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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 Zhang, Yang Li, Himadri Pathak, Takeshi Sato, Kenichi L. Ishikawa, Feng He

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 $ω-2ω$ 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.

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

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 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.
Paper Structure (3 sections, 21 equations, 2 figures)

This paper contains 3 sections, 21 equations, 2 figures.

Table of Contents

  1. acknowledgment
  2. Data availability
  3. End Matter

Figures (2)

  • Figure 1: (colored online) The channel-resolved PMD of $\mathrm{H^-}$ along the laser polarization by different approaches. See texts for laser parameters. (a) Comparison of TDHS+P and TDHS+T. (b) Comparison of TDHS+P and HS+P. (c) Comparison of TDHS+P and NO+P. See the legends for interpreting the plots. The results are extracted from a calculation with a two-electron complete active space constituting 31 orbitals.
  • Figure 2: Calculations of $\mathrm{Ne_2}$ with a fixed nuclear distance of 5.841 a.u., driven by $\omega$-$2\omega$ pulses with a fundamental frequency of 0.60 a.u., a sine-square envelope lasting for 5 fs, and a tunable phase delay $\varphi$. The peak intensities for the $\omega$ and $2\omega$ components are $10^{13}$ W/cm$^2$ and $10^{10}$ W/cm$^2$, respectively. (a)-(b) Magnitudes of the iRDM elements as functions of $\varphi$. Entry indices are indicated in the legend. Symmetry forbidden entries are zero and not shown. Channel-resolved and total PMDs at (c) $\varphi=0.7\pi$ (d) $\varphi=1.2\pi$. All PMDs are normalized to the individual maximum for clarity, and share the same range of axis. $k_{//}$, $k_\perp$ are parallel and perpendicular components of photoelectron momentum in a.u., respectively.