[Paper Review] Imaging charge-migration in chiral molecules using time-resolved x-ray diffraction

Sucharita Giri, Jean Christophe Tremblay+1 more|arXiv (Cornell University)|Apr 5, 2021

Advanced Chemical Physics StudiesPhysics and Astronomy82 references23 citations

TL;DR

This study demonstrates that time-resolved x-ray diffraction (TRXD) can image ultrafast charge migration in chiral molecules, specifically oriented epoxypropane, using a pump-probe setup with linearly polarized light. The key finding is that TRXD signals differ significantly between enantiomers due to chiral-dependent electronic flux dynamics, enabling direct discrimination of molecular handedness via x-ray scattering.

ABSTRACT

Four-dimensional imaging of charge migration is crucial to the understanding of several ubiquitous processes in nature. The present work focuses on imaging of charge migration in an oriented epoxypropane: a chiral molecule. A linearly polarized pulse is used to induce the charge migration, which is imaged by time-resolved x-ray diffraction. It is found that the total time-resolved diffraction signals are significantly different for both enantiomers. Furthermore, a connection between time-resolved x-ray diffraction and the electronic continuity equation is discussed by analyzing the time-dependent diffraction signal and the time derivative of the total electron density in the momentum space.

Motivation & Objective

• To image ultrafast charge migration dynamics in chiral molecules using time-resolved x-ray diffraction (TRXD).
• To investigate whether TRXD can distinguish between enantiomers of a chiral molecule based on their electronic response to a chiral pump field.
• To establish a connection between time-resolved x-ray diffraction signals and the electronic continuity equation in momentum space.
• To demonstrate that TRXD provides complementary information to electronic flux density analysis for probing non-equilibrium electron dynamics in chiral systems.

Proposed method

• Simulates ultrafast electron dynamics using hybrid time-dependent density functional theory–configuration interaction (TDDFT-CI) with 31 excited states below ionization threshold.
• Models the time evolution of the many-body wavefunction under a linearly polarized laser pulse using a preconditioned adaptive Runge-Kutta algorithm.
• Computes one-electron density and electronic flux density from the many-body wavefunction using the detCI@ORBKIT toolbox.
• Calculates the time-resolved x-ray diffraction signal via the differential scattering probability (DSP) expression, linking it to the time derivative of the momentum-space electron density.
• Analyzes the relationship between the TRXD signal and the quantum continuity equation: ∂tρ(r,t) = −∇·j(r,t).
• Performs simulations for both enantiomers of epoxypropane to compare their TRXD responses under identical excitation conditions.

Experimental results

Research questions

• RQ1 Can time-resolved x-ray diffraction (TRXD) detect and image charge migration dynamics in chiral molecules with enantiomeric specificity?
• RQ2 How does the time-resolved x-ray diffraction signal differ between the two enantiomers of epoxypropane under identical excitation?
• RQ3 To what extent does the TRXD signal encode information about electronic flux densities during ultrafast charge migration?
• RQ4 Is there a direct theoretical link between the time-resolved x-ray diffraction signal and the time derivative of the momentum-space electron density?
• RQ5 Can TRXD serve as a viable method for absolute configuration determination in chiral molecules?

Key findings

• The total time-resolved x-ray diffraction signals for the two enantiomers of epoxypropane are significantly different, indicating enantiomer-specific scattering responses.
• The TRXD signal is directly related to the time derivative of the momentum-space electron density, as predicted by the electronic continuity equation.
• The electronic flux density, derived from the time-dependent wavefunction, shows chiral asymmetry in response to linearly polarized light, which is encoded in the TRXD signal.
• The simulation results confirm that the continuity equation is satisfied with high accuracy, validating the reliability of the computed flux and density dynamics.
• The method provides a pathway to distinguish enantiomers without relying on chiral probes or circularly polarized light, using only linearly polarized pump and x-ray probe.
• The study establishes TRXD as a complementary tool to existing methods like photoelectron circular dichroism and high-harmonic generation for probing chiral electron dynamics.