Nuclear Wave Packet Dynamics Research Articles

Vibronic Correlations in Molecular Strong-Field Dynamics.

We investigate the ultrafast vibronic dynamics triggered by intense femtosecond infrared pulses in small molecules. Our study is based on numerical simulations performed with 2D model molecules and analyzed in the perspective of the renowned Lochfrass and bond-softening models. We give a new interpretation of the observed nuclear wave packet dynamics with a focus on the phase of the bond oscillations. Our simulations also reveal intricate features in the field-induced nuclear motion that are not accounted for by existing models. Our analyses assign these features to strong dynamical correlations between the active electron and the nuclei, which significantly depend on the carrier envelope phase of the pulse, even for relatively "long" pulses, which should make them experimentally observable.

Quantum tomography of molecules using ultrafast electron diffraction.

We propose a quantum tomography (QT) approach to retrieve the temporally evolving reduced density matrix in electronic state basis, where the populations and coherence between the ground state and excited state are reconstructed from the ultrafast electron diffraction signal. In order to showcase the capability of the proposed QT approach, we simulate the nuclear wavepacket dynamics and ultrafast electron diffraction of photoexcited pyrrole molecules using the abinitio quantum chemical CASSCF method. From the simulated time-resolved diffraction data, we retrieve the evolving density matrix in a crude diabatic representation basis and reveal the symmetry of the excited pyrrole wavepacket. Our QT approach opens the route to make a quantum version of "molecular movie" that covers the electronic degree of freedom and equips ultrafast electron diffraction with the power to reveal the coherence between electronic states, relaxation, and dynamics of population transfer.

Femtosecond Collisional Dissipation of Vibrating D_{2}^{+} in Helium Nanodroplets.

We explored the collision-induced vibrational decoherence of singly ionized D_{2} molecules inside a helium nanodroplet. By using the pump-probe reaction microscopy with few-cycle laser pulses, we captured in real time the collision-induced ultrafast dissipation of vibrational nuclear wave packet dynamics of D_{2}^{+} ion embedded in the droplet. Because of the strong coupling of excited molecular cations with the surrounding solvent, the vibrational coherence of D_{2}^{+} in the droplet interior only lasts for a few vibrational periods and completely collapses within 140fs. The observed ultrafast coherence loss is distinct from that of isolated D_{2}^{+} in the gas phase, where the vibrational coherence persists for a long time with periodic quantum revivals. Our findings underscore the crucial role of ultrafast collisional dissipation in shaping the molecular decoherence and solvation dynamics during solution chemical reactions, particularly when the solute molecules are predominantly in ionic states.

Rebuilding the vibrational wavepacket in TRAS using attosecond X-ray pulses

Time-resolved X-ray photoelectron spectroscopy (TXPS) is a well-established technique to probe coherent nuclear wavepacket dynamics using both table-top and free-electron-based ultrafast X-ray lasers. Energy resolution, however, becomes compromised for a very short pulse duration in the sub-femtosecond range. By resonantly tuning the X-ray pulse to core-excited states undergoing Auger decay, this drawback of TXPS can be mitigated. While resonant Auger-electron spectroscopy (RAS) can recover the vibrational structures not hidden by broadband excitation, the full reconstruction of the wavepacket is a standing challenge. Here, we theoretically demonstrate how the complete information of a nuclear wavepacket, i.e., the populations and relative phases of the vibrational states constituting the wavepacket, can be retrieved from time-resolved RAS (TRAS) measurements. Thus, TRAS offers key insights into coupled nuclear and electronic dynamics in complex systems on ultrashort timescales, providing an alternative to leverage femtosecond and attosecond X-ray probe pulses.

Vibrational wave-packet dynamics of the silver pentamer probed by femtosecond NeNePo spectroscopy.

