Discrimination of Diverse Coherences Allows Identification of

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Discrimination of Diverse Coherences Allows Identification of Electronic Transitions of a Molecular Nanoring Vytautas Butkus, Jan Alster, Egle Basinskaite, Ram#nas Augulis, Patrik Neuhaus, Leonas Valkunas, Harry L. Anderson, Darius Abramavicius, and Donatas Zigmantas J. Phys. Chem. Lett., Just Accepted Manuscript • Publication Date (Web): 26 Apr 2017 Downloaded from http://pubs.acs.org on April 28, 2017

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The Journal of Physical Chemistry Letters

Discrimination of Diverse Coherences Allows Identication of Electronic Transitions of a Molecular Nanoring Vytautas Butkus,†,‡,¶ Jan Alster,†,§,k Egl e Ba²inskait e,‡,§ Ram unas Augulis,§,¶ Patrik Neuhaus,⊥ Leonas Valkunas,‡,¶ Harry L. Anderson,⊥ Darius Abramavicius,‡ and Donatas Zigmantas∗,§ †These authors equally contributed to this work

‡Department of Theoretical Physics, Faculty of Physics, Vilnius University, Sauletekio

Avenue 9-III, 10222 Vilnius, Lithuania

¶Center for Physical Sciences and Technology, Sauletekio Avenue 3, 10257 Vilnius,

Lithuania

§Department of Chemical Physics, Lund University, P.O. Box 124, 22100 Lund, Sweden kCurrent address: Faculty of Mathematics and Physics, Charles University in Prague,

Ke Karlovu 3, 121 16 Prague, Czech Republic

⊥Department of Chemistry, University of Oxford, Chemistry Research Laboratory,

Manseld Road, Oxford OX1 3TA, United Kingdom E-mail: [email protected]

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ACS Paragon Plus Environment


Abstract The role of quantum coherence in photochemical functions of complex molecular systems such as photosynthetic units is a broadly debated topic. Coexistence and intermixing of electronic and/or vibrational coherences has been proposed to be responsible for the observed long-lived coherences and eciency of energy transport. However, clear experimental evidence of coherences with dierent origins operating at the same time has been elusive. We present analysis of multidimensional spectra of a six-porphyrin nanoring supported by theoretical modeling that uncovers a great diversity of separable electronic, vibrational and mixed coherences and show their cooperation in shaping the spectroscopic response. Results yield direct assignment of electronic and vibronic states and characterization of the excitation dynamics. Clear disentanglement of coherences in molecules with extended π -conjugation opens new avenues for exploring coherent phenomena and understanding its importance for the function of the complex systems.

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Versatile applications of organic polymers and other molecules with extended π -conjugation as electric charge-carrying or light-emitting/absorbing moieties allow facile and cheap production of optoelectronic devices 1 . Even though they have been intensively studied, many questions remain due to their enormous chemical diversity, variability of optical and electronic properties, as well as due to the complex electronic structures of these materials. Electronic energy transfer (EET) which is a ubiquitous process in large molecular systems could be sensitive to coherent phenomena, arising from the quantum mechanical nature of the inner microscopic constituents. In the condition of electronic-vibrational resonance, quantum mixing of electronic and nuclear degrees of freedom of vibronically coupled molecular systems were suggested to result in a host of phenomena beyond the adiabatic approximation 2,3 . Indeed, it has been shown that coupling to vibrational modes should enhance the rate of EET 47 and of the charge transfer 8,9 . Coherences or superposition of states in the form of quantum beats in large molecules has been observed for a long time 1012 . Recent developments of ultrafast nonlinear spectroscopic techniques, such as the two-dimensional electronic spectroscopy (2DES) facilitated more detailed investigations of various coherences 8,9,1317 . However, even with simultaneously high spectral and temporal resolution provided by 2DES, the experimental identication of coherences and determination of their origin remains a highly complex issue. The nature of the long-lived coherences in the iconic Fenna-Matthews-Olson (FMO) light-harvesting complex (whether electronic 18 or vibrational 2,19,20 ) is still hotly debated. Mechanisms related to electronic-vibrational mixing 2,6,21 and/or inter-pigment correlations 22 were proposed to be important, allowing FMO to maintain the quantum coherence for as long as a picosecond. Multiple aforementioned studies proposed coexistence of electronic and vibrational coherences in the same system and their interplay, however it has never been unambiguously revealed. To explore coherences of various origin we studied a six-porphyrin nanoring complex. By analyzing two-dimensional oscillation maps we clearly identied three dierent types of coherences. This enabled us to determine the electronic origin of the strongest optical

