Broadband Transient Absorption and Two-Dimensional Electronic Spectroscopy of Methylene Blue

From Coherence to Function: Exploring the Connection in Chemical Systems

ConspectusThe role of quantum mechanical coherences or coherent superposition states in excited state processes has received considerable attention in the last two decades largely due to advancements in ultrafast laser spectroscopy. These coherence effects hold promise for enhancing the efficiency and robustness of functionally relevant processes, even when confronted with energy disorder and environmental fluctuations. Understanding coherence deeply drives us to unravel mechanisms and dynamics controlled by order and synchronization at a quantum mechanical level, envisioning optical control of coherence to enhance functions or create new ones in molecular and material systems. In this frontier, the interplay between electronic and vibrational dynamics, specifically the influence of vibrations in directing electronic dynamics, has emerged as the leading principle. Here, two energetically disparate quantum degrees of freedom work in-sync to dictate the trajectory of an excited state reaction. Moreover, with the vibrational degree being directly related to the structural composition of molecular or material systems, new molecular designs could be inspired by tailoring certain structural elements.In the realm of chemical kinetics, our understanding of the dynamics of chemical transformations is underpinned by fundamental theories, such as transition state theory, activated rate theory, and Marcus theory. These theories elucidate reaction rates by considering the energy barriers that must be overcome for reactants to transform into products. Those barriers are surmounted by the stochastic nature of energy gap fluctuations within reacting systems, emphasizing that the reaction coordinate, the pathway from reactants to products, is not rigidly defined by a specific vibrational motion but encompasses a diverse array of molecular motions. While less is known about the involvement of specific intramolecular vibrational modes, their significance in certain cases cannot be overlooked.In this Account, we summarize key experimental findings that offer deeper insights into the complex electronic-vibrational trajectories encompassing excited states afforded from state-of-the-art ultrafast laser spectroscopy in three exemplary processes: photoinduced electron transfer, singlet-triplet intersystem crossing, and intramolecular vibrational energy flow in molecular systems. We delve into the rapid decoherence, or loss of phase and amplitude correlations, of vibrational coherences along promoter vibrations during subpicosecond intersystem crossing dynamics in a series of binuclear platinum complexes. This rapid decoherence illustrates the vibration-driven reactive pathways from the Franck-Condon state to the curve crossing region. We also explore the generation of new vibrational coherences induced by impulsive reaction dynamics rather than by the laser pulse in these systems, which sheds light on specific energy dissipation pathways and thereby on the progression of the reaction trajectory in the vicinity of the curve crossing on the product side. Another property of vibrational coherences, amplitude, reveals how energy can flow from one vibration to another in the electronic excited state of a terpyridine-molybdenum complex hosting a nonreactive dinitrogen substrate. A slight change in vibrational energy triggers a quasi-resonant interaction, leading to constructive wavepacket interference and ultimately intramolecular vibrational redistribution from a Franck-Condon active terpyridine vibration to a dinitrogen stretching vibration, energizing the dinitrogen bond.

Distinct vibrational motions promote disparate excited-state decay pathways in cofacial perylenediimide dimers

A complex interplay of structural, electronic, and vibrational degrees of freedom underpins the fate of molecular excited states. Organic assemblies exhibit a myriad of excited-state decay processes, such as symmetry-breaking charge separation (SB-CS), excimer (EX) formation, singlet fission, and energy transfer. Recent studies of cofacial and slip-stacked perylene-3,4:9,10-bis(dicarboximide) (PDI) multimers demonstrate that slight variations in core substituents and H- or J-type aggregation can determine whether the system follows an SB-CS pathway or an EX one. However, questions regarding the relative importance of structural properties and molecular vibrations in driving the excited-state dynamics remain. Here, we use a combination of two-dimensional electronic spectroscopy, femtosecond stimulated Raman spectroscopy, and quantum chemistry computations to compare the photophysics of two PDI dimers. The dimer with 1,7-bis(pyrrolidin-1'-yl) substituents (5PDI2) undergoes ultrafast SB-CS from a photoexcited mixed state, while the dimer with bis-1,7-(3',5'-di-t-butylphenoxy) substituents (PPDI2) rapidly forms an EX state. Examination of their quantum beating features reveals that SB-CS in 5PDI2 is driven by the collective vibronic coupling of two or more excited-state vibrations. In contrast, we observe signatures of low-frequency vibrational coherence transfer during EX formation by PPDI2, which aligns with several previous studies. We conclude that key electronic and structural differences between 5PDI2 and PPDI2 determine their markedly different photophysics.

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.

Deterministic positioning and alignment of a single-molecule exciton in plasmonic nanodimer for strong coupling

Experimental realization of strong coupling between a single exciton and plasmons remains challenging as it requires deterministic positioning of the single exciton and alignment of its dipole moment with the plasmonic fields. This study aims to combine the host-guest chemistry approach with the cucurbit[7]uril-mediated active self-assembly to precisely integrate a single methylene blue molecule in an Au nanodimer at the deterministic position (gap center of the nanodimer) with the maximum electric field (EFmax) and perfectly align its transition dipole moment with the EFmax, yielding a large spectral Rabi splitting of 116 meV for a single-molecule exciton-matching the analytical model and numerical simulations. Statistical analysis of vibrational spectroscopy and dark-field scattering spectra confirm the realization of the single exciton strong coupling at room temperature. Our work may suggest an approach for achieving the strong coupling between a deterministic single exciton and plasmons, contributing to the development of room-temperature single-qubit quantum devices.

