Vibrational coherence in ultrafast electron-transfer dynamics of oxazine 1 in N,N-dimethylaniline: simulation of a femtosecond pump-probe experiment

Modeling Excited-State Proton Transfer Using the Lindblad Equation: Quantification of Time-Resolved Spectroscopy with Mechanistic Insights

The quantum dynamics of excited-state intramolecular proton transfer (ESIPT) is studied using a multilevel vibronic Hamiltonian and the Lindblad master equation. We simulate time-resolved fluorescence spectroscopy of 2-(2'-hydroxyphenyl) benzothiazole (HBT) and 10-hydroxybenzo[h]quinoline (HBQ), which suggests that the underlying mechanism behind the initial ultrafast rise and decay in the spectra is electronic state population that evolves simultaneously with proton wave packet dynamics. The results predict that the initial rise and decay signals at different wavelengths vary significantly with system properties in terms of their shape, the time, and the intensity of the maximum. These findings provide clues for data interpretation, mechanism validation, and control of the dynamics, and the model serves as an attempt toward clarifying ESIPT by direct comparison to time-resolved spectroscopy.

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.

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.

From Fundamental Theories to Quantum Coherences in Electron Transfer

Photoinduced electron transfer (ET) is a cornerstone of energy transduction from light to chemistry. The past decade has seen tremendous advances in the possible role of quantum coherent effects in the light-initiated energy and ET processes in chemical, biological, and materials systems. The prevalence of such coherence effects holds a promise to increase the efficiency and robustness of transport even in the face of energetic or structural disorder. A primary motive of this Perspective is to work out how to think about "coherence" in ET reactions. We will discuss how the interplay of basic parameters governing ET reactions-like electronic coupling, interactions with the environment, and intramolecular high-frequency quantum vibrations-impact coherences. This includes revisiting the insights from the seminal work on the theory of ET and time-resolved measurements on coherent dynamics to explore the role of coherences in ET reactions. We conclude by suggesting that in addition to optical spectroscopies, validating the functional role of coherences would require simultaneous mapping of correlated electron motion and atomically resolved nuclear structure.

Excitation Wavelength Dependence of the Dynamics of Bimolecular Photoinduced Electron Transfer Reactions

The dynamics of photoinduced electron transfer between polar acceptors and donors has been investigated in apolar solvents using femtosecond-resolved fluorescence spectroscopy. It was found to be ultrafast and to continuously accelerate by varying the excitation wavelength from the maximum to the red edge of the absorption band of the acceptor, the overall difference being as large as a factor 4-5. This violation of the Kasha-Vavilov rule is explained by a correlation between the composition of the acceptor environment and its transition energy, that is, the more donors around an acceptor, the longer its absorption wavelength, and the faster the quenching. Because of preferential solvation, this dependence is already observed at low quencher concentrations. This effect, which requires quenching to be faster than the fluctuations of the environment composition, should be quite general for photoinduced charge transfer processes in low-polarity, viscous, or rigid media, such as those used in organic optoelectronic devices.

Ultrafast photochemistry in liquids

Ultrafast photochemical processes can occur in parallel with the relaxation of the optically populated excited state toward equilibrium. The latter involves both intra- and intermolecular modes, namely vibrational and solvent coordinates, and takes place on timescales ranging from a few tens of femtoseconds to up to hundreds of picoseconds, depending on the system. As a consequence, the reaction dynamics can substantially differ from those usually measured with slower photoinduced processes occurring from equilibrated excited states. For example, the decay of the excited-state population may become strongly nonexponential and depend on the excitation wavelength, contrary to the Kasha and Vavilov rules. In this article, we first give a brief account of our current understanding of vibrational and solvent relaxation processes. We then present an overview of important classes of ultrafast photochemical reactions, namely electron and proton transfer as well as isomerization, and illustrate with several examples how nonequilibrium effects can affect their dynamics.

Driving force dependence of charge recombination in reactive and nonreactive solvents

This study addresses the free energy dependence of charge recombination following photoinduced bimolecular electron transfer in three different solvents of either inert (acetonitrile and benzyl acetate) or reactive (N,N-dimethylaniline) character. Femtosecond time-resolved fluorescence and transient absorption have been used to determine the time scales for charge recombination. In pure N,N-dimethylaniline, charge recombination is found to be substantially slower than charge separation in a range of driving forces covering 1.5 eV. In all three solvents, the so-called Marcus inverted region is clearly observed for charge recombination. Additionally, the charge recombination step is found to be influenced by the solvent relaxation dynamics. A diffusion-reaction equation approach using an electron transfer model accounting for solvent relaxation is used to rationalize the experimental results.

