Electronic current density paramagnetic contributions

Employing Eqs. (35)-(37), the first-order electronic current density induced by the external magnetic field can be written as a sum of paramagnetic and diamagnetic contributions. 

The paramagnetic spin-orbital contributions to the electronic current density induced by the nuclear magnetic... 

Therefore, the total electron current density is origin independent. Explicit formulae expressing the change of diamagnetic and paramagnetic contributions to J are given elsewhere [3, 4]. 

Lazzeretti, P., 8c Zanasi, R. (1996). Molecular magnetic properties via formal annihilation of paramagnetic contribution to electronic current density. International Journal of Quantum Chemistry, 60, 249. 

The total quantum mechanical current density is an invariant quantity, mapped onto itself in a gauge transformation, in the ideal case of electronic wavefunctions satisfying hypervirial theorems, for example, optimal variational eigenfunctions [7]. In particular, it remains the same in a change of coordinate system, as recalled above. Then comparison between Eqs. (41) and (93) necessarily impUes that the new, formally paramagnetic, term should be equivalent to the diamagnetic contribution in the conventional formulation, that is. 

The contributions to Ja, Eq. (7.46), obtained from current density terms corresponding to a given Ramsey mechanism, e.g., the diamagnetic and paramagnetic contributions from the nuclear spin/electron orbit terms, Eqs. (7.12) and (7.14), are, respectively. 

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