Spin-orbit effects on the ring current strengths of the substituted cyclophosphazene: c $$ c $$ -P 3 $$ {}_3 $$ N 3 $$ {}_3 $$ X 6 $$ {}_6 $$ ( X=H, F, Cl, Br, I, At, Ts ) $$ \left(\mathbf{X}=\mathbf{H},\mathbf{F},\mathbf{Cl},\mathbf{Br},\mathbf{I},\mathbf{At},\mathbf{Ts}\right) $$

Abstract

This work reports the magnetic index of aromaticity of cyclophosphazene ($c$-P${}_3$N${}_3$H${}_6$) and their halogenated cyclic derivatives: $c$-P${}_3$N${}_3$F${}_6$, $c$-P${}_3$N${}_3$Cl${}_6$, $c$-P${}_3$N${}_3$Br${}_6$, $c$-P${}_3$N${}_3$I${}_6$, $c$-P${}_3$N${}_3$At${}_6$ and $c$-P${}_3$N${}_3$Ts${}_6$. This index, also known as ring-current strength, is calculated by numerical integration of the magnetically-induced current density vector field which is generated by a perturbing external magnetic field. Due to the presence of heavy $X=\mathrm{Br},I,\mathrm{At}$ atoms in $c$-P${}_3$N${}_3$X${}_6$, important relativistic were expected. Accordingly, 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 values were also compared with the corresponding spin-free (scalar relativistic) ones.