Vibrational Wave Packet Research Articles

Interplay of vibrational wavepackets during an ultrafast electron transfer reaction.

Electron transfer reactions facilitate energy transduction and photoredox processes in biology and chemistry. Recent findings show that molecular vibrations can enable the dramatic acceleration of some electron transfer reactions, and control it by suppressing and enhancing reaction paths. Here, we report ultrafast spectroscopy experiments and quantum dynamics simulations that resolve how quantum vibrations participate in an electron transfer reaction. We observe ballistic electron transfer (~30 fs) along a reaction coordinate comprising high-frequency promoting vibrations. Along another vibrational coordinate, the system becomes impulsively out of equilibrium as a result of the electron transfer reaction. This leads to the generation (by the electron transfer reaction, not the laser pulse) of a new vibrational coherence along this second reaction coordinate in a mode associated with the reaction product. These results resolve a complex reaction trajectory composed of multiple vibrational coordinates that, like a sequence of ratchets, progressively diminish the recurrence of the reactant state.

Quantum dynamics of vibrational energy flow in oscillator chains driven by anharmonic interactions

A new model of vibrational energy transfer in molecular systems taking into account anharmonic (third order) interactions of localized vibrations with a chain of harmonic oscillators is developed. The role of the energy spectrum of the chain and of the magnitude of the non-linear coupling is discussed in detail by an exact numerical solution of the quantum dynamical problem based on the tensor-train (matrix product state) representation of the vibrational wave function. Results show that the type of wave packet motion is determined by the eigen-spectrum of the chain and by its excitation time. It is found that when the excitation of the chain takes place on a much shorter timescale than the energy transfer along the chain the vibrational wave packet moves in a ballistic way independently of the length of the chain. On the other hand when the excitation of the chain takes place on the timescale of the energy transfer along the chain the overall motion becomes superballistic. These findings shed new light on recent observations of ballistic energy transfer along polymethylene chains.

Intermolecular conical intersections in molecular aggregates.

Conical intersections (CoIns) of multidimensional potential energy surfaces are ubiquitous in nature and control pathways and yields of many photo-initiated intramolecular processes. Such topologies can be potentially involved in the energy transport in aggregated molecules or polymers but are yet to be uncovered. Here, using ultrafast two-dimensional electronic spectroscopy (2DES), we reveal the existence of intermolecular CoIns in molecular aggregates relevant for photovoltaics. Ultrafast, sub-10-fs 2DES tracks the coherent motion of a vibrational wave packet on an optically bright state and its abrupt transition into a dark state via a CoIn after only 40 fs. Non-adiabatic dynamics simulations identify an intermolecular CoIn as the source of these unusual dynamics. Our results indicate that intermolecular CoIns may effectively steer energy pathways in functional nanostructures for optoelectronics.

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.

Evolution of a Molecular Shape Resonance along a Stretching Chemical Bond.

We report experiments on laser-assisted electron recollisions that result from strong-field ionization of photoexcited I_{2} molecules in the regime of low-energy electron scattering (<25 eV impact energy). By comparing differential scattering cross sections extracted from the angle-resolved photoelectron spectra to differential scattering cross sections from quantum-scattering calculations, we demonstrate that the electron-scattering dynamics is dominated by a shape resonance. When the molecular bond stretches during the evolution of a vibrational wave packet this shape resonance shifts to lower energies, both in experiment and theory. We explain this behavior by the nature of the resonance wave function, which closely resembles an antibonding molecular orbital of I_{2}.

Excited state dynamics of cis,cis-1,3-cyclooctadiene: UV pump VUV probe time-resolved photoelectron spectroscopy.

We present UV pump, vacuum ultraviolet probe time-resolved photoelectron spectroscopy measurements of the excited state dynamics of cis,cis-1,3-cyclooctadiene. A 4.75 eV deep UV pump pulse launches a vibrational wave packet on the first electronically excited state, and the ensuing dynamics are probed via ionization using a 7.92 eV probe pulse. The experimental results indicate that the wave packet undergoes rapid internal conversion to the ground state in under 100 fs. Comparing the measurements with electronic structure and trajectory surface hopping calculations, we are able to interpret the features in the measured photoelectron spectra in terms of ionization to several states of the molecular cation.

Mapping the emergence of molecular vibrations mediating bond formation.