Vibrational wave-packet dynamics on the ground electronic state of the neutral silver pentamer (Ag5) 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 2A1 state of Ag5via photodetachment of mass-selected, cryogenically cooled Ag5- anions using a fs pump pulse. The temporal evolution of the vibrational wave packet is then probed by an ultrafast probe pulse via resonant multiphoton ionization to Ag5+. Frequency analysis of the fs NeNePo transients for pump-probe delay times from 0.2 to 8 ps reveals three primary beating frequencies at 157 cm-1, 101 cm-1 and 56 cm-1 as well as four weaker features. A comparison of these experimentally obtained beating frequencies to harmonic normal mode frequencies calculated from electronic structure calculations confirms that Ag5 in the gas phase adopts a planar trapezoidal geometry, similar to that previously observed in solid argon. The dependence of the ionization yield on the laser polarization indicates a s-d wave electron photodetachment from a 'p-type' occupied molecular orbital of Ag5. Franck-Condon analysis shows that both processes, photodetachment and subsequent photoionization determine the beating frequencies probed in the time-dependent cation yield. The present study extends the applicability of fs NeNePo spectroscopy to characterize the vibrational spectra in the far-IR frequency range in the absence of perturbations from a medium or a messenger atom to mass-selected neutral metal clusters with more than three atoms in the ground electronic states.

Quantum dynamics of the internal motion of biphenyl-based molecular junctions.

Single molecule junctions based on selected 4,4'-biphenyldithiol and 4,4'-dicyanobiphenyl derivatives bonded to gold electrodes are analyzed from a dynamical point of view. A fully quantum mechanical description of the internal rotation of the biphenyl moiety is carried out in terms of the nuclear wavepacket dynamics obtained by the solution of the time-dependent Schrödinger equation expressed in terms of the torsion angle between the phenyl rings. The required potential energy surfaces are computed using abinitio electronic structure methods. The nature and positions of the substituents on the phenyl rings determine the features of the potential energy surfaces. The effect of the initial conditions on the time propagation of the nuclear wavepackets and, as a consequence, on the evolution of the conformational distribution is also analyzed. In addition, the conductances at zero bias for the nanojunctions were computed for different conformations of the biphenyl fragments. Weighted by the wavepacket amplitudes, non-stationary conductance expectation values, and time-averaged torsion angles and conductances for the entire simulation are obtained. The consequences of using the time-averaged values to perform a linear regression between the conductance and the square of the cosine of the dihedral angle between the phenyl rings are analyzed and compared to the usual static approach based only on the information for equilibrium geometries. The study of the time dependent conformational variations of the biphenyl moieties in the nanojunctions allows for a better understanding of the quantum chemical phenomena that affect their transport properties.

Information Theoretical Approach to Coupled Electron–Nuclear Wave Packet Dynamics: Time-Dependent Differential Shannon Entropies

We study differential Shannon entropies determined from position-space quantum probability densities in a coupled electron-nuclear system. In calculating electronic and nuclear entropies, one gains information about the localization of the respective particles and also about the correlation between them. For Born-Oppenheimer dynamics, the correlation decreases at times when the wave packet reaches the classical turning points of its motion. If a strong non-adiabtic coupling is present, leading to a large population transfer between different electronic states, the electronic entropy is approximately constant. Then the time dependence of the entropy reflects the information on the nucleus alone, and the correlation is absent. A decomposition of the entropy into contributions from the participating electronic states reveals insight into the state-specific population and nuclear wave packet localization.

Coincidence spectroscopy of molecular normal Auger decay by ultrashort x-ray pulses

When a core-shell electron is ionized by coherent ultrashort x-ray pulses with varied duration, different nuclear wave packets of a cationic molecule are formed, which can be effectively studied by detecting the photoelectron-Auger electron-ion fragment as it is proposed in the present paper. We develop the theory for the photoelectron, i.e., Auger electron, ion fragment three-body coincidence spectroscopy, where dissociative Auger final states are considered. Simulations to display the HF molecule show that the coincidence spectra encode the detailed information of coherent nuclear wave-packet dynamics. Our work paves the way for using currently available coherent ultrashort x-ray pulses to investigate and manipulate molecular nuclear wave packets. Moreover, we discuss possibilities for high-resolution coincidence experimental techniques.

(Invited, Digital Presentation) In silico Photochemical Experiments with Non-Born-Oppenheimer Molecular Dynamics

What happens to a molecule once it has absorbed UV or visible light? How does the molecule release or convert the extra energy it just received? Answering these questions clearly goes beyond a pure theoretical curiosity, as photochemical and photophysical processes are central to numerous domains like energy conversion and storage, radiation damages in DNA, or atmospheric chemistry. Different theoretical tools have been developed to address these questions by simulating the excited-state dynamics of molecules [1]. Two examples of such methods include ab initio multiple spawning (AIMS) and trajectory surface hopping (TSH). AIMS describes the dynamics of nuclear wavepackets using adaptive linear combinations of traveling frozen Gaussians [2]. TSH portrays the nuclear dynamics with a swarm of independent classical trajectories that can hop between potential energy surfaces for this task [3].In this talk, I intend to briefly survey some of our recent work aiming at understanding the approximations underlying AIMS [4] and developing new approximate techniques based on the multiple spawning framework [5]. I will also discuss the application of nonadiabatic methods to unravel photochemical and photophysical processes of interest for photovoltaics.

