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

Zhao-Han Zhang1,2, Yang Li1,*, Himadri Pathak4,5, Takeshi Sato6,7,8, Kenichi L. Ishikawa6,7,8,9, and Feng He1,3,†

  • *Contact author: liyang22@sjtu.edu.cn
  • †Contact author: fhe@sjtu.edu.cn
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Phys. Rev. Lett. 136, 013204 – Published 8 January, 2026

DOI: https://doi.org/10.1103/dcdw-ly16

Abstract

We introduce a framework for resolving electron-hole dynamics within wave-function-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 ab initio wave functions. As a demonstration, we employ an attosecond ω−2ω 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.

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Time-dependent hole states in multiconfigurational time-dependent Hartree-Fock approaches: Applications in photoionization of water molecule

Zhao-Han Zhang, Yang Li, Himadri Pathak, Takeshi Sato, Kenichi L. Ishikawa, and Feng He
Phys. Rev. Research 8, 013016 (2026)

Article Text

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Phys. Rev. Lett. 136, 013204– Published 8 January, 2026
  • Received 10 May 2025
  • Revised 1 December 2025
  • Accepted 18 December 2025
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