Vibrational Wave Packet Research Articles

Spin-vibronic coherence drives singlet-triplet conversion.

Design-specific control over the transitions between excited electronic states with different spin multiplicities is of the utmost importance in molecular and materials chemistry1-3. Previous studies have indicated that the combination of spin-orbit and vibronic effects, collectively termed the spin-vibronic effect, can accelerate quantum-mechanically forbidden transitions at non-adiabatic crossings4,5. However, it has been difficult to identify precise experimental manifestations of the spin-vibronic mechanism. Here we present coherence spectroscopy experiments that reveal the interplay between the spin, electronic and vibrational degrees of freedom that drive efficient singlet-triplet conversion in four structurally related dinuclear Pt(II) metal-metal-to-ligand charge-transfer (MMLCT) complexes. Photoexcitation activates the formation of a Pt-Pt bond, launching a stretching vibrational wavepacket. The molecular-structure-dependent decoherence and recoherence dynamics of this wavepacket resolve the spin-vibronic mechanism. We find that vectorial motion along the Pt-Pt stretching coordinates tunes the singlet and intermediate-state energy gap irreversibly towards the conical intersection and subsequently drives formation of the lowest stable triplet state in a ratcheting fashion. This work demonstrates the viability of using vibronic coherences as probes6-9 to clarify the interplay among spin, electronic and nuclear dynamics in spin-conversion processes, and this could inspire new modular designs to tailor the properties of excited states.

Charge Migration in HCCI Cations Probed by Strong Field Ionization: Time-Dependent Configuration Interaction and Vibrational Wavepacket Simulations.

Strong field ionization of neutral iodoacetylene (HCCI) can produce a coherent superposition of the X and A cations and results in charge migration between the CC π orbital and the iodine π-type lone pair. This charge migration causes oscillations in the rate of strong field ionization of the cation to the dication that can be monitored using intense few-cycle probe pulses. The dynamics and strong field ionization of the coherent superposition the X and A states of HCCI+ have been modeled by time-dependent configuration interaction (TDCI) simulations. When the nuclei are allowed to move, the electronic wavefunctions need to be multiplied by vibrational wavefunctions. Nuclear motion has been modeled by vibrational packets moving on quadratic approximations to the potential energy surfaces for the X and A states of the cation. The overlap of the vibrational wavepackets decays in about 10-15 fs. Consequently, the oscillations in the strong field ionization decay on the same time scale. A revival of the vibrational overlap and in the oscillations of the strong field ionization is seen at 60-110 fs. TDCI simulations show that the decay and revival of the charge migration can be monitored by strong field ionization with intense 2- and 4-cycle linearly polarized 800 nm pulses. The revival is also seen with 7-cycle pulses.

Mapping molecular potentials using pump-probe spectroscopy of vibrational wave packets' revival

Mapping molecular potentials using pump-probe spectroscopy of vibrational wave packets' revival

Torsional Wave-Packet Dynamics in 2-Fluorobiphenyl Investigated by State-Selective Ionization-Detected Impulsive Stimulated Raman Spectroscopy.

We report the creation and observation of vibrational wave packets pertinent to torsional motion in a biphenyl derivative in its electronic ground-state manifold. Adiabatically cooled molecular samples of 2-fluorobiphenyl were irradiated by intense nonresonant ultrashort laser pulses to drive impulsive stimulated Raman excitation of torsional motion. Spectral change due to the nonadiabatic vibrational excitation is probed in a state-selective manner using resonance-enhanced two-photon ionization through the S1 ← S0 electronic transition. The coherent nature of the excitation was exemplified by adopting irradiation with a pair of pump pulses: observed signals for excited torsional levels exhibit oscillatory variations against the mutual delay between the pump pulses due to wave-packet interference. By taking the Fourier transform of the time course of the signals, energy intervals among torsional levels with v = 0-3 were determined and utilized to calibrate a density functional theory (DFT)-calculated torsional potential-energy function. Time variation of populations in the excited torsional levels was assessed experimentally by measuring integrated intensities of the corresponding transitions while scanning the delay. Early time enhancement of the population (up to ∼2 ps) and gradual degradation of coherence (within ∼20 ps) appears. To explain the observed distinctive features, we developed a four-dimensional (4D) dynamical calculation in which one-dimensional (1D) quantum-mechanical propagation of the torsional motion was followed by solving the time-dependent Schrödinger equation, whereas three-dimensional (3D) molecular rotation was tracked by classical trajectory calculations. This hybrid approach enabled us to reproduce experimental results at a reasonable computational cost and provided a deeper insight into rotational effects on vibrational wave-packet dynamics.

