Nuclear Wave Packet Research Articles

Correlated electron–nuclear motion during non-adiabatic transitions in LiH and its isotopomers

Exciting molecules with a short strong few cycle IR pulse triggers coherent electronic–nuclear dynamics on multiple electronic states. This creates a new type of initial state where non-adiabatic transfer takes place between already populated electronic states. We explore this new feature using accurate quantal simulations of the ultrafast laser-induced dissociative dynamics in LiH-LiD-LiT series of isotopomers. In this novel type of initial state the non-adiabatic amplitude exchange between the coupled electronic states strongly depends on isotopic composition. The effective non-adiabatic coupling strength is modulated by two counteracting factors. On one hand, the 1/mass factor makes the non-Born–Oppenheimer coupling weaker for the heavier masses. On the other hand, the transfer is modulated by the momentum coupling of the two non-stationary nuclear wave packets on the two electronic states. The magnitude of this coupling tends to be larger for the heavier isotopes and varies in time as the wave packet dynamics unfold. The correlation in motion of the nuclear wave packets in R- and k-space is then critical. The direction of population transfer changes in time according to the evolution of the coherences built during the short fs excitation. In addition, heavier isotopomers move slower through the non-adiabatic interaction allowing a longer effective duration for the transfer. As a result, an initially very moderate isotope effect in the immediate post excitation population rapidly grows when the wave packets transverse the non-adiabatic coupling region. We compare and contrast with similar time dependent effect of the mass in the non-adiabatic transfer in N2 where the optically accessible singlet electronic states are all bound and the couplings are quite different.

Spiral nuclear momentum distribution for the dissociation of H2+ in a circularly polarized laser pulse

The dissociation of ${\mathrm{H}}_{2}{}^{+}$ in a circularly polarized laser pulse is numerically studied by simulating the time-dependent Schr\odinger equation. After absorbing one or three photons, the nuclear wave packets carrying the angular momenta $\ensuremath{\hbar}$ and $3\ensuremath{\hbar}$ dissociate along the $2p{\ensuremath{\sigma}}_{u}$ state. Due to the broad initial kinetic-energy distribution of the superimposed nuclear vibrational states, the one-photon and three-photon dissociation pathways may end with the same kinetic energy. These coexisting dissociation pathways with same parities but different orbital angular momenta interfere with each other, resulting in the spiral nuclear momentum distribution in the laser polarization plane. The interference structure in the nuclear momentum distribution offers another freedom to identify the dissociation pathways of molecules in strong laser fields.

Non-Born-Oppenheimer Molecular Dynamics Observed by Coherent Nuclear Wave Packets.

The reaction dynamics of a photochemical reaction is typically described by reaction coordinates based on the Born-Oppenheimer (BO) approximation. A strong interaction between electrons and nuclei, conventionally occurring at conical intersections, however, breaks the BO approximation and has major consequences for the efficiency of a photochemical reaction. Despite its importance, related studies into the non-BO dynamics are scarce. Here, we investigate the non-BO dynamics of excited-state intramolecular proton transfer (ESIPT) occurring in 10-hydroxybenzo[h]quinoline (HBQ). Two coherent vibrational modes at 237 and 794 cm-1 representing molecular dynamics on a diabatic surface in HBQ are identified by a wave packet analysis based on a transient absorption measurement with a time resolution of 11 fs and with a density functional theory-based model calculation. It is also revealed that the strong Coulomb field effect in HBQ leads to the completion of ESIPT within about two cycles of the OH stretching mode. The work paves the way for time-domain studies of molecular dynamics beyond the BO approximation in other photochemical reactions.

Role of coherent nuclear motion in the ultrafast intersystem crossing of ruthenium complexes.

Ultrafast intersystem crossing (ISC) in transition metal complexes leads to a long-lived active state with a high yield, which leads to efficient light energy conversion. The detailed mechanism of ISC may lead to a rational molecular design of superior transition metal complexes. Coherent nuclear wave packets observed in femtosecond time-resolved spectroscopies provide important information on the excited-state dynamics. In particular, analyzing the nuclear wave packets in both the reactant and the product may unveil the molecular dynamics of an ultrafast reaction. In this study, experimental evidence proving the reaction coordinates of the ultrafast ISC of ruthenium(ii) complexes is presented using coherent vibrational spectroscopy with a quantum chemical simulation of coherent vibrational motion. We observed vibrational modes strongly coupled to the ISC, whose vibrational coherences undergo remarkable attenuation after the ISC. The coupled modes contain metal-ligand stretching or symmetry breaking components, and the faster ISC rates of lower-symmetry ruthenium(ii) complexes support the significance of the latter.