Observation of Coherent Symmetry-Breaking Vibration by Polarization-Dependent Femtosecond Spectroscopy

Understanding photoinduced chemical reactions beyond the Born-Oppenheimer paradigm requires a comprehensive examination of vibronic interactions. Although femtosecond studies have unveiled the influence of vibrational modes strongly coupled to ultrafast intramolecular reactions in the excited state, they often lack direct observations of how vibrations modulate electronic properties due to the rapid disappearance of reactants. To address this gap, our research investigates the dynamics of photoexcited molecules that do not react. Specifically, we focus on the coherent librational motion of molecular transition dipole moments, discovering that the coherent libration primarily originates from symmetry-breaking components in vibronically excited vibrational modes. Symmetry breaking motion can significantly impact the excited-state dynamics of highly symmetric molecules, potentially leading to nonadiabatic transitions. In essence, the data analysis framework introduced in this study can be harnessed to uncover potential reactivity in photoexcited molecules, further enhancing our understanding of the mechanisms governing these reactions.

Ultrafast Symmetry-Breaking Charge Separation in a Perylene Bisimide Dimer Enabled by Vibronic Coupling and Breakdown of Adiabaticity

Perylene bisimides (PBIs) have received great attention in their applicability to optoelectronics. Especially, symmetry-breaking charge separation (SB-CS) in PBIs has been investigated to mimic the efficient light capturing and charge generation in natural light-harvesting systems. However, unlike ultrafast CS dynamics in donor-acceptor heterojunction materials, ultrafast SB-CS in a stacked homodimer has still been challenging due to excimer formation in the absence of rigidifying surroundings such as a special pair in the natural systems. Herein, we present the detailed mechanism of ultrafast photoinduced SB-CS occurring in a 1,7-bis(N-pyrrolidinyl) PBI dimer within a cyclophane. Through narrow-band and broad-band transient absorption spectroscopy, we demonstrate that ultrafast SB-CS in the dimer is enabled by the combination of (1) vibrationally coherent charge-transfer resonance-enhanced excimer formation and (2) breakdown of adiabaticity (formation of SB-CS diabats) in the excimer state via structural and solvent fluctuation. Quantum chemical calculations also underpin that the participation of strong electron-donating substituents in overall vibrational modes plays a crucial role in triggering the ultrafast SB-CS. Therefore, our work provides an alternative route to facilitate ultrafast SB-CS in PBIs and thereby establishes a novel strategy for the design of optoelectronic materials.

Ultrafast electron transfer at the interface of gold nanoparticles and methylene blue molecular adsorbates

Due to their unique property of possessing localized surface plasmon resonance (LSPR), metal nanoparticles (MNPs) have drastically impacted many applications. For instance, local field enhancement through LSPRs and plasmonic hot electron transfer are known to enhance the efficiency of MNP-based photoreactions. Here, we report on the ultrafast electron transfer from gold nanoparticles (Au-NPs) to methylene blue (MB) molecular adsorbate using femtosecond pump-probe and steady-state absorption and emission spectroscopy techniques. Although the energy band alignment of the interface allows both dipole-dipole Förster resonance energy transfer (FRET) and charge transfer, because the MB emission intensity at the Au-NPs/MB nanocomposite decreased by a factor of ∼3.6, the FRET process was ruled out. Selective excitation of LSPRs at the Au-NPs/MB nanocomposite sample in pump-probe experiments led to the formation of the MB ground-state depletion and a positive induced absorption at wavelengths shorter than ∼500 nm, which was attributed to the shoulder of the MB^- anion absorption. Furthermore, despite the fact that the concentration of Au-NPs in the nanocomposite sample is the same as that in the Au-NPs solution, the initial intensity of the LSPR depletion signal was about six times weaker than that in the Au-NPs sample. These observations suggest that electron transfer from excited Au-NPs to MB adsorbates took place on a time-scale that is shorter than the ∼50 fs experimental temporal resolution.

Characterizing Mode Anharmonicity and Huang-Rhys Factors Using Models of Femtosecond Coherence Spectra

Femtosecond laser pulses readily produce coherent quantum beats in transient-absorption spectra. These oscillatory signals often arise from molecular vibrations and therefore may contain information about the excited-state potential energy surface near the Franck-Condon region. Here, by fitting the measured spectra of two laser dyes to microscopic models of femtosecond coherence spectra (FCS) arising from molecular vibrations, we classify coherent quantum-beat signals as fundamentals or overtones and quantify their Huang-Rhys factors and anharmonicity values. We discuss the extracted Huang-Rhys factors in the context of quantum-chemical computations. This work solidifies the use of FCS for analysis of coherent quantum beats arising from molecular vibrations, which will aid studies of molecular aggregates and photosynthetic proteins.

Ultrafast proton transfer of the aqueous phenol radical cation

Proton transfer (PT) reactions are fundamental to numerous chemical and biological processes. While sub-picosecond PT involving electronically excited states has been extensively studied, little is known about ultrafast PT triggered by photoionization. Here, we employ femtosecond optical pump-probe spectroscopy and quantum dynamics calculations to investigate the ultrafast proton transfer dynamics of the aqueous phenol radical cation (PhOH˙⁺). Analysis of the vibrational wave packet dynamics reveals unusually short dephasing times of 0.18 ± 0.02 ps and 0.16 ± 0.02 ps for the PhOH˙⁺ O-H wag and bend frequencies, respectively, suggestive of ultrafast PT occurring on the ∼0.1 ps timescale. The reduced potential energy surface obtained from ab initio calculations shows that PT is barrierless when it is coupled to the intermolecular hindered translation between PhOH˙⁺ and the proton-acceptor water molecule. Quantum dynamics calculations yield a lifetime of 193 fs for PhOH˙⁺, in good agreement with the experimental results and consistent with the PT reaction being mediated by the intermolecular O⋯O stretch. These results suggest that photoionization can be harnessed to produce photoacids that undergo ultrafast PT. In addition, they also show that PT can serve as an ultrafast deactivation channel for limiting the oxidative damage potential of radical cations.

