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Functional derivatives of meta-generalized gradient approximation (meta-GGA) type exchange-correlation density

F Zahariev1, S S Leang, Mark S Gordon

  • 1Department of Chemistry, Iowa State University, Ames, Iowa 50011, USA.

The Journal of Chemical Physics
|July 5, 2013
PubMed
Summary

This study generalizes practical solutions for computing meta-generalized gradient approximation (meta-GGA) functional derivatives. It presents the first time time-dependent density functional theory (TDDFT) working equations for meta-GGAs, improving computational efficiency.

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Area of Science:

  • Computational Chemistry
  • Quantum Mechanics
  • Density Functional Theory

Background:

  • Meta-generalized gradient approximation (meta-GGA) functionals depend on Kohn-Sham (KS) orbitals via kinetic energy density.
  • The indirect functional dependence of KS orbitals on electron density complicates analytic functional derivative computation.

Purpose of the Study:

  • To generalize practical solutions for computing meta-GGA functional derivatives.
  • To present time-dependent density functional theory (TDDFT) working equations for meta-GGAs.
  • To analyze implicit assumptions in functional derivative computations.

Main Methods:

  • Abstraction and generalization of existing computational solutions for meta-GGA functional derivatives.
  • Derivation and presentation of TDDFT working equations for meta-GGA functionals.
  • Analysis of functional differentiation approximations and their impact on KS orbitals and potentials.

Main Results:

  • A generalized approach for computing functional derivatives applicable to a broader class of density functionals.
  • The first presentation of TDDFT working equations specifically for meta-GGA functionals.
  • Uncovering implicit assumptions in the computation of functional derivatives and their connection to potential non-locality.

Conclusions:

  • The generalized method enhances computational efficiency for meta-GGA functionals.
  • The presented TDDFT equations provide a foundation for excited-state calculations with meta-GGAs.
  • Understanding the approximations in functional differentiation is crucial for accurate electronic structure calculations.