Broken symmetry DFT calculations of exchange coupling constants for manganese–porphyrin quasi-one-dimensional molecular magnets

Abstract

We report the results of broken symmetry density functional theory (BS-DFT) calculations providing the exchange coupling constants for two quasi-one-dimensional manganese–porphyrin compounds, [MnOEP][HCBD] and [MnTtBuPP][HCBD] (OEP = octaethylporphyrinato, TtBuPP = meso-tetrakis-(4′-tert-butylphenyl)porphinato, HCBD = hexa-cyanobutadiene). The different magnetic behaviour of these materials is due mainly to the distinct binding modes of the cyanocarbon unit. We compare and contrast the results of BS-DFT calculations for magnetic dinuclears, which properly model the actual molecular magnets, to determine the geometry dependence of the exchange interaction. The exchange coupling constants resulting from BS-DFT calculations vary strongly with the functional used, hybrid functionals such as B3LYP leading to results that better correlate with the constants determined experimentally. Structure-properties correlations reveal the determinant role of the Mn–(N≡C)TCNE bond angle on the ferrimagnetic coupling between the S 1 = 2 spin located on the MnIII–porphyrin donor and the S 2 = 1/2 spin positioned on the cyanocarbon acceptor. Based on a phenomenological model providing the geometry dependence of the exchange coupling constants, we fitted the results of the DFT calculations and obtained parameters describing the ferromagnetic and the antiferromagnetic parts of the superexchange interaction. The large differences between the magnetic properties of the two Mn–HCBD systems are explained based on the correlation between the exchange coupling constant and the overlap between the Mn(III) d and the HCBD π* orbitals and on the torsion angle of the butadiene backbone, which affects dramatically the nature of the π* orbital in the case of the nonplanar HCBD.