A Revisit on Impulsive Stimulated Raman Spectroscopy: Importance of Spectral Dispersion of Chirped Broadband Probe

The usefulness of a chirped broadband probe and spectral dispersion to obtain Raman spectra under nonresonant/resonant impulsive excitation is revisited. A general methodology is presented that inherently takes care of phasing the time-domain low-frequency oscillations without probe pulse compression and retrieves the absolute phase of the oscillations. As test beds, neat solvents (CCl₄, CHCl₃, and CH₂Cl₂) are used. Observation of periodic intensity modulation along detection wavelengths for particular modes is explained using a simple electric field interaction picture. This method is extended to diatomic molecule (iodine) and polyatomic molecules (Nile blue and methylene blue) to assign vibrational frequencies in ground/excited electronic state that are supported by density functional theory calculations. A comparison between frequency-domain and time-domain counterparts, i.e., stimulated Raman scattering and impulsive stimulated Raman scattering using degenerate pump-probe pairs is presented, and most importantly, it is shown how impulsive stimulated Raman scattering using chirped broadband probe retains unique advantages offered by both.

Coherent Two-Dimensional and Broadband Electronic Spectroscopies

Over the past few decades, coherent broadband spectroscopy has been widely used to improve our understanding of ultrafast processes (e.g., photoinduced electron transfer, proton transfer, and proton-coupled electron transfer reactions) at femtosecond resolution. The advances in femtosecond laser technology along with the development of nonlinear multidimensional spectroscopy enabled further insights into ultrafast energy transfer and carrier relaxation processes in complex biological and material systems. New discoveries and interpretations have led to improved design principles for optimizing the photophysical properties of various artificial systems. In this review, we first provide a detailed theoretical framework of both coherent broadband and two-dimensional electronic spectroscopy (2DES). We then discuss a selection of experimental approaches and considerations of 2DES along with best practices for data processing and analysis. Finally, we review several examples where coherent broadband and 2DES were employed to reveal mechanisms of photoinitiated ultrafast processes in molecular, biological, and material systems. We end the review with a brief perspective on the future of the experimental techniques themselves and their potential to answer an even greater range of scientific questions.

The Influence of Electronic Polarization on Nonlinear Optical Spectroscopy

The environment surrounding a chromophore can dramatically affect the energy absorption and relaxation process, as manifested in optical spectra. Simulations of nonlinear optical spectroscopy, such as two-dimensional electronic spectroscopy (2DES) and transient absorption (TA), will be influenced by the computational model of the environment. We here compare a fixed point charge molecular mechanics model and a quantum mechanical (QM) model of the environment in computed 2DES and TA spectra of Nile red in water and the chromophore of photoactive yellow protein (PYP) in water and protein environments. In addition to simulating these nonlinear optical spectra, we directly juxtapose the computed excitation energy correlation function to the dynamic Stokes shift function often used to analyze environment dynamics. Overall, we find that for the three systems studied here the mutual electronic polarization provided by the QM environment manifests in broader 2DES signals, as well as a larger reorganization energy and a larger static Stokes shift due to stronger coupling between the chromophore and the environment.

Influence of non-adiabatic effects on linear absorption spectra in the condensed phase: Methylene blue

Modeling linear absorption spectra of solvated chromophores is highly challenging as contributions are present both from coupling of the electronic states to nuclear vibrations and from solute-solvent interactions. In systems where excited states intersect in the Condon region, significant non-adiabatic contributions to absorption line shapes can also be observed. Here, we introduce a robust approach to model linear absorption spectra accounting for both environmental and non-adiabatic effects from first principles. This model parameterizes a linear vibronic coupling (LVC) Hamiltonian directly from energy gap fluctuations calculated along molecular dynamics (MD) trajectories of the chromophore in solution, accounting for both anharmonicity in the potential and direct solute-solvent interactions. The resulting system dynamics described by the LVC Hamiltonian are solved exactly using the thermalized time-evolving density operator with orthogonal polynomials algorithm (T-TEDOPA). The approach is applied to the linear absorption spectrum of methylene blue in water. We show that the strong shoulder in the experimental spectrum is caused by vibrationally driven population transfer between the bright S₁ and the dark S₂ states. The treatment of the solvent environment is one of many factors that strongly influence the population transfer and line shape; accurate modeling can only be achieved through the use of explicit quantum mechanical solvation. The efficiency of T-TEDOPA, combined with LVC Hamiltonian parameterizations from MD, leads to an attractive method for describing a large variety of systems in complex environments from first principles.