Efficient Semiclassical Evaluation of Electronic Coherences in Polyatomic Molecules

Exposing a molecule to intense light pulses may bring this molecule to a nonstationary quantum state, thus launching correlated dynamics of electronic and nuclear subsystems. Although much had been achieved in the understanding of fundamental physics behind the electron-nuclear interactions and dynamics, accurate numerical simulations of light-induced processes taking place in polyatomic molecules remain a formidable challenge. Here, we review a recently developed theoretical approach for evaluating electronic coherences in molecules, in which the ultrafast electronic dynamics is coupled to nuclear motion. The presented technique, which combines accurate ab initio on-the-fly simulations of electronic structure with efficient semiclassical procedure to compute the dynamics of nuclear wave packets, is not only computationally efficient, but also can help shed light on the underlying physical mechanisms of decoherence and revival of the electronic coherences driven by nuclear rearrangement.

Time-Resolved Optical Pump-Resonant X-ray Probe Spectroscopy of 4-Thiouracil: A Simulation Study.

We theoretically monitor the photoinduced ππ* → nπ* internal conversion process in 4-thiouracil (4TU), triggered by an optical pump. The element-sensitive spectroscopic signatures are recorded by a resonant X-ray probe tuned to the sulfur, oxygen, or nitrogen K-edge. We employ high-level electronic structure methods optimized for core-excited electronic structure calculation combined with quantum nuclear wavepacket dynamics computed on two relevant nuclear modes, fully accounting for their quantum nature of nuclear motions. We critically discuss the capabilities and limitations of the resonant technique. For sulfur and nitrogen, we document a pre-edge spectral window free from ground-state background and rich with ππ* and nπ* absorption features. The lowest sulfur K-edge shows strong absorption for both ππ* and nπ*. In the lowest nitrogen K-edge window, we resolve a state-specific fingerprint of the ππ* and an approximate timing of the conical intersection via its depletion. A spectral signature of the nπ* transition, not accessible by UV-vis spectroscopy, is identified. The oxygen K-edge is not sensitive to molecular deformations and gives steady transient absorption features without spectral dynamics. The ππ*/nπ* coherence information is masked by more intense contributions from populations. Altogether, element-specific time-resolved resonant X-ray spectroscopy provides a detailed picture of the electronic excited-state dynamics and therefore a sensitive window into the photophysics of thiobases.

Non-adiabatic quantum wavepacket dynamics simulation based on electronic structure calculations using the variational quantum eigensolver

A non-adiabatic nuclear wavepacket dynamics simulation of the H$_2$O$^+$ de-excitation process is performed based on electronic structure calculations using the variational quantum eigensolver. The adiabatic potential energy surfaces and non-adiabatic coupling vectors are computed with algorithms for noisy intermediate-scale quantum devices, and time propagation is simulated with conventional methods for classical computers. The results of non-adiabatic transition dynamics from the $\tilde{B}$ state to $\tilde{A}$ state reproduce the trend reported in previous studies, which suggests that this quantum-classical hybrid scheme may be a useful application for noisy intermediate-scale quantum devices.

Probing Light-Induced Conical Intersections by Monitoring Multidimensional Polaritonic Surfaces.

The interaction of a molecule with the quantized electromagnetic field of a nanocavity gives rise to light-induced conical intersections between polaritonic potential energy surfaces. We demonstrate for a realistic model of a polyatomic molecule that the time-resolved ultrafast radiative emission of the cavity enables following both nuclear wavepacket dynamics on, and nonadiabatic population transfer between, polaritonic surfaces without applying a probe pulse. The latter provides an unambiguous (and in principle experimentally accessible) dynamical fingerprint of light-induced conical intersections.

