Resolving Vibrational from Electronic Coherences in Two-Dimensional Electronic Spectroscopy: The Role of the Laser Spectrum

Two-dimensional electronic spectroscopy of Betaine-30

Betaine-30 is well-established as a standard dye for solvatochromism and has long been studied by ultrafast spectroscopy. Electronic excitation leads to rapid intramolecular electron transfer, while the decay of the resulting state corresponds to back electron transfer to the electronic ground state. Thus, Betaine-30's photophysics offers a route to probing the role that vibrational excitation and solvent dynamics play in electron transfer reaction rates. Here, we probe the excited state dynamics of Betaine-30 in two solvents (ethanol and acetonitrile) by means of two-dimensional electronic spectroscopy. Population dynamics in ethanol are measured at two pump wavelengths, and global analysis reveals a wavelength dependence of the electron transfer rate. This is assigned to excitation of distinct ground state conformers, which is confirmed by quantum chemical calculations. "Beatmaps" of coherently excited vibrations are recovered and analyzed in terms of the contribution of Raman active modes in ground and excited states. The contribution of modes in the excited state is a strong function of the rate of the electron transfer reaction.

Two-Dimensional Electronic Spectroscopy of Rhodamine 700 Using an 8 fs Ultrabroadband Laser Source and Full-Wavelength Reference Detection

Two-dimensional electronic spectroscopy (2DES) is one of the premier tools for investigating photoinduced condensed phase dynamics, combining high temporal and spectral resolution to probe ultrafast phenomena. We have coupled an ultrabroadband laser source generated with a hollow-core fiber, compressing pulses to have a pulse duration of 8 fs, with a boxcars 2DES interferometer constructed from only conventional optics. The resulting ultrabroad bandwidth and high temporal resolution allow for superior spectral coverage of the typically broad molecular line shapes in the near-IR/visible region in room temperature solutions, and the exploration of the excited state dynamics at the earliest time epoch in complex systems. The new spectrometer is characterized by examining the dynamics of the dye molecule Rhodamine 700 in methanol solution. These data exhibit rich vibrational wavepacket dynamics, with 2DES data unraveling key molecular vibronic couplings between multiple vibrational modes. For the first time in a degenerate broadband 2DES experiment, we demonstrate the implementation of full-wavelength reference detection to correct wavelength-dependent laser intensity fluctuations. The net result is a 4-5× increased signal-to-noise (S/N) ratio compared to data acquired without reference detection, yielding a typical S/N ratio = 28. The increased S/N ratio facilitates more rapid data acquisition and examination of samples at lower optical densities, and thus concentrations, than typically used in 2DES experiments. These advances will help to alleviate the typical high demands on precious samples in 2DES measurements.

Symmetry-Breaking Charge-Separation in a Subphthalocyanine Dimer Resolved by Two-Dimensional Electronic Spectroscopy

Understanding the role of structural and environmental dynamics in the excited state properties of strongly coupled chromophores is of paramount importance in molecular photonics. Ultrafast, coherent, and multidimensional spectroscopies have been utilized to investigate such dynamics in the simplest model system, the molecular dimer. Here, we present a half-broadband two-dimensional electronic spectroscopy (HB2DES) study of the previously reported ultrafast symmetry-breaking charge separation (SB-CS) in the subphthalocyanine oxo-bridged homodimer μ-OSubPc2. Electronic structure calculations and 2D cross-peaks reveal the dimer's excitonic structure, while ultrafast evolution of the multidimensional spectra unveils subtle features of structural relaxation, solvation dynamics, and inhomogeneous broadening in the SB-CS. Analysis of coherently excited vibrational motions reveals dimer-specific low-frequency Raman active modes coupled to higher-frequency vibrations localized on the SubPc cores. Finally, beatmap amplitude distributions characteristic of excitonic dimers with multiple bright states are reported and analyzed.

