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Coherent Charge Transfer Exciton Formation in Regioregular P3HT: A Quantum-Dynamical Study Wjatscheslaw Popp, Matthias Polkehn, Robert Binder, and Irene Burghardt J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.9b01105 • Publication Date (Web): 28 May 2019 Downloaded from http://pubs.acs.org on May 29, 2019

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The Journal of Physical Chemistry Letters

Coherent Charge Transfer Exciton Formation in Regioregular P3HT: A Quantum-Dynamical Study Wjatscheslaw Popp, Matthias Polkehn, Robert Binder, and Irene Burghardt∗ Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Str. 7, 60438 Frankfurt, Germany E-mail: [email protected]

Supporting information placeholder Abstract The ultrafast formation of charge transfer excitons (CTX) in regioregular poly(3hexyl thiophene) (rrP3HT) domains is elucidated by electronic structure and quantum dynamical studies of an aggregate model system comprising five stacked quaterthiophene units. Using a multi-state vibronic coupling Hamiltonian parametrized by TDDFT calculations for 13 electronic states of Frenkel and CTX type, along with 78 vibrational modes, quantum dynamical simulations are carried out using the MultiLayer Multi-Configuration Time-Dependent Hartree (ML-MCTDH) method. In line with time-resolved spectroscopic results [De Sio et al., Nature Comm. 7, 13742 (2016)], it is found that CTX formation occurs immediately upon photoexcitation, accompanied by sustained regular oscillations with a ∼25 fs periodicity. These coherent features whose presence may seem surprising in a high-dimensional aggregate or thin

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film material, can be traced back to a dominant vibronic signature of CC stretch type high-frequency modes. These vibrational signatures are found to be enhanced due to a collective vibronic response which is prompted by the initial generation of a delocalized bright exciton and its subsequent relaxation, by internal conversion, to a polaronic local exciton ground state.

Graphical TOC Entry hν

Poly-3-hexylthiophene (P3HT) plays a key role as a donor material in organic photovoltaics,1–5 which has been employed in prototypical donor-acceptor blends with the fullerene derivative [6,6]-phenyl-C61 butyric acid methyl ester (PCBM), but also in combination with alternative acceptor species like perylene diimide (PDI),6 or in hybrid organic-inorganic heterojunctions exemplified by P3HT/ZnO.7 A noteworthy fact is that in lamellar, regioregular (rrP3HT) domains,4,5 charge transfer excitons (CTX) or polarons are observed,8–10 likely due to photoinduced inter-chain polaron pair formation that occurs even in the absence of an acceptor species. This raises the question whether the presence of CTX polarons affects the yield of charge separated species between donor and acceptor domains and, hence, the power conversion efficiency. Recent spectroscopic8–12 and theoretical13 work contributes to answering these questions from a molecular-level perspective. The present Letter focuses specifically on the ultrafast formation step of the CTX species in rrP3HT type materials. In the time-resolved spectroscopic observations of rrP3HT thin films reported in Ref. [10], an extremely short time scale of 30 fs) are less pronounced and the system remains in a coherent superposition state. This is likely due to the fact that energy dissipation is not complete within the observation interval. The regular oscillations observed in the integrated diabatic populations of panel a) are also visible in the adiabatic populations, but to a lesser extent. In a complementary representation, Figure 3 shows the time dependence of the XT