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absorption bands. The porphyrin nanoring, the structure of which is depicted in Figure 1A and Supporting Information Figure S1, features multiple closely-spaced electronic and vibronic transitions. Therefore it is a well suited model system for gaining insight into electronic/vibronic transitions. The nanoring consists of six zinc(II) porphyrin units forming a belt around an inner hexapyridyl template; the porphyrins contain aryl groups (3,5bis(trihexylsilyl)benzene) at meso-positions and are interconnected by butadiyne links, ensuring complete π -conjugation of the nanoring. The ne structure of the main peaks, labeled as S1 through S6 in its absorption spectrum in methylcyclohexane solvent at 77 K (Figure 1B), suggests that quantum superpositions of the states can be readily excited by short laser pulses and coherences could be clearly resolvable in 2DES measurements as oscillations. Previous quantum chemistry calculations, using the time-dependent density functional theory, estimated the lowest-energy Q-band ground-to-excited state S0 − S1 transition at ∼ 10566 cm−1 . The sequence of similarly-spaced strong absorption peaks (for the nanoring studied here found at 11655, 12295 and 12862 cm−1 ) was discussed in terms of the Franck-Condon progression of the vibrational mode of ∼ 605 cm−1 , which was not identied. The complex structure of the uorescence spectrum was explained by electronic-vibrational interaction induced HerzbergâTeller intensity borrowing from

S0 − S2 to S0 − S1 transitions 23 . We performed 2DES measurements on the hexamer nanorings at 77 K using laser pulses with spectrum centered either at 800 nm or 880 nm, thus covering dierent parts of the absorption (refer to the upper panels in Figure 2A-B). The 2D spectrum at 30 fs waiting time, shown in Figure 2A, was obtained with 880 nm laser pulses, which covered the lowest electronic transitions. The spectrum is dominated by a strong diagonal peak at ∼ 11655 cm−1 . Other features on the diagonal observed at 10941 cm−1 (S1 ) and

11373 cm−1 (S2 ) follow the peaks of the absorption spectrum. These features are substantially weaker in the 2DES spectrum. However, the cross-peaks above the diagonal (P12 , P13 and P23 ), correlating the three diagonal peaks can be clearly resolved. Ex-

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Figure 1: Structure (A) and absorption spectrum (B) of the porphyrin nanoring. (B) Measured (black solid line) and simulated by minimal vibronic model (blue dashed line) absorption spectra at 77 K. Energies of the electronic transitions to states S1 − S6 are indicated by vertical solid lines; vibronic transitions - by vertical dashed lines. Frequencies of resolved coherent beatings are shown as colored segments, connecting the states involved in the corresponding quantum superpositions. The dierent colors signify the dierent origin of observed coherences.

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cited state absorption shows up as negative features below the diagonal, masking positive cross-peaks. Abs. (a.u.)

