Magnetic Exchange Coupling Constants Research Articles

Unveiling the Low-Lying Spin States of [Fe3S4] Clusters via the Extended Broken-Symmetry Method.

Photosynthetic water splitting, when synergized with hydrogen production catalyzed by hydrogenases, emerges as a promising avenue for clean and renewable energy. However, theoretical calculations have faced challenges in elucidating the low-lying spin states of iron-sulfur clusters, which are integral components of hydrogenases. To address this challenge, we employ the Extended Broken-Symmetry method for the computation of the cubane-[Fe3S4] cluster within the [FeNi] hydrogenase enzyme. This approach rectifies the error caused by spin contamination, allowing us to obtain the magnetic exchange coupling constant and the energy level of the low-lying state. We find that the Extended Broken-Symmetry method provides more accurate results for differences in bond length and the magnetic coupling constant. This accuracy assists in reconstructing the low-spin ground state force and determining the geometric structure of the ground state. By utilizing the Extended Broken-Symmetry method, we further highlight the significance of the geometric arrangement of metal centers in the cluster's properties and gain deeper insights into the magnetic properties of transition metal iron-sulfur clusters at the reaction centers of hydrogenases. This research illuminates the untapped potential of hydrogenases and their promising role in the future of photosynthesis and sustainable energy production.

The performance and efficiency of twelve range-separated hybrid DFT functionals for calculation of the magnetic exchange coupling constants of di-nuclear first row transition metal complexes

The performance and efficiency of twelve range-separated hybrid functionals are compared with each other in calculating magnetic exchange coupling constant (J) data on eleven di-nuclear first-row transition metal complexes having di-copper (Cu) and di-vanadium (V) as their central atoms. The J values are then compared with the experimental findings. In addition to that we also computed the B3LYP results of these complexes. We compared them with the results obtained from range-separated functionals as well as with the experimental results to understand their performances in predicting the magnetic exchange coupling constant. When computing, we reoptimized all the structures of the complexes taken from the crystal data, and then the values of Js were determined. The performances are predicted in terms of four statistical error matrices, namely, the mean absolute error (MAE), mean fractional error (MFE), mean signed error (MSE), root mean square error (RMSE) in cm−1.

Antiaromatic Molecules as Magnetic Couplers: A Computational Quest.

In this study, we investigate a set of organic diradical structures in which two oxo-verdazyl radicals are selected as radical spin centers that are connected (coupled) via six coupler molecules (CM), resulting in various magnetic (ferromagnetic (FM) or antiferromagnetic (AFM)) characteristics, as reflected by their exchange coupling constants (J). We have designed 12 diradicals with 6-antiaromatic couplers coupled with bis-oxo-verdazyl diradicals with meta-meta (m-m) and para-meta (p-m) positional connectivities. The nature of the magnetic coupling (ferromagnetic, nonmagnetic, or antiferromagnetic) and the magnitude of the exchange constant J depend on the type of coupler, the connecting point between each radical center and CM, the degree of aromaticity of the coupler, and the length of the through-bond distance between radical centers. The computed magnetic exchange coupling constants J for these diradicals at the B3LYP/6-311++G(d,p) and MN12SX/6-311++G(d,p) levels of theory are large for many of these structures, indicating strong ferromagnetic coupling (with positive J values). In some cases, magnetic couplings are observed with J > 1000 cm-1 (B3LYP/6-311++G(d,p)) and strong antiferromagnetic coupling (with negative J values) with J < -1000 cm-1 (B3LYP/6-311++G(d,p)). Similarly, in some cases, magnetic couplings are observed with J > 289 cm-1 (MN12SX/6-311++G(d,p)) and strong antiferromagnetic coupling (with negative J values) with J < -568 cm-1 (MN12SX/6-311++G(d,p)). Furthermore, while numerous studies have reported that the degree of aromaticity of molecular couplers often favors strong ferromagnetic coupling, displaying the high-spin character of diradicals in their ground states, the couplers chosen in this study are characterized as antiaromatic or nonaromatic. The current investigation provides evidence that, remarkably, antiaromatic couplers are able to enhance stability by favoring electronic diradical structures with very strong ferromagnetic coupling when the length of the through-bond distance and connectivity pattern between radical centers are selected in such a way that the FM coupling is optimized. The findings in this study offer new strategies in the design of novel organic materials with interesting magnetic properties for practical applications.

