Breakdown of the pseudopotential approximation for magnetizabilities and electric multipole moments. II. The importance of gauge invariance for large-core semi-local pseudopotentials

In a previous paper we pointed out that core contributions to the static magnetizability are non-negligible, and can therefore lead to erroneous results within the pseudopotential approximation P. Schwerdtfeger, B. Assadollahzadeh, U. Rohrmann, R. Scha?fer, and J. R. Cheeseman, J. Chem. Phys. 134, 204102 (2011)]. In a recent paper van Wu?llen showed that additional terms arising from the gauge-invariant condition for the semi-local part of a pseudopotential operator can lead to non-negligible contributions to the magnetizability tensor, which are sensitive to the gauge origin and basis set chosen C. van Wu?llen, J. Chem. Phys. 136, 114110 (2012)]. These terms were neglected in previous calculations as they were assumed to be small. In this paper we analyze the importance of the gauge-dependent semi-local pseudopotential correction term in detail for AuF and clusters of Sn showing that it leads indeed to very large corrections to the paramagnetic term for large-core pseudopotentials. Without this correction the results become very sensitive to the basis set applied. This now resolves some of the unusual large paramagnetic contributions reported before for both AuF and Sn(2).