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Figure 2: Absorptive two-dimensional spectra at 30 fs waiting time. Spectra were obtained using laser pulses centered at 880 nm (A) and 800 nm (B), respectively. In the upper panels nanoring absorption spectrum and laser intensity spectra (gray shaded areas) are shown. In (A) the signal value is multiplied by a factor of 20 for the plot range where ω1 < 11157 cm−1 . (C) Zoomed in region of a degenerate peak in the 800 nm measurement (shown by red squares in (A) and (B)) and oscillatory dynamics of the P34 and P43 peaks. Spectra are drawn using linear color scale, normalized to the maximum of each spectrum. Dashed vertical and horizontal lines indicate the energies of states S1 − S6 . Laser pulses with the spectrum centered at 800 nm were used to investigate the spectral range of the three most prominent transitions. The corresponding 2D spectrum at 30 fs waiting time is shown in Figure 2B. The spectrum is abundant in features and at least 17 peaks can be resolved. Interestingly, a peak on the diagonal at around 11655 cm−1 consists of two previously unresolved 23,24 contributions separated by ∼ 80 cm−1 . It could be estimated from the position of the cross-peaks, indicated as P34 and P43 in Figure 2C, that the energies corresponding to these states are approximately 11600 cm−1 (S3 ) and 11680 cm−1 (S4 ). 6


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To measure coherent dynamics in the manifold of the excited states, 2DES data were acquired at a population time, t2 , up to 800 fs with 10 fs time step, forming a complete 3D data set. Feature-rich oscillatory evolution was observed throughout the whole (ω1 , ω3 ) 2D spectra as a function of t2 . Another data set with population times up to 1 ns was measured to capture slower excitation relaxation processes. Excitation population dynamics were extracted using a global tting procedure revealing three exponential decays: rst with a short lifetime of 160-250fs and the other two with much longer lifetimes of 235ps and >1ns, respectively. The shortest timescale is related to the downward energy relaxation in the singly-excited state manifold. This process is reected in the decay of diagonal peaks in the 2D spectrum alongside the simultaneous increase of cross-peaks below the diagonal if no other competing channels exist 25,26 . Note that presence of oscillatory signals with comparable amplitude made determination of lifetimes somewhat uncertain. This is especially the case for S3 and S4 states whose lifetimes are probably longer (for details, see Supporting Information). The longer timescales represent relaxation from the lowest (singlet) state (235 ps) and from some other (possibly triplet) long lived state (>1 ns) to the ground state (for more details see Supporting Information, Figures S2 and S3, and Table S1). Coherent beatings in the 2D spectra can be conveniently visualized by applying Fourier transforms t2 → ω2 to the residuals after subtraction of exponential decay components 27,28 . The resulting Fourier amplitude dependency is a three-dimensional (ω1 , ω2 , ω3 ) spectrum, which can be analyzed by producing 2D slices (ω1 ,ω3 ), so-called oscillation maps for a xed frequency ω2 . Notice that oscillations of conjugate coherences |aihb| and

|biha| appear at positive and negative ω2 frequencies, respectively 28,29 . The oscillation maps obtained from the rephasing part of the signal at a few selected

ω2 frequencies (see Supporting Information Figure S4 for the full summary of observed beating frequencies) are shown in Figure 3A-D. Three types of peak congurations can be distinguished in measurements of nanorings. (i) The maps at ω2 = ±80, ±307, ±570,

±615, ±695, and ±1150 cm−1 shown in Figure 3A-B are diagonally symmetric, i. e. positive and negative ω2 features are mirror images of each other with respect to the

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diagonal as explicitly shown in Figure 3A for ω2 = ±80 cm−1 . (ii) Oscillation maps at

ω2 = +380 cm−1 and −380 cm−1 , shown in Figure 3C, are diagonally asymmetric and the features below the diagonal in the ω2 = −380 cm−1 map are signicantly stronger than in the ω2 = +380 cm−1 map. (iii) Features in the ω2 = −235 cm−1 and ω2 = +235 cm−1

maps (Figure 3D) are diagonally asymmetric, but their amplitudes are of similar magnitude for positive and negative frequency maps. Refer to Supporting Information Figure S5 for extracted oscillation maps at the other distinguishable frequencies.