Fundamental studies of chemical reactions often consider the molecular dynamics along a reaction coordinate using a calculated or suggested potential energy surface1-5. But fully mapping such dynamics experimentally, by following all nuclear motions in a time-resolved manner-that is, the motions of wavepackets-is challenging and has not yet been realized even for the simple stereotypical bimolecular reaction6-8: A-B+C→A+B-C. Here we track the trajectories of these vibrational wavepackets during photoinduced bond formation of the gold trimer complex [Au(CN)2-]3 in an aqueous monomer solution, using femtosecond X-ray liquidography9-12 with X-ray free-electron lasers13,14. In the complex, which forms when three monomers A, Band C cluster together through non-covalent interactions15,16, the distance between Aand Bis shorter than that between Band C. Tracking the wavepacket in three-dimensional nuclear coordinates reveals that within the first 60femtoseconds after photoexcitation, a covalent bond forms between Aand B to give A-B+C. The second covalent bond, between Band C, subsequently forms within 360femtoseconds to give a linear and covalently bonded trimer complex A-B-C. The trimer exhibits harmonic vibrations that we map and unambiguously assign to specific normal modes using only the experimental data. In principle, more intense X-rays could visualize the motion not only of highly scattering atoms such as gold but also of lighter atoms such as carbon and nitrogen, which will open the door to the direct tracking of the atomic motions involved in many chemical reactions.

The shape of the electric dipole function determines the sub-picosecond dynamics of anharmonic vibrational polaritons

Vibrational strong coupling has emerged as a promising route for manipulating the reactivity of molecules inside infrared cavities. We develop a full-quantum methodology to study the unitary dynamics of a single anharmonic vibrational mode interacting with a quantized infrared cavity field. By comparing multi-configurational time-dependent Hartree simulations for an intracavity Morse oscillator with an equivalent formulation of the problem in Hilbert space, we describe for the first time the essential role of permanent dipole moments in the femtosecond dynamics of vibrational polariton wavepackets. We classify molecules into three general families according to the shape of their electric dipole function de(q) along the vibrational mode coordinate q. For polar species with a positive slope of the dipole function at equilibrium, an initial diabatic light-matter product state without vibrational or cavity excitations evolves into a polariton wavepacket with a large number of intracavity photons for interaction strengths at the conventional onset of ultrastrong coupling. This buildup of the cavity photon amplitude is accompanied by an effective lengthening of the vibrational mode that is comparable with a laser-induced vibrational excitation in free space. In contrast, polar molecules with a negative slope of the dipole function experience an effective mode shortening, under equivalent coupling conditions. We validate our predictions using realistic ab initio ground state potentials and dipole functions for HF and CO2 molecules. We also propose a non-adiabatic state preparation scheme to generate vibrational polaritons with molecules near infrared nanoantennas for the spontaneous radiation of infrared quantum light.

Low-Temperature Vibrational Energy Transport via PEG Chains.

We used relaxation-assisted two-dimensional infrared spectroscopy to study the temperature dependence (10-295 K) of end-to-end energy transport across end-decorated PEG oligomers of various chain lengths. The excess energy was introduced by exciting the azido end-group stretching mode at 2100 cm-1 (tag); the transport was recorded by observing the asymmetric C═O stretching mode of the succinimide ester end group at 1740 cm-1. The overall transport involves diffusive steps at the end groups and a ballistic step through the PEG chain. We found that at lower temperatures the through-chain energy transport became faster, while the end-group diffusive transport time and the tag lifetime increase. The modeling of the transport using a quantum Liouville equation linked the observations to the reduction of decoherence rate and an increase of the mean-free-path for the vibrational wavepacket. The energy transport at the end groups slowed down at low temperatures due to the decreased number and efficiency of the anharmonic energy redistribution pathways.

Ultrafast x-ray and electron scattering of free molecules: A comparative evaluation.

Resolving gas phase molecular motions with simultaneous spatial and temporal resolution is rapidly coming within the reach of x-ray Free Electron Lasers (XFELs) and Mega-electron-Volt (MeV) electron beams. These two methods enable scattering experiments that have yielded fascinating new results, and while both are important methods for determining transient molecular structures in photochemical reactions, it is important to understand their relative merits. In the present study, we evaluate the respective scattering cross sections of the two methods and simulate their ability to determine excited state molecular structures in light of currently existing XFEL and MeV source parameters. Using the example of optically excited N-methyl morpholine and simulating the scattering patterns with shot noise, we find that the currently achievable signals are superior with x-ray scattering for equal samples and on a per-shot basis and that x-ray scattering requires fewer detected signal counts for an equal fidelity structure determination. Importantly, within the independent atom model, excellent structure determinations can be achieved for scattering vectors only to about 5 Å−1, leaving larger scattering vector ranges for investigating vibrational motions and wavepackets. Electron scattering has a comparatively higher sensitivity toward hydrogen atoms, which may point to applications where electron scattering is inherently the preferred choice, provided that excellent signals can be achieved at large scattering angles that are currently difficult to access.