Magnetic Exchange Coupling in Macrocyclic Cobalt (II) Complexes: The Influence of Bridging Ligands and Choice of the Computational Methodologies

AbstractExchange‐coupled spin states of cobalt complexes represent the key to understanding the challenging nature of the magnetism of cobalt dimer. In this study, we introduce a comprehensive investigation of the nature of magnetic super‐exchange coupling interactions between two metallic centers in a macro ligand cobalt dimer. More importantly, we provide a detailed comparison between a series of bridging ligands and study their role in the magnetic exchange coupling constant in cobalt dimer with tetraaza macrocycle ligand scaffold. By varying the types of bridging and terminal ligands, we explored the nature of magnetic coupling in 24 species of cobalt dimers, which allowed us to draw a magneto‐structure relationship and monitor the effect of bridging/terminal ligands on the overall magnetism. We employed different density functional theory (DFT) methodologies and complete active space self‐consistent field (CASSCF) in our investigation. The results show that there are comprehensible functional dependencies, and the choice of exchange‐correlation functional is critical for calculating the magnetic properties. Using the experimental values of the exchange coupling, we found that hybrid functionals with 10–20 % Hartree‐Fock exchange integrals give acceptable accuracy. Furthermore, we adjusted the percentage of HF integrals to estimate the optimum value required to be included in the hybrid functionals. Finally, we used CASSCF to gain deeper understanding of the magnetic coupling for the valence magnetic electrons and to achieve the true ground state wavefunction, which is not feasible with conventional DFT calculations. However, the CASSCF calculations poorly underestimate the magnetic coupling, which can be significantly improved by including the dynamic correlations, as implemented in the NEVPT2 methodology.

Synthesis, structure, thermal and magnetic properties of new tetranuclear copper(II) complex supported by multidentate ligand and glutarate functionality

A new tetranuclear Cu(II) complex, [Cu(H2O)4][Cu4(cpdp)2(glut)]Cl2·6H2O (1) was successfully constructed by utilization of carboxylate-based multidentate ligand N,N'-bis[2-carboxybenzomethyl]-N,N'-bis[2-pyridylmethyl]-1,3-diaminopropan-2-ol (H3cpdp), in combination with glutarate (glut) and Cu(II) ions, and characterized systematically. Originally, the symmetrical flexible ligand cpdp3− is capable to bind two Cu(II) ions, leaving behind accessible binding sites for further coordination of exogenous glutarate anion which facilitates the assembly of two ligand-bound Cu(II) pairs. In MeOH/H2O, the reaction of CuCl2·2H2O with H3cpdp and sodium glutarate in the presence of NaOH results in the formation of 1. Complex 1 was characterized by different analytical techniques, including single crystal X-ray structure investigation. Analysis of single crystal X-ray structure shows that 1 is a self-assembled tetranuclear copper complex in which two dinuclear [Cu2(cpdp)]+ species are exclusively bridged by one glutarate functionality through μ4:η1:η1:η1:η1 manner, acting as a coligand. Thermoanalytical methods (TGA/DTA) were used to examine the thermal stability and it was observed that 1 is stable up to ∼190°C. Variable temperature (2-300 K) magnetic susceptibility studies show the weak antiferromagnetic interactions among the copper centers with the value of magnetic exchange coupling constant (J) of -0.5 cm−1.