Table 1: Classication of the observed coherences ( 600 80 200 190 -

στ (fs) 160 130 20 30 40 -

Origin of coherence Electronic |S3 ihS4 | Vibrational Mixed |S∗4 ihS5 | Electronic |S2 ihS4 | Vibrational Vibrational Electronic |S5 ihS6 | Electronic |S4 ihS5 | Electronic |S3 ihS5 | Electronic |S3 ihS5 |

It has been previously shown that electronic, vibrational, and mixed coherences are manifested by their characteristic patterns and symmetries in the oscillation maps 3,30 . The symmetry of the experimental maps at ω2 = ±80, ±307, ±570, ±615, ±695 cm−1 and ±1185 cm−1 (Figure 3A and B) indicate that the underlying coherences are predominantly of the electronic origin. Dephasing times of these coherences vary in the range of 80 - 500 fs, as determined by the time domain tting procedure (Table 1 and Supporting Information). These oscillations are present only on the o-diagonal regions in the rephasing 2D spectra (and only on the diagonal peaks in the non-rephasing 2D spectrum; see Supporting Information Figure S6), and the peaks at positive and negative ω2 8


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Diversity of coherences revealed by oscillation maps, obtained from rephasing 2D spectra. (A) experimental oscillation maps of electronic coherences at ω2 = ±80, ±307, ±570, ±695, and ±1150 cm−1 ; (B) experimental and simulated oscillation maps for the electronic coherence at ω2 = ±615 cm−1 ; (C) the vibrational coherence at ω2 = ±380 cm−1 ; (D) the mixed coherence at ω2 = ±235 cm−1 . The oscillation ampliFigure 3:

tude at each point of a map is indicated by the color scale. Contours show 2D rephasing spectrum at 30 fs waiting time. Each experimental and theoretical map for a particular frequency is independently normalized to the maximum amplitude of the positive or negative frequency map. Dashed lines parallel to the diagonal are separated by the value of ω2 . Dashed vertical and horizontal lines indicate transition frequencies of electronic states S1 through S6 . All, but ω2 ± 307 cm−1 oscillation maps are extracted from the measurement with the laser spectrum at 800 nm. The ω2 ± 307 cm−1 map was obtained from the 880 nm measurement.

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frequencies in 2D slices are of the same amplitude. The electronic coherence with ω2 = +80 cm−1 (and ω2 = −80 cm−1 ) can be assigned to the coherent superposition |S4 ihS3 | (and |S3 ihS4 |) of the closely-positioned electronic states in the vicinity of 11655 cm−1 . The electronic coherence at ω2 = ±307 cm−1 shows up only in the measurement using laser pulses at 880 nm, signifying electronic quantum beats between states S2 and S4 , that could not be excited by laser pulses at 800 nm. Beatings with the ±570, ±615, ±695 cm−1 and ±1150 cm−1 frequencies represent quantum coherences |S5 ihS6 |, |S4 ihS5 |, |S3 ihS5 | and |S4 ihS6 | (and their Hermitian conjugates). All listed electronic beatings originating from superpositions of electronic states provide direct evidence that the states S2 through S6 are of electronic origin in contrast to previous suggestions 23,24 . Since S2 and S3 are assigned to electronic states, the clear correlation between them and S1 state, as indicated by the cross-peaks in Figure 2A, enable us to conclude that S1 is also an electronic state in accordance with the earlier studies 23 . We nd that some parts of certain oscillation maps reemerge in oscillation maps at adjacent frequencies (ω2 = ±570, ±615, and ±695 cm−1 ). This is caused by the broadening of the peaks in frequency domain due to the limited lifetime of corresponding oscillatory signals in the time domain. For example, the appearance of two upper, weaker peaks in the map of ω2 = ±615 cm−1 is caused by the |S4 ihS5 | coherence with the ±570 cm−1 frequency (Figure 3B, this coherence has a lifetime of 80 fs, which results in a spectral width of Fourier amplitude with more than 140 cm−1 ). This partial overlap of coherences is supported by for the observation that in the ω2 = ±615 cm−1 oscillation map the weaker peaks are shifted away from the ω3 = ω1 ± 615 cm−1 locations towards the lower frequency (dashed lines, parallel to the diagonal). We assign beatings with the ω2 = ±380 cm−1 frequency to the vibrational coherence, which can be superposition of vibrational states in the ground and excited electronic state. This follows from the oscillation maps (Figure 3C), which show the characteristic pattern of the vibrational coherence 30 . The ω2 = −380 cm−1 map contains many features below the diagonal, while the ω2 = +380 cm−1 map is similar to the above diagonal part of electronic oscillation maps presented in Figure 3A and B, corresponding to positive