Revealing Excited-State Trajectories on Potential Energy Surfaces with Atomic Resolution in Real Time.

Photoexcited molecular trajectories on potential energy surfaces (PESs) prior to thermalization are intimately connected to the photochemical reaction outcome. The excited-state trajectories of a diplatinum complex featuring photo-activated metal-metal σ-bond formation and associated Pt-Pt stretching motions were detected in real time using femtosecond wide-angle X-ray solution scattering. The observed motions correspond well with coherent vibrational wavepacket motions detected by femtosecond optical transient absorption. Two key coordinates for intersystem crossing have been identified, the Pt-Pt bond length and the orientation of the ligands coordinated with the platinum centers, along which the excited-state trajectories can be projected onto the calculated PESs of the excited states. This investigation has gleaned novel insight into electronic transitions occurring on the time scales of vibrational motions measured in real time, revealing ultrafast nonadiabatic or non-equilibrium processes along excited-state trajectories involving multiple excited-state PESs.

Revealing Excited‐State Trajectories on Potential Energy Surfaces with Atomic Resolution in Real Time

AbstractPhotoexcited molecular trajectories on potential energy surfaces (PESs) prior to thermalization are intimately connected to the photochemical reaction outcome. The excited‐state trajectories of a diplatinum complex featuring photo‐activated metal–metal σ‐bond formation and associated Pt−Pt stretching motions were detected in real time using femtosecond wide‐angle X‐ray solution scattering. The observed motions correspond well with coherent vibrational wavepacket motions detected by femtosecond optical transient absorption. Two key coordinates for intersystem crossing have been identified, the Pt−Pt bond length and the orientation of the ligands coordinated with the platinum centers, along which the excited‐state trajectories can be projected onto the calculated PESs of the excited states. This investigation has gleaned novel insight into electronic transitions occurring on the time scales of vibrational motions measured in real time, revealing ultrafast nonadiabatic or non‐equilibrium processes along excited‐state trajectories involving multiple excited‐state PESs.

Vibrations That Do Not Promote Vibronic Coupling Can Dominate Observed Lineshapes in Two-Dimensional Electronic Spectroscopy.

Impulsively generated wavepackets can report on vibronic couplings underlying ultrafast electronic relaxation. Coherence maps (CMs) in multidimensional spectroscopy resolve beating amplitudes of such wavepackets as two-dimensional contour maps. A precise understanding of how these wavepackets manifest spectroscopically is vital for unambiguously deciphering their mechanistic significance and establishing CMs as a powerful tool for guiding the synthetic design of functional vibronic couplings. Here we take a step in this direction. We establish physically distinct origins of recently reported apparent similarities between diagonal node-like CM lineshapes in bacteriochlorophyll monomers and multichromophoric photosynthetic reaction centers (RCs). The former arise when vibrational wavepackets survive on both ground and excited electronic states, while nodal lines in RCs arise when vibrational wavepackets that do not participate in energy transfer are coherently transferred to the acceptor. We resolve recent spectroscopic observations and illustrate new mechanistic insights gained by connecting microscopic interference between electronic relaxation pathways and observed CMs.

Effects of Autoionizing Resonances on Wave-Packet Dynamics Studied by Time-Resolved Photoelectron Spectroscopy.

