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Adiabatic approximation of time-dependent density matrix functional response theory.

Katarzyna Pernal1, Klaas Giesbertz, Oleg Gritsenko

  • 1Afdeling Theoretische Chemie, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands.

The Journal of Chemical Physics
|December 11, 2007
PubMed
Summary

An improved adiabatic approximation (AA) for time-dependent density matrix functional theory accurately predicts molecular polarizability and excitation energies. This method overcomes limitations of the static approximation (SA) and adiabatic TDDFT, especially for two-electron systems like HeH(+).

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Theoretical Chemistry

Background:

  • Time-dependent density matrix functional theory (TD-DMF) requires approximations for solving coupled-perturbed response equations.
  • The adiabatic approximation in TD-DMF is critical due to the absence of a clear 'zero order' reference, unlike in time-dependent density functional theory (TDDFT).
  • Previous static approximations (SA) have shown deficiencies, particularly in the low-frequency limit.

Purpose of the Study:

  • To evaluate and improve adiabatic approximations within time-dependent density matrix functional theory.
  • To analytically compare approximations with exact equations for two-electron systems.
  • To test the accuracy of static approximation (SA) and adiabatic approximation (AA) against benchmark calculations.

Main Methods:

  • Formulation of time-dependent density matrix functional theory using coupled-perturbed response equations.
  • Development and application of an improved adiabatic approximation (AA).
  • Analytical derivation of exact coupled-perturbed equations for two-electron systems.
  • Testing approximations on the two-electron HeH(+) molecule at equilibrium and stretched geometries.

Main Results:

  • The static approximation (SA) underestimates frequency-dependent polarizability (alpha(omega)) and shows incorrect behavior at omega=0.
  • Adiabatic TDDFT overestimates alpha(omega) for HeH(+).
  • The improved adiabatic approximation (AA) accurately reproduces alpha(0) and improves upon SA, while adiabatic density matrix functional theory corrects excitation energies and overpolarization issues seen in adiabatic TDDFT for stretched HeH(+).

Conclusions:

  • The developed adiabatic approximation (AA) offers a significant improvement over the static approximation (SA) for TD-DMF.
  • Adiabatic density matrix functional theory provides accurate results for molecular properties, including frequency-dependent polarizability and excitation energies, showing excellent agreement with high-level correlated calculations.
  • The study highlights the importance of accurate approximations in TD-DMF for reliable predictions of molecular electronic structure and response properties.