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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Theoretical Chemistry

Background:

  • The adiabatic approximation in time-dependent density functional theory (TDDFT) inaccurately models the quadratic response function.
  • This inaccuracy leads to unphysical divergences in calculated excited state properties, such as transition probabilities and hyperpolarizabilities.

Purpose of the Study:

  • To identify the exact form of the quadratic response kernel in TDDFT.
  • To develop a practical and accurate approximation to the kernel that resolves the unphysical divergences.
  • To validate the new approximation using model systems and real molecular calculations.

Main Methods:

  • Derivation of the exact quadratic response kernel.
  • Development of a novel approximation to the kernel.
  • Application of the approximation to calculate excited state-to-state transition probabilities.

Main Results:

  • The exact form of the quadratic response kernel was determined.
  • A practical and accurate approximation was successfully derived, effectively removing unphysical divergences.
  • The approximation demonstrated reliable performance on both a model system and the LiH molecule.

Conclusions:

  • The derived approximation provides a robust solution to the divergence problem in TDDFT quadratic response calculations.
  • This advancement enables more accurate predictions of excited state properties and hyperpolarizabilities.
  • The method is validated for practical applications in quantum chemistry and materials science.