Separating single- from multi-particle dynamics in nonlinear spectroscopy.

Quantum states depend on the coordinates of all their constituent particles, with essential multi-particle correlations. Time-resolved laser spectroscopy1 is widely used to probe the energies and dynamics of excited particles and quasiparticles such as electrons and holes2,3, excitons4-6, plasmons7, polaritons8 or phonons9. However, nonlinear signals from single- and multiple-particle excitations are all present simultaneously and cannot be disentangled without a priori knowledge of the system4,10. Here, we show that transient absorption-the most commonly used nonlinear spectroscopy-with N prescribed excitation intensities allows separation of the dynamics into N increasingly nonlinear contributions; in systems well-described by discrete excitations, these N contributions systematically report on zero to N excitations. We obtain clean single-particle dynamics even at high excitation intensities and can systematically increase the number of interacting particles, infer their interaction energies and reconstruct their dynamics, which are not measurable via conventional means. We extract single- and multiple-exciton dynamics in squaraine polymers11,12 and, contrary to common assumption6,13, we find that the excitons, on average, meet several times before annihilating. This surprising ability of excitons to survive encounters is important for efficient organic photovoltaics14,15. As we demonstrate on five diverse systems, our procedure is general, independent of the measured system or type of observed (quasi)particle and straightforward to implement. We envision future applicability in the probing of (quasi)particle interactions in such diverse areas as plasmonics7, Auger recombination2 and exciton correlations in quantum dots5,16,17, singlet fission18, exciton interactions in two-dimensional materials19 and in molecules20,21, carrier multiplication22, multiphonon scattering9 or polariton-polariton interaction8.

Simulation of exciton spectra in disordered supramolecular polymers: exciton localization in cisoid indolenine squaraine hexamers.

In order to understand the effects of disorder and defects in oligomers and polymers on the localization of excitons, we investigated the spectral properties of the squaraine B hexamer using long range corrected tight-binding TDDFT (lc-TDDFTB) and Frenkel-exciton model based calculations. Employing classical molecular dynamics, the cisoid indolenine squaraine hexamers helix was propagated in DCM and acetone to obtain ensembles of realistic structures, which naturally exhibit considerable disorder. The trajectories together with several model squaraine systems were studied to show the profound effects of disorder in the superstructure and disorder of the local monomer geometry on optical properties like absorption and exciton localization. We further compared lc-TDDFTB and exciton theory derived spectral data to related experimental data on absorption, exciton transfer and localization in squaraine polymers and oligomers.

High-order pump-probe and high-order two-dimensional electronic spectroscopy on the example of squaraine oligomers.

Time-resolved spectroscopy is commonly used to study diverse phenomena in chemistry, biology, and physics. Pump-probe experiments and coherent two-dimensional (2D) spectroscopy have resolved site-to-site energy transfer, visualized electronic couplings, and much more. In both techniques, the lowest-order signal, in a perturbative expansion of the polarization, is of third order in the electric field, which we call a one-quantum (1Q) signal because in 2D spectroscopy it oscillates in the coherence time with the excitation frequency. There is also a two-quantum (2Q) signal that oscillates in the coherence time at twice the fundamental frequency and is fifth order in the electric field. We demonstrate that the appearance of the 2Q signal guarantees that the 1Q signal is contaminated by non-negligible fifth-order interactions. We derive an analytical connection between an nQ signal and (2n + 1)th-order contaminations of an rQ (with r < n) signal by studying Feynman diagrams of all contributions. We demonstrate that by performing partial integrations along the excitation axis in 2D spectra, we can obtain clean rQ signals free of higher-order artifacts. We exemplify the technique using optical 2D spectroscopy on squaraine oligomers, showing clean extraction of the third-order signal. We further demonstrate the analytical connection with higher-order pump-probe spectroscopy and compare both techniques experimentally. Our approach demonstrates the full power of higher-order pump-probe and 2D spectroscopy to investigate multi-particle interactions in coupled systems.

Solvent Induced Helix Folding of Defined Indolenine Squaraine Oligomers.

A protecting group strategy was employed to synthesise a series of indolenine squaraine dye oligomers up to the nonamer. The longer oligomers show a distinct solvent dependence of the absorption spectra, that is, either a strong blue shift or a strong red shift of the lowest energy bands in the near infrared spectral region. This behaviour is explained by exciton coupling theory as being due to H- or J-type coupling of transition moments. The H-type coupling is a consequence of a helix folding in solvents with a small Hansen dispersity index. DOSY NMR, small angle neutron scattering (SANS), quantum chemical and force field calculations agree upon a helix structure with an unusually large pitch and open voids that are filled with solvent molecules, thereby forming a kind of clathrate. The thermodynamic parameters of the folding process were determined by temperature dependent optical absorption spectra.

