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Time-dependent Dyson orbital theory.

O V Gritsenko1, E J Baerends

  • 1Section Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands.

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Time-dependent Dyson orbital theory (TDDOT) offers an exact solution for electron ionization probabilities, overcoming limitations of time-dependent density functional theory (TDDFT) by avoiding approximations and accurately describing electron behavior.

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Area of Science:

  • Quantum Chemistry
  • Theoretical Physics
  • Computational Many-Body Physics

Background:

  • Time-dependent density functional theory (TDDFT) is widely used for simulating electron dynamics but faces challenges.
  • Key TDDFT limitations include neglecting memory effects due to the adiabatic approximation and difficulties in calculating multiple ionization probabilities.
  • Accurate description of continuum states for ejected electrons in ionization processes remains a challenge for existing methods.

Purpose of the Study:

  • To introduce time-dependent Dyson orbital theory (TDDOT) as a novel approach for studying electron ionization.
  • To address the limitations of TDDFT in real-time electron density propagation and ionization probability calculations.
  • To provide a formally exact framework for describing photoinduced ionization dynamics, including multiple ionization events.

Main Methods:

  • Derivation of exact equations of motion for time-dependent Dyson orbitals.
  • Utilizing static, feasible potentials for electron-electron interactions, avoiding the adiabatic approximation.
  • Developing formally exact expressions for the time evolution of the outgoing electron wavefunction.

Main Results:

  • TDDOT provides exact solutions for the probabilities of single (P(1)(t)), multiple (P(n)(t)), and no ionization (P(0)(t)).
  • The theory formally resolves the issue of memory effects neglected in TDDFT.
  • For two-electron systems, TDDOT allows for the calculation of P(1)(t) and P(2)(t), including a proper description of continuum states.

Conclusions:

  • TDDOT offers a formally exact and robust alternative to TDDFT for studying photoinduced ionization.
  • The theory is expected to accurately reproduce phenomena like the 'knee structure' in non-sequential double ionization of Helium.
  • TDDOT provides a pathway for more reliable calculations of ionization processes, particularly multiple ionization events.