Electron-nuclear Motion Research Articles

First-Principles Nonadiabatic Dynamics of Molecules at Metal Surfaces withVibrationally Coupled Electron Transfer.

Accurate description of nonadiabatic dynamics of molecules at metal surfaces involving electron transfer has been a long-standing challenge for theory. Here, we tackle this problem by first constructing high-dimensional neural network diabatic potentials including state crossings determined by constrained density functional theory, then applying mixed quantum-classical surface hopping simulations to evolve coupled electron-nuclear motion. Our approach accurately describes the nonadiabatic effects in CO scattering from Au(111) without empirical parameters and yields results agreeing well with experiments under various conditions for this benchmark system. We find that both adiabatic and nonadiabatic energy loss channels have important contributions to the vibrational relaxation of highly vibrationally excited CO(v_{i}=17), whereas relaxation of low vibrationally excited states of CO(v_{i}=2) is weak and dominated by nonadiabatic energy loss. The presented approach paves the way for accurate first-principles simulations of electron transfer mediated nonadiabatic dynamics at metal surfaces.

Correlated electron-nuclear dynamics of photoinduced water dissociation on rutile TiO2.

Elucidating the mechanism of photoinduced water splitting on TiO2 is important for advancing the understanding of photocatalysis and the ability to control photocatalytic surface reactions. However, incomplete experimental information and complex coupled electron-nuclear motion make the microscopic understanding challenging. Here we analyse the atomic-scale pathways of photogenerated charge carrier transport and photoinduced water dissociation at the prototypical water-rutile TiO2(110) interface using first-principles dynamics simulations. Two distinct mechanisms are observed. Field-initiated electron migration leads to adsorbed water dissociation via proton transfer to a surface bridging oxygen. In the other pathway, adsorbed water dissociation occurs via proton donation to a second-layer water molecule coupled to photoexcited-hole transfer promoted by in-plane surface lattice distortions. Two stages of non-adiabatic in-plane lattice motion-expansion and recovery-are observed, which are closely associated with population changes in Ti3d orbitals. Controlling such highly correlated electron-nuclear dynamics may provide opportunities for boosting the performance of photocatalytic materials.

Rotation in attosecond vibronic coherence spectroscopy for molecules

Excitation or ionization of a molecule by ultrafast laser pulses can create a superposition of electronic states, whose dynamics is influenced by the interplay of electronic coherence and nuclear motion, resulting in charge migration and possibly charge transfer. Probing the vibronic coherence is therefore vital to monitoring electronic dynamics and controlling chemical reactivity, as recently demonstrated in molecules via attosecond transient absorption spectroscopy (ATAS). However, theories supporting the interpretation of ATAS experiments neglect the effects of molecular rotation, often leading to inaccurate interpretation of experimental data. Here, we develop a comprehensive theory for ATAS of molecules encompassing the entire pump-probe process. Applying the theory to N2, we demonstrate that the emergence of coherent signals critically depends on the consideration of molecular rotation. This work contributes to close the gap between theory and ATAS experiments, paving the way for monitoring electronic motion and controlling chemical reactivity in diverse molecular systems.