We report a combined experimental and theoretical study on the effect of autoionizing resonances in time-resolved photoelectron spectroscopy. The coherent excitation of N_{2} by ∼14.15 eV extreme-ultraviolet photons prepares a superposition of three dominant adjacent vibrational levels (v^{'}=14-16) in the valence b^{'} ^{1}Σ_{u}^{+} state, which are probed by the absorption of two or three near-infrared photons (800nm). The superposition manifests itself as coherent oscillations in the measured photoelectron spectra. A quantum-mechanical simulation confirms that two autoionizing Rydberg states converging to the excited A ^{2}Π_{u} and B ^{2}Σ_{u}^{+} N_{2}^{+} cores are accessed by the resonant absorption of near-infrared photons. We show that these resonances apply different filters to the observation of the vibrational wave packet, which results in different phases and amplitudes of the oscillating photoelectron signal depending on the nature of the autoionizing resonance. This work clarifies the importance of resonances in time-resolved photoelectron spectroscopy and particularly reveals the phase of vibrational quantum beats as a powerful observable for characterizing the properties of such resonances.

Transient Stimulated Raman Excited Fluorescence Spectroscopy

The pursuit of better sensitivity has always been one of the central themes in Raman spectroscopy. Recently, all-far-field single-molecule Raman spectroscopy has been demonstrated by a novel hybrid spectroscopy that couples Raman scattering with fluorescence emission. However, such frequency-domain spectroscopy lacks efficient hyperspectral excitation methods and encounters intrinsic strong fluorescence backgrounds from electronic transitions, hindering its applications in advanced Raman spectroscopy and microscopy. Here we report the ultrafast time-domain spectroscopy counterpart named transient stimulated Raman excited fluorescence (T-SREF): excited by two successive broadband femtosecond pulse pairs (i.e., the pump and Stokes pulses) with time-delay scanning, strong vibrational wave packet interference is revealed on the time-domain fluorescence trace, resulting in background-free spectra of the corresponding Raman modes after the Fourier transform. T-SREF achieves background-free Raman spectra of electronic-coupled vibrational modes with sensitivity up to the level of a few molecules, which paves the way for supermultiplexed fluorescence detection and molecular dynamics sensing.

Femtosecond Time-Resolved Observation of Relaxation and Wave Packet Dynamics of the S1 State in Electronically Excited o-Fluoroaniline

Quantum beat frequency is the basis for understanding interference effects and vibrational wave packet dynamics and has important applications. Using femtosecond time-resolved mass spectrometry and femtosecond time-resolved photoelectron image combined with theoretical calculations, we study the electronic excited-state relaxation of o-fluoraniline molecule and the time-dependent evolution of vibrational wave packets between different eigenstates. After the molecule absorbs a photon of 288.3 nm and is excited to the S1 state, intramolecular vibrational redistribution first occurs on the time scale τ1 = 349 fs, and then the transition to the triplet state occurs through the intersystem crossing on the time scale τ2 = 583 ps, and finally, the triplet state occurs decays slowly through the time scale τ3 = 2074 ps. We find the intramolecular vibrational redistribution is caused by the 00, 10b1 and 16a1 vibrational modes of the Sl state origin. That is, the 288.3 nm femtosecond laser excites the molecule to the S1 state, and the continuous flow of the vibrational wave packet prepares a coherent superposition state of three vibrational modes. Through extracting the oscillation of different peak intensities in the photoelectron spectrum, we observe reversible changes caused by mutual interference of the S1 00, S1 10b1 and S1 16a1 states when the wave packets flow. When the pump pulse is 280 nm, the beat frequency disappears completely. This is explained in terms of increases in the vibrational field density and characteristic period of oscillation, and statistical averaging makes the quantum effect smooth and indistinguishable. In addition, the Rydberg component of the S1 state is more clearly resolved by combining experiment and theory.