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and CTX populations with the spatial resolution of the 5-site lattice. This representation highlights several aspects: (i) First, the qualitative change of the excitonic density within the first 20-30 femtosecond, due to internal conversion, (ii) second, the coherent, concerted dynamics of the XT and CTX manifolds, i.e., the XT and CTX densities appear to evolve in phase across the lattice, (iii) third, the increasing contraction of the exciton – with its XT and CTX components – at the center of the lattice on a slower time scale of several hundred femtoseconds, which is associated with energy redistribution within the first few Sn states, and (iv) fourth, the collective displacements of the (QI ) modes (and (QII ) modes) across the lattice. These displacements appear within the first 20 femtoseconds, showing that exciton-polaron formation happens within a single vibrational period (as also observed for intra-chain dynamics32). This leads to the conclusion that the observed dynamics monitors the generation of a polaronic (self-trapped) local exciton ground state of mixed XT/CTX character, driven by collective vibronic effects. The nonstationary, oscillatory character of the dynamics is entirely in line with the experimental observations.10,11 To ascertain that the oscillatory traces in the integrated XT and CTX populations of Figures 2-3 are indeed due to collective vibrational motions — i.e., vibrational rather than electronic coherence — we carried out a Fourier transformation of the integrated CTX population, shown in Figure 4 and juxtaposed with the spectral density of Figure 1. The results of Figure 4 show an excellent agreement between the Fourier transform of the time-evolving populations and the SD peaks, including the lower-amplitude contributions to the SD. The latter contributions are also in good agreement with the frequency-domain signals reported in Ref. [10]. By contrast, the purely electronic spectrum obtained in the absence of vibrations (grey line in Figure 4a) does not agree with the observed frequencies. From our simulations, we also found an extremely rapid decay of the electronic coherence, characteristic of multi-state internal conversion processes (Figures S10-S12). Additional, more approximate simulations for larger (OT4)n aggregates — i.e., (OT4)7 (19 states, 114 effective modes), (OT4)9 (25 states, 150 effective modes), and (OT4)11 (31

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states, 186 effective modes) — are reported in the Supp. Information (see Sec. S4), to ascertain that the dynamics we analyzed for (OT4)5 is representative of larger aggregates. We found that both the bright-state excitation pattern and the relaxation towards the lowestlying exciton are similar (see Fig. S17). The extremely rapid internal conversion dynamics within 20-30 fs (see Figure 2 and Figure S18) is shared by all systems, even though the large aggregates tend to exhibit a longer period of S1/S2 mixing before the exciton fully relaxes towards the center of the lattice (see Figures S19-S21). Presumably for the same reasons, the asymptotic exciton delocalization ranges from 3 to 5 units (see Table S8). These findings are in line with combined experimental and theoretical analyses which report on delocalization lengths around 3 units in rrP3HT.33,34 To summarize, our analysis is in excellent agreement with the experimental observations of Refs. [10,11], both regarding the time scale of CTX formation and the presence of sustained high-frequency oscillations. Our first-principles analysis shows that the photogenerated state as such corresponds to a XT/CTX superposition, representing the high-lying bright state of the modified H-aggregate with strong CTX admixture. The subsequent vibronic dynamics triggers an ultrafast internal conversion process via a cascade of nonadiabatic curve crossings, leading to the local exciton ground state of the aggregate. The present analysis paves the way towards a better understanding of the role of polaronic CTX species in the charge separation at donor-acceptor interfaces, and establishing whether CTX polarons appear as a loss channel or promote interfacial charge separation.13 As highlighted above, the CTX formation dynamics is mainly driven by a small subset of high-frequency CC stretch modes which play a prominent role in the spectral density, and whose vibronic coupling effects are synchronized and enhanced by excitonic delocalization. The emergence of collective electron-phonon coupling in extended systems and the resulting dissipation and dephasing effects are indeed general phenomena that attract increasing attention in atomic and molecular quantum nanotechnology.35

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Associated Content Supporting Information The Supporting Information is available free of charge on the ACS Publications website: Details regarding the parametrization of the model Hamiltonian (Sec. S1), the set-up of the multiconfigurational (ML-MCTDH) calculations (Sec. S2), supplementary dynamical simulation results (Sec. S3), and detailed considerations regarding the size dependence of the exciton dynamics (Sec. S4) are presented.

Author Information Corresponding author ∗

E-mail:

[email protected]

Notes The authors declare no competing financial interest.

Acknowledgments We thank Hiroyuki Tamura, Rocco Martinazzo, and Keith Hughes for valuable discussions. Funding by the Deutsche Forschungsgemeinschaft (DFG) in the framework of the project BU-1032-2 is gratefully acknowledged.