Magnetic ground state of NiCl2/Br2 monolayers encapsulated in UiO-67 MOF, effect of partially filled pores: Ab-initio and Monte Carlo theoretical study

Ab initio calculations are used to study the properties of two dimensional (2D) Transition Metal Halides (TMH, TM=Ni; H = Cl, Br) encapsulated inside a derivative of UiO-67 Metal-Organic Frameworks (MOF). Two monolayers of TMHs (NiCl2 and NiBr2) were isolated from the experimental Crystallographic Information File (CIF) and used in this study. We found that the structure of both monolayers within the MOF (TMH@MOF) have very similar geometries compared to their perfect 2D sheets hypothetically derived from their bulk structures (TMH@bulk) with small distortions in the Metal–Metal (M–M) and Metal–Halide (M–H) bonds. NiCl2 and NiBr2 sheets have a Ferromagnetic (FM) ground state with large intrinsic magnetic moments localized at each metal site. The predicted FM ground state is also confirmed in the magnetic exchange coupling constant (J) calculations between M centers which are found all positive, but non isotropic within each sheet. Weaker interactions with J ≈0.2 meV are found among NN centers in the outer ring compared to J ≈0.85 meV in the inner rings of both monolayers. The calculated Jś are inserted in a Monte Carlo (MC) code to afford Curie temperatures of 27 K and 22 K for NiCl2/Br2 monolayers respectively. Finally, the experimentally collected structures at low metal loading were found to have distinct magnetic properties compared to the completely filled sheets.

Combined first principles and Heisenberg model studies of ferrimagnetic Tri-transition quaternary perovskites CaCu3B2Re2O12 (B = Mn, Fe, Co, and Ni)

In this study, density functional theory (DFT) showed that the electronic band profiles of CaCu3B2Re2O12 (B = Mn, Fe, Co, and Ni) indicate their half-metallic character. The optimized magnetic energy curves in different magnetic phases demonstrated the type-I ferrimagnetic order of all the compounds investigated in this study. The magnetic exchange coupling constants were calculated between the Cu–B, B–Re, and Cu–Re site spins using the Heisenberg model. These interactions generate strong long range Cu(↑)B(↑)Re(↓) order through a super-exchange mechanism. In these perovskites, the anti-parallel moments of Re with B and Cu reduce the net magnetic moments and they are responsible for the ferrimagnetism. The Cu and B 3d-electrons are localized and responsible for the magnetism, and the Re 5d-electrons are delocalized and responsible for the metallic nature. Magnetic susceptibility analysis verified the results estimated using DFT and the Heisenberg model. Due to the 100% spin polarization around the Fermi level, high Curie temperature TC and ferrimagnetism are expected, thereby making these materials suitable for spintronic applications.

Theoretical Simulation on Regulating the Magnetic Coupling Properties of Diradical Artificial Bases.

In this work, we computationally designed a series of diradical molecules with obvious magnetic coupling properties based on newly synthesized artificial bases, 6-amino-3-(1'-β-d-2'-deoxyribofuranosyl)-5-nitro-1H-pyridin-2-one (Z), 2-amino-8-(1'-β-d-2'-deoxyribofuranosyl)-imidazo-[1,2a]-1,3,5-triazin-[8H]-4-one (P), 6-amino-9[(1'-β-d-2'-deoxyribofuranosyl)-4-hydroxy-5-(hydroxymethyl)-oxolan-2-yl]-1H-purin-2-one (B), and found two methods (base pairing and nitro group rotation) of regulating the magnetic magnitude, making them become magnetic switches with promising prospects. On one hand, the modified diradical artificial base P3 possesses an excellent magnetic exchange coupling constant due to its spin density concentration on a unique spin polarization path. Because of the serious mismatch between the singly occupied molecular orbital (SOMO) and the lowest unoccupied molecular orbital (LUMO) of Z-P3 base pairing, the magnetic coupling property of the Z-P3 base pair disappears, which indicates that the base pairing can be used as an effective means to regulate the molecular magnetic coupling properties. On the other hand, the investigation shows that the rotation of the nitro group on Z has an influence on the energy gaps between the closed-shell (CS) singlet and triplet (T) states of the base pairs formed by Z-analogues and thereby the expression of magnetic coupling properties. This work can help to develop the modification strategy of the diradical base and provide theoretical guidance for the design and synthesis of magnetic coupling materials with controllable magnetic coupling properties.