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ω2 contributions. In contrast to the electronic coherences, the amplitude of the ω2 = −380 cm−1 map is signicantly larger than that of ω2 = +380 cm−1 2,31 . Detailed analysis of the maps implies that the vibrational ground state coherences |gihg∗ | (|g∗ i denotes vibrationally hot ground state) appear exclusively at ω2 < 0 in rephasing maps, whereas positive frequency maps feature only excited state coherences. The large amplitude of peaks in negative frequency map is related to the long dephasing time of ground state vibrational superpositions, whereas vibrational superpositions on excited states mapped onto ω2 = +380 cm−1 dephase faster due to the energy relaxation in the excited states manifold. The pattern of the weaker 450 cm−1 oscillation map is similar to the 380 cm−1 map, thus it can be assigned to the vibrational coherence. Maps at ω2 = 128 cm−1 ,

180 cm−1 have much lower amplitude and assignment of corresponding frequencies is more dicult (see the Supporting Information online). The pattern of the 450 cm−1 oscillation map is similar to the 380 cm−1 map, thus it can be assigned to vibrational coherence. Interestingly, beatings at ω2 = ±235 cm−1 clearly point to the mixed character of the coherence, signifying the quantum superposition of the S5 electronic state and vibronically hot state S∗4 (with excited 380 cm−1 vibrational mode). The beating frequency 235 cm−1 matches the energy gap between the identied states and the corresponding oscillation map is neither similar to vibrational nor to electronic coherences 3 (see Figure 3D). It is noteworthy to mention, that some contributions of ground-state coherences can be absent in oscillation maps due to a nite bandwidth of laser pulses in the experiment. It can make oscillation maps of vibrational coherences look like of purely electronic ones 32,33 . In this letter the distinction is unambiguous in oscillation maps, obtained using laser pulses with spectrum, centered at 880 nm, which fully covers lower-frequency transitions, including ground-state vibrational coherences. It is best seen in the ω2 = 307 cm−1 map in Figure 3A, where no features on the diagonal are seen (refer to Figure S7 in Supporting Information for oscillation maps at other frequencies). To support the assignment of the excited states and the nature of the broad range of coherences, the simple molecular vibronic model was considered. For qualitative simulations of the vibronic coupling in the porphyrin nanoring we used the theoretical approach

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developed for a vibronic molecular dimer 3,34 . Note that there have been several modeling studies published on purely exciton dynamics of porphyrin nanorings, see e.g. 35 . In our model we assume that two electronic states with the highest oscillator strengths, S4 and

S5 , are coupled to two vibrational modes with 380 cm−1 and 450 cm−1 frequencies with the Huang-Rhys factors of 0.03 and 0.01, respectively (see Supporting Information for details). The modeled absorption spectrum is presented in Figure 1B by the dashed blue line. The model does not attempts to match absorption spectrum very well, instead our aim is to qualitatively reproduce the oscillation maps observed in the experiments. We performed simulations of the full 3D spectrum and extracted oscillation maps at various ω2 values, corresponding to electronic, vibrational and mixed coherences (Figure 3B, C and D). Although we included only two molecular excitonic states in the vibronic model, calculated and experimental maps of the representative vibrational coherences at ±380 cm−1 , the electronic coherences at ±615 cm−1 , and the mixed coherences at ±235 cm−1 are in a very good agreement with the experimental ones, conrming our assignments. Information on the strongest transitions and coherences in hexamer nanorings is summarized in Figure 1B and Table 1, respectively. The absorption spectrum of the porphyrin nanoring is dominated by electronic transitions. Energy from higher-lying electronic and vibronic states relaxes to few lowest states within several hundred femtoseconds and decays from S1 state to the ground state in a few hundred picoseconds. The wide range of observed dephasing times of electronic coherences (80-500 fs) suggests a varied degree of correlation between the electronic states. This implies spatial delocalization of the electronic states in the nanoring, as it regulates dephasing times. The observation that dephasing times of electronic coherences are in the same range as excitation energy relaxation, points to the possibility that coherently prepared electronic wavepackets may relax coherently through the manifold of electronic states in nanorings. Concluding, analysis of coherences and their origin helps in disentangling the energy level structure of the excited states and provides a means to distinguish between electronic and vibronic features in spectroscopic signals. Due to the convoluted nature of electronic and vibrational degrees of freedom in molecular systems, the variety of co-