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(10) De Sio, A.; Troiani, F. F.; Maiuri, M.; Réhault, J.; Sommer, E.; Lim, J.; Huelga, S. F.; Plenio, M. B.; Rozzi, C.; Cerullo, G.; Molinari, E.; Lienau, C. Tracking the coherent generation of polaron pairs in conjugated polymers Nature Comm. 2016, 7, 13742. (11) Song, Y.; Hellmann, C.; Stingelin, N.; Scholes, G. D. The separation of vibrational coherence from ground- and excited-electronic states in P3HT film J. Chem. Phys. 2015, 142, 212410. (12) Sio, A. D.; Camargo, F.; Winte, K.; Sommer, E.; Branchi, F.; Cerullo, G.; Lienau, C. Ultrafast relaxation dynamics in a polymer: fullerene blend for organic photovoltaics probed by two-dimensional electronic spectroscopy Eur. Phys. J. B 2018, 91, 236. (13) Polkehn, M.; Tamura, H.; Burghardt, I. Impact of charge-transfer excitons in regioregular polythiophene on the charge separation at polythiophene-fullerene heterojunctions J. Phys. B: At. Mol. Opt. Phys. 2018, 51, 014003. (14) Dijkstra, A. G.; Wang, C.; Cao, J.; Fleming, G. R. Coherent Exciton Dynamics in the Presence of Underdamped Vibrations J. Phys. Chem. Lett. 2015, 6, 627. (15) Jonas, D. M. Vibrational and nonadiabatic coherence in 2D electronic spectroscopy, the Jahn-Teller effect, and energy transfer Annu. Rev. Phys. Chem. 2018, 69, 327. (16) Spano, F. C.; Silva, C. H- and J-aggregate behavior in polymeric semiconductors Annu. Rev. Phys. Chem. 2014, 65, 477–500. (17) Blancafort, L.; Voityuk, A. A. Exciton delocalization, charge transfer, and electronic coupling for singlet excitation energy transfer between stacked nucleobases in DNA: An MS-CASPT2 study J. Chem. Phys. 2014, 140, 095102. (18) Polkehn, M.; Eisenbrandt, P.; Tamura, H.; Burghardt, I. Quantum Dynamical Studies of Ultrafast Charge Separation in Nanostructured Organic Polymer Materials: Effects of Vibronic Interactions and Molecular Packing Int. J. Quant. Chem. 2018, 118 . 14


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(19) Popp, W.; Hughes, K. H.; Martinazzo, R.; Burghardt, I. Vibronic coupling models for donor-acceptor aggregates using an effective-mode scheme: Application to mixed Frenkel and charge-transfer excitons in oligothiophene aggregates. 2019; submitted to J. Chem. Phys.. (20) Beck, M. H.; Jäckle, A.; Worth, G. A.; Meyer, H. D. The Multiconfiguration TimeDependent Hartree (MCTDH) method: A highly efficient algorithm for propagating wavepackets Phys. Rep. 2000, 324, 1–105. (21) Vendrell, O.; Meyer, H. Multilayer Multiconfiguration Time-Dependent Hartree method: Implementation and applications to a Henon-Heiles Hamiltonian and to pyrazine J. Chem. Phys. 2011, 134, 044135. (22) Clark, J.; Chang, J.; Spano, F. C.; Friend, R. H.; Silva, C. Determining exciton bandwidth and film microstructure in polythiophene films using linear absorption spectroscopy Appl. Phys. Lett. 2009, 94, 163306. (23) Tamura, H.; Martinazzo, R.; Ruckenbauer, M.; Burghardt, I. Quantum dynamics

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ultrafast charge transfer at a polymer-fullerene interface J. Chem. Phys. 2012, 137, 22A540. (24) Casado, J.; Hotta, S., Hernández, V., Lo´pez Navarrete, J. T. Vibrational spectroscopic study of a series of α, α!-diethyl end-capped oligothiophenes with different chain lengths in the neutral state J. Phys. Chem. A 1999, 103, 816-822. (25) Chai, J.-D.; Head-Gordon, M. Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections Phys. Chem. Chem. Phys. 2008, 10, 6615– 6620. (26) Li, H.; Nieman, R.; Lischka, A. J. A. A. H.; Tretiak, S. Comparison of LC-TDDFT and ADC(2) methods in computations of bright and charge transfer states in stacked oligothiophenes J. Chem. Theory Comput. 2014, 10, 3280 – 3289. 15



