Dark Electronic States Research Articles

Role of Dark States and Stokes Shift Simulations for Tetraphenylpyrazine Compared to Other Donor-Acceptor Photosensitizers.

An excellent agreement for simulated and measured absorption and emission spectra is found for four donor-acceptor aromatic molecules (tetraphenylpyrazine, tetraphenylethene, distirylanthracene and hexaphenylsilole) whose derivatives serve as solid state photosensitizers. After comparing several hybrid TDDFT functionals, EOM-CCSD, and experiments, the best agreement was found with TD-B3LYP and double zeta basis sets (6-31G** and def2-SVP) for one molecule in gas phase. A full characterisation of twelve to twenty electronic excited states was performed in every system. Symmetry-forbidden bands are found in the absorption spectra by sampling fifty to hundred geometries from a Wigner distribution. The density of states in the region 2-6 eV was also analysed, showing a very packed region of excited states and suggesting that dark electronic states may play a role in the dynamics of some of the photoexcited systems. Further calculations were done with QM/xTB at geometries extracted from previously published X-ray data to evaluate the influence of the environment on the excitations of the four aggregated molecular crystals.

Bose–Einstein condensation of light in a semiconductor quantum well microcavity

When particles with integer spin accumulate at low temperature and high density, they undergo Bose–Einstein condensation (BEC). Atoms, magnons, solid-state excitons, surface plasmon polaritons and excitons coupled to light exhibit BEC, which results in high coherence due to massive occupation of the respective system’s ground state. Surprisingly, photons were shown to exhibit BEC recently in organic-dye-filled optical microcavities, which—owing to the photon’s low mass—occurs at room temperature. Here we demonstrate that photons within an inorganic semiconductor microcavity also thermalize and undergo BEC. Although semiconductor lasers are understood to operate out of thermal equilibrium, we identify a region of good thermalization in our system where we can clearly distinguish laser action from BEC. Semiconductor microcavities are a robust system for exploring the physics and applications of quantum statistical photon condensates. In practical terms, photon BECs offer their critical behaviour at lower thresholds than lasers. Our study shows two further advantages: the lack of dark electronic states in inorganic semiconductors allows these BECs to be sustained continuously; and quantum wells offer stronger photon–photon scattering. We measure an unoptimized interaction parameter (g̃\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ilde{{{{{g}}}}}$$\\end{document} ≳ 10–3), which is large enough to access the rich physics of interactions within BECs, such as superfluid light.

Non-adiabatic electronic relaxation of tetracene from its brightest singlet excited state.

The ultrafast relaxation dynamics of tetracene following UV excitation to the bright singlet state S6 has been studied with time-resolved photoelectron spectroscopy. With the help of high-level abinitio multireference perturbation theory calculations, we assign photoelectron signals to intermediate dark electronic states S3, S4, and S5 as well as to a low-lying electronic state S2. The energetic structure of these dark states has not been determined experimentally previously. The time-dependent photoelectron yields assigned to the states S6, S5, and S4 have been analyzed and reveal the depopulation of S6 within 60fs, while S5 and S4 are populated with delays of about 50 and 80fs. The dynamics of the lower-lying states S3 and S2 seem to agree with a delayed population coinciding with the depopulation of the higher-lying states S4-S6 but could not be elucidated in full detail due to the low signal levels of the corresponding two-photon ionization probe processes.

Embrace the darkness: An experimental perspective on organic exciton–polaritons

Organic polaritonics has emerged as a captivating interdisciplinary field that marries the complexities of organic photophysics with the fundamental principles of quantum optics. By harnessing strong light–matter coupling in organic materials, exciton–polaritons offer unique opportunities for advanced device performance, including enhanced energy transport and low-threshold lasing, as well as new functionalities like polariton chemistry. In this review, we delve into the foundational principles of exciton–polaritons from an experimental perspective, highlighting the key states, processes, and timescales that govern polariton phenomena. Our review centers on the spectroscopy of exciton–polaritons. We overview the primary spectroscopic approaches that reveal polariton phenomena, and we discuss the challenges in disentangling polaritonic signatures from spectral artifacts. We discuss how organic materials, due to their complex photophysics and disordered nature, not only present challenges to the conventional polariton models but also provide opportunities for new physics, like manipulating dark electronic states. As the research field continues to grow, with increasingly complex materials and devices, this review serves as a valuable introductory guide for researchers navigating the intricate landscape of organic polaritonics.

