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

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.