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Real-time linear response for time-dependent density-functional theory.

Roi Baer1, Daniel Neuhauser

  • 1Department of Physical Chemistry and the Lise Meitner Minerva-Center for Quantum Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel.

The Journal of Chemical Physics
|November 20, 2004
PubMed
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We developed a linear-response theory for time-dependent density-functional theories (TD-DFT) using time-adiabatic functionals. This approach allows calculations in both time and frequency domains, enhancing computational efficiency for electronic structure.

Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Theoretical Chemistry

Background:

  • Time-dependent density-functional theory (TD-DFT) is a powerful method for studying excited states and electronic dynamics.
  • Existing TD-DFT methods can be computationally intensive, particularly for large systems or long time scales.
  • The development of efficient and accurate linear-response formalisms is crucial for advancing TD-DFT applications.

Purpose of the Study:

  • To present a novel linear-response approach for TD-DFT utilizing time-adiabatic functionals.
  • To enable calculations in both the time and frequency domains within a unified framework.
  • To provide a computationally tractable method for investigating time-dependent electronic properties.

Main Methods:

  • Derivation of a linear-response theory based on time-adiabatic functionals.

Related Experiment Videos

  • Transformation to a symplectic real-spinor representation to reveal inherent linearity.
  • Development of a modified Chebyshev expansion for numerical integration of time-dependent equations.
  • Adaptation of the Chebyshev expansion for frequency-domain calculations via Green's operator expansion.

    • Main Results:

    • The developed theory successfully describes the autonomous time evolution of Kohn-Sham orbitals under impulsive perturbation.
    • Linearity of the response equations is explicitly demonstrated in the symplectic real-spinor representation.
    • A modified Chebyshev expansion method is presented for efficient numerical integration in the time domain.
    • The frequency domain is readily accessible by modifying Chebyshev polynomial coefficients, yielding a formal symplectic Green's operator.

    Conclusions:

    • The presented linear-response approach offers a versatile and efficient method for TD-DFT calculations.
    • The ability to perform calculations in both time and frequency domains expands the applicability of TD-DFT.
    • This work provides a foundation for more accurate and efficient simulations of electronic dynamics and excited states.