Designing Red-Shifted Molecular Emitters Based on the Annulated Locked GFP Chromophore Derivatives.

Bioimaging techniques require development of a wide variety of fluorescent probes that absorb and emit red light. One way to shift absorption and emission of a chromophore to longer wavelengths is to modify its chemical structure by adding polycyclic aromatic hydrocarbon (PAH) fragments, thus increasing the conjugation length of a molecule while maintaining its rigidity. Here, we consider four novel classes of conformationally locked Green Fluorescent Protein (GFP) chromophore derivatives obtained by extending their aromatic systems in different directions. Using high-level ab initio quantum chemistry calculations, we show that the alteration of their electronic structure upon annulation may unexpectedly result in a drastic change of their fluorescent properties. A flip of optically bright and dark electronic states is most prominent in the symmetric fluorene-based derivative. The presence of a completely dark lowest-lying excited state is supported by the experimentally measured extremely low fluorescence quantum yield of the newly synthesized compound. Importantly, one of the asymmetric modes of annulation provides a very promising strategy for developing red-shifted molecular emitters with an absorption wavelength of ∼600 nm, having no significant impact on the character of the bright S-S1 transition.

ExoMol line lists – XLIV. Infrared and ultraviolet line list for silicon monoxide (28Si16O)

ABSTRACT A new silicon monoxide (28Si16O) line list covering infrared, visible, and ultraviolet regions called SiOUVenIR is presented. This line list extends the infrared EBJT ExoMol line list by including vibronic transitions to the $A\, {}^{1}\Pi$ and $E\, {}^{1}\Sigma ^{+}$ electronic states. Strong perturbations to the $A\, {}^{1}\Pi$ band system are accurately modelled through the treatment of six dark electronic states: $C\, {}^{1}\Sigma ^{-}$, $D\, {}^{1}\Delta$, $a\, {}^{3}\Sigma ^{+}$, $b\, {}^{3}\Pi$, $e\, {}^{3}\Sigma ^{-}$, and $d\, {}^{3}\Delta$. Along with the $X\, {}^{1}\Sigma ^{+}$ ground state, these nine electronic states were used to build a comprehensive spectroscopic model of SiO using a combination of empirical and ab initio curves, including the potential energy (PE), spin–orbit, electronic angular momentum, and (transition) dipole moment curves. The ab initio PE and coupling curves, computed at the multireference configuration interaction level of theory, were refined by fitting their analytical representations to 2617 experimentally derived SiO energy levels determined from 97 vibronic bands belonging to the X–X, E–X, and A–X electronic systems through the MARVEL (Measured Active Rotational–Vibrational Energy Levels) procedure. 112 observed forbidden transitions from the C–X, D–X, e–X, and d–X bands were assigned using our predictions, and these could be fed back into the MARVEL procedure. The SiOUVenIR line list was computed using published ab initio transition dipole moments for the E–X and A–X bands; the line list is suitable for temperatures up to 10 000 K and for wavelengths longer than 140 nm. SiOUVenIR is available from www.exomol.com and the CDS data base.

Controlling Defect-State Photophysics in Covalently Functionalized Single-Walled Carbon Nanotubes.