(27) Trofimov, A. B.; Schirmer, J. An efficient polarization propagator approach to valence electron excitation spectra J. Phys. B: At. Mol. Opt. 1995, 28, 2299–2324. (28) Hestand, N. J.; Spano, F. C. Interference between Coulombic and CT-mediated couplings in molecular aggregates: H- to J-aggregate transformation in perylene-based πstacks J. Chem. Phys. 2015, 143, 244707. (29) Plasser, F.; Lischka, H. Analysis of excitonic and charge transfer interactions from quantum chemical calculations J. Chem. Theory Comput. 2012, 8, 2777 – 2789. (30) Huix-Rotllant, M.; Tamura, H.; Burghardt, I. Concurrent effects of delocalization and internal conversion tune charge separation at regioregular polythiophenefullerene heterojunctions J. Phys. Chem. Lett. 2015, 6, 1702. (31) Nelson, T.; Fernandez-Alberti, S.; Roitberg, A. E.; Tretiak, S. Electronic Delocalization, Vibrational Dynamics, and Energy Transfer in Organic Chromophores J. Phys. Chem. Lett. 2017, 8, 3020. (32) Binder, R.; Lauvergnat, D.; Burghardt, I. Conformational dynamics guides coherent exciton migration in conjugated polymer materials: A first-principles quantum dynamical study Phys. Rev. Lett. 2018, 120, 227401. (33) Spano, F. C.; Clark, J.; Silva, C.; Friend, R. H. Determining exciton coherence from the photoluminescence spectral line shape in poly(3-hexylthiophene) thin films J. Chem. Phys. 2009, 130, 074904. (34) Paquin, F.; Yamagata, H.; Hestand, N. J.; Sakowicz, M.; Bérubé, N.; Côté, M.; Reynolds, L. X.; Haque, S. A.; Stingelin, N.; Spano, F. C.; Silva, C. Two-dimensional spatial coherence of excitons in semicrystalline polymeric semiconductors: Effect of molecular weight Phys. Rev. B 2013, 88, 155202.

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(35) Galve, F.; Mandarino, A.; Paris, M.; Benedetti, C.; Zambrini, R. Microscopic description for the emergence of collective dissipation in extended quantum systems Sci. Rep. 2017, 7, 42050.

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Tables Table 1: On-site energies and diabatic couplings obtained from ab initio calculations (ωB97XD//SVP) in conjunction with the diabatization procedure of Ref. [ 17]. All parameters are given in eV. on-site energies [eV] EXT

ECTX

0.00

0.41

diabatic couplings [eV] κ1

κ2

j

l11

l02

l−11

0.21 −0.06 0.09 −0.12 −0.06 0.06

Table 2: Adiabatic state energies (in [eV]) resulting from explicit supermolecular TDDFT calculations of the (OT4)5 aggregate (ETDDFT) as compared with the energies obtained by diagonalizing the diabatic model Hamiltonian of Eq. (1) (Emodel) at the Franck-Condon geometry. dominant state character

adiabatic state

ETDDFT [eV]

Emodel [eV]

|∆E| [eV]

XT

S1 S2 S3 S4 S5

3.08 3.11 3.18 3.35 3.41

3.05 3.13 3.23 3.34 3.35

0.03 0.02 0.05 0.01 0.06

CTX

S6 S7 S8 S9 S10 S11 S12 S13

3.73 3.74 3.78 3.81 3.83 3.85 3.91 3.99

3.66 3.72 3.81 3.82 3.93 3.96 4.01 4.13

0.07 0.02 0.03 0.01 0.10 0.11 0.10 0.14

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Figures b)

c)

d)

I 1562

II

1617

vibronic coupling C

XT

(eV)

a)

0.1

spectral density J(ω) (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


J(ω)

8 6

CXT

4 2 0

0

-0.1

0

500

1000

- 1500

wavenumber ω (cm 1)

2000

Figure 1. Panels a) and b): stacked (OT4)5 pentamer in aligned geometry,5 shown in sideways view (a) and top view (b). The structure was obtained by excited-state geometry optimization of the supermolecular system. Panel c): high-frequency modes of an OT4 fragment exhibiting the strongest vibronic couplings, denoted QI and QII in the text; frequencies are indicated in cm−1. Panel d): vibronic couplings {cXT,j } and associated spectral density JXT(ω) for a single OT4 fragment, obtained by projecting the excited-state gradient of the bright state of an (OT4)2 dimer onto one of the fragments.