Challenges in constructing accurate methods for hydrogen transfer reactions in large biological assemblies: rare events sampling for mechanistic discovery and tensor networks for quantum nuclear effects.

We present two methods that address the computational complexities arising in hydrogen transfer reactions in enzyme active sites. To address the challenge of reactive rare events, we begin with an ab initio molecular dynamics adaptation of the Caldeira-Leggett system-bath Hamiltonian and apply this approach to the study of the hydrogen transfer rate-determining step in soybean lipoxygenase-1. Through direct application of this method to compute an ensemble of classical trajectories, we discuss the critical role of isoleucine-839 in modulating the primary hydrogen transfer event in SLO-1. Notably, the formation of the hydrogen bond between isoleucine-839 and the acceptor-OH group regulates the electronegativity of the donor and acceptor groups to affect the hydrogen transfer process. Curtailing the formation of this hydrogen bond adversely affects the probability of hydrogen transfer. The second part of this paper deals with complementing the rare event sampled reaction pathways obtained from the aforementioned development through quantum nuclear wavepacket dynamics. Essentially the idea is to construct quantum nuclear dynamics on the potential surfaces obtained along the biased trajectories created as noted above. Here, while we are able to obtain critical insights on the quantum nuclear effects from wavepacket dynamics, we primarily engage in providing an improved computational approach for efficient representation of quantum dynamics data such as potential surfaces and transmission probabilities using tensor networks. We find that utilizing tensor networks yields an accurate and efficient description of time-dependent wavepackets, reduced dimensional nuclear eigenstates and associated potential energy surfaces at much reduced cost.

Statistical distributions of the tuning and coupling collective modes at a conical intersection using the hierarchical equations of motion.

We investigate the possibility of extracting the probability distribution of the effective environmental tuning and coupling modes during the nonadiabatic relaxation through a conical intersection. Dynamics are dealt with an open quantum system master equation by partitioning a multistate electronic subsystem out of all the nuclear vibrators. This is an alternative to the more usual partition retaining the tuning and coupling modes of a conical intersection in the active subsystem coupled to a residual bath. The minimal partition of the electronic system generally leads to highly structured spectral densities for both vibrational baths and requires a strongly nonperturbative non-Markovian master equation, treated here by the hierarchical equations of motion (HEOMs). We extend-for a two-bath situation-the procedure proposed by Shi et al. [J. Chem. Phys. 140, 134106 (2014)], whereby the information contained in the auxiliary HEOM matrices is exploited in order to derive the nuclear dissipative wave packet, i.e., the statistical distribution of the displacement of the two tuning and coupling collective coordinates in each electronic state and the coherence. This allows us to visualize the distribution, all along the nonadiabatic decay. We explore a large parameter space for a symmetrical conical intersection model and a symmetrical initial Franck-Condon preparation. Some parameters could be controlled by external fields, while others are molecule dependent and could be designed by molecular engineering. We illustrate the relation between the strongly coupled electronic and bath dynamics together with a geometric measure of non-Markovianity.

Subfemtosecond Tracing of Molecular Dynamics during Strong-Field Interaction.

We introduce and experimentally demonstrate a method where the two intrinsic timescales of a molecule, the slow nuclear motion and the fast electronic motion, are simultaneously measured in a photoelectron photoion coincidence experiment. In our experiment, elliptically polarized, 750nm, 4.5fs laser pulses were focused to an intensity of 9×10^{14} W/cm^{2} onto H_{2}. Using coincidence imaging, we directly observe the nuclear wave packet evolving on the 1sσ_{g} state of H_{2}^{+} during its first round-trip with attosecond temporal and picometer spatial resolution. The demonstrated method should enable insight into the first few femtoseconds of the vibronic dynamics of ionization-induced unimolecular reactions of larger molecules.

Non-condon Effect on Ultrafast Excited-State Intramolecular Proton Transfer.