Astronomical CH3+ rovibrational assignments

Context. The methyl cation (CH3+) has recently been discovered in the interstellar medium through the detection of 7 μm (1400 cm−1) features toward the d203-506 protoplanetary disk by the JWST. Line-by-line spectroscopic assignments of these features, however, were unsuccessful due to complex intramolecular perturbations preventing a determination of the excitation and abundance of the species in that source. Aims. Comprehensive rovibrational assignments guided by theoretical and experimental laboratory techniques provide insight into the excitation mechanisms and chemistry of CH3+ in d203-506. Methods. The rovibrational structure of CH3+ was studied theoretically by a combination of coupled-cluster electronic structure theory and (quasi-)variational nuclear motion calculations. Two experimental techniques were used to confirm the rovibrational structure of CH3+:(1) infrared leak-out spectroscopy of the methyl cation, and (2) rotationally resolved photoelectron spectroscopy of the methyl radical (CH3). In (1), CH3+ ions, produced by the electron impact dissociative ionization of methane, were injected into a 22-pole ion trap where they were probed by the pulses of infrared radiation from the FELIX free electron laser. In (2), neutral CH3, produced by CH3NO2 pyrolysis in a molecular beam, was probed by pulsed-field ionization zero-kinetic-energy photoelectron spectroscopy. Results. The quantum chemical calculations performed in this study have enabled a comprehensive spectroscopic assignment of the v2+ and v4+ bands of CH3+ detected by the JWST. The resulting spectroscopic constants and derived Einstein A coefficients fully reproduce both the infrared and photoelectron spectra and permit the rotational temperature of CH3+ (T = 660 ± 80 K) in d203-506 to be derived. A beam-averaged column density of CH3+ in this protoplanetary disk is also estimated.

Differential Shannon Entropies Characterizing Electron-Nuclear Dynamics and Correlation: Momentum-Space Versus Coordinate-Space Wave Packet Motion.

We calculate differential Shannon entropies derived from time-dependent coordinate-space and momentum-space probability densities. This is performed for a prototype system of a coupled electron-nuclear motion. Two situations are considered, where one is a Born-Oppenheimer adiabatic dynamics, and the other is a diabatic motion involving strong non-adiabatic transitions. The information about coordinate- and momentum-space dynamics derived from the total and single-particle entropies is discussed and interpreted with the help of analytical models. From the entropies, we derive mutual information, which is a measure for the electron-nuclear correlation. In the adiabatic case, it is found that such correlations are manifested differently in coordinate- and momentum space. For the diabatic dynamics, we show that it is possible to decompose the entropies into state-specific contributions.

Differential Shannon entropies and correlation measures for Born-Oppenheimer electron-nuclear dynamics: numerical results and their analytical interpretation.

We study the Born-Oppenheimer dynamics within a model for a coupled electron-nuclear motion. Differential Shannon entropies are calculated from the time-dependent probability densities of the combined system and, using single particle densities, entropies for the electronic and nuclear degrees of freedom are derived. These functions provide information on details of the wave packet motion. From the entropies, we determine the mutual information which characterizes particle correlations. This quantity is compared to other measures of electron-nuclear entanglement. Numerical results are interpreted within an analytically solvable approach, and it is documented how these functions depend on properties of the Born-Oppenheimer wave function and, in particular, how dynamical effects like wave packet focusing and dispersion influence the correlation between the particles.

Coherent polaron dynamics of electrons solvated in polar liquids.

An electron solvated in a polar liquid is an elementary quantum system with properties governed by electric interactions with a fluctuating molecular environment. In the prevailing single particle picture, the quantum ground and excited states are determined by a self-consistent potential, as defined by the particular local configuration of the solvation shell. This description neglects collective many-body excitations, which arise from the coupling of electronic degrees of freedom and nuclear motions of the environment. While recent experiments have demonstrated collective nonequilbrium electronic-nuclear motion, i.e. polaron excitations in liquid water, their relevance in the broader context of polar liquids has remained unexplored. Here, we study the nonequilibrium dielectric response of the, compared to water, less polar alcohols isopropanol, and ethylene glycol, that also display a different hydrogen bond pattern. We demonstrate that ultrafast relaxation of photogenerated electrons impulsively induces coherent charge oscillations, which persist for some 10ps. They emit electric waves in a frequency range from 0.1 to 2 THz, depending on electron concentration. Oscillation frequencies and line shapes are reproduced by a unified polaron picture for alcohols and water, which is based on a Clausius-Mossotti local field approach for the THz dielectric function. The analysis suggests a longitudinal character of many-body polaron excitations and a weak coupling to transverse excitations, supported by the underdamped character of charge oscillations. Polaron dynamics are governed by the long-range Coulomb interaction between an excess electron and several thousands of polar solvent molecules, while local electron solvation geometries play a minor role.

