4-Component relativistic calculation of the magnetically induced current density in the group 15 heteroaromatic compounds

We present a 4-component relativistic implementation for calculating the magnetically induced current density within Hartree-Fock and Kohn-Sham linear response theory using a common gauge origin. We demonstrate how the current density can be decomposed into paramagnetic and diamagnetic contributions by calculating separately the contributions from rotations between positive-energy orbitals and contributions from rotations between the occupied positive-energy orbitals and the virtual negative-energy orbitals, respectively. This methodology is applied to the study of the magnetically induced current density in benzene and the group 15 heteroaromatic compounds C5H5E (E = N, P, As, Sb, Bi). Quantitative values for the magnetically induced ring currents are obtained by numerical integration over the current flow. We have found that the diatropic ring current is sustained for the entire series of the group 15 heteroaromatic compounds-the induced ring current susceptibility of bismabenzene being 76% of the benzene result. Having employed two hybrid and two nonhybrid generalized gradient approximation functionals, the results are found to be rather insensitive to the choice of the density functional approximation. The relativistic effect is relatively small, reaching its maximum of 8% for bismabenzene. The presented 4-component relativistic methodology opens up the possibility to visualize magnetically induced current densities of aromatic heavy-element systems with both scalar relativistic and spin-orbit effects included.