The reaction dynamics of excited-state intramolecular proton transfer (ESIPT) of 2,2'-dihydroxyazobenzene (2,2'-DHAB) was investigated by means of white-light supercontinuum femtosecond transient absorption spectroscopy. A coherent in-phase oscillation was observed in the entire wavelength range where stimulated emission of the photoproduct is dominant. This result indicates that the transition strength of the product state is dynamically modulated by a nuclear wavepacket motion (non-Condon effect). The observed vibration was assigned to the mode which modulates the distance between oxygen and hydrogen atoms. By integrating the result of time-dependent density functional theory calculation, the origin of the non-Condon effect was attributed to a dynamical change of configuration interaction between enol and keto characters along the vibrational coordinate, indicating that this vibration is strongly related to the reaction coordinate of ESIPT.

Nonadiabatic excited-state intramolecular proton transfer in 3-hydroxyflavone: S2 state involvement via multi-mode effect.

The excited-state intramolecular proton transfer process in 3-hydroxyflavone is investigated based on the computed structural parameters and energetics of stationary points of vibronically coupled S1-S2 potential energy surfaces. A conical intersection close to the Franck-Condon point on S1 is identified. The minimum energy of the conical intersection is found to be near-degenerate with the equilibrium minimum of S2. Quantum nuclear wavepacket simulations revealed a small population transfer from the "bright" S1 to "dark" S2 on a time scale shorter than the O-H stretching vibrational period. Such a nonadiabatic transition opens up the possibility of new photophysical and photochemical pathways, including the proton transfer via S2.

Angle-dependent strong-field ionization of halomethanes.

We study, experimentally and theoretically, the ionization probability of singly halogenated methane molecules, CH3Cl and CH3Br, in intense linearly polarized 800 nm laser pulses as a function of the angle between the molecular axis and the laser polarization. Experimentally, the molecules are exposed to two laser pulses with a relative time delay. The first, weaker pulse induces a nuclear rotational wave packet within the molecules, which are then ionized by the second, stronger pulse. The angle-dependent ionization yields are extracted from fits of the measured delay-dependent ionization signal to a superposition of moments of the rotational wave packet's angular distribution. Angle-dependent strong-field ionization (SFI) yields are also calculated using time-dependent density functional theory. Good agreement between measurements and theory is obtained. Interestingly, we find a marked difference between the angle-dependence of the ionization yields for these two halomethane species despite the similar structure of their highest occupied molecular orbitals. Calculations reveal that these differences are a result of multichannel (CH3Cl) vs single-channel (CH3Br) ionization and of increased hole localization on Br vs Cl. By adding calculations for CH3F, we can discern clear trends in the ionization dynamics with increasing halogen mass. These results are illustrative, as chemical functionalization and molecular alignment are likely to be important parameters for initiating and controlling charge migration dynamics via SFI.

Hovering States of Ammonia in a High-Intensity, High-Frequency Oscillating Field: Trapped into Planarity by Laser-Induced Hybridization.

A high-intensity, high-frequency laser can create an oscillating induced dipole moment in a molecule. At high laser frequencies with a long pulse width, a stable non-ionizing state with a laser-induced hybridization of the electrons is formed. For ammonia, aligned with the linear polarization direction of the laser, such stable states can be realized. Electronic hybridization in the presence of the high-frequency field is such that the lone pair propensity is dynamically equalized on either side of ammonia. This leads to a destabilization of pyramidal ammonia and hovering states with the electron density flipping to either side of the geometry. Electronic structure calculations in an oscillating frame of reference anticipate this effect with a predicted classical quiver distance of 0.1 Å. Electronic dynamics at a laser intensity of 1.14 × 1013 W/cm2 and a frequency of 8.16 eV predicts negligible ionization for the planar geometry. Approximate nuclear wave packet dynamics in the oscillating potential energy generated by the electrons predicts a trapping of ammonia in its planar transition state geometry.

Time-resolved near-edge X-ray absorption fine structure of pyrazine from electronic structure and nuclear wave packet dynamics simulations.