Fate of Optical Excitons in FAPbI3 Nanocube Superlattices

Understanding the nature of the photoexcitation and ultrafast charge dynamics pathways in organic halide perovskite nanocubes and their aggregation into superlattices is key for potential applications as tunable light emitters, photon-harvesting materials, and light-amplification systems. In this work, we apply two-dimensional coherent electronic spectroscopy (2DES) to track in real time the formation of near-infrared optical excitons and their ultrafast relaxation in CH(NH2)2PbI3 nanocube superlattices. Our results unveil that the coherent ultrafast dynamics is limited by the combination of the inherent short exciton decay time (≃40 fs) and the dephasing due to the coupling with selective optical phonon modes at higher temperatures. On the picosecond time scale, we observe the progressive formation of long-lived localized trap states. The analysis of the temperature dependence of the excitonic intrinsic line width, as extracted by the antidiagonal components of the 2D spectra, unveils a dramatic change of the excitonic coherence time across the cubic to tetragonal structural transition. Our results offer a new way to control and enhance the ultrafast coherent dynamics of photocarrier generation in hybrid halide perovskite synthetic solids.

On-the-Fly Simulation of Two-Dimensional Fluorescence-Excitation Spectra

Two-dimensional (2D) fluorescence-excitation (2D-FLEX) spectroscopy is a recently proposed nonlinear femtosecond technique for the detection of photoinduced dynamics. The method records a time-resolved fluorescence signal in its excitation- and detection-frequency dependence and hence combines the exclusive detection of excited state dynamics (fluorescence) with signals resolved in both excitation and emission frequencies (2D electronic spectroscopy). In this work, we develop an on-the-fly protocol for the simulation of 2D-FLEX spectra of molecular systems, which is based on interfacing the classical doorway-window representation of spectroscopic responses with trajectory surface hopping simulations. Applying this methodology to gas-phase pyrazine, we show that femtosecond 2D-FLEX spectra can deliver detailed information that is otherwise obtainable via attosecond spectroscopy.

Vibrational coherences in half-broadband 2D electronic spectroscopy: Spectral filtering to identify excited state displacements

Vibrational coherences in ultrafast pump-probe (PP) and 2D electronic spectroscopy (2DES) provide insights into the excited state dynamics of molecules. Femtosecond coherence spectra and 2D beat maps yield information about displacements of excited state surfaces for key vibrational modes. Half-broadband 2DES uses a PP configuration with a white light continuum probe to extend the detection range and resolve vibrational coherences in the excited state absorption (ESA). However, the interpretation of these spectra is difficult as they are strongly dependent on the spectrum of the pump laser and the relative displacement of the excited states along the vibrational coordinates. We demonstrate the impact of these convoluting factors for a model based upon cresyl violet. A careful consideration of the position of the pump spectrum can be a powerful tool in resolving the ESA coherences to gain insights into excited state displacements. This paper also highlights the need for caution in considering the spectral window of the pulse when interpreting these spectra.

Quantum phase synchronization via exciton-vibrational energy dissipation sustains long-lived coherence in photosynthetic antennas

The lifetime of electronic coherences found in photosynthetic antennas is known to be too short to match the energy transfer time, rendering the coherent energy transfer mechanism inactive. Exciton-vibrational coherence time in excitonic dimers which consist of two chromophores coupled by excitation transfer interaction, can however be much longer. Uncovering the mechanism for sustained coherences in a noisy biological environment is challenging, requiring the use of simpler model systems as proxies. Here, via two-dimensional electronic spectroscopy experiments, we present compelling evidence for longer exciton-vibrational coherence time in the allophycocyanin trimer, containing excitonic dimers, compared to isolated pigments. This is attributed to the quantum phase synchronization of the resonant vibrational collective modes of the dimer, where the anti-symmetric modes, coupled to excitonic states with fast dephasing, are dissipated. The decoupled symmetric counterparts are subject to slower energy dissipation. The resonant modes have a predicted nearly 50% reduction in the vibrational amplitudes, and almost zero amplitude in the corresponding dynamical Stokes shift spectrum compared to the isolated pigments. Our findings provide insights into the mechanisms for protecting coherences against the noisy environment.

