On the topology of total and diamagnetic induced electronic currents in molecules

An application of the continuous transformation of the origin of the current density (CTOCD) scheme to constrain the diamagnetic induced charge current density (J_d) to be divergenceless is introduced. This results in a family of J_d fields perpendicular and proportional to both the gradient of the electron density and the external magnetic field. Since, in the limit of a complete basis set calculation, the paramagnetic component J_p also becomes divergenceless, we call this scheme CTOCD-DC (CTOCD for Divergenceless Components). CTOCD-DC allows for a topological characterization of both J_d and J_p in terms of their stagnation graphs. All stagnation graphs of J_d from CTOCD-DC contain the zero points of the gradient of the unperturbed electron density (∇ρ). In this way, an intimate topological relation between ρ and the diamagnetic current contribution is revealed. Numerical experiments exemplified by the case of LiNHF in point group symmetry C₁ suggest that the corresponding paramagnetic current contributions J_p can show tendencies to accumulate pseudo-stagnation lines in proximity of some kind of the zero points of ∇ρ. Common zero points of ∇ρ and the total currents are exactly zero points of the mechanical momentum density.