Vibronic dynamics resolved by global and target analysis of ultrafast transient absorption spectra

We present a methodology that provides a complete parametric description of the time evolution of the electronically and vibrationally excited states as detected by ultrafast transient absorption (TA). Differently from previous approaches, which started fitting the data after ≈100 fs, no data are left out in our methodology, and the "coherent artifact" and the instrument response function are fully taken into account. In case studies, the method is applied to solvents, the dye Nile blue, and all-trans β-carotene in cyclohexane solution. The estimated Damped Oscillation Associated Spectra (DOAS) and phases express the most important vibrational frequencies present in the molecular system. By global fit alone of the experimental data, it is difficult to interpret in detail the underlying dynamics. Since it is unfeasible to directly fit the data by a theoretical simulation, our enhanced DOAS methodology thus provides a useful "middle ground" where the theoretical description and the fit of the experimental data can meet. β-carotene in cyclohexane was complementarily studied with femtosecond stimulated Raman spectroscopy (FSRS). The fs-ps dynamics of β-carotene in cyclohexane in TA and FSRS experiments can be described by a sequential scheme S2 → hot S1 → S1' → S1 → S0 with lifetimes of 167 fs (fixed), 0.35, 1.1, and 9.6 ps. The correspondence of DOAS decaying concomitantly with hot S1 and the Species Associated Difference Spectra of hot S1 in TA and FSRS suggest that we observe here features of the vibrational relaxation and nuclear reorganization responsible for the hot S1 to S1 transition.

Ultrafast vibrational wave packet dynamics of the aqueous tyrosyl radical anion induced by photodetachment

The ultrafast dynamics triggered by the photodetachment of the tyrosinate dianion in aqueous environment shed light on the elementary processes that accompany the interaction of ionizing radiation with biological matter. Photodetachment of the tryosinate dianion yields the tyrosyl radical anion, an important intermediate in biological redox reactions, although the study of its ultrafast dynamics is limited. Here, we utilize femtosecond optical pump-probe spectroscopy to investigate the ultrafast structural reorganization dynamics that follow the photodetachment of the tyrosinate dianion in aqueous solution. Photodetachment of the tyrosinate dianion leads to vibrational wave packet motion along seven vibrational modes that are coupled to the photodetachment process. The vibrational modes are assigned with the aid of density functional theory (DFT) calculations. Our results offer a glimpse of the elementary dynamics of ionized biomolecules and suggest the possibility of extending this approach to investigate the ionization-induced structural rearrangement of other aromatic amino acids and larger biomolecules.

Vibronic and Environmental Effects in Simulations of Optical Spectroscopy

Including both environmental and vibronic effects is important for accurate simulation of optical spectra, but combining these effects remains computationally challenging. We outline two approaches that consider both the explicit atomistic environment and the vibronic transitions. Both phenomena are responsible for spectral shapes in linear spectroscopy and the electronic evolution measured in nonlinear spectroscopy. The first approach utilizes snapshots of chromophore-environment configurations for which chromophore normal modes are determined. We outline various approximations for this static approach that assumes harmonic potentials and ignores dynamic system-environment coupling. The second approach obtains excitation energies for a series of time-correlated snapshots. This dynamic approach relies on the accurate truncation of the cumulant expansion but treats the dynamics of the chromophore and the environment on equal footing. Both approaches show significant potential for making strides toward more accurate optical spectroscopy simulations of complex condensed phase systems.

Signatures of Vibrational and Electronic Quantum Beats in Femtosecond Coherence Spectra

Femtosecond laser pulses can produce oscillatory signals in transient-absorption spectroscopy measurements. The quantum beats are often studied using femtosecond coherence spectra (FCS), the Fourier domain amplitude, and phase profiles at individual oscillation frequencies. In principle, one can identify the mechanism that gives rise to each quantum-beat signal by comparing its measured FCS to those arising from microscopic models. To date, however, most measured FCS deviate from the ubiquitous harmonic oscillator model. Here, we expand the inventory of models to which the measured spectra can be compared. We develop quantum-mechanical models of the fundamental, overtone, and combination-band FCS arising from harmonic potentials, the FCS of anharmonic potentials, and the FCS of a purely electronic dimer. This work solidifies the use of FCS for identifying electronic coherences that can arise in measurements of molecular aggregates including photosynthetic proteins. Furthermore, future studies can use the derived expressions to fit the measured FCS and thereby extract microscopic parameters of molecular potential-energy surfaces.

First principles theoretical spectroscopy of methylene blue: Between limitations of time-dependent density functional theory approximations and its realistic description in the solvent

Methylene blue [3,7-Bis(di-methylamino) phenothiazin-5-ium chloride] is a phenothiazine dye with applications as a sensitizer for photodynamic therapy, photoantimicrobials, and dye-sensitized solar cells. Time-dependent density functional theory (TDDFT), based on (semi)local and global hybrid exchange-correlation functionals, fails to correctly describe its spectral features due to known limitations for describing optical excitations of π-conjugated systems. Here, we use TDDFT with a non-empirical optimally tuned range-separated hybrid functional to explore the optical excitations of gas phase and solvated methylene blue. We compute solvated configurations using molecular dynamics and an iterative procedure to account for explicit solute polarization. We rationalize and validate that by extrapolating the optimized range separation parameter to an infinite amount of solvating molecules, the optical gap of methylene blue is well described. Moreover, this method allows us to resolve contributions from solvent-solute intermolecular interactions and dielectric screening. We validate our results by comparing them to first-principles calculations based on the GW+Bethe-Salpeter equation approach and experiment. Vibronic calculations using TDDFT and the generating function method account for the spectra's subbands and bring the computed transition energies to within 0.15 eV of the experimental data. This methodology is expected to perform equivalently well for describing solvated spectra of π-conjugated systems.

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.