Synthesis, characterization, DFT calculations and bromoperoxidase activity of binuclear oxidovanadium complexes containing vitamin B6

Two binucelar oxidovanadium complexes, [(VO2)2(µ-Hpydn)2] (1) and [(VO)2(µ-pydn)2(bpy)2]·5H2O (2), where pydn = pyridoxine and bpy = 2,2’-bipyridine, were synthesized and characterized by elemental analysis and infrared (IR), electron paramagnetic resonance (EPR), and electronic (UV-vis) spectroscopies. The structure of 2 was determined by single-crystal X-ray diffraction analysis. It is comprised of two distorted octahedral oxidovanadium(IV) centers with a terminal bpy ligand and bridged by the methoxido group of the pydn ligands, forming the {VIVO(µ-OR)2}2+ core with anti-orthogonal configuration. Density functional theory (DFT) calculations at the B3LYP/LANL2DZ level were used to obtain the optimized geometries and to study the electronic structure of 1 and 2. For 2, EPR analysis in the solid state, magnetic susceptibility measurements and the theoretical magnetic exchange coupling constant (J) of 20.1 cm−1 indicate a weak ferromagnetic coupling. 51V NMR and EPR spectroscopies suggest partial breakage of both binuclear structures in solution. Both complexes act as pre-catalysts for the bromination of phenol red to phenol blue in the presence of KBr, H2O2 and perchloric acid.

Direct and inverse magnetocaloric effects in FeRh alloy

There are two types of magnetocaloric effects that are the so-called direct and inverse effects originating from ferromagnetic–paramagnetic (FM–PM) and antiferromagnetic–ferromagnetic (AFM–FM) phase transitions, respectively. Here, the magnetocaloric effects of FeRh alloy, which exhibit both the direct and inverse effects, have been studied by combining first-principles calculations and Monte Carlo simulations. The magnetic exchange coupling constants in the AFM and FM phases are evaluated by first-principles calculations based on the Liechtenstein formula. The Monte Carlo calculations considering the two-phase mixtures of AFM and FM well reproduce the experimental magnetization curves at zero external magnetic field. It is also shown that the isothermal magnetic entropy changes near the AFM–FM transition temperature under magnetic fields are successfully reproduced based on the Maxwell relation. The entropy changes in a wide range of the magnetic fields near the AFM–FM and FM–PM transition temperatures are investigated and the direct and inverse magnetocaloric effects of FeRh are discussed. The giant relative cooling power of FeRh alloy is achieved due to the large saturation magnetizations and the first-order AFM–FM phase transition.

Study of Self-Interaction Errors in Density Functional Calculations of Magnetic Exchange Coupling Constants Using Three Self-Interaction Correction Methods.

We examine the role of self-interaction error (SIE) removal on the evaluation of magnetic exchange coupling constants. In particular, we analyze the effect of scaling down the self-interaction correction (SIC) for three nonempirical density functional approximations (DFAs) namely, the local spin density approximation, the Perdew-Burke-Ernzerhof generalized gradient approximation, and the recent SCAN family of meta-GGA functionals. To this end, we employ three one-electron SIC methods: Perdew-Zunger SIC [Perdew, J. P.; Zunger, A. Phys. Rev. B, 1981, 23, 5048.], the orbitalwise scaled SIC method [Vydrov, O. A. et al. J. Chem. Phys. 2006, 124, 094108.], and the recent local scaling method [Zope, R. R. et al. J. Chem. Phys. 2019, 151, 214108.]. We compute the magnetic exchange coupling constants using the spin projection and nonprojection approaches for sets of molecules composed of dinuclear and polynuclear H···He models, organic radical molecules, and chlorocuprate and compare these results against accurate theories and experiment. Our results show that for the systems that mainly consist of single-electron regions, PZSIC performs well, but for more complex organic systems and the chlorocuprates, an overcorrecting tendency of PZSIC combined with the DFAs utilized in this work is more pronounced, and in such cases, LSIC with kinetic energy density ratio performs better than PZSIC. Analysis of the results in terms of SIC corrections to the density and to the total energy shows that both density and energy correction are required to obtain an improved prediction of magnetic exchange couplings.