Two-Dimensional Electronic Spectroscopy Resolves Relative Excited-State Displacements

Knowledge of relative displacements between potential energy surfaces (PES) is critical in spectroscopy and photochemistry. Information on displacements is encoded in vibrational coherences. Here we apply ultrafast two-dimensional electronic spectroscopy in a pump-probe half-broadband (HB2DES) geometry to probe the ground- and excited-state potential landscapes of cresyl violet. 2D coherence maps reveal that while the coherence amplitude of the dominant 585 cm-1 Raman-active mode is mainly localized in the ground-state bleach and stimulated emission regions, a 338 cm-1 mode is enhanced in excited-state absorption. Modeling these data with a three-level displaced harmonic oscillator model using the hierarchical equation of motion-phase matching approach (HEOM-PMA) shows that the S1 ← S0 PES displacement is greater along the 585 cm-1 coordinate than the 338 cm-1 coordinate, while Sn ← S1 displacements are similar along both coordinates. HB2DES is thus a powerful tool for exploiting nuclear wavepackets to extract quantitative multidimensional, vibrational coordinate information across multiple PESs.

Electronic Structure of Isolated Graphene Nanoribbons in Solution Revealed by Two-Dimensional Electronic Spectroscopy

Structurally well-defined graphene nanoribbons (GNRs) are nanostructures with unique optoelectronic properties. In the liquid phase, strong aggregation typically hampers the assessment of their intrinsic properties. Recently we reported a novel type of GNRs, decorated with aliphatic side chains, yielding dispersions consisting mostly of isolated GNRs. Here we employ two-dimensional electronic spectroscopy to unravel the optical properties of isolated GNRs and disentangle the transitions underlying their broad and rather featureless absorption band. We observe that vibronic coupling, typically neglected in modeling, plays a dominant role in the optical properties of GNRs. Moreover, a strong environmental effect is revealed by a large inhomogeneous broadening of the electronic transitions. Finally, we also show that the photoexcited bright state decays, on the 150 fs time scale, to a dark state which is in thermal equilibrium with the bright state, that remains responsible for the emission on nanosecond time scales.

Multimode vibrational dynamics and orientational effects in fluorescence-encoded infrared spectroscopy. II. Analysis of early-time signals

Developing fluorescence-encoded infrared (FEIR) vibrational spectroscopy for single-molecule applications requires a detailed understanding of how the molecular response and external experimental parameters manifest in the detected signals. In Paper I [L. Whaley-Mayda, A. Guha, and A. Tokmakoff, J. Chem. Phys. 159, 194201 (2023)] we introduced a nonlinear response function theory to describe vibrational dynamics, vibronic coupling, and transition dipole orientation in FEIR experiments with ultrashort pulses. In this second paper, we apply the theory to investigate the role of intermode vibrational coherence, the orientation of vibrational and electronic transition dipoles, and the effects of finite pulse durations in experimental measurements. We focus on measurements at early encoding delays-where signal sizes are largest and therefore of most value for single-molecule experiments, but where many of these phenomena are most pronounced and can complicate the appearance of data. We compare experiments on coumarin dyes with finite-pulse response function simulations to explain the time-dependent behavior of FEIR spectra. The role of the orientational response is explored by analyzing polarization-dependent experiments and their ability to resolve relative dipole angles in the molecular frame. This work serves to demonstrate the molecular information content of FEIR experiments, and develop insight and guidelines for their interpretation.

Coherent Phonon-Mediated Many-Body Interaction in Monolayer WSe2

Due to the strong Coulomb interaction, the optical and electrical properties of two-dimensional transition metal dichalcogenides (TMDCs) are greatly determined by the emergence of many-body complexes such as excitons or trions. To fully realize the potential functionalities of these atomically thin materials, a comprehensive understanding of their many-body interaction mechanism is essential. Here, using the advanced femtosecond two-dimensional electronic spectroscopy technique combined with broadband transient absorption spectroscopy, a strong electron-exciton coupling effect in monolayer WSe₂ following the ultrafast photoexcitation is revealed. We demonstrate that such many-body complexes can be generated effectively through the band-edge optical excitation, with a ∼1.5 ps stabilization process. The coherent optical phonon plays a dominant role in this electron-exciton interaction, and the coherence of the electron (exciton)-phonon coupling can last for ∼4.5 ps. This finding offers new insight into the formation mechanism of photoinduced many-body complexes in TMDCs.

