Probing Electronic Fluxes via Time-Resolved X-Ray Scattering

Abstract

The current flux density is a vector field that can be used to describe theoretically how electrons flow in a system out-of-equilibrium. In this work, we unequivocally demonstrate that the signal obtained from time-resolved X-ray scattering does not only map the time-evolution of the electronic charge distribution, but also encodes information about the associated electronic current flux density. We show how the electronic current flux density qualitatively maps the distribution of electronic momenta and reveals the underlying mechanism of ultrafast charge migration processes, while also providing quantitative information about the timescales of electronic coherences.Time-resolved imaging (TRI) of dynamically evolving electronic charge distribution is essential for complete understanding of complex chemical and biological processes in nature. Moreover, TRI of valence electron charge distribution is paramount to understand different instances during chemical reactions such as conformational changes, charge migration, and bond formation and breakage [1][2][3][4]. Following the quantum mechanical version of continuity equation, the flow of electron charge distribution is accompanied by associated electronic fluxes [5]. The concept of quantum electronic fluxes offers a wealth of crucial informations and has played a decisive role for understanding the mechanism of chemical reactions [6][7][8]. However, the notion of electronic fluxes has been restricted to theoretical modelling [9-18] and there is no general way to probe them directly in experiment. In this work, we will demonstrate a real-space and real-time imaging of electronic fluxes associated with attosecond non-stationary charge migration using time-resolved X-ray scattering (TRXS). For this purpose, we will consider benzene molecule as a test system in which a pump pulse will induce an adiabatic charge migration and ultrashort X-ray pulses will probe the electronic fluxes accompanying charge migration.Scattering of X-rays from matter is an indispensable technique to unveil the real-space structure of solids, biomolecules and molecules with atomic-scale spatial resolution [19]. Tremendous technological progress has been made to generate tunable ultraintense and ultrashort Xray pulses from X-ray free-electron lasers (XFELs) [20][21][22]. X-ray pulses with few femtoseconds pulse duration are routinely generated at various XFELs (LCLS, SACLA, European XFEL). Moreover, few successful attempts have been demonstrated to generate attosecond X-ray pulses [23][24][25][26][27][28]. The availability of these ultrashort X-ray pulses offer to extend X-ray scattering from static to time domain with unprecedented temporal resolution [29,30]. Scattering of ultrashort X-ray pulses from the temporarily evolving electronic charge distribution promises to provide stroboscopic snap-shots of matter in action with atomic-scale spatial and temporal resolutions [31,32]. A direct approach to envision TRXS is a pump-probe experiment, where the pump pulse triggers the ultrafast dynamics ...

Imaging conical intersection dynamics during azobenzene photoisomerization by ultrafast X-ray diffraction

“…This is especially true for excited molecules, being in a time-evolving superposition of many-body states. Inelastic scattering from different electronic states (25)(26)(27), as well as electronic and vibrational coherences (27)(28)(29)(30), contributes to the signal.…”

Electron Symmetry Breaking during Attosecond Charge Migration Induced by Laser Pulses: Point Group Analyses for Quantum Dynamics

“…This scenario has also been used in Refs. [2][3][4]6,[9][10][11][12]. An alternative orientation of the nuclear scaffold-i.e., again with the molecular plane in the laboratory x-y-plane, but with two carbon nuclei on the x-axis instead of the y-axis-is considered in Refs.…”

“…[1], as in Refs. [2][3][4]6,[9][10][11][12], cf. Figure 1), whereas for Mg-porphyrin, e' 1 = e x and e' 2 = e y (this is in accord with Refs.…”

Time-resolved x-ray scattering from impulsively aligned or oriented molecules

“…The theory of time-resolved x-ray scattering has been developed in step with the experimental XFEL facilities [21,[26][27][28][29][30][31][32][33][34][35]. For the present purpose, the standard theory of timeresolved x-ray scattering based on the independent atom model (IAM) suffices.…”

“…Though deviations from the IAM can reveal important electronic effects such as chemical bonding or electronic excitations [36,37], they do not concern the signatures of rotational alignment or orientation considered here. Thus, the electron density is expressed as a sum of free atomic densities and contributions from coherently populated electronic states [30,[32][33][34][35] are neglected.…”