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b)

a) 1

3.82 3.76 3.74 3.69 3.63 3.56 3.52 3.46 3.37 3.29 3.22

CTX states

1

4.2

4.12 3.95

Adiabatic eigenvectors

-1

4.13 4.01

4.0

3.96 3.93 3.82 3.81 3.72 3.66 3.35 3.34 3.23 3.13

3.8 3.6

S5

3.4

3.2

XT states

3.05

S1

3.0

f)

CTX states 0.16 0.14

XT states

XT manifold CTX manifold

0.12

hole

E [eV]

fosc.

|c|2

electron

d)

c)

Eigenenergies (eV)

e)

E [eV]

-1

Eigenenergies (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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S5

S1 3.08

S2 3.11

S3 3.18

S4 3.35

3.41

0.0006

0.0000

0.1370

0.0000

2.824 7

0.1 0.08

S5

0.06 0.04 0.02

Diabatic basis states

Scheme 1. Electronic manifolds and energetics for the (OT4)5 system at the FC geometry. Panels (a)-(d) show the electronic eigenstates in ascending energetic order; in panels (a) and (d), the abscissa defines a series of electron-hole basis states, of XT and CTX character. For reference, panels (a) illustrates eigenstates for a local adiabatic representation where the electronic coupling between the XT and CTX manifolds was removed (κ1 = κ2 = 0); panel (b) shows the corresponding energies for the decoupled XT manifold (red) and CTX manifold (blue). In panels (c)-(d), the corresponding energies and eigenvectors are shown for the strongly mixed XT and CTX manifolds in the fully adiabatic representation. Panel e) shows e-h plots resulting from a transition density analysis,29 along with vertical excitation energies and oscillator strengths (fosc) of the first five singlet states, based on supermolecular TDDFT calculations for (OT4)5. The excitation energies are in good agreement with the energies resulting from the model Hamiltonian Eq. (1) as reported in panel (d), see also Table 2. The S5 state carries the dominant oscillator strength; panel (f) shows the composition of the S5 state in terms of XT and CTX diabatic components.

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a) 0.8 integrated population

0.7 0.6

ΣXT

0.5

ΣCTX

0.4 0.3

b)

0.2

M1

[a.u.]

0.4

M2

M3

M4

M5

0.2 0

-0.2 -0.4

c) adiabatic state population

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.2

S1

S5

1

S2

S7

S3

S8

0.8

0

20 S4

time [fs]

0.6 0.4 0.2 0 0

50

100

150

Time [fs]

200

250

300

Figure 2. Population dynamics and high-frequency mode expectation values of the (OT4)5 aggregate. Panel a) shows integrated diabatic XT and CTX state populations; panel b) shows expectation values of the strongly coupled high-frequency mode QI , for the individual OT4 monomer units Mn (see Fig. 1), noting that the final displacement from the reference geometry is largest for the center fragment M3; panel c) shows adiabatic state populations which were computed using a simplified diabatic-to-adiabatic transformation along the paths defined by the full set of time-evolving expectation values; the inset shows the the details of the first 20 fs of the dynamics. 21



XT State CTX State

a)

b)

c)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 3. Spatially resolved population dynamics in the diabatic picture; the ordinate indicate lattice sites in the case of |XTn) states and the high-frequency mode QI , or pairs of neighboring sites in the case of | CTXn,n ) / states. Top panel: CTX state populations; center panel: XT state populations; bottom panel: expectation values of the site-specific highfrequency modes QI .

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FFT(ΣCTX)

a) 15

FFT

10

FFTel*10

b)

J(ω) [eV]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


5 0

J(ω)×10

5

J(ω)

3 1 0

500

ω[cm

-1

1000

]

1500

23

2000

ω[cm


-1

2500

]

3000


Figure 4. (a) Fourier transform of the integrated CTX state populations of Figure 2a (blue), and Fourier transform of the corresponding purely electronic dynamics (grey). (b) Spectral density of Figure 1d, with a scaled representation of the lower-frequency part. The correspondence between the spectral features of the upper and lower panels is emphasized by red dashed lines. Both the dominant high-frequency spectral features and the lower-amplitude features are in good correspondence with the observations of Ref. [10], see especially Figure 2b-c) of this reference.

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