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

TL;DR

This paper develops a time-domain extension of Koopmans' theorem within MCTDHF theory to accurately analyze electron-hole dynamics and extract observables in ultrafast laser-driven multielectron systems.

Contribution

It introduces a novel framework for defining and computing time-dependent hole states and related observables directly from wavefunctions, advancing multielectron dynamics simulations.

Findings

Demonstrated control of hole dynamics using attosecond laser pulses

Derived exact equations of motion for Dyson orbitals in time-dependent systems

Enabled direct extraction of photoelectron distributions from wavefunctions

Abstract

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 \textit{ab 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.