As a demonstration of the analysis of the electronic structure and the nuclear dynamics from time-resolved near-edge X-ray absorption fine structure (TR-NEXAFS), we present the TR-NEXAFS spectra of pyrazine following the excitation to the 1B2u(ππ*) state. The spectra are calculated combining the frozen-core/core-valence separated equation-of-motion coupled cluster singles and doubles approach for the spectral signatures and the multiconfiguration time-dependent Hartree method for the wave packet propagation. The population decay from the 1B2u(ππ*) state to the 1B3u(nπ*) and 1Au(nπ*) states, followed by oscillatory flow of population between the 1B3u(nπ*) and 1Au(nπ*) states, is interpreted by means of visualization of the potential energy curves and the reduced nuclear densities. By examining the electronic structure of the three valence-excited states and the final core-excited states, we observe that the population dynamics is explicitly reflected in the TR-NEXAFS spectra, especially when the heteroatoms are selected as the X-ray absorption sites. This work illustrates the feasibility of extracting fine details of molecular photophysical processes from TR-NEXAFS spectra by using currently available theoretical methods.

Time resolved mechanism of the isotope selectivity in the ultrafast light induced dissociation in N2.

The time evolution of a vacuum ultraviolet excited N2 molecule is followed all the way from an ultrafast excitation to dissociation by a quantum mechanical simulation. The primary aim is to discern the role of the excitation by a pulse short compared to the vibrational period, to discern the different coupling mechanisms between different electronic states, nonadiabatic, spin orbit, and to analyze the origin of any isotopic effect. We compare the picture in the time and energy domains. The initial ultrafast excitation pumps the molecule to a coherent electronic wave packet to which several singlet bound electronic states contribute. The total nonstationary wave function is given as a coherent sum of nuclear wave packets on each electronic state times the stationary electronic wave function. When the wave packets on different electronic states overlap, they are coupled in a mass-dependent manner whether one uses an adiabatic or a diabatic electronic basis. A weak spin-orbit coupling acts as a bottleneck between the bound singlet part of phase space and the triplet manifold of states in which dissociation takes place. To describe the spin-orbit perturbation that is ongoing in time, an energy-resolved eigenstate representation appears to be more intuitive. In the eigenstate basis, the singlet-to-triplet population transfer is large only between those vibronic eigenstates that are quasiresonant in energy. The states in resonance are different for different excitation energy ranges. The resonances are mass dependent, which explains the control of the isotope effect through the profile of the pulse.

Femtosecond gas-phase mega-electron-volt ultrafast electron diffraction.

The development of ultrafast gas electron diffraction with nonrelativistic electrons has enabled the determination of molecular structures with atomic spatial resolution. It has, however, been challenging to break the picosecond temporal resolution barrier and achieve the goal that has long been envisioned—making space- and-time resolved molecular movies of chemical reaction in the gas-phase. Recently, an ultrafast electron diffraction (UED) apparatus using mega-electron-volt (MeV) electrons was developed at the SLAC National Accelerator Laboratory for imaging ultrafast structural dynamics of molecules in the gas phase. The SLAC gas-phase MeV UED has achieved 65 fs root mean square temporal resolution, 0.63 Å spatial resolution, and 0.22 Å−1 reciprocal-space resolution. Such high spatial-temporal resolution has enabled the capturing of real-time molecular movies of fundamental photochemical mechanisms, such as chemical bond breaking, ring opening, and a nuclear wave packet crossing a conical intersection. In this paper, the design that enables the high spatial-temporal resolution of the SLAC gas phase MeV UED is presented. The compact design of the differential pump section of the SLAC gas phase MeV UED realized five orders-of-magnitude vacuum isolation between the electron source and gas sample chamber. The spatial resolution, temporal resolution, and long-term stability of the apparatus are systematically characterized.

Electronic and nuclear flux dynamics at a conical intersection

A combined electronic-nuclear wave packet motion is accompanied by temporal changes of probability flux densities. Using a two dimensional model, we study such densities in the vicinity of a conical intersection (CI) between the potential energy surfaces of two electronically excited states. When the dynamics is accompanied by an efficient population transfer, the electronic flux density behaves nearly time-independent although the nuclear flux does not. The second case involves a nuclear motion where the CI is surrounded. There, the nuclear wave packet undergoes a bifurcation, and the electronic density shows characteristics of a rotation. The electronic flux, however, exhibits a constant directional dynamics during the nuclear motion. The geometrical phase which appears in comparing the nuclear dynamics derived from the coupled motion and the Born-Oppenheimer calculation is also seen in the nuclear flux dynamics.