Nonlinear spectroscopy in the condensed phase: The role of Duschinsky rotations and third order cumulant contributions

First-principles modeling of nonlinear optical spectra in the condensed phase is highly challenging because both environment and vibronic interactions can play a large role in determining spectral shapes and excited state dynamics. Here, we compute two dimensional electronic spectroscopy (2DES) signals based on a cumulant expansion of the energy gap fluctuation operator, with specific focus on analyzing mode mixing effects introduced by the Duschinsky rotation and the role of the third order term in the cumulant expansion for both model and realistic condensed phase systems. We show that for a harmonic model system, the third order cumulant correction captures effects introduced by a mismatch in curvatures of ground and excited state potential energy surfaces, as well as effects of mode mixing. We also demonstrate that 2DES signals can be accurately reconstructed from purely classical correlation functions using quantum correction factors. We then compute nonlinear optical spectra for the Nile red and methylene blue chromophores in solution, assessing the third order cumulant contribution for realistic systems. We show that the third order cumulant correction is strongly dependent on the treatment of the solvent environment, revealing the interplay between environmental polarization and the electronic-vibrational coupling.

Transient Two-Dimensional Electronic Spectroscopy: Coherent Dynamics at Arbitrary Times along the Reaction Coordinate

Recent advances in two-dimensional electronic spectroscopy (2DES) have enabled identification of fragile quantum coherences in condensed-phase systems near the equilibrium molecular geometry. In general, traditional 2DES cannot measure such coherences associated with photophysical processes that occur at times significantly after the initially prepared state has dephased, such as the evolution of the initial excited state into a charge transfer state. We demonstrate the use of transient two-dimensional electronic spectroscopy (t-2DES) to probe coherences in an electron donor-acceptor dyad consisting of a perylenediimide (PDI) acceptor and a perylene (Per) donor. An actinic pump pulse prepares the lowest excited singlet state of PDI followed by formation of the PDI^•--Per^•+ ion pair, which is probed at different times following the actinic pulse using 2DES. Analysis of the observed coherences provides information about electronic, vibronic, and vibrational interactions at any time along the reaction coordinate for ion pair formation.

Ultrafast structural rearrangement dynamics induced by the photodetachment of phenoxide in aqueous solution

The elementary processes that accompany the interaction of ionizing radiation with biologically relevant molecules are of fundamental importance. However, the ultrafast structural rearrangement dynamics induced by the ionization of biomolecules in aqueous solution remain hitherto unknown. Here, we employ femtosecond optical pump-probe spectroscopy to elucidate the vibrational wave packet dynamics that follow the photodetachment of phenoxide, a structural mimic of tyrosine, in aqueous solution. Photodetachment of phenoxide leads to wave packet dynamics of the phenoxyl radical along 12 different vibrational modes. Eight of the modes are totally symmetric and support structural rearrangement upon electron ejection. Comparison to a previous photodetachment study of phenoxide in the gas phase reveals the important role played by the solvent environment in driving ultrafast structural reorganization induced by ionizing radiation. This work provides insight into the ultrafast molecular dynamics that follow the interaction of ionizing radiation with molecules in aqueous solution.

The interaction of biomolecules with ionizing radiation induces structural changes which are still largely unknown. The authors use femtosecond wave packet spectroscopy to observe ultrafast structural dynamics that follow the photodetachment of phenoxide in aqueous solution.

Photophysical properties of methylene blue in water and in aqueous solutions of dimethylsulfoxide

A detailed study of the effect of aprotic polar solvents such as dimethylsulfoxide on methylene blue (MB) was carried out through a combination of UV-vis absorption and steady-state fluorescence spectroscopy techniques at 293.15 K. In aqueous solutions MB tends to exhibit strong tendency to aggregate. The dimerization behavior of MB in water was analyzed in terms of monomer-dimer equilibrium. The addition of dimethylsulfoxide prevents dimerization of dye molecules. From absorption spectra the dimerization constants and changes of standard Gibbs energy were calculated. From the steady-state fluorescence spectra the quantum yields and Stokes shifts were determined. To explain the effect of dimethylsulfoxide properly the other polar aprotic solvents such as N, N-dimethylformamide, acetonitrile and acetone were used. It is suggested that water structural effect is the major factor in aggregation phenomenon. Moreover the quantum yield increases drastically in dimethylsulfoxide compared with water assuming that MB may be characterized as viscosity probe.

Ultrafast charge transfer coupled with lattice phonons in two-dimensional covalent organic frameworks

Covalent organic frameworks (COFs) have emerged as a promising light-harvesting module for artificial photosynthesis and photovoltaics. For efficient generation of free charge carriers, the donor–acceptor (D-A) conjugation has been adopted for two-dimensional (2D) COFs recently. In the 2D D-A COFs, photoexcitation would generate a polaron pair, which is a precursor to free charge carriers and has lower binding energy than an exciton. Although the character of the primary excitation species is a key factor in determining optoelectronic properties of a material, excited-state dynamics leading to the creation of a polaron pair have not been investigated yet. Here, we investigate the dynamics of photogenerated charge carriers in 2D D-A COFs by combining femtosecond optical spectroscopy and non-adiabatic molecular dynamics simulation. From this investigation, we elucidate that the polaron pair is formed through ultrafast intra-layer hole transfer coupled with coherent vibrations of the 2D lattice, suggesting a mechanism of phonon-assisted charge transfer.

The donor–acceptor (D-A) conjugation has been adopted for two-dimensional (2D) covalent organic frameworks (COFs) for efficient generation of free charge carriers. Here, the authors investigate the dynamics of photogenerated charge carriers in 2D D-A COFs by combining femtosecond optical spectroscopy and non-adiabatic molecular dynamics simulation.

