Error of relativistic effective core potentials for closed-shell diatomic molecules of p-block heavy and superheavy elements in DFT and TDDFT calculations.

Pseudopotentials (PP) are extensively used in electronic structure calculations, particularly for molecules containing heavy elements. Parameters in PPs are mainly determined from ab initio results, and errors of such PPs in density functional theory (DFT) calculations have been studied previously. However, PP errors on results with spin-orbit coupling and those in time-dependent DFT (TDDFT) calculations have not been reported previously. In this work, we investigate the error of the small-core energy-consistent Stuttgart/Koln pseudopotentials in DFT and TDDFT calculations with and without spin-orbit coupling. Ground state bond lengths, harmonic frequencies, dissociation energies, and vertical excitation energies for a series of closed-shell diatomic heavy and superheavy p-block molecules are calculated using several popular exchange-correlation functionals. PP errors are estimated by comparing with results using the all-electron Dirac-Coulomb (-Gaunt) Hamiltonian. Our results show that the difference between ground state properties and most excitation energies in scalar-relativistic calculations with the PP and those of all-electron calculations is quite small. This difference becomes somewhat larger when spin-orbit coupling (SOC) is present, especially for properties that are affected by SOC to some extent. In addition, the errors of the PPs are insensitive to the employed exchange-correlation functionals in most cases. Our results indicate that reasonable DFT and TDDFT results can be obtained using the small-core energy-consistent Stuttgart/Koln pseudopotentials for heavy and super-heavy p-block molecules.