Spin-orbit effects on magnetically induced current densities in the M₄^2- (M=B,Al,Ga,In,Tl) clusters

We report about the spin-orbit effects on the aromaticity of the B₄^2-,Al₄^2-,Ga₄^2-, In₄^2-and Tl₄^2-clusters via the magnetically-induced current density method. All-electron density functional theory (DFT) calculations were carried out using the four-component Dirac-Coulomb (DC) Hamiltonian, including scalar and spin-orbit relativistic effects. The relativistic values for ring current strengths were obtained by numerical integration over the current flow. These values were compared to the scalar relativistic and non-relativistic values, in order to assess the corresponding contributions to aromaticity. It was found that in the heavy cluster, Tl₄^2-, there is a significant influence of both scalar and spin-orbit relativistic effects.