Conical Intersection Passages of Molecules Probed by X-ray Diffraction and Stimulated Raman Spectroscopy

Conical intersections (CoIns) play an important role in ultrafast relaxation channels. Their monitoring remains a formidable experimental challenge. We theoretically compare the probing of the S2 → S1 CoIn passage in 4-thiouracil by monitoring its vibronic coherences, using off-resonant X-ray-stimulated Raman spectroscopy (TRUECARS) and time-resolved X-ray diffraction (TRXD). The quantum nuclear wavepacket (WP) dynamics provides an accurate picture of the photoinduced dynamics. Upon photoexcitation, the WP oscillates among the Franck-Condon point, the S2 minimum, and the CoIn with a 70 fs period. A vibronic coherence first emerges at 20 fs and can be observed until the S2 state is fully depopulated. The distribution of the vibronic frequencies involved in the coherence is recorded by the TRUECARS spectrogram. The TRXD signal provides spatial images of electron densities associated with the CoIn. In combination, the two signals provide a complementary picture of the nonadiabatic passage, which helps in the study of the underlying photophysics in thiobases.

Wave Packet Control and Simulation Protocol for Entangled Two-Photon Absorption of Molecules.

Quantum light spectroscopy, providing novel molecular information nonaccessible by classical light, necessitates new computational tools when applied to complex molecular systems. We introduce two computational protocols for the molecular nuclear wave packet dynamics interacting with an entangled photon pair to produce an entangled two-photon absorption signal. The first involves summing over transition pathways in a temporal grid defined by two light-matter interaction times accompanied by the field correlation functions of quantum light. The signal is obtained by averaging over the two time distribution characteristics of the entangled photon state. The other protocol involves a Schmidt decomposition of the entangled light and requires summing over the Schmidt modes. We demonstrate how photon entanglement can be used to control and manipulate the two-photon excited nuclear wave packets in a displaced harmonic oscillator model.

Photoisomerization transition state manipulation by entangled two-photon absorption

We demonstrate how two-photon excitation with quantum light can influence elementary photochemical events. The azobenzene trans → cis isomerization following entangled two-photon excitation is simulated using quantum nuclear wave packet dynamics. Photon entanglement modulates the nuclear wave packets by coherently controlling the transition pathways. The photochemical transition state during passage of the reactive conical intersection in azobenzene photoisomerization is strongly affected with a noticeable alteration of the product yield. Quantum entanglement thus provides a novel control knob for photochemical reactions. The distribution of the vibronic coherences during the conical intersection passage strongly depends on the shape of the initial wave packet created upon quantum light excitation. X-ray signals that can experimentally monitor this coherence are simulated.

Dynamics near a conical intersection-A diabolical compromise for the approximations of ab initio multiple spawning.

Full multiple spawning (FMS) offers an exciting framework for the development of strategies to simulate the excited-state dynamics of molecular systems. FMS proposes to depict the dynamics of nuclear wavepackets by using a growing set of traveling multidimensional Gaussian functions called trajectory basis functions (TBFs). Perhaps the most recognized method emanating from FMS is the so-called ab initio multiple spawning (AIMS). In AIMS, the couplings between TBFs-in principle exact in FMS-are approximated to allow for the on-the-fly evaluation of required electronic-structure quantities. In addition, AIMS proposes to neglect the so-called second-order nonadiabatic couplings and the diagonal Born-Oppenheimer corrections. While AIMS has been applied successfully to simulate the nonadiabatic dynamics of numerous complex molecules, the direct influence of these missing or approximated terms on the nonadiabatic dynamics when approaching and crossing a conical intersection remains unknown to date. It is also unclear how AIMS could incorporate geometric-phase effects in the vicinity of a conical intersection. In this work, we assess the performance of AIMS in describing the nonadiabatic dynamics through a conical intersection for three two-dimensional, two-state systems that mimic the excited-state dynamics of bis(methylene)adamantyl, butatriene cation, and pyrazine. The population traces and nuclear density dynamics are compared with numerically exact quantum dynamics and trajectory surface hopping results. We find that AIMS offers a qualitatively correct description of the dynamics through a conical intersection for the three model systems. However, any attempt at improving the AIMS results by accounting for the originally neglected second-order nonadiabatic contributions appears to be stymied by the hermiticity requirement of the AIMS Hamiltonian and the independent first-generation approximation.

