dynamics”, J. Phys. Chem. A, 112, 9650–9656 (2008) [doi:10.1021/jp805360v].

  53. [53]

    J. S. Graves and R. E. Allen, “Response of GaAs to fast intense laser pulses”, Phys. Rev. B, 58, 13627–13633 (1998) [doi: S0163-18299801843-8].

  54. [54]

    A. Castro, M. A. L. Marques, and A. Rubio, “Propagators for the time-dependent Kohn — Sham equations”, J. Chem. Phys., 121, 3425–3433 (2004) [doi: 10.1063/1.1774980].

  55. [55]

    G. Ashkenazi, R. Kosloff, and M. A. Ratner, “Photoexcited electron transfer: Short-time dynamics and turnover control by dephasing, relaxation, and mixing”, J. Am. Chem. Soc., 121, 3386–3395 (1999) [10.1021/ja981998p].

  56. [56]

    G. S. Engel, T. R. Calhoun, E. L. Read EL, T. K. Ahn, T. Mancal, Y.-C. Cheng, R. E. Blankenship, and G. R. Fleming, “Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems”, Nature, 446, 782–786 (2007) [doi:10.1038/nature05678].

  57. [57]

    H. Lee, Y-. C. Cheng, and G. R. Fleming, “Coherence dynamics in photosynthesis: Protein protection of excitonic coherence’, Science, 316, 1462–1465 (2007) [doi:10.1126/science.1142188]

  58. [58]

    E. Collini, C. Y. Wong, K. E. Wilk, P. M. G. Curmi, P. Brumer, and G. D. Scholes, “Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature”, Nature, 463, 664–669 (2010) [doi: 10.1038/nature08811].

Download references

Author information



Corresponding author

Correspondence to David L. Andrews.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Andrews, D.L., Jones, G.A. Primary Photonic Processes in Energy Harvesting: Quantum Dynamical Analysis of Exciton Energy Transfer over Three-Dimensional Dendrimeric Geometries. MRS Online Proceedings Library 1325, 501 (2011).

Download citation