ConspectusSingle-walled carbon nanotubes (SWCNTs) show promise as light sources for modern fiber optical communications due to their emission wavelengths tunable via chirality and diameter dependency. However, the emission quantum yields are relatively low owing to the existence of low-lying dark electronic states and fast excitonic diffusion leading to carrier quenching at defects. Covalent functionalization of SWCNTs addresses this problem by brightening their infrared emission. Namely, introduction of sp3-hybridized defects makes the lowest energy transitions optically active for some defect geometries and enables further control of their optical properties. Such functionalized SWCNTs are currently the only material exhibiting room-temperature single photon emission at telecom relevant infrared wavelengths. While this fluorescence is strong and has the right wavelength, functionalization introduces a variety of emission peaks resulting in spectrally broad inhomogeneous photoluminescence that prohibits the use of SWCNTs in practical applications. Consequently, there is a strong need to control the emission diversity in order to render these materials useful for applications. Recent experimental and computational work has attributed the emissive diversity to the presence of multiple localized defect geometries each resulting in distinct emission energy. This Account outlines methods by which the morphology of the defect in functionalized SWCNTs can be controlled to reduce emissive diversity and to tune the fluorescence wavelengths. The chirality-dependent trends of emission energies with respect to individual defect morphologies are explored. It is demonstrated that defect geometries originating from functionalization of SWCNT carbon atoms along bonds with strong π-orbital mismatch are favorable. Furthermore, the effect of controlling the defect itself through use of different chemical groups is also discussed. Such tunability is enabled due to the formation of specific defect geometries in close proximity to other existing defects. This takes advantage of the changes in π-orbital mismatch enforced by existing defects and the resulting changes in reactivities toward formation of specific defect morphologies. Furthermore, the trends in emissive energies are highly dependent on the value of mod(n-m,3) for an (n,m) tube chirality. These powerful concepts allow for a targeted formation of defects that emit at desired energies based on SWCNT single chirality enriched samples. Finally, the impact of functionalization with specific types of defects that enforce certain defect geometries due to steric constraints in bond lengths and angles to the SWCNT are discussed. We further relate to a similar effect that is present in systems where high density of surface defects is formed due to high reactant concentration. The outlined strategies suggested by simulations are instrumental in guiding experimental efforts toward the generation of functionalized SWCNTs with tunable emission energies.

Excited state non-adiabatic dynamics of the smallest polyene, trans 1,3-butadiene. I. Time-resolved photoelectron-photoion coincidence spectroscopy.

The ultrafast excited state dynamics of the smallest polyene, trans-1,3-butadiene, were studied by femtosecond time-resolved photoelectron-photoion coincidence (TRPEPICO) spectroscopy. The evolution of the excited state wavepacket, created by pumping the bright 1Bu (ππ*) electronic state at its origin of 216 nm, is projected via one- and two-photon ionization at 267 nm onto several ionization continua. The results are interpreted in terms of Koopmans' correlations and Franck-Condon factors for the excited and cationic states involved. The known predissociative character of the cation excited states is utilized to assign photoelectron bands to specific continua using TRPEPICO spectroscopy. This permits us to report the direct observation of the famously elusive S1(21Ag) dark electronic state during the internal conversion of trans 1,3-butadiene. Our phenomenological analysis permits the spectroscopic determination of several important time constants. We report the overall decay lifetimes of the 11Bu and 21Ag states and observe the re-appearance of the hot ground state molecule. We argue that the apparent dephasing time of the S2(11Bu) state, which leads to the extreme breadth of the absorption spectrum, is principally due to large amplitude torsional motion on the 1Bu surface in conjunction with strong non-adiabatic couplings via conical intersections, whereupon nuclear wavepacket revivals to the initial Franck-Condon region become effectively impossible. In Paper II [W. J. Glover et al., J. Chem. Phys. 148, 164303 (2018)], ab initio multiple spawning is used for on-the-fly computations of the excited state non-adiabatic wavepacket dynamics and their associated TRPEPICO observables, allowing for direct comparisons of experiment with theory.

Detection of dark states in two-dimensional electronic photon-echo signals via ground-state coherence.

Several recent experiments report on possibility of dark-state detection by means of so called beating maps of two-dimensional photon-echo spectroscopy [Ostroumov et al., Science 340, 52 (2013); Bakulin et al., Ultrafast Phenomena XIX (Springer International Publishing, 2015)]. The main idea of this detection scheme is to use coherence induced upon the laser excitation as a very sensitive probe. In this study, we investigate the performance of ground-state coherence in the detection of dark electronic states. For this purpose, we simulate beating maps of several models where the excited-state coherence can be hardly detected and is assumed not to contribute to the beating maps. The models represent strongly coupled electron-nuclear dynamics involving avoided crossings and conical intersections. In all the models, the initially populated optically accessible excited state decays to a lower-lying dark state within few hundreds femtoseconds. We address the role of Raman modes and of interstate-coupling nature. Our findings suggest that the presence of low-frequency Raman active modes significantly increases the chances for detection of dark states populated via avoided crossings, whereas conical intersections represent a more challenging task.

Femtosecond time-resolved electronic relaxation dynamics in tetrathiafulvalene.