New anti-ferromagnetic tri-transition quaternary perovskites for magnetic cloaking and spintronic applications

Magnetism in new tri-transition A-site ordered quaternary perovskites ACu3V4O12 (A = Mn and Cu) are studied using generalized gradient approximation with Hubbard potential (GGA + U) in the domain of density functional theory. The effective Heisenberg model estimates the magnetic exchange coupling constants (J1, J2 and J3) between the spins of Mn and Cu sites. The exchange constants J1 and J3 in MnCu3V4O12 and Cu(1)Cu3(2)V4O12 reveal their long rang interactions through super exchange mechanism. The ground state magnetic order is explained from the optimized energy curves; which reveal the G-type anti-ferromagnetic (AFM) order of MnCu3V4O12 and A-type AFM order of Cu(1)Cu3(2)V4O12. Heisenberg model and magnetic susceptibility are in well agreement in the estimation of Neel temperature 15.1/50 and 15.6/25 K respectively. There is a strong correlation between the magnetism of the A-site atoms (Mn, Cu(1), and Cu(2)), as well as the metallic character of the B-site atoms (V, as well as the tiny contribution of A-site Cu(2) and Mn atoms). Due to AFM metallic nature it is expected that these compounds could be used in spintronic technology and magnetic cloaking devices.

Magnetic Modulation in Heteroallene and Heterocumulene Based tert‐butyl Nitroxide Diradicals: Spin Delocalization and Conformation Play Crucial Roles

We have theoretically investigated the magnetic properties of heteroallene (>C=C=X-) and heterocumulene (>C=C=C=X-) based tert-butyl nitroxide diradicals (X is P/As). Calculation of magnetic exchange coupling constant (J) shows ferromagnetic interaction in heteroallene based diradicals. Whereas, in heterocumulene based diradicals, tuning of J value from antiferro- to ferro-magnetic state is observed from Z- to E- isomer. Delocalization of spin density from radical site to the coupler (in planar arrangement) is observed in spin distribution analysis which is also advocated by molecular orbital analysis. The typical feature of tert-butyl nitroxide radical creates spin delocalization along with spin polarization within the coupler. The J values of all the diradicals strongly depend on the dihedral angle between radical center and coupler. Magneto-structural correlation shows that the change in dihedral angle tunes the magnetic property for both the Z- and E- isomers of heterocumulenes depending on the spin accumulation on two nearby magnetic centers. The extent of spin delocalization and conformation of spin centers on the molecular axis are important for the different J values observed in our designed systems.

Pragmatic Improvement of Magnetic Exchange Couplings from Subsystem Density-Functional Theory through Orthogonalization of Subsystem Orbitals

We explore a pragmatic way of correcting magnetic exchange coupling constants from subsystem density-functional theory (sDFT). Our previous work [ Faraday Discuss. 2020, 224, 201−226] showed that s...

Direct and Inverse Magnetocaloric Effects in FeRh Alloy: A Theoretical Study

There are two types of magnetocaloric effects that are the so-called direct and inverse effects originating from ferromagnetic-paramagnetic (FM-PM) and antiferromagnetic--ferromagnetic (AFM-FM) phase transitions, respectively. Here, the magnetocaloric effects of FeRh alloy, which exhibit both the direct and inverse effects, have been studied by combining first-principles calculations and Monte-Carlo simulations. The magnetic exchange coupling constants in the AFM and FM phases are evaluated by first-principles calculations based on the Liechtenstein formula. The Monte-Carlo calculations considering the two-phase mixtures of AFM and FM well reproduce the experimental magnetization curves at zero external magnetic field. It is also shown that the isothermal magnetic entropy changes near the AFM-FM transition temperature under magnetic fields are successfully reproduced based on the Maxwell relation. The entropy changes in a wide range of the magnetic fields near the AFM-FM and FM-PM transition temperatures are investigated and the direct and inverse magnetocaloric effects of FeRh are discussed. The giant relative cooling power of FeRh alloy is achieved due to the large saturation magnetizations and the first-order AFM-FM phase transition.

Substituent Effects on Exchange Coupling and Magnetic Relaxation in 2,2'-Bipyrimidine Radical-Bridged Dilanthanide Complexes.