Fluorescence band exchange narrowing in a series of squaraine oligomers: energetic vs. structural disorder.

The influence of oligosquaraine chain length on the energies and shape of absorption and emission bands and the exciton coherence length is studied in CHCl3 where the oligomers adopt a random coil structure. From the observed fluorescence band narrowing an effective coherence length of Ncoh = 2.5 was estimated for the nonamer. Applying a theoretical Frenkel exciton model the absorption and emission spectra were simulated which confirmed the experimental results. From the relative amplitude of the 00 peak to the vibronic shoulder the coherence length was estimated which yields a somewhat higher saturation value of Ncoh≈ 3 for the nonamer, which is in very good agreement with the theoretical amplitude ratio. The coherence length is much smaller than the geometrical length because the electronic delocalisation is reduced by structural disorder. Taking into account the energetic (diagonal) and structural (off-diagonal) disorder we observed a different influence on the absorption and fluorescence spectra. For the emission spectra, exciton delocalisation leads to a narrowing of the band caused by averaging over energetic disorder, but for the absorption band the spectra are broadened by excitonic splitting and structural disorder.

Ultrafast Energy Transfer Dynamics in a Squaraine Heterotriad.

A squaraine heterotriad consisting of three different covalently linked squaraine chromophores was synthesized, and its absorption spectra were interpreted in terms of Kasha's exciton coupling theory. Using the exciton couplings derived from model dyads (ca. 700 cm-1) as the input, we were able to predict the exciton state energies of the heterotriad. Transient absorption spectroscopy with femtosecond time resolution showed that excitation of the highest exciton state populates a state mainly localized at one terminal squaraine chromophore, and energy transfer to the lowest exciton state localized at the other terminal squaraine occurs within 30 fs. Field-induced surface hopping dynamics simulations support the assumption of ultrafast energy transfer. Moreover, they show the close relationship between internal conversion and energy transfer in the intermediate to weak coupling regime. The latter is a consequence of excitation localization caused by molecular vibrations.

Facile Access to Unprecedented Electron-Precise Monohydrodiboranes(4), cis-1,2-Dihydrodiboranes(4), and a 1,1-Dihydrodiborane(5).

2,3-Bis(dimethylamino)-substituted B2 N2 C2 heterocycles underwent selective dimethylamino/hydride exchange with either one or two equivalents of BH3 ⋅SMe2 to give the corresponding cyclic monohydrido- or (cis)1,2-dihydridodiboranes(4), respectively. Upon either heating or irradiation in solution, the latter underwent ring contraction to the corresponding five-membered BN2 C2 heterocycles, whereas irradiation of the 1,2-dimethylaminoethene-supported 1,2-dihydridodiborane(4) in the presence of PEt3 gave an unprecedented unsymmetrical 1,1-dihydrodiborane(5) phosphine adduct.

Correction: From wavelike to sub-diffusive motion: exciton dynamics and interaction in squaraine copolymers of varying length.

[This corrects the article DOI: 10.1039/C9SC04367E.].

From wavelike to sub-diffusive motion: exciton dynamics and interaction in squaraine copolymers of varying length.

Exciton transport and exciton-exciton interactions in molecular aggregates and polymers are of great importance in natural photosynthesis, organic electronics, and related areas of research. Both the experimental observation and theoretical description of these processes across time and length scales, including the transition from the initial wavelike motion to the following long-range exciton transport, are highly challenging. Therefore, while exciton dynamics at small scales are often treated explicitly, long-range exciton transport is typically described phenomenologically by normal diffusion. In this work, we study the transition from wavelike to diffusive motion of interacting exciton pairs in squaraine copolymers of varying length. To this end we use a combination of the recently introduced exciton-exciton-interaction two-dimensional (EEI2D) electronic spectroscopy and microscopic theoretical modelling. As we show by comparison with the model, the experimentally observed kinetics include three phases, wavelike motion dominated by immediate exciton-exciton annihilation (10-100 fs), sub-diffusive behavior (0.1-10 ps), and excitation relaxation (0.01-1 ns). We demonstrate that the key quantity for the transition from wavelike to diffusive dynamics is the exciton delocalization length relative to the length of the polymer: while in short polymers wavelike motion of rapidly annihilating excitons dominates, in long polymers the excitons become locally trapped and exhibit sub-diffusive behavior. Our findings indicate that exciton transport through conjugated systems emerging from the excitonic structure is generally not governed by normal diffusion. Instead, to characterize the material transport properties, the diffusion presence and character should be determined.