Perturbed free induction decay obscures early time dynamics in two-dimensional electronic spectroscopy: The case of semiconductor nanocrystals

Two-dimensional electronic spectroscopy (2DES) has recently been gaining popularity as an alternative to the more common transient absorption spectroscopy due to the combination of high frequency and time resolution of 2DES. In order to advance the reliable analysis of population dynamics and to optimize the time resolution of the method, one has to understand the numerous field matter interactions that take place at an early and negative time. These interactions have historically been discussed in one-dimensional spectroscopy as coherent artifacts and have been assigned to both resonant and non-resonant system responses during or before the pulse overlap. These coherent artifacts have also been described in 2DES but remain less well-understood due to the complexity of 2DES and the relative novelty of the method. Here, we present 2DES results in two model nanocrystal samples, CdSe and CsPbI₃. We demonstrate non-resonant signals due to solvent response during the pulse overlap and resonant signals, which we assign to perturbed free induction decay (PFID), both before and during the pulse overlap. The simulations of the 2DES response functions at early and negative time delays reinforce the assignment of the negative time delay signals to PFID. Modeling reveals that the PFID signals will severely distort the initial picture of the resonant population dynamics. By including these effects in models of 2DES spectra, one is able to push forward the extraction of early time dynamics in 2DES.

Revealing Intermolecular Electronic and Vibronic Coherence with Polarization-Dependent Two-Dimensional Beating Maps

Two-dimensional electronic spectroscopy (2DES) has been widely employed as an efficient tool to reveal the impact of intermolecular electronic and/or vibronic quantum coherence on excitation energy transfer in light-harvesting complexes. However, intramolecular vibrational coherence would also contribute to oscillating signals in 2D spectra, along with the intermolecular coherence signals that are directly related to energy transfer. In this work, the possibility of screening the vibrational coherence signals is explored through polarization-dependent 2DES. The all-parallel (AP) and double-crossed (DC) polarization-dependent two-dimensional rephasing spectra (2DRS) are simulated for a minimalist heterodimer model with vibrational coupling. By combining the DC-2DRS and the 2D beating maps, we demonstrate that the population and vibrational coherence signals can be largely suppressed, resulting in highlighted intermolecular electronic and vibronic coherence signals. Moreover, the AP- and DC-2DBMs show rather different patterns at the vibrational frequency, indicating a possible way to identify pure vibrational coherence.

π-Stacking-Dependent Vibronic Couplings Drive Excited-State Dynamics in Perylenediimide Assemblies

Vibronic coupling, the interplay of electronic and nuclear vibrational motion, is considered a critical mechanism in photoinduced reactions such as energy transfer, charge transfer, and singlet fission. However, our understanding of how particular vibronic couplings impact excited-state dynamics is lacking due to the limited number of experimental studies of model molecular systems. Herein, we use two-dimensional electronic spectroscopy (2DES) to launch and interrogate a range of vibronic coherences in two distinct types of perylenediimide slip stacks─along the short and long molecular axes, which form either an excimer or a mixed state between the Frenkel exciton (FE) and charge transfer states. We explore the functionality of these vibronic coherences using quantum beatmaps, which display the Fourier amplitude signal oscillations as a function of pump and probe frequencies, along with knowledge of the characteristic signatures of the FE, ionic, and excimer species. We find that a low-frequency vibrational mode of the short-axis slip stack appears concomitantly with the formation of the excimer state, survives 2-fold longer than in the FE state in the reference monomer, and shows a phase shift compared to other modes. For the long-axis slip stacks, a pair of low-frequency modes coupled to a high-frequency coordinate of the FE state were found to play a critical role in mixed-state generation. Our findings thus experimentally reveal the complex and varying roles of vibronic couplings in tightly packed multimers undergoing a range of photoinduced processes.