Time-dependent variational dynamics for nonadiabatically coupled nuclear and electronic quantum wavepackets in molecules

We propose a methodology to unify electronic and nuclear quantum wavepacket dynamics in molecular processes including nonadiabatic chemical reactions. The canonical and traditional approach in the full quantum treatment both for electrons and nuclei rests on the Born–Oppenheimer fixed nuclei strategy, the total wavefunction of which is described in terms of the Born–Huang expansion. This approach is already realized numerically but only for small molecules with several number of coupled electronic states for extremely hard technical reasons. Besides, the stationary-state view of the relevant electronic states based on the Born–Oppenheimer approximation is not always realistic in tracking real-time electron dynamics in attosecond scale. We therefore incorporate nuclear wavepacket dynamics into the scheme of nonadiabatic electron wavepacket theory, which we have been studying for a long time. In this scheme thus far, electron wavepackets are quantum mechanically propagated in time along nuclear paths that can naturally bifurcate due to nonadiabatic interactions. The nuclear paths are in turn generated simultaneously by the so-called matrix force given by the electronic states involved, the off-diagonal elements of which represent the force arising from nonadiabatic interactions. Here we advance so that the nuclear wavepackets are directly taken into account in place of path (trajectory) approximation. The nuclear wavefunctions are represented in terms of the Cartesian Gaussians multiplied by plane waves, which allows for feasible calculations of atomic and molecular integrals together with the electronic counterparts in a unified manner. The Schrödinger dynamics of the simultaneous electronic and nuclear wavepackets are to be integrated by means of the dual least action principle of quantum mechanics [K. Takatsuka, J. Phys. Commun. 4, 035007 (2020)], which is a time-dependent variational principle. Great contributions of Vincent McKoy in the electron dynamics in the fixed nuclei approximation and development in time-resolved photoelectron spectroscopy are briefly outlined as a guide to the present work.

A quantum Langevin equation approach for two-dimensional electronic spectra of coupled vibrational and electronic dynamics.

We present an efficient method to simulate two-dimensional (2D) electronic spectra of condensed-phase systems with an emphasis on treating quantum nuclear wave packet dynamics explicitly. To this end, we combine a quantum Langevin equation (QLE) approach for dissipation and a perturbative scheme to calculate three-pulse photon-echo polarizations based on wave packet dynamics under the influence of external fields. The proposed dynamical approach provides a consistent description of nuclear quantum dynamics, pulse-overlap effects, and vibrational relaxation, enabling simulations of 2D electronic spectra with explicit and non-perturbative treatment of coupled electronic-nuclear dynamics. We apply the method to simulate 2D electronic spectra of a displaced-oscillator model in the condensed phase and discuss the spectral and temporal evolutions of 2D signals. Our results show that the proposed QLE approach is capable of describing vibrational relaxation, decoherence, and vibrational coherence transfer, as well as their manifestations in spectroscopic signals. Furthermore, vibrational quantum beats specific for excited-state vs ground-state nuclear wave packet dynamics can also be identified. We anticipate that this method will provide a useful tool to conduct theoretical studies of 2D spectroscopy for strong vibronically coupled systems and to elucidate intricate vibronic couplings in complex molecular systems.

Electron Dynamics in Molecular Elementary Processes and Chemical Reactions

Abstract This account places a particular emphasis on recent progress in the theory and its applications of nonadiabatic electron dynamics in chemical science. After a brief description of the fundamental relevance of the breakdown of the Born-Oppenheimer approximation, we show examples of our extensive and systematic application of electron dynamics to highlight the significance and necessity of beyond-Born-Oppenheimer chemistry. The chemical subjects presented herewith cover (1) characteristic phenomena arising from nonadiabatic dynamics, (2) flow of electrons during chemical reactions and ionization dynamics, (3) symmetry breaking and its possible control in chemical reactions emerging from multi-dimensional nonadiabatic interactions, a special example which can cause possible breakdown of molecular mirror symmetry, (4) physical mechanism of charge separation in organic compounds and biomolecules, (5) essential roles of charge separation and elementary chemical reaction mechanisms in catalytic cycles of Mn oxo complexes up to Mn4CaO5 in water splitting dynamics (2H2O → 4H+ + 4e− + O2), (6) chemical bonds and huge electronic state fluctuation in densely quasi-degenerate electronic manifolds, which make chemistry without the notion of potential energy surfaces, and so on. All these materials and issues have been chosen because they are not directly resolved by the method of energetics based on time-independent quantum chemistry. We thus have been exploring, developing, and cultivating a new chemical realm beyond the Born-Oppenheimer paradigm. This account is closed with a scope about the theory of simultaneous electronic and nuclear quantum wavepacket dynamics.