Quantum flux densities for electronic-nuclear motion: exact versus Born-Oppenheimer dynamics.

We study the coupled electronic-nuclear dynamics in a model system to compare numerically exact calculations of electronic and nuclear flux densities with those obtained from the Born-Oppenheimer (BO) approximation. Within the adiabatic expansion of the total wave function, we identify the terms which contribute to the flux densities. It is found that only off-diagonal elements that involve the interaction between different electronic states contribute to the electronic flux whereas in the nuclear case the major contribution belongs to the BO electronic state. New flux densities are introduced where in both, the electronic and the nuclear case, the main contribution is contained in the component corresponding to the BO state. As a consequence, they can be determined within the BO approximation, and an excellent agreement with the exact results is found. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.

Correlated three-dimensional electron-nuclear motion: Adiabatic dynamics vs passage of conical intersections.

We study the three-dimensional correlated motion of an electron and a proton. In one situation, the dynamics is restricted to the electronic ground state and is, thus, well described within the Born-Oppenheimer (BO) approximation. The probability and flux densities yield information about the coupled dynamics. Because the electronic flux density vanishes if determined from the BO wave function, another flux density is regarded, which provides insight into the directional motion of the electron. This flux density can be calculated within the BO approximation and agrees numerically well with the one derived from the full-dimensional calculation. Starting in the first excited electronic state at a similar geometry as chosen for the ground state dynamics results in a short-time dynamics that takes place in the same regions of the configuration space. Adopting the picture that evolves from the adiabatic expansion of the wave function, the nuclear wave packet motion in the two coupled adiabatic electronic states proceeds through a ring of conical intersections (CIs), which is accompanied by an effective population transfer. Nevertheless, the total nuclear probability and flux densities resemble very much those obtained for the ground state dynamics. While passing the CI, the electronic densities remain nearly constant, as expected for a diabatic dynamics. This confirms the conclusions obtained from our former two-dimensional study, namely, that also in three-dimensional space the wave packet dynamics does not exhibit features of the non-adiabatic dynamics.

Gaussian-Type Orbital Calculations for High Harmonic Generation in Vibrating Molecules: Benchmarks for H2.

The response of the hydrogen molecular ion, H2+, to few-cycle laser pulses of different intensities is simulated. To treat the coupled electron-nuclear motion, we use adiabatic potentials computed with Gaussian-type basis sets together with a heuristic ionization model for the electron and a grid representation for the nuclei. Using this mixed-basis approach, the time-dependent Schrödinger equation is solved, either within the Born-Oppenheimer approximation or with nonadiabatic couplings included. The dipole response spectra are compared to all-grid-based solutions for the three-body problem, which we take as a reference to benchmark the Gaussian-type basis set approaches. Also, calculations employing the fixed-nuclei approximation are performed, to quantify effects due to nuclear motion. For low intensities and small ionization probabilities, we get excellent agreement of the dynamics using Gaussian-type basis sets with the all-grid solutions. Our investigations suggest that high harmonic generation (HHG) and high-frequency response, in general, can be reliably modeled using Gaussian-type basis sets for the electrons for not too high harmonics. Further, nuclear motion destroys electronic coherences in the response spectra even on the time scale of about 30 fs and affects HHG intensities, which reflect the electron dynamics occurring on the attosecond time scale. For the present system, non-Born-Oppenheimer effects are small. The Gaussian-based, nonadiabatically coupled, time-dependent multisurface approach to treat quantum electron-nuclear motion beyond the non-Born-Oppenheimer approximation can be easily extended to approximate wavefunction methods, such as time-dependent configuration interaction singles (TD-CIS), for systems where no benchmarks are available.