Vibrational and vibronic coherences in the energy transfer process of light-harvesting complex II revealed by two-dimensional electronic spectroscopy

The presence of quantum coherence in light-harvesting complex II (LHCII) as a mechanism to understand the efficiency of the light-harvesting function in natural photosynthetic systems is still debated due to its structural complexity and weak-amplitude coherent oscillations. Here, we revisit the coherent dynamics and clarify different types of coherences in the energy transfer processes of LHCII using a joint method of the high-S/N transient grating and two-dimensional electronic spectroscopy. We find that the electronic coherence decays completely within 50 fs at room temperature. The vibrational coherences of chlorophyll a dominate over oscillations within 1 ps, whereas a low-frequency mode of 340 cm−1 with a vibronic mixing character may participate in vibrationally assisted energy transfer between chlorophylls a. Our results may suggest that vibronic mixing is relevant for rapid energy transfer processes among chlorophylls in LHCII.

The influence of a Hamiltonian vibration vs a bath vibration on the 2D electronic spectra of a homodimer

We elucidate the influence of the system–bath boundary placement within an open quantum system, with emphasis on the two-dimensional electronic spectra, through the application of the hierarchical equations of motion formalism for an exciton system. We apply two different models, the Hamiltonian vibration model (HVM) and bath vibration model (BVM), to a monomer and a homodimer. In the HVM, we specifically include the vibronic states in the Hamiltonian capturing vibronic quenching, whereas in the BVM, all vibrational details are contained within the bath and described by an underdamped spectral density. The resultant spectra are analyzed in terms of energetic peak position and thermodynamic broadening precision in order to evaluate the efficacy of the two models. The HVM produces 2D spectra with accurate peak positional information, while the BVM is well suited to modeling dynamic peak broadening. For the monomer, both models produce equivalent spectra in the limit where additional damping associated with the underdamped vibration in the BVM approaches zero. This is supported by analytical results. However, for the homodimer, the BVM spectra are redshifted with respect to the HVM due to an absence of vibronic quenching in the BVM. The computational efficiency of the two models is also discussed in order to inform us of the most appropriate use of each method.

Visualizing Ultrafast Electron Transfer Processes in Semiconductor-Metal Hybrid Nanoparticles: Toward Excitonic-Plasmonic Light Harvesting

Recently, it was demonstrated that charge separation in hybrid metal-semiconductor nanoparticles (HNPs) can be obtained following photoexcitation of either the semiconductor or of the localized surface plasmon resonance (LSPR) of the metal. This suggests the intriguing possibility of photocatalytic systems benefiting from both plasmon and exciton excitation, the main challenge being to outcompete other ultrafast relaxation processes. Here we study CdSe-Au HNPs using ultrafast spectroscopy with high temporal resolution. We describe the complete pathways of electron transfer for both semiconductor and LSPR excitation. In the former, we distinguish hot and band gap electron transfer processes in the first few hundred fs. Excitation of the LSPR reveals an ultrafast (<30 fs) electron transfer to CdSe, followed by back-transfer from the semiconductor to the metal within 210 fs. This study establishes the requirements for utilization of the combined excitonic-plasmonic contribution in HNPs for diverse photocatalytic applications.

Electronic State-Resolved Multimode-Coupled Vibrational Wavepackets in Oxazine 720 by Two-Dimensional Electronic Spectroscopy

The difference between the excited- and ground-state vibrational wavepackets remains to be fully explored when multiple vibrational modes are coherently excited simultaneously by femtosecond pulses. In this work, we present a series of one- and two-dimensional electronic spectroscopy for studying multimode wavepackets of oxazine 720 in solution. Fourier transform (FT) maps combined with time-frequency transform (TFT) are employed to unambiguously distinguish the origin of low-frequency vibrational wavepackets, that is, an excited-state vibrational wavepacket of 586 cm^-1 with a dephasing time of 0.7 ps and a ground-state vibrational wavepacket of 595 cm^-1 with a dephasing time of 1.3-1.7 ps. We also found the additional low-frequency vibrational wavepackets resulting from the coupling of the 595 cm^-1 mode to a series of high-frequency modes centered at 1150 cm^-1 via electronic transitions. The combined use of FT maps and TFT analysis allows us to reveal the potential vibrational coupling of wavepackets and offers the possibility of disentangling the coupling between the electronic and vibrational degrees of freedom in condensed-phase systems.

