The Ehrenfest method with fully quantum nuclear motion (Qu-Eh): Application to charge migration in radical cations

Controlling Electronic Coherences and the Curvature Induced by the Derivative Coupling at a Conical Intersection: A Quantum Ehrenfest (QuEh) Protocol for Reaction Path Following Application to "Channel 3" Benzene Photochemistry

We report a protocol for the implementation of "reaction path following" from a transition state through a conical intersection, including both the path curvature induced by the derivative coupling and the corresponding induced electronic coherences. This protocol focuses on the "central" Gaussian wavepacket (initially unexcited) in the quantum Ehrenfest (QuEh) method. Like the reaction path following, the normal mode corresponding to the imaginary frequency at the transition state is given an initial momentum. The protocol is applied to the "channel 3" radiationless decay of benzene. We also demonstrate that one can enhance the effect of the derivative coupling and the electronic coherence with an IR pulse.

Time dependent vibrational electronic coupled cluster (VECC) theory for non-adiabatic nuclear dynamics

A time-dependent vibrational electronic coupled-cluster (VECC) approach is proposed to simulate photo-electron/UV-VIS absorption spectra as well as time-dependent properties for non-adiabatic vibronic models, going beyond the Born-Oppenheimer approximation. A detailed derivation of the equations of motion and a motivation for the ansatz are presented. The VECC method employs second-quantized bosonic construction operators and a mixed linear and exponential ansatz to form a compact representation of the time-dependent wave-function. Importantly, the method does not require a basis set, has only a few user-defined inputs, and has a classical (polynomial) scaling with respect to the number of degrees of freedom (of the vibronic model), resulting in a favorable computational cost. In benchmark applications to small models and molecules, the VECC method provides accurate results compared to multi-configurational time-dependent Hartree calculations when predicting short-time dynamical properties (i.e., photo-electron/UV-VIS absorption spectra) for non-adiabatic vibronic models. To illustrate the capabilities, the VECC method is also successfully applied to a large vibronic model for hexahelicene with 14 electronic states and 63 normal modes, developed in the group by Aranda and Santoro [J. Chem. Theory Comput. 17, 1691, (2021)].

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.

Coherent Mixing of Singlet and Triplet States in Acrolein and Ketene: A Computational Strategy for Simulating the Electron-Nuclear Dynamics of Intersystem Crossing

We present a theoretical study of intersystem crossing (ISC) in acrolein and ketene with the Ehrenfest method that can describe a superposition of singlet and triplet states. Our simulations illustrate a new mechanistic effect of ISC, namely, that a superposition of singlets and triplets yields nonadiabatic dynamics characteristic of that superposition rather than the constituent state potential energy surfaces. This effect is particularly significant in ketene, where mixing of singlet and triplet states along the approach to a singlet/singlet conical intersection occurs, with the spin-orbit coupling (SOC) remaining small throughout. In both cases, the effects require many recrossings of the singlet/triplet state crossing seam, consistent with the textbook treatment of ISC.

How electronic superpositions drive nuclear motion following the creation of a localized hole in the glycine radical cation

In this work, we have studied the nuclear and electron dynamics in the glycine cation starting from localized hole states using the quantum Ehrenfest method. The nuclear dynamics is controlled both by the initial gradient and by the instantaneous gradient that results from the oscillatory electron dynamics (charge migration). We have used the Fourier transform (FT) of the spin densities to identify the “normal modes” of the electron dynamics. We observe an isomorphic relationship between the electron dynamics normal modes and the nuclear dynamics, seen in the vibrational normal modes. The FT spectra obtained this way show bands that are characteristic of the energy differences between the adiabatic hole states. These bands contain individual peaks that are in one-to-one correspondence with atom pair (+·) ↔ (·+) resonances, which, in turn, stimulate nuclear motion involving the atom pair. With such understanding, we anticipate “designer” coherent superpositions that can drive nuclear motion in a particular direction.

