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

Abstract

σ-Functionals are promising new developments for the Kohn–Sham correlation energy based upon the direct Random Phase Approximation (dRPA) within the adiabatic connection formalism, providing impressive improvements over dRPA for a broad range of benchmarks. However, σ-functionals exhibit a high amount of self-interaction inherited from the approximations made within dRPA. Inclusion of an exchange kernel in deriving the coupling-strength-dependent density–density response function leads to so-called τ-functionals, which – apart from a fourth-order Taylor series expansion – have only been realized in an approximate fashion so far to the best of our knowledge, most notably in the form of scaled σ-functionals. In this work, we derive, optimize, and benchmark three types of σ- and τ-functionals including approximate exchange effects in the form of an antisymmetrized Hartree kernel. These functionals, based on a second-order screened exchange type contribution in the adiabatic connection formalism, the electron–hole time-dependent Hartree–Fock kernel (eh-TDHF) otherwise known as RPA with exchange (RPAx), and an approximation thereof known as approximate exchange kernel (AXK), are optimized on the ASCDB database using two new parametrizations named A1 and A2. In addition, we report a first full evaluation of σ- and τ-functionals on the GMTKN55 database, revealing our exchange-including functionals to considerably outperform existing σ-functionals while being highly competitive with some of the best double-hybrid functionals of the original GMTKN55 publication. In particular, the σ-functionals based on AXK and τ-functionals based on RPAx with PBE0 reference stand out as highly accurate approaches for a wide variety of chemically relevant problems.