Towards a spectroscopic protocol for unambiguous detection of quantum coherence in excitonic energy transport

We propose a witness for quantum coherence in EET that can be extracted directly from two-pulse pump–probe spectroscopy experimental data.

Correction of spectral distortion in two-dimensional electronic spectroscopy arising from the wedge-based delay line

Unlike the probe wavelength, which is spectrally resolved by monochromator, the excitation wavelength in two-dimensional electronic spectroscopy is retrieved by means of Fourier transform of the interference signal introduced by the coherence delay time between the first and second excitation laser pulses. Hence, the calibration of delay lines would determine its accuracy. In this work, we showed that an inaccurate calibration factor of wedge-based delay line would result in a global peak shift and asymmetric spectral twists along the excitation axis. Both theoretical analysis and experiments have shown that such spectral distortions can be corrected by an accurately predetermined calibration factor. The relative accuracy of calibration factor reaches 3 × 10^-5 in our setup. The dispersion effect of wedges also has been considered for the broadband excitation.

Coherent two-dimensional electronic and infrared crystallography

The two-dimensional electronic and infrared spectroscopy of oriented single crystals is sensitive to structure and point group symmetry. The third order response of crystals is generally different from measurements of isotropic solutions because each coherence path that contributes to the measured field scales to the ensemble average of the four-point correlation functions of the four field-dipole interactions involved in the respective Feynman paths. An analytical evaluation of 2D optical crystallography which depends on the crystal symmetry, laboratory orientation, and the orientation in the crystallographic frame is presented. Applying a symmetry operator in the basis of the allowed polarised radiation modes provides a method for evaluation of non-zero fourth rank tensor elements alternative to direct inspection methods. Uniaxial and biaxial systems are distinguished and the contributions to the rephasing and non-rephasing directions are evaluated for isolated and coupled oscillators. By exploiting coordinate analysis, the extension of non-linear electronic and infrared crystallography for coupled oscillators demonstrates the structural, directional, and symmetry dependent selection of coherences to the four-wave mixing signal.

Characterization of Vibrational Coherence in Monomeric Bacteriochlorophyll a by Two-Dimensional Electronic Spectroscopy

Bacteriochlorophyll a (BChla) is the most abundant pigment found in the Bacterial Reaction Center (BRC) and light-harvesting proteins of photosynthetic purple and green bacteria. Recent two-dimensional electronic spectroscopy (2DES) studies of photosynthetic pigment-protein complexes including the BRC and the Fenna-Matthews-Olson (FMO) complex have shown oscillatory signals, or coherences, whose physical origin has been hotly debated. To better understand the observations of coherence in larger photosynthetic systems, it is important to carefully characterize the spectroscopic signatures of the monomeric pigments. Prior spectroscopic studies of BChla have differed significantly in their observations, with some studies reporting little to no coherence. Here we present evidence of strong coherences in monomeric BChla in isopropanol using 2DES at 77 K. We resolve many modes with frequencies that correspond well with known vibrational modes. We confirm their vibrational origin by comparing the 2D spectroscopic signatures with expectations based on a purely vibrational model.

Ultrafast Carotenoid to Retinal Energy Transfer in Xanthorhodopsin Revealed by the Combination of Transient Absorption and Two-Dimensional Electronic Spectroscopy

By comparing two-dimensional electronic spectroscopy (2DES) and Pump-Probe (PP) measurements on xanthorhodopsin (XR) and reduced-xanthorhodopsin (RXR) complexes, the ultrafast carotenoid-to-retinal energy transfer pathway is revealed, at very early times, by an excess of signal amplitude at the associated cross-peak and by the carotenoid bleaching reduction due to its ground state recovery. The combination of the measured 2DES and PP spectroscopic data with theoretical modelling allows a clear identification of the main experimental signals and a comprehensive interpretation of their origin and dynamics. The remarkable velocity of the energy transfer, despite the non-negligible energy separation between the two chromophores, and the analysis of the underlying transport mechanism, highlight the role played by the ground state carotenoid vibrations in assisting the process.