SVD-aided non-orthogonal decomposition (SANOD) method to exploit prior knowledge of spectral components in the analysis of time-resolved data

Analysis of time-resolved data typically involves discriminating noise against the signal and extracting time-independent components and their time-dependent contributions. Singular value decomposition (SVD) serves this purpose well, but the extracted time-independent components are not necessarily the physically meaningful spectra directly representing the actual dynamic or kinetic processes but rather a mathematically orthogonal set necessary for constituting the physically meaningful spectra. Converting the orthogonal components into physically meaningful spectra requires subsequent posterior analyses such as linear combination fitting (LCF) and global fitting (GF), which takes advantage of prior knowledge about the data but requires that all components are known or satisfactory components are guessed. Since in general not all components are known, they have to be guessed and tested via trial and error. In this work, we introduce a method, which is termed SVD-aided Non-Orthogonal Decomposition (SANOD), to circumvent trial and error. The key concept of SANOD is to combine the orthogonal components from SVD with the known prior knowledge to fill in the gap of the unknown signal components and to use them for LCF. We demonstrate the usefulness of SANOD via applications to a variety of cases.

Vibronic Wavepackets and Energy Transfer in Cryptophyte Light-Harvesting Complexes

Determining the key features of high-efficiency photosynthetic energy transfer remains an ongoing task. Recently, there has been evidence for the role of vibronic coherence in linking donor and acceptor states to redistribute oscillator strength for enhanced energy transfer. To gain further insights into the interplay between vibronic wavepackets and energy-transfer dynamics, we systematically compare four structurally related phycobiliproteins from cryptophyte algae by broad-band pump-probe spectroscopy and extend a parametric model based on global analysis to include vibrational wavepacket characterization. The four phycobiliproteins isolated from cryptophyte algae are two "open" structures and two "closed" structures. The closed structures exhibit strong exciton coupling in the central dimer. The dominant energy-transfer pathway occurs on the subpicosecond timescale across the largest energy gap in each of the proteins, from central to peripheral chromophores. All proteins exhibit a strong 1585 cm^-1 coherent oscillation whose relative amplitude, a measure of vibronic intensity borrowing from resonance between donor and acceptor states, scales with both energy-transfer rates and damping rates. Central exciton splitting may aid in bringing the vibronically linked donor and acceptor states into better resonance resulting in the observed doubled rate in the closed structures. Several excited-state vibrational wavepackets persist on timescales relevant to energy transfer, highlighting the importance of further investigation of the interplay between electronic coupling and nuclear degrees of freedom in studies on high-efficiency photosynthesis.

Quantum transition probabilities during a perturbing pulse: Differences between the nonadiabatic results and Fermi's golden rule forms

For a perturbed quantum system initially in the ground state, the coefficient c_k(t) of excited state k in the time-dependent wave function separates into adiabatic and nonadiabatic terms. The adiabatic term a_k(t) accounts for the adjustment of the original ground state to form the new ground state of the instantaneous Hamiltonian H(t), by incorporating excited states of the unperturbed Hamiltonian H₀ without transitions; a_k(t) follows the adiabatic theorem of Born and Fock. The nonadiabatic term b_k(t) describes excitation into another quantum state k; b_k(t) is obtained as an integral containing the time derivative of the perturbation. The true transition probability is given by b_k(t) ², as first stated by Landau and Lifshitz. In this work, we contrast b_k(t) ² and c_k(t) ². The latter is the norm-square of the entire excited-state coefficient which is used for the transition probability within Fermi's golden rule. Calculations are performed for a perturbing pulse consisting of a cosine or sine wave in a Gaussian envelope. When the transition frequency ω_k0 is on resonance with the frequency ω of the cosine wave, b_k(t) ² and c_k(t) ² rise almost monotonically to the same final value; the two are intertwined, but they are out of phase with each other. Off resonance (when ω_k0 ≠ ω), b_k(t) ² and c_k(t) ² differ significantly during the pulse. They oscillate out of phase and reach different maxima but then fall off to equal final values after the pulse has ended, when a_k(t) ≡ 0. If ω_k0 < ω, b_k(t) ² generally exceeds c_k(t) ², while the opposite is true when ω_k0 > ω. While the transition probability is rising, the midpoints between successive maxima and minima fit Gaussian functions of the form a exp[-b(t - d)²]. To our knowledge, this is the first analysis of nonadiabatic transition probabilities during a perturbing pulse.

Photophysical characterization and time-resolved spectroscopy of a anthradithiophene dimer: exploring the role of conformation in singlet fission

Quantitative singlet fission has been observed for a variety of acene derivatives such as tetracene and pentacene, and efforts to extend the library of singlet fission compounds is of current interest. Preliminary calculations suggest anthradithiophenes exhibit significant exothermicity between the first optically-allowed singlet state, S₁, and 2 × T₁ with an energy difference of >5000 cm^-1. Given the fulfillment of this ingredient for singlet fission, here we investigate the singlet fission capability of a difluorinated anthradithiophene dimer (2ADT) covalently linked by a (dimethylsilyl)ethane bridge and derivatized by triisobutylsilylethynyl (TIBS) groups. Photophysical characterization of 2ADT and the single functionalized ADT monomer were carried out in toluene and acetone solution via absorption and fluorescence spectroscopy, and their photo-initiated dynamics were investigated with time-resolved fluorescence (TRF) and transient absorption (TA) spectroscopy. In accordance with computational predictions, two conformers of 2ADT were observed via fluorescence spectroscopy and were assigned to structures with the ADT cores trans or cis to one another about the covalent bridge. The two conformers exhibited markedly different excited state deactivation mechanisms, with the minor trans population being representative of the ADT monomer showing primarily radiative decay, while the dominant cis population underwent relaxation into an excimer geometry before internally converting to the ground state. The excimer formation kinetics were found to be solvent dependent, yielding time constants of ∼1.75 ns in toluene, and ∼600 ps in acetone. While the difference in rates elicits a role for the solvent in stabilizing the excimer structure, the rate is still decidedly long compared to most singlet fission rates of analogous dimers, suggesting that the excimer is neither a kinetic nor a thermodynamic trap, yet singlet fission was still not observed. The result highlights the sensitivity of the electronic coupling element between the singlet and correlated triplet pair states, to the dimer conformation in dictating singlet fission efficiency even when the energetic requirements are met.

