Coherence Vibrations and Electronic Excitation Dynamics in Molecular Aggregates and Photosynthetic Pigment-Proteins

Transcription

1 VILNIUS UNIVERSITY Coherence Vibrations and Electronic Excitation Dynamics in Molecular Aggregates and Photosynthetic Pigment-Proteins L. Valkunas Department of Theoretical Physics, Faculty of Physics, Vilnius University, Institute of Physics, Center for Physical Sciences and Technology, Vilnius Lithuania

2 Contents Coherent vs. Incoherent Processes Coherences and oscillations in 2D ES Model systems Coupled two-level systems (electronic dimer) Displaced harmonic oscillator Coupled displaced harmonic oscillators (molecular dimer) Real stuff PSII RC, FCP

3 Energy transfer and charge separation

4 Resonance of energy transfer Electronic excited state Vibronic states Resonance energy transfer to nearby molecule Electronic ground state Molecule 1 Molecule 2

5 Are excitons the excitons? The system evolves into new equilibrium with respect to the excited system configuration. The initial exciton becomes not the eigenstate A. Gelzinis, D. Abramavicius, L. Valkunas, Phys. Rev. B. 84, , 2011.

6 Are excitons the excitons? The systems evolves into new equilibrium with respect to the excited system configuration. The initial exciton becomes not the eigenstate Absorption A. Gelzinis, D. Abramavicius, L. Valkunas, Phys. Rev. B. 84, , 2011.

7 Are excitons the excitons? The systems evolves into new equilibrium with respect to the excited system configuration. The initial exciton becomes not the eigenstate Emission A. Gelzinis, D. Abramavicius, L. Valkunas, Phys. Rev. B. 84, , 2011.

8 Are excitons the excitons? The system evolves into new equilibrium with respect to the excited system configuration. The initial exciton becomes not the eigenstate Emission A. Gelzinis, D. Abramavicius, L. Valkunas, Phys. Rev. B. 84, , 2011.

9 Are excitons the excitons? The system evolves into new equilibrium with respect to the excited system configuration. The initial exciton becomes not the eigenstate Mixed picture where all excitons are more localized Emission A. Gelzinis, D. Abramavicius, L. Valkunas, Phys. Rev. B. 84, , 2011.

10 Search for the preferred basis The exciton basis is given by: The global basis is different: The density matrix is diagonal in the global basis at equilibrium What happens in the molecular representation? EFFECTIVE PARAMETERS A. Gelzinis, D. Abramavicius, L. Valkunas, Phys. Rev. B. 84, , 2011.

11 The effective polaronic Hamiltonian The real effective Hamiltonian is a function of the system-bath coupling Initial excitons are no longer relevant A. Gelzinis, D. Abramavicius, L. Valkunas, Phys. Rev. B. 84, , 2011.

12 Absorption lineshape calculations A. Gelzinis, D. Abramavicius, L. Valkunas, J. Chem. Phys. 142, , 2015.

13 Different levels of theory for off-diagonal fluctuations A. Gelzinis, D. Abramavicius, L. Valkunas, J. Chem. Phys. 142, , 2015.

14 Coherence vs. Incoherence

15 FMO G. S. Engel et al. Nature 446, 782 (2007) G. Panitchayangkoon et al. PNAS 107, (2010)

16 Scheme 2D photon echo spectroscopy (3) (3) r P (, t) dt dt dt S ( t, t, t ) E( r, t t ) E( r, t t t ) E( r, t t t t )

17 Classification of third order techniques: Possible phase-matching directions: ks u k u k u k Assuming that each laser pulse interacts with the system only once, we get 4 linearly independent signals ki k k k rephasing non-rephasing kii k k k double quantum coherence k k k k III 1 2 3

18 Two-level system Inhomogeneous linewidth Homogeneous linewidth

19 Noninteracting molecules Two diagonal peaks present Peaks getting round shape due to losing correlation

20 Interacting molecules (a dimer) Excited state absorption Excitation relaxation

21 Quantum transport in 2D spectroscopy Diagonal peaks represent state populations Off-diagonal peaks are mixed: populations and coherences Off-diagonal oscillate due to quantum coherences this does not show quantum transport Exponential decay/rise of the diagonal peaks signify Classical Transport regime Oscillatory diagonal peaks signify Quantum Transport regime

