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, Delta sigma=sigma(parallel to)-sigma(perpendicular to), 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 sigma center dot pi U/2c, in which pi=p+A, U is a nonunitary transformation operator, and c congruent to 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 Delta sigma for halogen nuclei found in our previous studies is related to the neglect of the U-(0,U-1) perturbation operator of U, which is independent of the external magnetic field and of the first order with respect to the nuclear magnetic dipole moment. Introduction of gauge-including atomic orbitals and a finite-size nuclear model is also discussed.