In the present paper, the ultrafast electronic relaxation of tetrathiafulvalene (TTF) initiated around 4 eV is studied by femtosecond time-resolved velocity-map imaging. The goal is to investigate the broad double structure observed in the absorption spectrum at this energy. By monitoring the transients of the parent cation and its fragments and by varying the pump and the probe wavelengths, two internal conversions and intramolecular vibrational relaxation are detected both on the order of a few hundred of femtoseconds. Photoelectron images permit the assignment of a dark electronic state involved in the relaxation. In addition, the formation of the dimer of TTF has been observed.

Electronic spectra and excited state dynamics of pentafluorophenol: Effects of low-lying πσ(∗) states.

Multiple fluorine atom substitution effect on photophysics of an aromatic chromophore has been investigated using phenol as the reference system. It has been noticed that the discrete vibronic structure of the S1←S0 absorption system of phenol vapor is completely washed out for pentafluorophenol (PFP), and the latter also shows very large Stokes shift in the fluorescence spectrum. For excitations beyond S1 origin, the emission yield of PFP is reduced sharply with increase in excess vibronic energy. However, in a collisional environment like liquid hydrocarbon, the underlying dynamical process that drives the non-radiative decay is hindered drastically. Electronic structure theory predicts a number of low-lying dark electronic states of πσ(∗) character in the vicinity of the lowest valence ππ(∗) state of this molecule. Tentatively, we have attributed the excitation energy dependent non-radiative decay of the molecule observed only in the gas phase to an interplay between the lowest ππ(∗) and a nearby dissociative πσ(∗) state. Measurements in different liquids reveal that some of the dark excited states light up with appreciable intensity only in protic liquids like methanol and water due to hydrogen bonding between solute and solvents. Electronic structure theory methods indeed predict that for PFP-(H2O)n clusters (n = 1-11), intensities of a number of πσ(∗) states are enhanced with increase in cluster size. In contrast with emitting behavior of the molecule in the gas phase and solutions of nonpolar and polar aprotic liquids, the fluorescence is completely switched off in polar protic liquids. This behavior is a chemically significant manifestation of perfluoro effect, because a very opposite effect occurs in the case of unsubstituted phenol for which fluorescence yield undergoes a very large enhancement in protic liquids. Several dynamical mechanisms have been suggested to interpret the observed photophysical behavior.

Hot Injection Processes in Optically Excited States: Molecular Design for Optimized Photocapture

Design principles for efficient solar photocapture using a single molecule are presented. The proposed molecular model is composed of ground and excited bright and dark electronic states. Once photoexcited to the bright states, vibrational relaxation and dissipation to the ground vibrational level of the bright state commonly occur. This degrades a substantial amount of the incoming photon energy into heat, further reducing the efficiency of molecular photocells. One way to circumvent this energy flow from electronic excitation into heat is the hot injection process, by which the original excited bright state undergoes a rapid crossing to an acceptor dark state, with a higher potential energy minimum, and is trapped in the region of that minimum. By choosing an appropriate pair of vibrational modes, the overall energy gain can be increased substantially and the constraints on the bath behavior substantially simplified. We present calculations in a two-dimensional vibrational space, along with energy relaxation and transfer to the bath (using a Stochastic Surrogate Hamiltonian model). We find that the second degree of vibrational freedom, if carefully chosen, strongly increases the efficiency and the possibility of successful hot injection. In addition, the same molecular model can be designed to utilize the red part of the solar spectrum. Excited state absorption can recycle the wasted bright state population thus increasing the efficiency of solar capture.

The role of the low-lying dark nπ* states in the photophysics of pyrazine: a quantum dynamics study.

The excited state dynamics of pyrazine has attracted considerable attention in the last three decades. It has long been recognized that after UV excitation, the dynamics of the molecule is impacted by strong non-adiabatic effects due to the existence of a conical intersection between the B2u(ππ*) and B3u(nπ*) electronic states. However, a recent study based on trajectory surface hopping dynamics simulations suggested the participation of the Au(nπ*) and B2g(nπ*) low-lying dark electronic states in the ultrafast radiationless decay of the molecule after excitation to the B2u(ππ*) state. The purpose of this work was to pursue the investigation of the role of the Au(nπ*) and B2g(nπ*) states in the photophysics of pyrazine. A linear vibronic coupling model hamiltonian including the four lowest excited electronic states and the sixteen most relevant vibrational degrees of freedom was constructed using high level XMCQDPT2 electronic structure calculations. Wavepacket propagations using the MCTDH method were then performed and used to simulate the absorption spectrum and the electronic state population dynamics of the system. Our results show that the Au(nπ*) state plays an important role in the photophysics of pyrazine.

