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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
VILNIUS
UNIVERSITY
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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
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Energy transfer and charge separation
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Resonance of energy transfer
Electronic
excited state
Electronic
ground state
Vibronic
states
Resonance
energy
transfer to
nearby
molecule
Molecule 1 Molecule 2
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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, 245430, 2011.
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Are excitons the excitons?
• The systems 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, 245430, 2011.
Absorption
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Are excitons the excitons?
• The systems 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, 245430, 2011.
Emission
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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, 245430, 2011.
Emission
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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, 245430, 2011.
Emission
Mixed picture where all “excitons” are more localized
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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?
A. Gelzinis, D. Abramavicius, L. Valkunas, Phys. Rev. B. 84, 245430, 2011.
EFFECTIVEPARAMETERS
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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, 245430, 2011.
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Absorption lineshape calculations
A. Gelzinis, D. Abramavicius, L. Valkunas, J. Chem. Phys. 142, 154107, 2015.
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Different levels of theory for off-diagonal fluctuations
A. Gelzinis, D. Abramavicius, L. Valkunas, J. Chem. Phys. 142, 154107, 2015.
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Coherence vs. Incoherence
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FMO
G. S. Engel et al. Nature 446, 782 (2007)G. Panitchayangkoon et al. PNAS 107, 12766-12770 (2010)
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2D photon echo spectroscopy
Scheme
(3) (3)
3 2 1 3 2 1
0 0 0
3 3 2 3 2 1
( , ) ( , , )
( , ) ( , ) ( , ).
P t dt dt dt S t t t
E t t E t t t E t t t t
r
r r r
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Classification of third order techniques:
1 1 2 2 3 3s u u u k k k k
1 2 3I k k k k
1 2 3II k k k k
1 2 3III k k k k
Possible phase-matching directions:
Assuming that each laser pulse interacts with the system only once, we get 4 linearly independent signals
rephasing
non-rephasing
double quantum coherence
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Two-level system
Homogeneous linewidth
Inhomogeneous linewidth
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Noninteracting molecules
• Two diagonal peaks present
• Peaks getting round shape due to losing correlation
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Interacting molecules (a dimer)
Excited state absorption
Excitation relaxation
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Quantum transport in 2D spectroscopy
• Diagonal peaks representstate populations
• Off-diagonal peaks aremixed: populations and coherences
• Off-diagonal oscillate due to quantum coherencesthis does not show quantum transport
• Exponential decay/rise of the diagonal peaks signify Classical Transport regime
• Oscillatory diagonal peaks signify Quantum Transport regime
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Oscillation Fourier maps
• One contribution of the rephasing signal
assuming no bath-induced relaxation and Green’s function , gives
Oscillating cross-peak:
Phase and amplitude of oscillations is obtained by Fourier transform of time-dependent spectra,
V. Butkus, D. Zigmantas, L. Valkunas, D. Abramavicius, CPL 545, 40 (2012)
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Purely electronic/vibrational systems
Electronicdimer
Vibrationalmonomer
Electronic dimer
Vibrational monomer
V. Butkus, D. Zigmantas, L. Valkunas, D. Abramavicius, CPL 545, 40 (2012)
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Oscillations in model systems (rephasing signal only)
Inte
nsy
vum
as
Inte
nsi
ty
Inte
nsi
ty
Inte
nsi
tyDiagonal elements
Diagonal elements
Off-diagonal elements
Off-diagonalelements
Population time (fs) Population time (fs)
Population time (fs) Population time (fs)
Cross-peak oscillations IN PHASE
V. Butkus, D. Zigmantas, L. Valkunas, D. Abramavicius, CPL 545, 40 (2012)
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Purely electronic/vibrational systems
Electronic dimer
Vibrational monomer
V. Tiwari et al. PNAS 110 (2013)
V. Butkus, D. Zigmantas, L. Valkunas, D. Abramavicius, CPL 545, 40 (2012)
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Oscillation map in experiment
© Jan Alster
http://www.chemphys.lu.se/2Dgroup/
Water-Soluble Chlorophyll-Binding Protein
from Lepidium virginicumJ. Alster, H. Jokstein, J. Dostàl, A. Uchida,
D. Zigmantas, JPCB 118, 3524 (2014)
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Time-resolved phenomena
• Coherent beats of vibrationaldegrees of freedom(internal structure of excitons)
V. Butkus, D. Zigmantas, L. Valkunas, D. Abramavicius, CPL 545, 40 (2012)
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Excitonvibronic Hamiltonian of a dimer
• Electronic basis of a dimer consists of a common ground state 0 and molecular excited states
𝑚 = 𝐵𝑚†
0 .
• Hamiltonian of a single molecule:
• Of a dimer:
A. Ground-state basis B. Shifted basis
A.
