Chemical accuracy with σ-functionals for the Kohn-Sham correlation energy optimized for different input orbitals and...

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Orbital-dependent functionals for Kohn-Sham (KS) correlation energy, specifically σ-functionals, represent a novel approach.
• These functionals are conceptually linked to the direct random phase approximation (dRPA) but feature an optimized function.
• Previous work established a PBE-based σ-functional, necessitating further development with diverse input functionals.

Purpose of the Study:

• To introduce and evaluate new σ-functionals derived from meta-GGA (TPSS) and hybrid-functional (PBE0, B3LYP) KS calculations.
• To expand the optimization of σ-functionals using a larger set of reference data, including 3d-transition metal compounds.
• To reparameterize the PBE-based σ-functional with the expanded dataset.

Main Methods:

• Development of σ-functionals utilizing input orbitals and eigenvalues from TPSS, PBE0, and B3LYP exchange-correlation functionals.
• Optimization of these functionals against extensive reference datasets covering atomization, reaction, transition state, and non-covalent interaction energies.
• Inclusion of 3d-transition metal compounds in the reference sets for broader applicability.

Main Results:

• σ-functionals based on PBE0 and B3LYP achieve chemical accuracy for main group chemistry.
• The B3LYP-based σ-functional shows excellent performance for a large reaction dataset (W4-11RE), rivaling coupled cluster methods.
• Accuracies of approximately 2 kcal/mol are obtained for 3d-transition metal chemistry, with lower computational cost than preceding hybrid calculations.

Conclusions:

• The developed σ-functionals offer a highly accurate and computationally efficient route to calculating correlation energies.
• These functionals demonstrate significant potential for applications in both main group and transition metal chemistry.
• The findings suggest σ-functionals are a promising advancement in electronic structure theory.