Ionization of HCCI Neutral and Cations by Strong Laser Fields Simulated With Time Dependent Configuration Interaction

Strong field ionization of neutral iodoacetylene (HCCI) can produce a coherent superposition of the X and A cations. This superposition results in charge migration between the CC π orbital and the iodine π-type lone pair which can be monitored by strong field ionization with short, intense probe pulses. Strong field ionization of the X and A states of HCCI cation was simulated with time-dependent configuration interaction using singly ionized configurations and singly excited, singly ionized configurations (TD-CISD-IP) and an absorbing boundary. Studies with static fields were used to obtain the 3-dimensional angular dependence of instantaneous ionization rates by strong fields and the orbitals involved in producing the cations and dications. The frequency of charge oscillation is determined by the energy separation of the X and A states; this separation can change depending on the direction and strength of the field. Furthermore, fields along the molecular axis can cause extensive mixing between the field-free X and A configurations. For coherent superpositions of the X and A states, the charge oscillations are characterized by two frequencies-the driving frequency of the laser field of the probe pulse and the intrinsic frequency due to the energy separation between the X and A states. For linear and circularly polarized pulses, the ionization rates show marked differences that depend on the polarization direction of the pulse, the carrier envelope phase and initial phase of the superposition. Varying the initial phase of the superposition at the beginning of the probe pulse is analogous to changing the delay between the pump and probe pulses. The charge oscillation in the coherent superposition of the X and A states results in maxima and minima in the ionization yield as a function of the superposition phase.

Nonadiabatic Dynamics with Coupled Trajectories

In this paper, we discuss coupled-trajectory schemes for molecular-dynamics simulations of excited-state processes. New coupled-trajectory strategies to capture decoherence effects, revival of coherence and nonadiabatic interferences in long-time dynamics are proposed, and compared to independent-trajectory schemes. The working framework is provided by the exact factorization of the electron-nuclear wave function, and it exploits ideas emanating from various surface-hopping schemes. The new coupled-trajectory algorithms are tested on a one-dimensional two-state system using different model parameters which allow one to induce different dynamics. The benchmark is provided by the numerically exact solution of the time-dependent Schrödinger equation.

Attochemistry: Is Controlling Electrons the Future of Photochemistry?

Controlling matter with light has always been a great challenge, leading to the ever-expanding field of photochemistry. In addition, since the first generation of light pulses of attosecond (1 as = 10^-18 s) duration, a great deal of effort has been devoted to observing and controlling electrons on their intrinsic time scale. Because of their short duration, attosecond pulses have a large spectral bandwidth populating several electronically excited states in a coherent manner, i.e., an electronic wavepacket. Because of interference, such a wavepacket has a new electronic distribution implying a potentially different and totally new reactivity as compared to traditional photochemistry, leading to the novel concept of "attochemistry". This nascent field requires the support of theory right from the start. In this Perspective, we discuss the opportunities offered by attochemistry, the related challenges, and the current and future state-of-the-art developments in theoretical chemistry needed to model it accurately.

Unlocking the Double Bond in Protonated Schiff Bases by Coherent Superposition of S1 and S2

The primary event occurring during the E-to-Z photoisomerization reaction of retinal protonated Schiff base (rPSB) is single-to-double bond inversion. In this work we examine the nuclear dynamics that occurs when the initial excited state is a superposition of the S₁ and S₂ electronic excited states that might be created in a laser experiment. The nuclear dynamics is dominated by double bond inversion that is parallel to the derivative coupling vector of S₁ and S₂. Thus, the molecule behaves as if it were at a conical intersection even if the states are nondegenerate.

