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Top-Down versus Bottom-Up Approaches for σ-Functionals Based on the Approximate Exchange Kernel.

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This summary is machine-generated.

New "bottom-up" functionals (σ↑AXK) improve density functional theory calculations by addressing self-interaction and delocalization errors, outperforming previous methods on key benchmarks.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Density Functional Theory

Background:

  • Investigated σ- and τ-functionals based on the adiabatic-connection fluctuation-dissipation theorem (ACFDT).
  • Previous work utilized a "top-down" approach for σ-functionals, showing good performance with hybrid PBE0 orbitals.
  • The approximate exchange kernel (AXK) introduced nonlinear spline function contributions.

Purpose of the Study:

  • To examine the analytic "bottom-up" approach for σ-functionals, inserting the spline function before analytic coupling strength integration.
  • To develop and evaluate new bottom-up functionals, denoted σ↑AXK, for improved accuracy in density functional theory.

Main Methods:

  • Employed the analytic "bottom-up" approach, integrating the spline function prior to the coupling strength integral within ACFDT.
  • Evaluated the performance of the new σ↑AXK functionals, specifically σ↑AXK@PBE0, against existing functionals.
  • Utilized the GMTKN55 database, including WTMAD-1 and WTMAD-2 metrics, for comprehensive benchmarking.

Main Results:

  • The new bottom-up σ↑AXK functionals significantly improve upon "top-down" counterparts for systems with self-interaction and delocalization errors.
  • σ↑AXK@PBE0 functionals demonstrate superior performance compared to regular σ-functionals, scaled σ-functionals, and prior σ+SOSEX- and τ-functionals.
  • A minor reduction in accuracy for noncovalent interactions was observed, but overall performance on the GMTKN55 database is enhanced.

Conclusions:

  • The "bottom-up" approach for constructing σ-functionals offers substantial improvements, particularly for challenging electronic structure problems.
  • σ↑AXK@PBE0 represents a significant advancement in density functional approximations, providing more accurate results for various chemical systems.
  • These findings pave the way for more reliable and accurate computational chemistry predictions using ACFDT-based functionals.