Spectral Filtering as a Tool for Two-Dimensional Spectroscopy: A Theoretical Model

Two-dimensional optical spectroscopy is a powerful technique for the probing of coherent quantum superpositions. Recently, the finite width of the laser spectrum has been employed to selectively tune experiments for the study of particular coherences. This involves the exclusion of certain transition frequencies, which results in the elimination of specific Liouville pathways. The rigorous analysis of such experiments requires the use of ever more sophisticated theoretical models for the optical spectroscopy of electronic and vibronic systems. Here we develop a nonimpulsive and non-Markovian model, which combines an explicit definition of the laser spectrum, via the equation of motion-phase matching approach (EOM-PMA), with the hierarchical equations of motion (HEOM). This theoretical framework is capable of simulating the 2D spectroscopy of vibronic systems with low frequency modes, coupled to environments of intermediate and slower time scales. In order to demonstrate the spectral filtering of vibronic coherences, we examine the elimination of lower energy peaks from the 2D spectra of a zinc porphyrin monomer upon blue-shifting the laser spectrum. The filtering of Liouville pathways is revealed through the disappearance of peaks from the amplitude spectra for a coupled vibrational mode.

Signatures of vibronic coupling in two-dimensional electronic-vibrational and vibrational-electronic spectroscopies

Two-Dimensional Electronic-Vibrational (2D EV) spectroscopy and Two-Dimensional Vibrational-Electronic (2D VE) spectroscopy are new coherent four-wave mixing spectroscopies that utilize both electronically resonant and vibrationally resonant field-matter interactions to elucidate couplings between electronic and vibrational degrees of freedom. A system Hamiltonian is developed here to lay a foundation for interpreting the 2D EV and 2D VE signals that arise from a vibronically coupled molecular system in the condensed phase. A molecular system consisting of one anharmonic vibration and two electronic states is modeled. Equilibrium displacement of the vibrational coordinate and vibrational frequency shifts upon excitation to the first electronic excited state are included in our Hamiltonian through linear and quadratic vibronic coupling terms. We explicitly consider the nuclear dependence of the electronic transition dipole moment and demonstrate that these spectroscopies are sensitive to non-Condon effects. A series of simulations of 2D EV and 2D VE spectra obtained by varying parameters of the system, system-bath, and interaction Hamiltonians demonstrate that one of the following conditions must be met to observe signals: (1) non-zero linear and/or quadratic vibronic coupling in the electronic excited state, (2) vibrational-coordinate dependence of the electronic transition dipole moment, or (3) electronic-state-dependent vibrational dephasing dynamics. We explore how these vibronic interactions are manifested in the positions, amplitudes, and line shapes of the peaks in 2D EV and 2D VE spectroscopies.

Vibronic Coherence in the Charge Separation Process of the Rhodobacter sphaeroides Reaction Center

Two-dimensional electronic spectroscopy was applied to a variant of the reaction center (RC) of purple bacterium Rhodobacter sphaeroides lacking the primary acceptor ubiquinone in order to understand the ultrafast separation and transfer of charge between the bacteriochlorin cofactors. For the first time, characteristic 2D spectra were obtained for the participating excited and charge-transfer states, and the electron-transfer cascade (including two different channels, the P* and B* channels) was fully mapped. By analyzing quantum beats using 2D frequency maps, excited-state vibrational modes at 153 and 33 cm-1 were identified. We speculate that these modes couple to the charge separation (CS) process and collectively optimize the CS and are responsible for the superhigh efficiency.