22 Oscillation Fourier maps One contribution of the rephasing signal Phase and amplitude of oscillations is obtained by Fourier transform of time-dependent spectra, assuming no bath-induced relaxation and Green s function, gives Oscillating cross-peak: V. Butkus, D. Zigmantas, L. Valkunas, D. Abramavicius, CPL 545, 40 (2012)

23 Purely electronic/vibrational systems Vibrational monomer Vibrational monomer Electronic dimer Electronic dimer V. Butkus, D. Zigmantas, L. Valkunas, D. Abramavicius, CPL 545, 40 (2012)

24 Intensity Intensyvumas Intensity Intensity Oscillations in model systems (rephasing signal only) Cross-peak oscillations IN PHASE Diagonal elements Off-diagonal elements Population time (fs) Population time (fs) Diagonal elements Population time (fs) Population time (fs) Off-diagonal elements V. Butkus, D. Zigmantas, L. Valkunas, D. Abramavicius, CPL 545, 40 (2012)

25 Purely electronic/vibrational systems Vibrational monomer Electronic dimer V. Tiwari et al. PNAS 110 (2013) V. Butkus, D. Zigmantas, L. Valkunas, D. Abramavicius, CPL 545, 40 (2012)

26 Oscillation map in experiment Jan Alster Water-Soluble Chlorophyll-Binding Protein from Lepidium virginicum J. Alster, H. Jokstein, J. Dostàl, A. Uchida, D. Zigmantas, JPCB 118, 3524 (2014)

27 Time-resolved phenomena Coherent beats of vibrational degrees of freedom (internal structure of excitons) V. Butkus, D. Zigmantas, L. Valkunas, D. Abramavicius, CPL 545, 40 (2012)

28 Exciton vibronic Hamiltonian of a dimer Electronic basis of a dimer consists of a common ground state 0 and molecular excited states m = B m 0. Hamiltonian of a single molecule: A. Ground-state basis B. Shifted basis A. Of a dimer: B. E. Basinskaite, V. Butkus, D. Abramavicius, L. Valkunas, Photosynth. Res. 121, (2014)

29 Choosing the basis GS basis and shifted basis are equivalent from the physical point of view In the GS basis approach, a larger number vibrational levels have to be considered A. Ground-state basis B. Shifted basis H = A. B. 0 (11) 0 0 (22) 0 H = 0 0 (21) (12) 0 0 Multi-particle states e i g j first molecule is vibronically excited; second molecule is vibrationally excited g i e j first molecule is vibrationally excited; second molecule is vibronically excited One-particle approximation e i g 0 first molecule is vibronically excited; second molecule in zero-quantum GS. g 0 e j first molecule is in zero-quantum GS; second molecule is vibronically excited E. Basinskaite, V. Butkus, D. Abramavicius, L. Valkunas, Photosynth. Res. 121, (2014)

30 In which cases the one-particle approximation works? Let s consider linear absorption dependence on resonant coupling Multi-particle states Two-particle approx. Electronic Vibronic Huang-Rhys s=0.05 Huang-Rhys s=0.5 One-particle approximation (OPA) can be used to simulate stationary spectra with low values of Huang Rhys factor or large inhomogeneous broadening OPA fails completely if the system is in the vicinity of the exciton vibronic resonance Validity of OPA in calculations with different laser pulse polarizations is highly questionable OPA will not give oscillations associated to mixed coherences. E. Basinskaite, V. Butkus, D. Abramavicius, L. Valkunas, Photosynth. Res. 121, (2014)

31 Effects of the inhomogeneous disorder on coherences The amplitude of the electronic-character beats is dramatically reduced by the disorder Vibrational-character beats weakly depend on the disorder σ σ D =20 σ D =0 D =50 cm -1-1 ω 0 =600 cm -1 ΔE=850 cm -1 s 1 =s 2 =0.05 σ D =200 cm -1 V. Butkus, D. Zigmantas, D. Abramavicius, L. Valkunas, CPL 587, 93 (2013)