Coherence Spectroscopy in the Condensed Phase: Insights into Molecular Structure, Environment, and Interactions

The role of coherences, or coherently excited superposition states, in complex condensed-phase systems has been the topic of intense interest and debate for a number of years. In many cases, coherences have been utilized as spectators of ultrafast dynamics or for identifying couplings between electronic states. In rare cases, they have been found to drive excited state dynamics directly. Interestingly though, the utilization of coherences as a tool for high-detail vibronic spectroscopy has largely been overlooked until recently, despite their encoding of key information regarding molecular structure, electronically sensitive vibrational modes, and intermolecular interactions. Furthermore, their detection in the time domain makes for a highly comprehensive spectroscopic technique wherein the phase and dephasing times are extracted in addition to amplitude and intensity, an element not afforded in analogous frequency domain "steady-state" measurements. However, practical limitations arise in disentangling the large number of coherent signals typically accessed in broadband nonlinear spectroscopic experiments, often complicating assignment of the origin and type of coherences generated. Two-dimensional electronic spectroscopy (2DES) affords an avenue by which to disperse and decompose the large number of coherent signals generated in nonlinear experiments, facilitating the assignment of various types of quantum coherences. 2DES takes advantage of the broad bandwidth necessary for achieving the high time resolution desired for ultrafast dynamics and coherence generation by resolving the excitation axis to detect all excitation channels independently. This feature is beneficial for following population dynamics such as electronic energy transfer, and 2DES has become the choice method for such studies. Simultaneously, coherences arise as oscillations at well-defined coordinates across the 2D map often atop those evolving population signals. By isolating the coherent contribution to the 2DES data and Fourier transforming along the population time, a 3D spectral representation of the coherent 2D data is generated, and coherences are then ordered by their oscillation frequency, ν₂. Individual coherences can then be selected by their frequency and evaluated via their distinct "2D coherence" spectra, yielding a significantly more distinctive set of spectroscopic signatures over other 1D methodologies and single-point 2DES analysis. Given that coherences of different origin result in unique 2D coherence spectra, these characteristics can be catalogued and compared directly against experiment for prompt assignment, a strategy not afforded by traditional 2DES analysis. In this Account, a structure-driven time-independent spectral model is discussed and employed to compare the 2D fingerprints of various coherences to experimental 2D coherence spectra. The frequency-domain approach can easily integrate ab initio derived vibronic parameters, and its correspondence with experimental coherence spectra of a model compound is demonstrated. Several examples and applications are discussed herein, from 2D Franck-Condon analysis of a model compound, to identifying the signatures of interpigment vibronic coupling in a photosynthetic light-harvesting complex. The 3D spectral approach to 2DES provides remarkable spectroscopic detail, in turn leading to new insights in molecular structure and interactions, which complement the time-resolved dynamics simultaneously recorded. The approach presented herein has the potential to distill down the convoluted set of nonlinear signals appearing in 2D coherent spectra, making the technique more amenable to high-detail vibronic spectroscopy in inherently complex condensed phase systems.

Ultrafast Solvation Dynamics and Vibrational Coherences of Halogenated Boron-Dipyrromethene Derivatives Revealed through Two-Dimensional Electronic Spectroscopy

Boron-dipyrromethene (BODIPY) chromophores have a wide range of applications, spanning areas from biological imaging to solar energy conversion. Understanding the ultrafast dynamics of electronically excited BODIPY chromophores could lead to further advances in these areas. In this work, we characterize and compare the ultrafast dynamics of halogenated BODIPY chromophores through applying two-dimensional electronic spectroscopy (2DES). Through our studies, we demonstrate a new data analysis procedure for extracting the dynamic Stokes shift from 2DES spectra revealing an ultrafast solvent relaxation. In addition, we extract the frequency of the vibrational modes that are strongly coupled to the electronic excitation, and compare the results of structurally different BODIPY chromophores. We interpret our results with the aid of DFT calculations, finding that structural modifications lead to changes in the frequency, identity, and magnitude of Franck-Condon active vibrational modes. We attribute these changes to differences in the electron density of the electronic states of the structurally different BODIPY chromophores.

