Computational approach to molecular magnetic properties by continuous transformation of origin of current density

The continuous set of gauge transformations method (CSGT) for calculating magnetic susceptibilities and nuclear magnetic shieldings reported by Keith and Bader is analyzed. To avoid numerical integration, analytical expressions are obtained for direct computation of the magnetic properties, which are written in closed form as a sum of the conventional paramagnetic terms and contributions which, in the limit of exact eigenfunctions to a model Hamiltonian, reduce to the conventional diamagnetic terms. The latter can also be expressed as the expectation value of certain commutators over the reference electronic state. It is shown that the CSGT method is related to the Geertsen procedure. The magnetic shielding within the CSGT method is origin independent, but the CSGT susceptibility depends on the origin of the vector potential, whereas the Geertsen average susceptibility is independent of the origin of the vector potential, but depends on the origin of the reference frame.