Laser-induced Coulomb explosion imaging of alkali-metal dimers on helium nanodroplets

Alkali dimers, $\mathrm{Ak}_2$, residing on the surface of He nanodroplets are doubly ionized due to multiphoton absorption from an intense, 50-fs laser pulse leading to fragmentation into a pair of alkali cations. Based on the measured kinetic energy distributions, $P(E_{\text{kin}})$, of the $\mathrm{Ak}^+$ fragment ions, we retrieve the distribution of internuclear distances, $P(R)$, via the $\mathrm{Ak}_2^{2+}$ potential curve. Results are obtained for $\mathrm{{Na}_2}$, $\mathrm{K}_2$, $\mathrm{Rb}_2$, and $\mathrm{Cs}_2$ in both the 1 $^1\Sigma_{g}^+$ ground state and in the lowest-lying triplet state 1 $^3\Sigma_{u}^+$, and for $\mathrm{Li}_2$ in the 1 $^3\Sigma_{u}^+$ state. For $\mathrm{Li}_2$, $\mathrm{K}_2$, and $\mathrm{Rb}_2$, the center of the measured $P(R)$'s is close to the center of the wave function, $\Psi(R)$, of the vibrational ground state in the 1 $^1\Sigma_{g}^+$ and 1 $^3\Sigma_{u}^+$ states, whereas for $\mathrm{{Na}_2}$ and $\mathrm{{Cs}_2}$ small shifts are observed. For all the $\mathrm{{Ak}_2}$, the width of the measured $P(R)$ is broader than $|\Psi(R)|^2$ by a factor of 2-4. We discuss that resonance effects in the multiphoton ionization and interaction of the $\mathrm{Ak}^+$ ion with the He droplet give rise to the observed deviations of $P(R)$ from $|\Psi(R)|^2$. Despite these deviations, we deem that timed Coulomb explosion will allow imaging of vibrational wave packets in alkali dimers on He droplets surfaces.

Steering thermal photoassociation of magnesium atoms by two time-delayed femtosecond laser pulses

By solving the full-dimensional time-dependent Schrödinger equation with the thermal-random-phase wavepacket method, we investigate the photoassociation (PA) process of hot (1000 K) magnesium atoms induced by two time-delayed femtosecond laser pulses. Driven by the 840 nm fs laser pulses, the Mg2 molecules can be formed on the four excited states, (1)1Πg, (1)1Πu, (2)1Πu, and (2)1Σu+, from the initial electronic ground state X1Σg+. It is found that the three-photon couplings between X1Σg+ and the three ungerade states [(1)1Πu (2)1Πu, and (2)1Σu+], play dominant roles in the population transfer process. By scanning the pulse duration τ from 50 to 200 fs, and varying the delay time δt0 from 0 to 2τ fs, we find that the final PA population is strongly dependent on the two parameters. For a given δt0, the parameter τ can induce a significant variation (2 ∼ 6.8 times) for the final PA population transfer, and for a given τ, one can also obtain a significant variation (2.7 ∼ 3.5 times) of the final PA population by varying δt0. Additionally, the dynamics of the coherently vibrational wavepackets of the four excited states are also influenced by the two parameters.

High-sensitivity fluorescence-detected multidimensional electronic spectroscopy through continuous pump-probe delay scan.

Fluorescence-detected multidimensional electronic spectroscopy (fMES) promises high sensitivity compared to conventional approaches and is an emerging spectroscopic approach toward combining the advantages of MES with the spatial resolution of a microscope. Here, we present a visible white light continuum-based fMES spectrometer and systematically explore the sensitivity enhancement expected from fluorescence detection. As a demonstration of sensitivity, we report room temperature two-dimensional coherence maps of vibrational quantum coherences in a laser dye at optical densities of ∼2-3 orders of magnitude lower than conventional approaches. This high sensitivity is enabled by a combination of biased sampling along the optical coherence time axes and a rapid scan of the pump-probe waiting time T at each sample. A combination of this approach with acousto-optic phase modulation and phase-sensitive lock-in detection enables measurements of room temperature vibrational wavepackets even at the lowest ODs. Alternative faster data collection schemes, which are enabled by the flexibility of choosing a non-uniform undersampled grid in the continuous T scanning approach, are also demonstrated.

Nuclear quantum dynamics on the ground electronic state of neutral silver dimer 107Ag109Ag probed by femtosecond NeNePo spectroscopy.