Dynamic Symmetry in Dozy-Chaos Mechanics

All kinds of dynamic symmetries in dozy-chaos (quantum-classical) mechanics (Egorov, V.V. Challenges 2020, 11, 16; Egorov, V.V. Heliyon Physics 2019, 5, e02579), which takes into account the chaotic dynamics of the joint electron-nuclear motion in the transient state of molecular “quantum” transitions, are discussed. The reason for the emergence of chaotic dynamics is associated with a certain new property of electrons, consisting in the provocation of chaos (dozy chaos) in a transient state, which appears in them as a result of the binding of atoms by electrons into molecules and condensed matter and which provides the possibility of reorganizing a very heavy nuclear subsystem as a result of transitions of light electrons. Formally, dozy chaos is introduced into the theory of molecular “quantum” transitions to eliminate the significant singularity in the transition rates, which is present in the theory when it goes beyond the Born–Oppenheimer adiabatic approximation and the Franck–Condon principle. Dozy chaos is introduced by replacing the infinitesimal imaginary addition in the energy denominator of the full Green’s function of the electron-nuclear system with a finite value, which is called the dozy-chaos energy γ. The result for the transition-rate constant does not change when the sign of γ is changed. Other dynamic symmetries appearing in theory are associated with the emergence of dynamic organization in electronic-vibrational transitions, in particular with the emergence of an electron-nuclear-reorganization resonance (the so-called Egorov resonance) and its antisymmetric (chaotic) “twin”, with direct and reverse transitions, as well as with different values of the electron–phonon interaction in the initial and final states of the system. All these dynamic symmetries are investigated using the simplest example of quantum-classical mechanics, namely, the example of quantum-classical mechanics of elementary electron-charge transfers in condensed media.

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.

Born-Oppenheimer and non-Born-Oppenheimer contributions to time-dependent electron momenta.

Using a model system for a coupled electron-nuclear motion, we calculate time-dependent expectation values of the electronic momentum operator. Whereas, within the velocity form, this quantity vanishes if the Born-Oppenheimer (BO) approximation is applied, it differs from zero if the calculation employs the length form of the expectation value. Using the adiabatic expansion of the total wave function, it is analyzed which terms contribute to the mean electronic momentum. For an adiabatic motion, where the BO approximation holds, it is shown that in the length form, the BO wave function yields an excellent estimate of the momentum. On the other hand, in the velocity form, it is necessary to include non-BO terms to calculate its value. This illustrates the different convergence behavior of the matrix elements in the two formulations. In the diabatic limit where the electron density does only marginally change upon the nuclear motion, both approaches converge to a vanishing mean electronic momentum.

H2 photoionization induced by XUV pulses and X-ray free electron lasers

SynopsisWe present a theoretical study on H2 photionization taking into account coupled electron-nuclear motion and non-dipole effects. In the first part we study the effects of harmonic filtering in a pump-probe scheme using attosecond train pulses (ATP) in dipole approximation. In the second part we investigate nondipole effects in XUV and soft X-ray regimes.

A classical ride through a conical intersection

Regarding the correlated electron-nuclear motion in a model system, we investigate the dynamics in the vicinity of a conical intersection (CoIn) between two excited state potential surfaces. It is documented that an ensemble of classical trajectories which move in the complete electronic-nuclear phase space tracks the quantum wave-packet motion through the CoIn which is accompanied by a non-adiabatic population transfer. On the contrary, for an adiabatic circular motion around the position of the CoIn, the quantum mechanical and classical densities deviate substantially. In the latter case, the Born-Oppenheimer classical nuclear motion on a single potential surface is able to track the quantum dynamics.

Ultrafast imaging of laser-controlled non-adiabatic dynamics in NO2 from time-resolved photoelectron emission.

