Calculation of divergenceless magnetically induced current density in molecules

A method for the calculation of divergenceless, magnetically induced quantum mechanical current densities in molecules that approximates the exact current is presented. This was achieved by adding to the calculated conventional current density, i.e., a current that typically has a non-zero divergence, a corrective term that is the negative of the irrotational field of its Helmholtz decomposition. The solenoidal field of the decomposition is the divergence-free current density, which is still an approximation of the exact current but which now satisfies the continuity requirement regardless of the quality of the basis set. Based on calculations performed on several simple molecules (LiH, H2O, benzene, and zethrene), adopting different kinds of low-level theoretical approaches, clear improvements are observed in the correspondence of vortices, sources, and sinks for which the conventional current density shows a lack of continuity. A little improvement is also observed for the calculated diagonal components of the magnetizability tensor.