Highly accurate σ- and τ-functionals for beyond-RPA methods with approximate exchange kernels.

Area of Science:

• Quantum Chemistry
• Computational Materials Science
• Electronic Structure Theory

Background:

• σ-functionals, based on direct Random Phase Approximation (dRPA), improve correlation energy calculations but suffer from self-interaction errors.
• τ-functionals aim to mitigate these errors by including exchange kernels, though they have been largely approximated.

Purpose of the Study:

• To derive, optimize, and benchmark new σ- and τ-functionals that include approximate exchange effects.
• To evaluate the performance of these novel functionals against existing methods and state-of-the-art double-hybrid functionals.

Main Methods:

• Development of functionals based on antisymmetrized Hartree kernel, second-order screened exchange, electron-hole time-dependent Hartree-Fock (eh-TDHF/RPAx), and approximate exchange kernel (AXK).
• Optimization using two new parametrizations (A1, A2) on the ASCDB database.
• Comprehensive benchmarking on the GMTKN55 database.

Main Results:

• Exchange-including σ- and τ-functionals demonstrate superior performance compared to standard σ-functionals.
• The developed functionals show high accuracy, competitive with leading double-hybrid functionals.
• σ-functionals with AXK and τ-functionals with RPAx (PBE0 reference) are particularly effective for diverse chemical problems.

Conclusions:

• Incorporating exchange effects significantly enhances the accuracy of σ- and τ-functionals.
• The new functionals present a promising advancement in electronic correlation energy calculations.
• These methods offer a robust and accurate approach for tackling complex chemical challenges.