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herences unraveled in this report should be present in any large molecule or molecular aggregate. The 2DES analysis of excitation dynamics presented here can be applied to an arbitrary molecular system with a complex coupling network between electronic and vibrational transitions that dictates coherent and incoherent energy transfer dynamics.

Methods Diractive-beamsplitter-based four-wave mixing setup with phase-matched boxcar geometry and heterodyne detection was used in 2DES experiments 36,37 . The lab-built noncollinear optical parametric amplier (NOPA) pumped by the Yb:KGW amplied laser (Pharos, Light Conversion) operating at 20 kHz repetition rate was used as the source of laser pulses. NOPA produced pulses with duration of 17 fs and 14 fs centered at 800 nm and 880 nm, respectively . Double modulation lock-in detection was employed, discussed in details in 37 . Coherence time delay was scanned within the -200 - 450 fs interval with 2 fs step by employing movable fused-silica wedges. In most experiments population time

t2 was scanned from 0 to 800 fs with 10 fs step using a mechanical delay stage. In one experiment, population time was scanned up to 1 ns to access the lifetimes of slower processes. Data acquired for population time delays up to 20 fs were omitted from the analysis to avoid pulse overlap eects. Spectrometer and dispersive delay line calibrations were performed using procedures described in 38 . The energy of excitation pulses was 1-2 nJ/pulse and 1/e diameter of the focused beams at the sample was ~160 µm. All the measurements were done at 77 K in methylcyclohexane, employing a liquid N2 bath cryostat (Optistat-DN2, Oxford Instruments). Spectral interferometry detection allowed for determination of the amplitude and phase of the 2D signal. The real (absorptive) part of the total response or alternatively the real part of the rephasing and non-rephasing signal were analyzed. The resolution of the collected data was 37 cm−1 on the excitation (ω1 ) and 33 cm−1 on the detection (ω3 ) axis. 2D spectra and oscillation maps presented in the paper were Fourier interpolated for clarity. Transition energies of states S1 through

S6 were determined from the absorption spectrum and positions of the cross-peaks in the 2D spectra and in the oscillation maps. 13



Acknowledgement The work in Lund was supported by Swedish Research Council, the Knut and Alice Wallenberg Foundation, and the Wenner-Gren Foundation. The work in Oxford was supported by European Commission (Marie Curie Individual Fellowship to P. N. under contract PIEF-GA-2011-301336, the ERC), the EPSRC. E. B. and D. A. acknowledge the support of the Research Council of Lithuania (Grant No. MIP-090/2015). V.B. acknowledges support by project Promotion of Student Scientic Activities (VP1-3.1MM-01-V-02-003) from the Research Council of Lithuania.

Supporting Information Available The Supporting Information is available free of charge on the ACS Publications website.

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2013, 110, 12031208.

(3) Butkus, V.; Valkunas, L.; Abramavicius, D. Vibronic phenomena and exciton vibrational interference in two-dimensional spectra of molecular aggregates. J.

Chem. Phys. 2014, 140, 034306. (4) Womick, J.; Moran, A. Vibronic Enhancement of Exciton Sizes and Energy Transport in Photosynthetic Complexes. J. Phys. Chem. B

2011, 115, 13471356.

(5) Kolli, A.; O'Reilly, E.; Scholes, G.; Olaya-Castro, A. The fundamental role of quan-

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