Time-resolved pump-probe spectroscopy with spectral domain ghost imaging

An atomic-level picture of molecular and bulk processes, such as chemical bonding and charge transfer, necessitates an understanding of the dynamical evolution of these systems. On the ultrafast timescales associated with nuclear and electronic motion, the temporal behaviour of a system is often interrogated in a 'pump-probe' scheme. Here, an initial 'pump' pulse triggers dynamics through photoexcitation, and after a carefully controlled delay a 'probe' pulse initiates projection of the instantaneous state of the evolving system onto an informative measurable quantity, such as electron binding energy. In this paper, we apply spectral ghost imaging to a pump-probe time-resolved experiment at an X-ray free-electron laser (XFEL) facility, where the observable is spectral absorption in the X-ray regime. By exploiting the correlation present in the shot-to-shot fluctuations in the incoming X-ray pulses and measured electron kinetic energies, we show that spectral ghost imaging can be applied to time-resolved pump-probe measurements. In the experiment presented, interpretation of the measurement is simplified because spectral ghost imaging separates the overlapping contributions to the photoelectron spectrum from the pump and probe pulse.

Control of nuclear dynamics in the benzene cation by electronic wavepacket composition

The study of coupled electron-nuclear dynamics driven by coherent superpositions of electronic states is now possible in attosecond science experiments. The objective is to understand the electronic control of chemical reactivity. In this work we report coherent 8-state non-adiabatic electron-nuclear dynamics simulations of the benzene radical cation. The computations were inspired by the extreme ultraviolet (XUV) experimental results in which all 8 electronic states were prepared with significant population. Our objective was to study the nuclear dynamics using various bespoke coherent electronic state superpositions as initial conditions in the Quantum-Ehrenfest method. The original XUV measurements were supported by Multi-configuration time-dependent Hartree (MCTDH) simulations, which suggested a model of successive passage through conical intersections. The present computations support a complementary model where non-adiabatic events are seen far from a conical intersection and are controlled by electron dynamics involving non-adjacent adiabatic states. It proves to be possible to identify two superpositions that can be linked with two possible fragmentation paths.

Relaxation dynamics through a conical intersection: Quantum and quantum-classical studies

We study the relaxation process through a conical intersection of a photo-excited retinal chromophore model. The analysis is based on a two-electronic-state two-dimensional Hamiltonian developed by Hahn and Stock [J. Phys. Chem. B 104 1146 (2000)] to reproduce, with a minimal model, the main features of the 11-cis to all-trans isomerization of the retinal of rhodopsin. In particular, we focus on the performance of various trajectory-based schemes to nonadiabatic dynamics, and we compare quantum-classical results to the numerically exact quantum vibronic wavepacket dynamics. The purpose of this work is to investigate, by analyzing electronic and nuclear observables, how the sampling of initial conditions for the trajectories affects the subsequent dynamics.

On-the-Fly Ab Initio Semiclassical Evaluation of Electronic Coherences in Polyatomic Molecules Reveals a Simple Mechanism of Decoherence

Irradiation of a molecular system by an intense laser field can trigger dynamics of both electronic and nuclear subsystems. The lighter electrons usually move on much faster, attosecond timescale but the slow nuclear rearrangement damps ultrafast electronic oscillations, leading to the decoherence of the electronic dynamics within a few femtoseconds. We show that a simple, single-trajectory semiclassical scheme can evaluate the electronic coherence time in polyatomic molecules accurately by demonstrating an excellent agreement with full-dimensional quantum calculations. In contrast to numerical quantum methods, the semiclassical one reveals the physical mechanism of decoherence beyond the general blame on nuclear motion. In the propiolic acid, the rate of decoherence and the large deviation from the static frequency of electronic oscillations are quantitatively described with just two semiclassical parameters-the phase space distance and signed area between the trajectories moving on two electronic surfaces. Because it evaluates the electronic structure on the fly, the semiclassical technique avoids the "curse of dimensionality" and should be useful for preselecting molecules for experimental studies.