Long-Lived Nuclear Coherences inside Helium Nanodroplets.

Much of our knowledge about dynamics and functionality of molecular systems has been achieved with femtosecond time-resolved spectroscopy. Despite extensive technical developments over the past decades, some classes of systems have eluded dynamical studies so far. Here, we demonstrate that superfluid helium nanodroplets, acting as a thermal bath of 0.4K temperature to stabilize weakly bound or reactive systems, are well suited for time-resolved studies of single molecules solvated in the droplet interior. By observing vibrational wave packet motion of indium dimers (In_{2}) for tens of picoseconds, we demonstrate that the perturbation imposed by this quantum liquid can be lower by a factor of 10-100 compared to any other solvent, which uniquely allows us to study processes depending on long nuclear coherence in a dissipative environment. Furthermore, tailor-made microsolvation environments inside droplets will enable us to investigate the solvent influence on intramolecular dynamics in a wide tuning range from molecular isolation to strong molecule-solvent coupling.

Vibrational coherences in manganese single-molecule magnets after ultrafast photoexcitation.

Magnetic recording using femtosecond laser pulses has recently been achieved in some dielectric media, showing potential for ultrafast data storage applications. Single-molecule magnets (SMMs) are metal complexes with two degenerate magnetic ground states and are promising for increasing storage density, but remain unexplored using ultrafast techniques. Here we have explored the dynamics occurring after photoexcitation of a trinuclear µ3-oxo-bridged Mn(III)-based SMM, whose magnetic anisotropy is closely related to the Jahn-Teller distortion. Ultrafast transient absorption spectroscopy in solution reveals oscillations superimposed on the decay traces due to a vibrational wavepacket. Based on complementary measurements and calculations on the monomer Mn(acac)3, we conclude that the wavepacket motion in the trinuclear SMM is constrained along the Jahn-Teller axis due to the µ3-oxo and µ-oxime bridges. Our results provide new possibilities for optical control of the magnetization in SMMs on femtosecond timescales and open up new molecular-design challenges to control the wavepacket motion in the excited state of polynuclear transition-metal complexes.

Vibrational wavepacket dynamics in Fe carbene photosensitizer determined with femtosecond X-ray emission and scattering

The non-equilibrium dynamics of electrons and nuclei govern the function of photoactive materials. Disentangling these dynamics remains a critical goal for understanding photoactive materials. Here we investigate the photoinduced dynamics of the [Fe(bmip)2]2+ photosensitizer, where bmip = 2,6-bis(3-methyl-imidazole-1-ylidine)-pyridine, with simultaneous femtosecond-resolution Fe Kα and Kβ X-ray emission spectroscopy (XES) and X-ray solution scattering (XSS). This measurement shows temporal oscillations in the XES and XSS difference signals with the same 278 fs period oscillation. These oscillations originate from an Fe-ligand stretching vibrational wavepacket on a triplet metal-centered (3MC) excited state surface. This 3MC state is populated with a 110 fs time constant by 40% of the excited molecules while the rest relax to a 3MLCT excited state. The sensitivity of the Kα XES to molecular structure results from a 0.7% average Fe-ligand bond length shift between the 1 s and 2p core-ionized states surfaces.

Limitations of Generic Chromophore Concept for Femtosecond Vibrational Coherences

The spectrum of vibrational coherences modulating transient triplet–triplet absorption of bis-triisopropylsilylethynylpentacene that propagate in the course of the fission process from the singlet state of this molecule to the triplet manifold has been lately reproduced by ab initio calculations. This has led to the conclusion that, contrary to a recent hypothesis, spontaneous generation of coherent vibrational wave packets is not a constitutive feature of singlet exciton fission. Here we demonstrate by calculations that the corresponding spectrum of unsubstituted pentacene is significantly different, so that the two systems cannot be viewed as different models of the same generic chromophore. This shows that femtosecond pump–probe spectra of vibrational coherences are sensitive to subtle features of molecular structure, which we identify here, thereby rationalizing the registered spectral differences. The crucial factor is the substituent-induced coupling between some pentacene normal modes that in other...