The nuclear quantum dynamics on the ground electronic state of the neutral silver dimer 107Ag109Ag are studied by femtosecond (fs) pump-probe spectroscopy using the 'negative ion - to neutral - to positive ion' (NeNePo) excitation scheme. A vibrational wave packet is prepared on the X1Σ+g state of Ag2via photodetachment of mass-selected, cryogenically cooled Ag2- using a first ultrafast pump laser pulse. The temporal evolution of the wave packet is then probed by an ultrafast probe pulse via resonant multiphoton ionization to Ag2+. Frequency analysis of the fs-NeNePo spectra obtained for a single isotopologue and pump-probe delay times up to 60 ps yields the harmonic (ωe = 192.2 cm-1), quadratic anharmonic (ωexe = 0.637 cm-1) and cubic anharmonic (ωeye = 3 × 10-4 cm-1) constants for the X1Σ+g state of neutral Ag2. The fs-NeNePo spectra obtained at different pump wavelengths provide insight into the excitation mechanism. At a pump wavelength of 510 nm instead of 1010 nm, resonant excitation of a short-lived electronically excited state of the anion followed by autodetachment results in population of higher-energy vibrational levels of the neutral ground state. In contrast, at 1140 nm dynamics with a slightly shorter beating period and different relative phase are observed. The present study demonstrates that isotopologue-specific fs-NeNePo spectroscopy provides accurate vibrational constants of mass-selected neutral clusters in their electronic ground state in the terahertz spectral region, which remains difficult to obtain directly in the frequency domain with any other type of spectroscopy of comparable sensitivity.

Nonadiabatic wave packet dynamics and predissociation resonances in sodium hydride.

Vibrational wave packet dynamics provides an opportunity to explore the energy landscape and the population transfer between nonadiabatically coupled excited electronic states. Here the coupled nonadiabatic dynamics of the C1Σ+ and D1Σ+ states of sodium hydride (NaH) in the gas phase in the adiabatic picture is studied, using a sequence of ultra-fast laser pulses in the femtosecond region. Emergence of different population dynamics and dissociation probabilities is shown by carefully choosing the pulse wavelength, duration and time-shift between the pulses, exciting the molecule from the ground X1Σ+ state via the immediate A1Σ+ state. Quantum dynamics simulations were performed in the adiabatic picture, avoiding the adiabatic to diabatic transformation. Predissociation resonances, i.e. vibrational states with finite lifetimes, arise due to nonadiabatic couplings between bound and continuum states. Here accurate resonance energies and widths are computed providing further insight into the dissociation dynamics.

Signatures of Duschinsky Rotation in Femtosecond Coherence Spectra

The motions of nuclei in a molecule can be mathematically described by using normal modes of vibration, which form a complete orthonormal basis. Each normal mode describes oscillatory motion at a frequency determined by the momentum of the nuclei. Near equilibrium, it is common to apply the quantum harmonic-oscillator model, whose eigenfunctions intimately involve combinatorics. Each electronic state has distinct force constants; therefore, each normal-mode basis is distinct. Duschinsky proposed a linearized approximation to the transformation between the normal-mode bases of two electronic states using a rotation matrix. The rotation angles are typically obtained by using quantum-chemical computations or via gas-phase spectroscopy measurements. Quantifying the rotation angles in the condensed phase remains a challenge. Here, we apply a two-dimensional harmonic model that includes a Duschinsky rotation to condensed-phase femtosecond coherence spectra (FCS), which are created in transient–absorption spectroscopy measurements through impulsive excitation of coherent vibrational wavepackets. Using the 2D model, we simulate spectra to identify the signatures of Duschinsky rotation. The results suggest that peak multiplicities and asymmetries may be used to quantify the rotation angle, which is a key advance in condensed-phase molecular spectroscopy.

Wavepacket dynamics of the excited (S1) state of 2,5-difluoroaniline by accidental resonance with the Rydberg states.