B.
E. Basinskaite, V. Butkus, D. Abramavicius, L. Valkunas, Photosynth. Res. 121, 95-106 (2014)
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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
• Multi-particle states– 𝑒𝑖𝑔𝑗 first molecule is
vibronically excited; second molecule is vibrationallyexcited
– 𝑔𝑖𝑒𝑗 first molecule is vibrationally excited; second molecule is vibronicallyexcited
• One-particle approximation– 𝑒𝑖𝑔0 first molecule is
vibronically excited; second molecule in zero-quantum GS.
– 𝑔0𝑒𝑗 first molecule is in zero-quantum GS; second molecule is vibronicallyexcited
A. Ground-state basis B. Shifted basis
𝐻 =
(11)
(22)
0
0
0
0 𝐻 =
(12)
(21)0
0
0
0
A.
B.
E. Basinskaite, V. Butkus, D. Abramavicius, L. Valkunas, Photosynth. Res. 121, 95-106 (2014)
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In which cases the one-particle approximation works?
• Let’s consider linear absorption dependence on resonant coupling
• 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†.
Huang-Rhys
s=0.05
Huang-Rhys
s=0.5
Multi-particle states
Two-particle approx.
ElectronicVibronic
E. Basinskaite, V. Butkus, D. Abramavicius, L. Valkunas, Photosynth. Res. 121, 95-106 (2014)
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Effects of the inhomogeneous disorder on
coherences
• The amplitude of theelectronic-character beats isdramatically reduced by thedisorder
• Vibrational-character beatsweakly depend on thedisorder
ω0=600 cm-1
ΔE=850 cm-1
s1=s2=0.05
σD=0
σD=200 cm-1
σD=20 cm-1σD=50 cm-1
V. Butkus, D. Zigmantas, D. Abramavicius, L. Valkunas, CPL 587, 93 (2013)
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Amplitude dependence on disorder
σD=200 cm-1
σD=0
V. Butkus, D. Zigmantas, D. Abramavicius, L. Valkunas, CPL 587, 93 (2013)
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Tight binding hamiltonian
A. Gelzinis et al. New J. Phys. 15, 075013 (2013)
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CT pathways
A. Gelzinis et al. New J. Phys. 15, 075013 (2013)
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CT states
A. Gelzinis et al. New J. Phys. 15, 075013 (2013)
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Spectral density
A. Gelzinis et al. New J. Phys. 15, 075013 (2013)
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Absorption of PSII RC
A. Gelzinis et al. New J. Phys. 15, 075013 (2013)
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Monomer absorption
A. Gelzinis et al. New J. Phys. 15, 075013 (2013)
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PSII RC 2D at 77 K
A. Gelzinis et al. New J. Phys. 15, 075013 (2013
A. Gelzinis et al. New J. Phys. 15, 075013 (2013)
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PSII RC 2D at 77 K
A. Gelzinis et al. New J. Phys. 15, 075013 (2013)
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PSII RC 2D at 77 K
A. Gelzinis et al. New J. Phys. 15, 075013 (2013)
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Excited state energy distributions
A. Gelzinis et al. New J. Phys. 15, 075013 (2013)
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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, 706-711 (2014)
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Physical origin of coherencesEx
cito
nic
stat
es
Experiment TheoryVib
ron
ic
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, 706-711 (2014)
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Enhancement of the charge transfer
Excitonic splittings
Pop
ula
tio
n o
fC
T st
ate
Spe
ctra
l de
nsi
ty
D. Abramavicius et al. Acceleration of charge separation by oscillations
of the environment polarization. Chem Phys Lett 368 (2003)
Groundstate
CT state
Separated charges
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.
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, 706-711 (2014)
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Enhancement of charge transfer
D. Abramavicius, L. Valkunas, Photosynth. Res. (2015)
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Fucoxanthin-chlorophyll protein - FCP
V. Butkus et al. JCP 142 (2015)
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FCP absorption
V. Butkus et al. JCP 142 (2015)
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V. Butkus et al. JCP 142 (2015)
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Oscillation frequencies
V. Butkus et al. JCP 142 (2015)
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Fourier maps
V. Butkus et al. JCP 142 (2015)
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Proposed pigment arrangement
V. Butkus et al. JCP 142 (2015)
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Conclusions
• Two types of oscillations of either vibronic orelectronic character can be distinguished by the useof Fourier oscillation maps, constructed from thesequences of time-resolved 2D spectra.
• Inhomogeneous disorder influencesvibronic/electronic coherences differently.
• Vibrational coherences evolving in the ground stateand vibronic coherences in the excited state are equally significant.
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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 supportLSC grant no:
VP1-3.1-ŠMM-07-K-01-007.