Direct Observation of a Dark State in Lycopene Using Pump-DFWM

We apply pump-degenerate four-wave-mixing (pump-DFWM) for the investigation of the ultrafast internal relaxation of the excited states of lycopene. A unique feature in the pump-DFWM signal, appearing at small temporal delays between the initial pump pulse and the DFWM sequence, provides direct evidence for the participation of an additional excited state located between the S(2) and S(1) states. Our experimental findings are corroborated by a detailed numerical simulation of lycopene's pump-DFWM signal using the Brownian oscillator model. A very fast dynamics directly after excitation of the S(2) state manifests as a component populated with a time constant of about 20 fs and which decays to S(1) with a lifetime of 110 fs. This ultrafast dynamics is discussed under the light of several different models suggested for the relaxation pathway of carotenoids. In this context, we show that the dynamics can be explained in terms of a dark electronic state between the S(2) and S(1) states.

Electronic and Vibrational Spectroscopy of 1‐Methylthymine and its Water Clusters: The Dark State Survives Hydration

Electronic and vibrational gas phase spectra of 1-methylthymine (1MT) and 1-methyluracil (1MU) and their clusters with water are presented. Mass selective IR/UV double resonance spectra confirm the formation of pyrimidine-water clusters and are compared to calculated vibrational spectra obtained from ab initio calculations. In contrast to Y. He, C. Wu, W. Kong; J. Phys. Chem. A, 2004, 108, 94 we are able to detect 1MT/1MU and their water clusters via resonant two-photon delayed ionization under careful control of the applied water-vapor pressure. The long-living dark electronic state of 1MT and 1MU detected by delayed ionization, survives hydration and the photostability of 1MT/1MU cannot be attributed solely to hydration. Oxygen coexpansions and crossed-beam experiments indicate that the triplet state population is probably small compared to the (1)n pi* and/or hot electronic ground state population. Ab initio theory shows that solvation of 1MT by water does not lead to a substantial modification of the electronic relaxation and quenching of the (1)n pi* state. Relaxation pathways via (1)pi pi*(1)-n pi*(1) and (1)pi pi*-S(0) conical intersections and barriers have been identified, but are not significantly altered by hydration.

Fluorescence Studies of Terrylene in a Supersonic Jet: Indication of A Dark Electronic State Below the Allowed Transition

Jet-cooled terrylene has been studied in helium buffer gas using a pulsed nozzle by means of laser-induced fluorescence. Fluorescence excitation and two-color depletion experiments (resulting in hole burning spectra) are presented. Analysis of the spectra leads to the conclusion that another excited electronic state is present in the vicinity of the allowed 1B1u state. Assuming (according to previous literature suggestions Karabunarliev, S.; Baumgarten, M.; Müllen, K. J. Phys. Chem. A 1998, 102, 7029) that this dark state is the 21Ag state, we discuss the vibrational structure of the fluorescence excitation spectrum in terms of two manifolds of vibronic states belonging to Sd(21Ag) and S1(1B1u) states. The anomalous shift between excitation and dispersed fluorescence spectra observed earlier for terrylene in a neon matrix is discussed as a consequence of terrylene electronic relaxation to the low-energy dark state.

The photophysics of metalloporphyrins excited in their Soret and higher energy UV absorption bands

Photophysical processes involving the higher electronic excited states of diamagnetic porphyrins and metalloporphyrins are critically reviewed. Intramolecular electronic relaxation of one-photon Soret-excited molecules in solution is now known to involve processes other than S 2 - S 1 internal conversion; dark electronic states are implicated. Sequential two-photon excitation to produce gerade excited singlet states ( S n , n > 2) results in relaxation dynamics that are quantitatively different from those resulting from one-photon excitation to ungerade states of about the same energy. Intermolecular electron and electronic energy transfer involving Soret-excited metalloporphyrins and intramolecular electron and electronic energy transfer in Soret-excited dyads and larger arrays containing porphyrins are reviewed. Metalloporphyrins containing main group metals or transition metals with filled d orbitals exhibit relaxation dynamics that differ from metalloporphyrins containing transition metals with unfilled d orbitals. Non-linear phenomena associated with multi-photon excitation of diamagnetic metalloporphyrins are also reviewed.