Monte carlo wave packet theory of dissociative double ionization

Nuclear dynamics in strong-field double ionization processes is predicted using a stochastic Monte Carlo wave packet technique. Using input from electronic structure calculations and strong-field electron dynamics the description allows for field-dressed dynamics within a given molecule as well as transitions between several different charge states. The description is computationally efficient and applicable to a wide range of systems. As a proof of principle, theoretical nuclear kinetic energy release spectra for H2 (D2) in strong near-infrared laser pulses of 40 fs duration are compared to experiments and very good agreement is obtained.

Theoretical description of femtosecond fluorescence depletion spectrum of molecules in solution

A theoretical model used for calculating the fluorescence depletion spectrum (FDS) of molecules in liquids induced by femtosecond pump-probe laser pulses is proposed based on the reduced density matrix theory. The FDS intensity is obtained by calculating the stimulated emission of the excited electronic state. As an application of the theoretical model, the FDS of oxazine 750 (OX-750) molecule in acetone solution is calculated. The simulated FDS agrees with the experimental result of Liu et al. [J. Y. Liu et al., J. Phys. Chem. A 107, 10857 (2003)]. The calculated vibrational relaxation rate is 2.5 ps(-1) for the OX-750 molecule. Vibrational population dynamics and wave packet evolution in the excited state are described in detail. The effect of the probe pulse parameter on the FDS is also discussed.

Ultrafast Photoinduced Electron Transfer in Directly Linked Porphyrin−Ferrocene Dyads

The ultrafast electron transfer occurring upon Soret excitation of three new porphyrin-ferrocene (XP-Fc) dyads has been studied by femtosecond up-conversion and pump-probe techniques. In the XP-Fc dyads (XP-Fcs) designed in this study, the ferrocene moiety is covalently bonded to the meso positions of 3,5-di-tert-butylphenyl zinc porphyrin (BPZnP-Fc), pentafluorophenyl zinc porphyrin (FPZnP-Fc), and 3,5-di-tert-butylphenyl free-base porphyrin (BPH2P-Fc). Charge separation and recombination in the XP-Fcs were confirmed by transient absorption spectra, and the lifetimes of the charge-separated states were estimated from the decay rate of the porphyrin radical anion band to be approximately 20 ps. The charge-separation rates of the XP-Fcs were found to be >10(13) s-1 from the S2 state and 6.3x10(12) s-1 from the S1 state. Charge separation from the S2 state was particularly efficient for BPZnP-Fc, whereas the main reaction pathway was from the S1 state for BPH2P-Fc. Charge separation from the S2 and S1 states occurred at virtually the same rate in benzene and tetrahydrofuran and was much faster than their solvation times. Analysis of these results using semiquantum Marcus theory indicates that the magnitude of the electronic-tunneling matrix element is rather large and far outside the range of nonadiabatic approximation. The pump-probe data show the presence of vibrational coherence during the reactions, suggesting that wavepacket dynamics on the adiabatic potential energy surface might regulate the ultrafast reactions.

Three-centered model of ultrafast photoinduced charge transfer: Continuum dielectric approach

A theoretical description of photoinduced charge transfer involves explicit treating both the optical formation of the nuclear wave packet on the excited free energy surface and its ensuing dynamics. The reaction pathway constitutes two-stage charge transfer between three centers. Manifestations of fractional charge transfer at first stage are explored. An expression for time dependent rate constant of photoinduced charge transfer is found in the framework of the linear dielectric continuum model of the medium. The model involves both the intramolecular vibrational reorganization and the Coulombic interaction of the transferred charge with the medium polarization fluctuations and allows to express the rate in terms of intramolecular reorganization parameters and complex dielectric permittivity. The influence of the vibrational coherent motion in the locally excited state on the charge transfer dynamics has been explored. The dependence of the ultrafast photoinduced charge transfer dynamics on the excitation pulse carrier frequency (spectral effect) has been investigated. The spectral effect has been shown to depend on quantity of the fractional charge.

Effect of the excitation pulse frequency on the ultrafast photoinduced electron transfer dynamics

The dependence of the ultrafast photoinduced electron transfer dynamics in donor-acceptor complexes on the excitation pulse carrier frequency (spectral effect) has been investigated in the framework of a model involving three electronic state. The spectral effect has been shown to strongly depend on the angle theta between the reaction coordinate directions corresponding to optical and charge transfer transitions. Describing the solvent as a linear homogenous polar medium and accounting for Coulombic interaction of the transferred charge with the medium polarization fluctuations, the angle theta has been found out to be typically in the area 40 degrees -85 degrees. Exactly in this area of theta the spectral effect is predicted to be most pronounced.