Attosecond Charge Migration Induced by Core-Level Ionization: A Relativistic Real-Time Time-Dependent Density Functional Theory Perspective

Abstract

Core-ionization induced charge migration in molecular systems has been widely studied, but the influence of relativistic effects on such dynamics remains relatively unexplored from a relativistic theory perspective. This issue is particularly important because core orbitals exhibit strong scalar-relativistic and spin-orbit imprints, and these effects are further enhanced in heavy-element systems, where relativistic signatures also alter the valence orbitals. To address this, we formulate four-component Dirac-Coulomb and two-component atomic mean-field exact two-component (and non-relativistic) Hamiltonian approaches for studying charge migration within real-time time-dependent density functional theory. The time-dependent induced electric dipole moment is used as a marker of the characteristic charge-migration time scales. We apply the method to nitrosobenzene (N $1s$ electron removal), iodoacetylene (I $2p$ electron removal) and interhalogen series (I $2p$, Cl $2p$ electron removal). For iodoacetylene, the charge migration timescale is relatively insensitive to the choice of Hamiltonian but they show weak relativistic phase and amplitude modifications. However, it would be misleading to conclude that relativistic effects are generally unimportant. In interhalogen systems, we observe significant deviations between relativistic and non-relativistic dynamics. These results demonstrate that relativistic signatures in core-ionization-induced charge migration are not determined by heavy-atom core ionization alone, but by the relativistic sensitivity of the valence orbital manifold that drives core-hole screening and charge redistribution. Moreover, consistently across all systems, we observe a delay in the emergence of the relativistic imprints.