The quantum-Ehrenfest method with the inclusion of an IR pulse: Application to electron dynamics of the allene radical cation

We describe the implementation of a laser control pulse in the quantum-Ehrenfest method, a molecular quantum dynamics method that solves the time-dependent Schrödinger equation for both electrons and nuclei. The oscillating electric field-dipole interaction is incorporated directly in the one-electron Hamiltonian of the electronic structure part of the algorithm. We then use the coupled electron-nuclear dynamics of the π-system in the allene radical cation (•CH₂=C=CH₂)⁺ as a simple model of a pump-control experiment. We start (pump) with a two-state superposition of two cationic states. The resulting electron dynamics corresponds to the rapid oscillation of the unpaired electron between the two terminal methylenes. This electron dynamics is, in turn, coupled to the torsional motion of the terminal methylenes. There is a conical intersection at 90° twist, where the electron dynamics collapses because the adiabatic states become degenerate. After passing the conical intersection, the electron dynamics revives. The IR pulse (control) in our simulations is timed to have its maximum at the conical intersection. Our simulations show that the effect of the (control) pulse is to change the electron dynamics at the conical intersection and, as a consequence, the concomitant nuclear dynamics, which is dominated by the change in the torsional angle.

Shannon Entropy and Fisher Information from a Non-Born-Oppenheimer Perspective

We study the Shannon entropy and the Fisher information in a non-Born-Oppenheimer (nBO) regime, where these quantities are constructed from one-particle densities obtained from an exact nBO analytic wave function for a Coulomb-Hooke model of a four-particle system. This model consists of two electrons and two protons with Coulombic interactions between like particles and Hookean interactions otherwise [ Becerra , M. et al. Int. J. Quantum Chem 2013 , 113 ( 10 ), 1584 - 1590 ]. In the nBO case, there arise densities for both the nuclei and electrons. Furthermore, these densities vary with respect to a particular point of reference from which they are calculated. We consider, in the present work, electron and nuclear densities calculated from the following reference points: a global center of mass, the geometric center between the electrons, and the geometric center between the protons. A comparison of the nBO Shannon entropy and Fisher information, with respect to their counterparts computed from Born-Oppenheimer densities, suggests that the former quantities provide more insights into the chemical reactivity because of the nonuniqueness nature of the nBO electron density as well as the availability and access to the nBO nuclear density. Finally, some comments are made concerning the nBO vs the BO regimes in relation to this particular chemical reactivity indicator.

Competition between charge migration and charge transfer induced by nuclear motion following core ionization: Model systems and application to Li2. J Chem Phys 2019;151:124108. [PMID: 31575213 DOI: 10.1063/1.5117246]

Attosecond and femtosecond spectroscopies present opportunities for the control of chemical reaction dynamics and products, as well as for quantum information processing; we address the somewhat unique situation of core-ionization spectroscopy which, for dimeric chromophores, leads to strong valence charge localization and hence tightly paired potential-energy surfaces of very similar shape. Application is made to the quantum dynamics of core-ionized Li₂ ⁺. This system is chosen as Li₂ is the simplest stable molecule facilitating both core ionization and valence ionization. First, the quantum dynamics of some model surfaces are considered, with the surprising result that subtle differences in shape between core-ionization paired surfaces can lead to dramatic differences in the interplay between electronic charge migration and charge transfer induced by nuclear motion. Then, equation-of-motion coupled-cluster calculations are applied to determine potential-energy surfaces for 8 core-excited state pairs, calculations believed to be the first of their type for other than the lowest-energy core-ionized molecular pair. While known results for the lowest-energy pair suggest that Li₂ ⁺ is unsuitable for studying charge migration, higher-energy pairs are predicted to yield results showing competition between charge migration and charge transfer. Central is a focus on the application of Hush's 1975 theory for core-ionized X-ray photoelectron spectroscopy to understand the shapes of the potential-energy surfaces and hence predict key features of charge migration.

De- and Recoherence of Charge Migration in Ionized Iodoacetylene

During charge migration, electrons flow rapidly from one site of a molecule to another, perhaps inducing subsequent processes (e.g., selective breaking of chemical bonds). The first joint experimental and theoretical preparation and measurement of the initial state and subsequent quantum dynamics simulation of charge migration for fixed nuclei was demonstrated recently for oriented, ionized iodoacetylene. Here, we present new quantum dynamics simulations for the same system with moving nuclei. They reveal the decisive role of the nuclei, i.e. they switch charge migration off (decoherence) and on (recoherence). This is a new finding in attosecond-to-femtosecond chemistry and physics which opens new prospects for laser control over electronic dynamics via nuclear motions.