32 Amplitude dependence on disorder σ D =0 σ D =200 cm -1 V. Butkus, D. Zigmantas, D. Abramavicius, L. Valkunas, CPL 587, 93 (2013)

33 Tight binding hamiltonian A. Gelzinis et al. New J. Phys. 15, (2013)

34 CT pathways A. Gelzinis et al. New J. Phys. 15, (2013)

35 CT states A. Gelzinis et al. New J. Phys. 15, (2013)

36 Spectral density A. Gelzinis et al. New J. Phys. 15, (2013)

37 Absorption of PSII RC A. Gelzinis et al. New J. Phys. 15, (2013)

38 Monomer absorption A. Gelzinis et al. New J. Phys. 15, (2013)

39 PSII RC 2D at 77 K A. Gelzinis et al. New J. Phys. 15, (2013 A. Gelzinis et al. New J. Phys. 15, (2013)

40 PSII RC 2D at 77 K A. Gelzinis et al. New J. Phys. 15, (2013)

41 PSII RC 2D at 77 K A. Gelzinis et al. New J. Phys. 15, (2013)

42 Excited state energy distributions A. Gelzinis et al. New J. Phys. 15, (2013)

43 2D spectrum of the PSII RC at 77K at a waiting time of 170 fs. F. D. Fuller, J. Pan, A. Gelzinis, V. Butkus, S. S. Senlik, D. E. Wilcox, C. F. Yocum, L. Valkunas, D. Abramavicius, J. P. Ogilvie, Vibronic coherence in oxygenic photosynthesis. Nature Chemistry 6, (2014)

44 Excitonic states Physical origin of coherences Experiment Theory Vibronic Experiment Theory F. D. Fuller, J. Pan, A. Gelzinis, V. Butkus, S. S. Senlik, D. E. Wilcox, C. F. Yocum, L. Valkunas, D. Abramavicius, J. P. Ogilvie, Vibronic coherence in oxygenic photosynthesis. Nature Chemistry 6, (2014)

45 Spectral density Population of CT state Enhancement of the charge transfer Separated charges Ground state CT state Excitonic splittings After the excitation, the electron appears in the initial state A. The transition along overdamped and underdamped coordinates are indicated as states B, C and D. The charge transfer may take place at any time while the most probable event happens in the state D. D. Abramavicius et al. Acceleration of charge separation by oscillations of the environment polarization. Chem Phys Lett 368 (2003) F. D. Fuller, J. Pan, A. Gelzinis, V. Butkus, S. S. Senlik, D. E. Wilcox, C. F. Yocum, L. Valkunas, D. Abramavicius, J. P. Ogilvie, Vibronic coherence in oxygenic photosynthesis. Nature Chemistry 6, (2014)

46 Enhancement of charge transfer D. Abramavicius, L. Valkunas, Photosynth. Res. (2015)

47 Fucoxanthin-chlorophyll protein - FCP V. Butkus et al. JCP 142 (2015)

48 FCP absorption V. Butkus et al. JCP 142 (2015)

49 V. Butkus et al. JCP 142 (2015)

50 Oscillation frequencies V. Butkus et al. JCP 142 (2015)

51 Fourier maps V. Butkus et al. JCP 142 (2015)

52 Proposed pigment arrangement V. Butkus et al. JCP 142 (2015)

53 Conclusions Two types of oscillations of either vibronic or electronic character can be distinguished by the use of Fourier oscillation maps, constructed from the sequences of time-resolved 2D spectra. Inhomogeneous disorder influences vibronic/electronic coherences differently. Vibrational coherences evolving in the ground state and vibronic coherences in the excited state are equally significant.

54 Acknowledgements Vilnius: Michigan: Saclay: D. Abramavicius J. P. Ogilvie B. Robert V. Butkus F. D. Fuller A. Gall A. Gelzinis Lund: Frankfurt: R. Augulis D. Zigmantas C. Büchel E. Basinskaite Financial support LSC grant no: VP1-3.1-ŠMM-07-K