Tracking multiple components of a nuclear wavepacket in photoexcited Cu(I)-phenanthroline complex using ultrafast X-ray spectroscopy

Disentangling the strong interplay between electronic and nuclear degrees of freedom is essential to achieve a full understanding of excited state processes during ultrafast nonadiabatic chemical reactions. However, the complexity of multi-dimensional potential energy surfaces means that this remains challenging. The energy flow during vibrational and electronic relaxation processes can be explored with structural sensitivity by probing a nuclear wavepacket using femtosecond time-resolved X-ray Absorption Near Edge Structure (TR-XANES). However, it remains unknown to what level of detail vibrational motions are observable in this X-ray technique. Herein we track the wavepacket dynamics of a prototypical [Cu(2,9-dimethyl-1,10-phenanthroline)2]+ complex using TR-XANES. We demonstrate that sensitivity to individual wavepacket components can be modulated by the probe energy and that the bond length change associated with molecular breathing mode can be tracked with a sub-Angstrom resolution beyond optical-domain observables. Importantly, our results reveal how state-of-the-art TR-XANES provides deeper insights of ultrafast nonadiabatic chemical reactions.

Diffractive imaging of dissociation and ground-state dynamics in a complex molecule

We have investigated the structural dynamics in photoexcited 1,2-diiodotetrafluoroethane molecules (C2F4I2) in the gas phase experimentally using ultrafast electron diffraction and theoretically using FOMO-CASCI excited state dynamics simulations. The molecules are excited by an ultra-violet femtosecond laser pulse to a state characterized by a transition from the iodine 5p orbital to a mixed 5p|| hole and CF2 antibonding orbital, which results in the cleavage of one of the carbon-iodine bonds. We have observed, with sub-Angstrom resolution, the motion of the nuclear wavepacket of the dissociating iodine atom followed by coherent vibrations in the electronic ground state of the C2F4I radical. The radical reaches a stable classical (non-bridged) structure in less than 200 fs.

Ultrafast Internal Conversion and Solvation of Electrons in Water, Methanol, and Ethanol.

Ultrafast internal conversion from the first excited state of a solvated electron in water, methanol, and ethanol is investigated using time-resolved photoelectron spectroscopy of liquid microjets and a spectral retrieval method. Photoelectron spectra corrected for inelastic scattering clearly reveal well-separated signals from the excited and ground states, and the latter enables us to analyze the solvation dynamics in the ground state after internal conversion. Measurements with 25 fs time resolution identify a rapid increase in the vertical electron binding energy of the solvated electron owing to nuclear wave packet motions in the excited state and allow us to precisely determine the internal conversion time.

Femtosecond wave-packet revivals in ozone

Photodissociation of ozone following absorption of biologically harmful solar ultraviolet radiation is the key mechanism for the life protecting properties of the atmospheric ozone layer. Even though ozone photolysis is described successfully by post-Hartree-Fock theory, it has evaded direct experimental access so far, due to the unavailability of intense ultrashort deep ultraviolet radiation sources. The rapidity of ozone photolysis with predicted values of a few tens of femtoseconds renders both ultrashort pump and probe pulses indispensable to capture this manifestation of ultrafast chemistry. Here, we present the observation of femtosecond time-scale electronic and nuclear dynamics of ozone triggered by \ensuremath{\sim}10-fs, \ensuremath{\sim}2-\textmu{}J deep ultraviolet pulses and, in contrast to conventional attochemistry experiments, probed by extreme ultraviolet isolated pulses. An electronic wave packet is first created. We follow the splitting of the excited B-state related nuclear wave packet into a path leading to molecular fragmentation and an oscillating path, revolving around the Franck-Condon point with 22-fs wave-packet revival time. Full quantum-mechanical ab initio multiconfigurational time-dependent Hartree simulations support this interpretation.

Cover Feature: Molecular Dynamics of Excited State Intramolecular Charge Transfer in Solution by Coherent Nuclear Wave Packets (ChemPhysChem 11/2019)

The Cover Feature illustrates the trajectory of the wave packets on the excited state following photoexcitation and coherent intramolecular charge transfer reaction. Amplitude of the wave packet of the ring deformation mode is modified by the reaction rate, whereas the ring breathing mode is orthogonal to the reaction coordinate and therefore impervious to the reaction rate. More information can be found in the Article by W. Heo and T. Joo on page 1448 in Issue 11, 2019 (DOI: 10.1002/cphc.201801103).