Gauge-origin dependence of NMR shielding constants in the Douglas–Kroll–Hess method

We investigate whether the second-order Douglas–Kroll–Hess (DKH2) method combined with gauge-including atomic orbitals (GIAO) provides gauge-origin invariant NMR shielding constants. It is difficult to correctly evaluate the DKH2-GIAO integrals due to the approximate use of the resolution of identity and, therefore, we propose two approximations for calculating the DKH1-GIAO integrals, which sufficiently reduce the gauge-origin dependence in most cases. Additionally, we show two useful approximations: the DKH2 method combined with the common gauge origin (CGO) method of Malkina et al., and the DKH2-GIAO method, where the DKH2 magnetic operators are replaced with the Breit–Pauli magnetic operators.