Echo in a single vibrationally excited molecule

Echo is a ubiquitous phenomenon found in many physical systems, ranging from spins in magnetic fields to particle beams in hadron accelerators. It is typically observed in inhomogeneously broadened ensembles of nonlinear objects, and is used to eliminate the effects of environmental-induced dephasing, enabling observation of proper, inherent object properties. Here, we report experimental observation of quantum wave packet echoes in a single isolated molecule. In contrast to conventional echoes, here the entire dephasing-rephasing cycle occurs within a single molecule without any inhomogeneous spread of molecular properties, or any interaction with the environment. In our experiments, we use a short laser pulse to impulsively excite a vibrational wave packet in an anharmonic molecular potential, and observe its oscillations and eventual dispersion with time. A second delayed pulsed excitation is applied, giving rise to an echo: a partial recovery of the initial coherent wavepacket. The vibrational dynamics of single molecules is visualized by time-delayed probe pulse dissociating them one at a time. Two mechanisms for the echo formation are discussed: ac Stark-induced molecular potential shaking and creation of depletion-induced "hole" in the nuclear spatial distribution. Interplay between the optically induced echoes and quantum revivals of the vibrational wave packets is observed and theoretically analyzed. The single molecule wave packet echoes may lead to the development of new tools for probing ultrafast intramolecular processes in various molecules.

The vibronic absorption spectra and exciton dynamics of plasmon-exciton hybrid systems in the regimes ranged from Fano antiresonance to Rabi-like splitting.

The complex interplay between molecules and plasmonic metal nanoparticles (MNPs) presents a set of particular characteristics in absorption/scattering spectra such as excitonic splitting, asymmetric line shapes, plasmon-induced absorption enhancement and transparencies, etc. Although the MNP-molecule systems have been intensively investigated experimentally and theoretically, the construction of a theoretical framework which can produce all the disparate experimental observations and account for the electron-phonon (e-p) coupling is still in progress. Here, we present a theoretical approach which can account for both the plasmon-exciton coupling and the e-p interaction and produce all the spectral line shapes ranging from Fano antiresonance to Rabi splitting by simply tuning the coupling strength or plasmon damping rate. Additionally, we demonstrate the evolution of vibronic spectra and exciton dynamics with the coupling strength, plasmon damping rate, and detuning energy. It is found that the vibronic structures appearing in Rabi-like spectra are worse resolved, wider, and more largely shifted than those appearing in the Fano regime, attributed to the more significant deformation of the molecular vibrational wavepacket in the Rabi-like regime than that in the Fano regime as the molecular e-p interaction increases. The positive/negative value of detuning energy can induce different degrees of the vibrational wavepacket deformation and subsequently a different effect on the spectra in different coupling regimes.

Ultrafast dissociative ionization and large-amplitude vibrational wave packet dynamics of strong-field-ionized di-iodomethane.

We employ few-cycle pulses to strong-field-ionize di-iodomethane (CH2I2) and femtosecond extreme ultraviolet (XUV) transient absorption spectroscopy to investigate the subsequent ultrafast dissociative ionization and vibrational wave packet dynamics. Probing in the spectral region of the I 4d core-level transitions, the time-resolved XUV differential absorption spectra reveal the population of several electronic states of CH2I2 + by strong-field ionization. Global analysis reveals three distinct time scales for the observed dynamics: 20 ± 2 fs, 49 ± 6 fs, and 157 ± 9 fs, ascribed to relaxation of the CH2I2 + parent ion from the Franck-Condon region, dissociation of high-lying excited states of CH2I2 + to I+ (3P2), CH2I, and I2 + (2Π3/2,g), and dissociation of CH2I2 + to I (2P3/2) and CH2I+, respectively. Oscillatory features in the time-resolved XUV differential absorption spectra point to the generation of vibrational wave packets in both the residual CH2I2 and the CH2I2 + parent ion. Analysis of the oscillation frequencies and phases reveals, in the case of neutral CH2I2, C-I symmetric stretching induced by bond softening and I-C-I bending driven by a combination of bond softening and R-selective depletion. In the case of CH2I2 +, both the fundamental and first overtone frequencies of the I-C-I bending mode are observed, indicating large-amplitude I-C-I bending motion, in good agreement with results obtained from ab initio simulations of the XUV transition energy along the I-C-I bend coordinate. These results show that femtosecond XUV absorption spectroscopy is well-suited for studying ultrafast photodissociation and vibrational wave packet dynamics.

