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Developing new and understanding old approximations in TDDFT.

Lionel Lacombe1, Neepa T Maitra

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Adiabatic approximations in time-dependent density functional theory (TDDFT) calculations often fail for systems far from their ground state. This study investigates why, exploring new memory-dependent approximations beyond the adiabatic approximation.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Theoretical Chemistry

Background:

  • Adiabatic approximations in time-dependent density functional theory (TDDFT) are widely used but their accuracy is not well understood, especially for systems far from their ground state.
  • Developing improved approximations beyond the adiabatic approximation is crucial for advancing TDDFT applications.

Purpose of the Study:

  • To investigate the reasons behind the varying accuracy of adiabatic approximations in TDDFT.
  • To explore new theoretical frameworks for approximations that go beyond the standard adiabatic approximation.
  • To derive a new expression for the exact exchange-correlation potential.

Main Methods:

  • Analysis of the exact time-dependent exchange-correlation potential to understand the relationship between adiabatic approximation accuracy and natural orbital occupation numbers.
  • Exploration of exactly-solvable model systems to test theoretical insights.
  • Development and discussion of a new class of memory-dependent approximations.
  • Derivation of a novel expression for the exact exchange-correlation potential using coupling-constant path integration.

Main Results:

  • The accuracy of adiabatic approximations in TDDFT is linked to the deviation between natural orbital occupation numbers of the physical system and the Kohn-Sham system.
  • A new class of memory-dependent approximations has been proposed as a potential improvement over adiabatic approximations.
  • A new expression for the exact exchange-correlation potential has been derived.

Conclusions:

  • Understanding the deviation in natural orbital occupation numbers is key to assessing and improving TDDFT adiabatic approximations.
  • Memory-dependent approximations offer a promising avenue for more accurate TDDFT calculations.
  • The derived exact exchange-correlation potential expression may lead to further theoretical advancements.