Estimation of damped oscillation associated spectra from ultrafast transient absorption spectra

When exciting a complex molecular system with a short optical pulse, all chromophores present in the system can be excited. The resulting superposition of electronically and vibrationally excited states evolves in time, which is monitored with transient absorption spectroscopy. We present a methodology to resolve simultaneously the contributions of the different electronically and vibrationally excited states from the complete data. The evolution of the excited states is described with a superposition of damped oscillations. The amplitude of a damped oscillation cos(ω_nt)exp(-γ_nt) as a function of the detection wavelength constitutes a damped oscillation associated spectrum DOAS_n(λ) with an accompanying phase characteristic φ_n(λ). In a case study, the cryptophyte photosynthetic antenna complex PC612 which contains eight bilin chromophores was excited by a broadband optical pulse. Difference absorption spectra from 525 to 715 nm were measured until 1 ns. The population dynamics is described by four lifetimes, with interchromophore equilibration in 0.8 and 7.5 ps. We have resolved 24 DOAS with frequencies between 130 and 1649 cm^-1 and with damping rates between 0.9 and 12 ps^-1. In addition, 11 more DOAS with faster damping rates were necessary to describe the "coherent artefact." The DOAS contains both ground and excited state features. Their interpretation is aided by DOAS analysis of simulated transient absorption signals resulting from stimulated emission and ground state bleach.

Photovoltaic concepts inspired by coherence effects in photosynthetic systems

The past decade has seen rapid advances in our understanding of how coherent and vibronic phenomena in biological photosynthetic systems aid in the efficient transport of energy from light-harvesting antennas to photosynthetic reaction centres. Such coherence effects suggest strategies to increase transport lengths even in the presence of structural disorder. Here we explore how these principles could be exploited in making improved solar cells. We investigate in depth the case of organic materials, systems in which energy and charge transport stand to be improved by overcoming challenges that arise from the effects of static and dynamic disorder - structural and energetic - and from inherently strong electron-vibration couplings. We discuss how solar-cell device architectures can evolve to use coherence-exploiting materials, and we speculate as to the prospects for a coherent energy conversion system. We conclude with a survey of the impacts of coherence and bioinspiration on diverse solar-energy harvesting solutions, including artificial photosynthetic systems.

Black-Box, Real-Time Simulations of Transient Absorption Spectroscopy

We introduce an atomistic, all-electron, black-box electronic structure code to simulate transient absorption (TA) spectra and apply it to simulate pyrazole and a GFP-chromophore derivative. The method is an application of OSCF2, our dissipative extension of time-dependent density functional theory. We compare our simulated spectra directly with recent ultrafast spectroscopic experiments. We identify features in the TA spectra to Pauli-blocking, which may be missed without a first-principles model. An important ingredient in this method is the stationary-TDDFT correction scheme recently put forward by Fischer, Govind, and Cramer that allows us to overcome a limitation of adiabatic TDDFT. We demonstrate that OSCF2 is able to reproduce the energies of bleaches and induced absorptions as well as the decay of the transient spectrum with only the molecular structure as input.

Methylene Blue Exciton States Steer Nonradiative Relaxation: Ultrafast Spectroscopy of Methylene Blue Dimer

The photochemistry and aggregation properties of methylene blue (MB) lead to its popular use in photodynamic therapy. The facile formation of strongly coupled "face-to-face" H-aggregates in concentrated aqueous solution, however, significantly changes its spectroscopic properties and photophysics. The photoinitiated dynamics of the simplest MB aggregate, MB2, was investigated over femtosecond to nanosecond time scales revealing sequential internal conversion events that fully relax the excited population. MB monomer dynamics were analyzed in tandem for a direct comparison. First, ultrafast internal conversion from the electric-dipole allowed upper exciton state to the lower forbidden exciton state was evaluated by use of broadband transient absorption (BBTA) and two-dimensional electronic spectroscopy (2DES) with a time resolution of ∼ 10 fs. Lineshape analysis of MB and MB2 2DES bands at 298 and 77 K show effectively no difference in the diagonal/antidiagonal line width ratio for the dimer, in marked contrast to the distinct reduction of the homogeneous line width for MB. This result is interpreted as ultrafast population relaxation imposing a limitation to the homogeneous line width, instead of pure dephasing as in the case of the monomer. Narrowband transient absorption was performed with the aid of target analysis, to model the dynamics at longer times. The MB dynamics were described by a sequential model featuring vibrational relaxation (1-10 ps) followed by intersystem crossing and internal conversion (τ ∼ 370 ps) leaving behind MB triplet species. Alternatively, the dimer dynamics were entirely quenched within ∼ 10 ps, yielding a ground state recovery time of 3-4 ps. Such fast and complete relaxation to the ground state demonstrates the effect of concentration quenching when monomers are brought into close proximity. The formation of exciton states introduces an initial energy funnel that eventually leads to population relaxation to the ground state, preventing even the dissociation of dimers despite having internal energies well above its binding energy.

Observing Vibrational Wavepackets during an Ultrafast Electron Transfer Reaction

Recent work has proposed that coherent effects impact ultrafast electron transfer reactions. Here we report studies using broadband pump-probe and two-dimensional electronic spectroscopy of intramolecular nuclear motion on the time scale of the electron transfer between oxazine 1 (Ox1) and dimethylaniline (DMA). We performed time-frequency analysis on the time domain data to assign signal amplitude modulations to ground or excited electronic states in the reactive system (Ox1 in DMA) relative to the control system (Ox1 in chloronaphthalene). It was found that our ability to detect vibrational coherence via the excited electronic state of Ox1 diminishes on the time scale that population is lost by electron transfer. However, the vibrational wavepacket is not damped by the electron transfer process and has been observed previously by detecting the Ox1 radical transient absorption. The analysis presented here indicates that the "addition" of an electron to the photoexcited electron acceptor does not significantly perturb the vibrational coherence, suggesting its presence as a spectator, consistent with the Born-Oppenheimer separation of electronic and nuclear degrees of freedom.