Vibronic coherence evolution in multidimensional ultrafast photochemical processes

The complex choreography of electronic, vibrational, and vibronic couplings used by photoexcited molecules to transfer energy efficiently is remarkable, but an unambiguous description of the temporally evolving vibronic states governing these processes has proven experimentally elusive. We use multidimensional electronic-vibrational spectroscopy to identify specific time-dependent excited state vibronic couplings involving multiple electronic states, high-frequency vibrations, and low-frequency vibrations which participate in ultrafast intersystem crossing and subsequent relaxation of a photoexcited transition metal complex. We discover an excited state vibronic mechanism driving long-lived charge separation consisting of an initial electronically-localized vibrational wavepacket which triggers delocalization onto two charge transfer states after propagating for ~600 femtoseconds. Electronic delocalization consequently occurs through nonadiabatic internal conversion driven by a 50 cm−1 coupling resulting in vibronic coherence transfer lasting for ~1 picosecond. This study showcases the power of multidimensional electronic-vibrational spectroscopy to elucidate complex, non-equilibrium energy and charge transfer mechanisms involving multiple molecular coordinates.

Tracking the Metal-Centered Triplet in Photoinduced Spin Crossover of Fe(phen)32+ with Tabletop Femtosecond M-Edge X-ray Absorption Near-Edge Structure Spectroscopy.

Fe(II) coordination complexes are promising alternatives to Ru(II) and Ir(III) chromophores for photoredox chemistry and solar energy conversion, but rapid deactivation of the initial metal-to-ligand charge transfer (MLCT) state to low-lying (d,d) states limits their performance. Relaxation to a long-lived quintet state is postulated to occur via a metal-centered triplet state, but this mechanism remains controversial. We use femtosecond extreme ultraviolet (XUV) transient absorption spectroscopy to measure the excited-state relaxation of Fe(phen)32+ and conclusively identify a 3T intermediate that forms in 170 fs and decays to a vibrationally hot 5T2g state in 39 fs. A coherent vibrational wavepacket with a period of 249 fs and damping time of 0.63 ps is observed on the 5T2g surface, and the spectrum of this oscillation serves as a fingerprint for the Fe-N symmetric stretch. The results show that the shape of the M2,3-edge X-ray absorption near-edge structure (XANES) spectrum is sensitive to the electronic structure of the metal center, and the high-spin sensitivity, fast time resolution, and tabletop convenience of XUV transient absorption make it a powerful tool for studying the complex photophysics of transition metal complexes.

Characterizing dissociative motion in time-resolved x-ray scattering from gas-phase diatomic molecules

Time-resolved x-ray scattering (TRXS) measures internuclear separations in a molecule following laser-induced photoexcitation. The molecular dynamics induced by the excitation laser may lie on one or several bound or dissociative electronic states. Time-resolved x-ray scattering from these states can be difficult to isolate because they generally overlap in the angle-resolved x-ray scattering pattern $I(x,y,\ensuremath{\tau})$, where $\ensuremath{\tau}$ is the pump-probe delay and $(x,y)$ are the physical pixel positions. Here we show how standard transform methods can isolate the dynamics from individual states. We form the temporal Fourier transform $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{I}(x,y,\ensuremath{\omega})={\ensuremath{\int}}_{\ensuremath{-}\ensuremath{\infty}}^{+\ensuremath{\infty}}d\ensuremath{\tau}\phantom{\rule{0.16em}{0ex}}{e}^{\ensuremath{-}i\ensuremath{\omega}\ensuremath{\tau}}I(x,y,\ensuremath{\tau})$. This frequency-resolved x-ray scattering (FRXS) signal segregates the bound states according to their vibrational frequencies ${\ensuremath{\omega}}_{i}$ and also displays dissociative states along straight lines $\ensuremath{\omega}=vQ$, where the slope $v$ is the rate of increase of the internuclear distance and $Q$ is the momentum transfer between the incident and scattered x-ray photon. We derive this relation and use FRXS to extract state-specific dynamics from experimental TRXS from molecular iodine following a 520-nm pump. Dynamics observed include one- and two-photon dissociation of the ${}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}$ and ${}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}{}^{+}$ excited states and vibrational wave packets on the $B{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Pi}}}_{0u}{}^{+}$ state.