Exciton-Phonon Spectroscopy of Quantum Dots Below the Single-Particle Homogeneous Line Width

We demonstrate that high-dimensionality coherent spectroscopy yields "super-resolved" spectra whereby peaks may be localized far below their homogeneous line width by resolving them across multiple, coherently coupled dimensions. We implement this technique using a fifth-order photon-echo spectroscopy called Gradient-Assisted Multidimensional Electronic-Raman Spectroscopy (GAMERS) that combines resonant and nonresonant excitation to disperse the optical response across three spectral dimensions: two involving excitonic transitions and one that encodes phonon energies. In analogy to super-resolution localization microscopies, which separate spatially overlapping signals in time, GAMERS isolates signals spectrally using combined electronic and nuclear resolution. Optical phonon lines in a colloidal solution of CdSe quantum dots at room temperature separated by less than 150 μeV are resolved despite the homogeneous line width of these transitions being nearly an order of magnitude broader. The frequency difference between these phonon modes is attributed to softening of the longitudinal phonon mode upon excitation to the lowest exciton state. Further, such phonon mode selectivity yields spectra with electronic line widths that approach the single particle limit. Through this enhanced spectral resolution, the GAMERS method yields insights into the nature of coupling between longitudinal optical and acoustic phonons and specific excitonic transitions that were previously hidden.

Detection of a weak ring current in a nonaromatic porphyrin nanoring using magnetic circular dichroism

We compare the absorption and magnetic circular dichroism (MCD) spectra of a series of porphyrin oligomers - dimer, tetramer, and hexamer - bound in a linear or cyclic fashion. The MCD signal is extremely weak for low energy transitions in the linear oligomers, but it is amplified when the cyclic porphyrin hexamer binds a template, restricting rotational freedom. The appearance of Faraday A terms in the MCD spectra demonstrates the presence of a magnetic moment, and thus, uncompensated electronic current. The value of the excited state magnetic moment estimated from the A term is very low compared with those of monomeric porphyrins, which confirms the nonaromatic character of the cyclic array and the lack of a global ring current in the ground state of the neutral nanoring. DFT calculations predict the absorption and MCD patterns reasonably well, but fail to reproduce the MCD sign inversion observed in substituted monomeric zinc porphyrins ("soft" chromophores). Interestingly, a correct sign pattern is predicted by INDO/S calculations. Analysis of the MCD spectra of the monomeric porphyrin unit allowed us to distinguish between two close-lying lowest energy transitions, which some previous assignments placed further apart. The present results prove the usefulness of MCD not only for deconvolution and assignment of electronic transitions, but also as a sensitive tool for detecting electronic ring currents.

Mechanistic insight into internal conversion process within Q-bands of chlorophyll a

The non-radiative relaxation of the excitation energy from higher energy states to the lowest energy state in chlorophylls is a crucial preliminary step for the process of photosynthesis. Despite the continuous theoretical and experimental efforts to clarify the ultrafast dynamics of this process, it still represents the object of an intense investigation because the ultrafast timescale and the congestion of the involved states makes its characterization particularly challenging. Here we exploit 2D electronic spectroscopy and recently developed data analysis tools to provide more detailed insights into the mechanism of internal conversion within the Q-bands of chlorophyll a. The measurements confirmed the timescale of the overall internal conversion rate (170 fs) and captured the presence of a previously unidentified ultrafast (40 fs) intermediate step, involving vibronic levels of the lowest excited state.

Discrimination of Diverse Coherences Allows Identification of Electronic Transitions of a Molecular Nanoring

The role of quantum coherence in photochemical functions of molecular systems such as photosynthetic complexes is a broadly debated topic. Coexistence and intermixing of electronic and vibrational coherences has been proposed to be responsible for the observed long-lived coherences and high energy transfer efficiency. However, clear experimental evidence of coherences with different origins operating at the same time has been elusive. In this work, multidimensional spectra obtained from a six-porphyrin nanoring system are analyzed in detail with support from theoretical modeling. We uncover a great diversity of separable electronic, vibrational, and mixed coherences and show their cooperation in shaping the spectroscopic response. The results permit direct assignment of electronic and vibronic states and characterization of the excitation dynamics. The clear disentanglement of coherences in molecules with extended π-conjugation opens up new avenues for exploring coherent phenomena and understanding their importance for the function of complex systems.