Time-resolving and controlling coupled electronic and nuclear dynamics at conical intersections on the sub-femtosecond to few-femtosecond time scale is among the challenging goals of attosecond physics. Here we present numerical simulations of time-resolved photoelectron spectroscopy of such dynamics in NO2, where the coupled electron-nuclear motion at the 2A1/2B2 conical intersection is steered on the sub-laser-cycle time scale by a nearly single-cycle, waveform controlled mid-infrared laser pulse. For a rigorous description of the photoionization dynamics, we employ ab initio energy- and geometry-resolved photoionization matrix elements obtained with the multichannel R-matrix method, using a multiconfigurational description of the molecule and a newly developed algorithm to generate photoionization dipoles that are phase consistent on the level of both the neutral and the ionic states. We find that for sufficient molecular alignment, the time- and energy-resolved anisotropy parameters of the photoelectron angular distributions provide a particularly clear picture of both the ultrafast natural molecular dynamics at the conical intersection and its modifications by the control pulse. In particular, changes in the electronic and nuclear configurations induced by the control pulse lead to the appearance of non-vanishing odd anisotropy parameters in the photoelectron spectra. These are absent in the spectra obtained without the control pulse and therefore provide sensitive, background-free diagnostic of the control.

Time-dependent electron momenta from Born-Oppenheimer calculations

The time-dependent expectation value of the electron momentum is zero if determined within the Born-Oppenheimer (BO) approximation. We show that one arrives at non-zero values, if the mean momentum is calculated from the time-derivative of the electronic coordinate. This is illustrated for the case of a coupled electron-nuclear motion in a one-dimensional model system. Regarding a situation where the BO approximation is valid, we find that the BO results are in perfect agreement with those derived from the numerically exact calculations. This holds for cases where the involved wave packets are well localized and also if a large spreading of the probability density occurs.

Intertwined electron-nuclear motion in frustrated double ionization in driven heteronuclear molecules

We study frustrated double ionization (FDI) in a strongly-driven heteronuclear molecule HeH+ and compare with H2. We compute the probability distribution of the sum of the final kinetic energies of the nuclei for strongly-driven HeH+. We find that this distribution has more than one peak for strongly-driven HeH+, a feature we do not find to be present for strongly-driven H2. Moreover, we compute the probability distribution of the principal quantum number n of FDI. We find that this distribution has several peaks for strongly-driven HeH+, while the respective distribution has one main peak and a ‘shoulder’ at lower principal quantum numbers n for strongly-driven H2. Surprisingly, we find this feature to be a clear signature of the intertwined electron-nuclear motion.

Time-dependent density-functional-theory investigation of the collisions of protons and α particles with uracil and adenine

Time-dependent density-functional theory was employed to study the effects of proton and $\ensuremath{\alpha}$-particle radiation on uracil and adenine. This method has the advantage of treating nuclear motion and electronic motion simultaneously, allowing for the study of electronic excitation, charge transfer, ionization, and nuclear motion. Particle energies were surveyed in the range of 15--500 keV for protons and 100--2000 keV for $\ensuremath{\alpha}$ particles in conjunction with impact points both on and off carbon bonds in order to investigate the electron and nuclear dynamics of irradiated molecules and the form and quantity of transferred energy. The stopping power, energy transferred, and ionization were found, and the relationship between incident particle energy and electron density of the target molecule was characterized for proton and $\ensuremath{\alpha}$-particle radiation incident on adenine and uracil.

Electron-nuclear correlation in above-threshold double ionization of molecules

We report on the experimental observation of photon energy sharing among two electrons and two ions ejected from a doubly ionized molecule exposed to an intense ultraviolet femtosecond laser pulse. Although two electrons are successively released one after the other, bridged by the nuclear motion via their interactions, photon energy sharing among four particles is observed as multiple energy conservation lines in their joint energy spectrum. For sequential double ionization of ${\mathrm{H}}_{2}$, the electron-nuclear joint energy spectrum allows us to identify three pathways towards the charge-resonance enhanced ionization of the stretching ${\mathrm{H}}_{2}{}^{+}$ in strong laser fields. By counting the photon number absorbed by the molecule, we trace the accessibility, enhancement, and suppression of various pathways. The correlated electron-nuclear motion provides profound insights of the complicated strong-field dynamics of molecules.