Coherent nuclear wavepacket behavior obtained by time-resolved spectroscopy is a good choice to capture the real-time evolution of molecular configuration. Using femtosecond time-resolved photoelectron imaging, we investigate the real-time evolution of the vibrational wavepacket of 2,5-difluoroaniline following the coherent excitation of an out-of-plane vibrational mode in the S1 state at 289.8nm. Probed by an accidental resonance with the Rydberg states, the periodic oscillations with the frequency of 99cm-1 are observed from the photoelectron kinetic energy (PKE) distributions, corresponding to the energy difference between the out-of-plane mode X1 0 of C-F bond and the band origin. Moreover, phase reversal of π rad between 0.66-0.75 and 1.00-1.08eV is also observed in the PKE region. Combined with the scan of the potential energy surface in the ground cationic D0 state, the observed two ionization channels corresponding to different phases are attributed to the periodic geometry changes between the planar and the non-planar structures when the coherent wavepacket evolves from the initial vertical Franck-Condon region toward the global minimum of the S1 potential energy surface.

Franck-Condon spectra of unbound and imaginary-frequency vibrations via correlation functions: A branch-cut free, numerically stable derivation.

Molecular electronic spectra can be represented in the time domain as auto-correlation functions of the initial vibrational wavepacket. We present a derivation of the harmonic vibrational auto-correlation function that is valid for both real and imaginary harmonic frequencies. The derivation rests on Lie algebra techniques that map otherwise complicated exponential operator arithmetic to simpler matrix formulas. The expressions for the zero- and finite-temperature harmonic auto-correlation functions have been carefully structured both to be free of branch-cut discontinuities and to remain numerically stable with finite-precision arithmetic. Simple extensions correct the harmonic Franck-Condon approximation for the lowest-order anharmonic and Herzberg-Teller effects. Quantitative simulations are shown for several examples, including the electronic absorption spectra of F2, HOCl, CH2NH, and NO2.

Vibrational wave packet dynamics of H2O+ and H2O by strong-field Fourier transform spectroscopy

The vibrational wave packet dynamics of H2O+ and H2O are investigated by pump–probe measurements using few-cycle intense laser pulses. By a Fourier transform (FT) of the time-dependent yields of the two-body Coulomb explosion pathway, H2O2+ → H+ + OH+, and the parent ion, H2O+, the vibrational excitation processes in the electronic ground states of H2O+ and H2O induced by the intense laser field are retrieved from the phases of the respective vibrational peaks in the FT spectrum. Accurate quantum-dynamics simulations on H2O+ confirm both the peak assignment and the origin of the time-dependent ionization yields of the vibrational wave packet.

Coherent Control of Molecular Dissociation by Selective Excitation of Nuclear Wave Packets.

We report on pump-probe control schemes to manipulate fragmentation product yields in p-nitrotoluene (PNT) cation. Strong field ionization of PNT prepares the parent cation in the ground electronic state, with coherent vibrational excitation along two normal modes: the C–C–N–O torsional mode at 80 cm−1 and the in-plane ring-stretching mode at 650 cm−1. Both vibrational wave packets are observed as oscillations in parent and fragment ion yields in the mass spectrum upon optical excitation. Excitation with 650 nm selectively fragments the PNT cation into , whereas excitation with 400 nm selectively produces and . In both cases the ion yield oscillations result from torsional wave packet excitation, but 650 and 400 nm excitation produce oscillations with opposite phases. Ab initio calculations of the ground and excited electronic potential energy surfaces of PNT cation along the C–C–N–O dihedral angle reveal that 400 nm excitation accesses an allowed transition from D0 to D6 at 0° dihedral angle, whereas 650 nm excitation accesses a strongly allowed transition from D0 to D4 at a dihedral angle of 90°. This ability to access different electronic excited states at different locations along the potential energy surface accounts for the selective fragmentation observed with different probe wavelengths. The ring-stretching mode, only observed using 800 nm excitation, is attributed to a D0 to D2 transition at a geometry with 90° dihedral angle and elongated C–N bond length. Collectively, these results demonstrate that strong field ionization induces multimode coherent excitation and that the vibrational wave packets can be excited with specific photon energies at different points on their potential energy surfaces to induce selective fragmentation.