Time-dependent Hole States in Multiconfigurational Time-Dependent Hartree-Fock Approaches: A Time-Domain Generalization of Extended Koopmans' Theorem

We introduce a framework for resolving electron-hole dynamics within wavefunction-based multiconfigurational time-dependent Hartree-Fock (MCTDHF) theory. Central to this framework is a time-domain generalization of the extended Koopmans’ theorem, which rigorously defines time-dependent hole states through single-electron removal. From this foundation, we prove the existence of exact equations of motion for time-dependent Dyson orbitals, enabling instantaneous construction of photofragments’ reduced density matrices. The formalism further yields a systematic procedure to extract hole-resolved observables, such as channel-resolved photoelectron momentum distributions, directly from time-dependent $\mathit{\text{ab}}\mathit{\text{initio}}$ wavefunctions. As a demonstration, we employ an attosecond $\omega -2\omega$ laser strategy to control hole dynamics, thereby resolving a long-standing challenge in MCTDHF simulations. This advance opens a pathway for exploring correlated multielectron dynamics in atoms and molecules under ultrafast laser fields.