Correlated-gauge invariant calculations of nuclear magnetic shielding constants using the continuous transformation of the origin of the current density approach. II. Coupled cluster and density-functional theory results for eight small molecules

The quantum mechanical current density induced in a molecule by an external magnetic field isinvariant to translations of the coordinate system. This fundamental symmetry is exploited toformally annihilate the diamagnetic contribution to the current density via the approach of“continuous transformation of the origin of the current density-diamagnetic zero” CTOCD-DZ.The relationships obtained by this method for the magnetic shielding at the nuclei are intrinsicallyindependent of the origin of the coordinate system for any approximate computational schemerelying on the algebraic approximation. The authors report for the first time an extended series oforigin-independent estimates of nuclear magnetic shielding constants using the CTOCD-DZapproach at the level of density functional theory DFT with four different types of functionals andunrelaxed coupled cluster singles and doubles linear response CCSD-LR theory. The resultsobtained indicate that in the case of DFT the procedure employed is competitive with currentlyadopted computational methods allowing for basis sets of gauge-including atomic orbitals, whereaslarger differences between CTOCD-DZ and common origin CCSD-LR results are observed due tothe incomplete fulfillment of hypervirial relations in standard CCSD-LR theory. It was foundfurthermore that the unrelaxed CCSD-LR calculations predict larger correlation corrections for theshielding constants of almost all nonhydrogen atoms in their set of molecules than the usual relaxedenergy derivative CCSD calculations. Finally the results confirm the excellent performance of Kealand Tozer’s third functional, in particular, for the multiply bonded systems with a lot of electroncorrelation, but find also that the simple local density functional gives even better results for the fewsingly bonded molecules in their study where correlation effects are small.