Numerical local "hybrid" functional treatment of selected diatomic molecules: comparison of energies and multipole moments to conventional hybrid functionals

TL;DR

This study benchmarks new local hybrid density functionals against traditional nonlocal hybrids for diatomic molecules, demonstrating comparable energy accuracy and highlighting computational advantages due to their differential equation-based approach.

Contribution

The paper introduces and benchmarks a new class of local hybrid functionals, showing they achieve similar energy results to nonlocal hybrids with simpler differential equations.

Findings

Total energies agree within basis set errors.

Multipole moments show small discrepancies, smaller than basis set errors.

Local hybrid functionals are computationally advantageous.

Abstract

New local "hybrid" functionals proposed by V. V. Karasiev in [J. Chem. Phys. {\bf 118}, 8567 (2003)] are benchmarked against nonlocal hybrid functionals. Their performance is tested on the total and high occupied orbital energies, as well as the electric moments of selected diatomic molecules. The new functionals, along with the Hartree-Fock and non-hybrid functionals, are employed for finite-difference calculations, which are basis-independent. Basis set errors in the total energy and electric moments are calculated for the 6-311G, 6-311G++G(3df,3pd) and AUG-cc-pVnZ (n=3,4,6) basis sets used in conjunction with the Hartree-Fock and conventional density functional methods. A comparison between the results of the finite-difference local "hybrid" and basis set nonlocal hybrid functional shows that total energies of local and nonlocal hybrid functionals agree to within the basis set error. Discrepancies for multipole moments are larger in magnitude when compared to the basis set errors, but still reasonably small (smaller than errors produced by the 6-311G basis set). Thus, we recommend using the new local "hybrid" functionals whenever the accuracy is expected to be sufficient, because they require a solution of just differential Kohn-Sham equations, instead of integro-differential ones in the case of hybrid functionals.