Relativistic calculation of nuclear magnetic shielding tensor using the regular approximation to the normalized elimination of the small component. III. Introduction of gauge-including atomic orbitals and a finite-size nuclear model

The relativistic calculation of nuclear magnetic shielding tensors in hydrogen halides is performed using the second-order regular approximation to the normalized elimination of the small component (SORA-NESC) method with the inclusion of the perturbation terms from the metric operator. This computational scheme is denoted as SORA-Met. The SORA-Met calculation yields anisotropies, Δσ=σ∥−σ⊥, for the halogen nuclei in hydrogen halides that are too small. In the NESC theory, the small component of the spinor is combined to the large component via the operator σ⋅πU/2c, in which π=p+A, U is a nonunitary transformation operator, and c≅137.036 a.u. is the velocity of light. The operator U depends on the vector potential A (i.e., the magnetic perturbations in the system) with the leading order c−2 and the magnetic perturbation terms of U contribute to the Hamiltonian and metric operators of the system in the leading order c−4. It is shown that the small Δσ for halogen nuclei found in our previous studies is...