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

Recently, a new type of orbital-dependent functional for the Kohn-Sham (KS) correlation energy, sigma-functionals, was introduced. Technically, sigma-functionals are closely related to the well-known direct random phase approximation (dRPA). Within the dRPA, a function of the eigenvalues sigma of the frequency-dependent KS response function is integrated over purely imaginary frequencies. In sigma-functionals, this function is replaced by one that is optimized with respect to reference sets of atomization, reaction, transition state, and non-covalent interaction energies. The previously introduced sigma-functional uses input orbitals and eigenvalues from KS calculations with the generalized gradient approximation (GGA) exchange-correlation functional of Perdew, Burke, and Ernzerhof (PBE). Here, sigma-functionals using input orbitals and eigenvalues from the meta-GGA TPSS and the hybrid-functionals PBE0 and B3LYP are presented and tested. The number of reference sets taken into account in the optimization of the sigma-functionals is larger than in the first PBE based sigma-functional and includes sets with 3d-transition metal compounds. Therefore, also a reparameterized PBE based sigma-functional is introduced. The sigma-functionals based on PBE0 and B3LYP orbitals and eigenvalues reach chemical accuracy for main group chemistry. For the 10 966 reactions from the highly accurate W4-11RE reference set, the B3LYP based sigma-functional exhibits a mean average deviation of 1.03 kcal/mol compared to 1.08 kcal/mol for the coupled cluster singles doubles perturbative triples method if the same valence quadruple zeta basis set is used. For 3d-transition metal chemistry, accuracies of about 2 kcal/mol are reached. The computational effort for the post-self-consistent evaluation of the sigma-functional is lower than that of a preceding PBE0 or B3LYP calculation for typical systems.

Automated summary

The newly introduced sigma-functionals for the Kohn-Sham correlation energy show higher accuracy in energy optimization, particularly for main group chemistry. Compared to PBE-based sigma-functionals, the ones based on PBE0 and B3LYP exhibit advantages in terms of computational accuracy and efficiency.