Structural and Spectroscopic Properties of Mg−Bacteriochlorin and Methyl Bacteriochlorophyllidesa,b,g, andhStudied by Semiempirical, ab Initio, and Density Functional Molecular Orbital Methods

Ab initio HF/6-31G* and density functional B3LYP/6-31G* methods have been used to calculate fully optimized structures of methyl bacteriochlorophyllides a, b, g, and h and magnesium-bacteriochlorin. Semiempirical ZINDO/S CIS and ab initio CIS/6-31G* and CIS/6-311G** configuration interaction methods and time dependent HF/6-31G*, HF/6-311G**, B3LYP/6-31G*, and B3LYP/6-311G** methods were used to estimate corresponding spectroscopic transition energies of the chromophores. The effects of solvent coordination were also studied by optimizing structures of 1:1 complexes of the methyl bacteriochlorophyllides and acetone. The self-consistent reaction field model was used to estimate bulk solvent effects. Differences in B3LYP and HF bond lengths of the bacteriochlorin had a strong influence on the calculated transition energies. Large variations of calculated transition energies were also observed when coordinates from different X-ray structure determinations were used for the same pigment. In the five coordinated solvent complex, the Mg atom is shifted from the bacteriochlorin plane, inducing red shifts of the Qx and Soret transitions. Linear correlations of the calculated and experimental solution transition energies were obtained with characteristic slopes and intercepts for each method used, reflecting inadequacy of the methods to describe transition energies in bacteriochlorins. Such correlations were shown to be useful in prediction of site transition energies for a pigment (pigment group) in solution or in protein under a given computational approach. Best correlations and the best calculated transition energies were obtained by using the ZINDO/S CIS method with B3LYP/6-31G* optimized structures. Calculations suggested the existence of a number of dark electronic states of bacteriochlorophylls below the main Soret transition. The density of these states was dependent on pigment surroundings. Dark states may have an important role in carotenoid to chlorophyll or to bacteriochlorophyll energy transfer in photosynthetic light harvesting complexes. It was also shown that conformation of an acetyl group of methyl bacteriochlorophyll a has an effect on calculated transition energies.

The [formula omitted] transition in jet-cooled 4H-pyran-4-thione: evidence for a dark [formula omitted] state below [formula omitted

The 3 A 2(n π ∗)→ X 1 A 1 phosphorescence excitation spectrum of jet-cooled 4H-pyran-4-thione (PT) was investigated in the region of the 1 A 1( ππ ∗)← X 1 A 1 absorption band between 27 300 and 28 800 cm −1 . The spectrum exhibits complex features, which are typical for the (strong) vibronic coupling case of two adjacent electronic states. The observed intermediate level structure was attributed to the coupling with a lower lying dark electronic state 1 B 1(n π 2 ∗) , whose origin was estimated to be ∼825–1025 cm −1 below the origin 1 A 1( ππ ∗) 0 , using calculations of vibronic state densities in combination with symmetry considerations. Consequences of the vibronic coupling on the decay dynamics of 1 A 1( ππ ∗) as well as tentative assignments of vibronic transitions 1 A 1( ππ ∗) ν← X 1 A 1 are also briefly discussed.

Model calculation on the pump-probe measurement of ultrafast electronic population decay in polyatomic molecules

We consider the common situation of strong vibronic coupling of an optically bright (in absorption from the ground state) excited electronic state to a lower-lying dark electronic state in a polyatomic molecule. It is shown that for sufficiently short pump and probe laser pulses a time-resolved experiment measures the total time-dependent population probability P( t) of the bright state. For a realistic model problem (representing the three lowest electronic states of the benzene cation) a conical intersection of the potential energy surfaces of the bright and the dark state causes an ultrafast initial decay of P(t) on a femtosecond time scale, followed by quasiperiodic recurrences. These recurrences show up as femtosecond quantum beats in the time-resolved pump-probe signal. The beating frequency is related to the vibrational frequency of the dominant accepting mode of the system.