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Meta-Local Density Functionals: A New Rung on Jacob's Ladder.

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  • 1Department of Chemistry, University of Helsinki, P.O. Box 55 (A.I. Virtasen aukio 1), FI-00014 University of Helsinki, Finland.

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We introduce meta-local density approximations (meta-LDAs), a new class of density-functional theory functionals. Optimized meta-LDAs improve atomic and molecular energies, significantly reducing errors from the local density approximation (LDA).

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Area of Science:

  • Quantum Chemistry
  • Computational Materials Science
  • Theoretical Physics

Background:

  • The homogeneous electron gas (HEG) is fundamental for constructing exchange-correlation functionals in density-functional theory (DFT).
  • The local density approximation (LDA) parameterizes HEG energy using spin density, but has limitations for inhomogeneous systems.
  • Generalizing LDA requires incorporating kinetic energy density information.

Purpose of the Study:

  • To develop a new family of density functionals, termed meta-local density approximations (meta-LDAs), by generalizing the LDA.
  • To investigate the stability and accuracy of meta-LDAs, particularly the local tau approximation (LTA) and its variants.
  • To optimize a meta-LDA parameter for improved energetic predictions in atomic and molecular systems.

Main Methods:

  • Generalized the LDA by evaluating functionals on a geometric average of local spin density and HEG spin density with matching kinetic energy density.
  • Introduced meta-LDAs, a new rung on Jacob's ladder of DFT functionals, exact for HEG and derived from HEG properties.
  • Assessed numerical stability and accuracy of meta-LDAs through self-consistent field calculations and atomic/molecular energy benchmarks.

Main Results:

  • The initial LTA (x=1) is numerically unstable due to divergent potentials.
  • Geometric averaging of LDA and LTA densities with smaller x values yields stable meta-LDAs.
  • The optimized meta-LDA (x=0.50) provides more accurate exchange energies than LDA, LTA, and tLDA, and significantly improves molecular atomization energies, reducing LDA's overbinding error by two-thirds.

Conclusions:

  • Meta-LDAs offer a stable and accurate generalization of the LDA by incorporating kinetic energy density.
  • The optimized meta-LDA (x=0.50) represents a significant improvement over existing functionals for electronic structure calculations.
  • This work establishes a new, promising direction for developing more accurate DFT functionals.