Exchange interactions in systems with multiple magnetic sites.

Nonequivalent magnetic interactions in systems with multiple magnetic centers can be explored through a proper description of exchange coupling. The magnetic exchange coupling constant (J) in systems with two magnetic sites is reliably estimated using Heisenberg-Dirac-van Vleck (HDVV) model through broken symmetry approach (BS) within a density functional theory (DFT) framework. However, in case of systems with multiple magnetic centers, exchange coupling constants, evaluated through state-of-the-art techniques, are often found to be inadequate to produce a correct fingerprint of the nature of magnetic interactions therein. This work suggests a new scheme to estimate exchange coupling constants in such systems. In this strategy, distribution of spins on magnetic sites in the ground state of systems with multiple magnetic centers is computed. On the basis of this spin mapping, exchange coupling constants between specific pairs are estimated through BS-DFT approach while keeping all other paramagnetic atoms magnetically inactive. Nonetheless, the effect of magnetically inert paramagnetic sites is already taken into account by the process of spin mapping, which is further justified through expressing the HDVV Hamiltonian in terms of spin density operators. We employ this technique to hypothetical benchmark systems, H(3)He(3) and H(4)He(4) followed by real molecules, cationic manganese trimer, 1,3,5-benzenetriyltris (N-tert-butyl nitroxide), and a pentanuclear manganese complex. Results are found to be concordant with the already established nature of magnetic interaction in these systems. This strategy is different from the most popular scheme to compute J in systems with multiple magnetic centers in the sense that it avoids the formation of a large matrix out of different spin configurations and thus provides a reliable and computationally economic way to address the magnetic interactions in non isotropic systems with multiple magnetic sites.