The program mpshift calculates nuclear magnetic shielding constants using the GIAO (Gauge Including Atomic Orbital) method.
At present the following methods are implemented:
the coupled perturbed Hartree–Fock (CPHF) equations in the AO basis are solved using a semi-direct iterative algorithm  similar to dscf.
using either non-hybrid functionals where no iterations are needed  or hybrid functionals where the same algorithm as at the HF-SCF level is used.
semi-direct method, see ref. .