Systematic analysis of related compounds is crucial to the design of single-molecule magnets with improved properties, yet such studies on multinuclear lanthanide complexes with strong magnetic coupling remain rare. Herein, we present the synthesis and magnetic characterization of the series of radical-bridged dilanthanide complex salts [(Cp*2Ln)2(μ-5,5'-R2bpym)](BPh4) (Ln = Gd, Dy; R = NMe2 (1), OEt (2), Me (3), F (4); bpym = 2,2'-bipyrimidine). Modification of the substituent on the bridging 5,5'-R2bpym radical anion allows the magnetic exchange coupling constant, JGd-rad, for the gadolinium compounds in this series to be tuned over a range from -2.7 cm-1 (1) to -11.1 cm-1 (4), with electron-withdrawing or -donating substituents increasing or decreasing the strength of exchange coupling, respectively. Modulation of the exchange coupling interaction has a significant impact on the magnetic relaxation dynamics of the single-molecule magnets 1-Dy through 4-Dy, where stronger JGd-rad for the corresponding Gd3+ compounds is associated with larger thermal barriers to magnetic relaxation (Ueff), open magnetic hysteresis at higher temperatures, and slower magnetic relaxation rates for through-barrier processes. Further, we derive an empirical linear correlation between the experimental Ueff values for 1-Dy through 4-Dy and the magnitude of JGd-rad for the corresponding gadolinium derivatives that provides insight into the electronic structure of these complexes. This simple model applies to other organic radical-bridged dysprosium complexes in the literature, and it establishes clear design criteria for increasing magnetic operating temperatures in radical-bridged molecules.

Magnetocaloric effect in MnCoGe alloys studied by first-principles calculations and Monte-Carlo simulation

The magnetocaloric effect in orthorhombic MnCoGe1−xCux (x = 0.0–0.35) alloys are investigated by combining density functional theory (DFT) and Monte-Carlo simulation. The long-range interactions of the magnetic exchange coupling constants evaluated by the DFT calculations are considered for the Monte-Carlo simulation. The magnetic phase transition temperature is estimated by the divergence of the specific heat, and the isothermal entropy change is computed by integrating the isothermal magnetization curves with the Maxwell relation. The magnetic exchange coupling constants of the Mn-Mn pairs is decreased significantly with increasing of the concentration of Cu from 0.0 to 0.35, resulting in the rapid decrease of the Curie temperature from 618 K to 28 K. Not only the Curie temperature of the MnCoGe alloy is controllable by changing the concentration of Cu at Ge site, but also the magnetocaloric properties such as isothermal magnetic entropy change and relative cooling power are strongly dependent on the concentration of Cu.

Tuning structural-transformation temperature toward giant magnetocaloric effect in MnCoGe alloy: A theoretical study

We propose a new model and scheme to consider the effect of structural transformation on magnetocaloric properties of Mn1-xCuxCoGe. The magnetic exchange coupling constants are estimated from first-principles calculations based on density functional theory. The magnetic phase diagram is semi-quantitatively reproduced by using mean-field approximation. The giant isothermal magnetic entropy change with the magnetostructural coupling of Mn0.89Cu0.11CoGe alloy is well reproduced by using the modified Potts model. The enhancement of magnetostructural coupling on the isothermal magnetic entropy change strongly depends on the condition of the magnetic phase transition temperature of orthorhombic and hexagonal phases.

Theoretical prediction of magnetic exchange coupling constants from broken-symmetry coupled cluster calculations.

Exchange coupling constants (J) are fundamental to the understanding of spin spectra of magnetic systems. Here, we investigate the broken-symmetry (BS) approaches of Noodleman and Yamaguchi in conjunction with coupled cluster (CC) methods to obtain exchange couplings. J values calculated from CC in this fashion converge smoothly toward the full configuration interaction result with increasing level of CC excitation. We compare this BS-CC scheme to the complementary equation-of-motion CC approach on a selection of bridged molecular cases and give results from a few other methodologies for context.

Coupling Constants, High Spin, and Broken Symmetry States of Organic Radicals: an Assessment of the Molecules-in-Molecules Fragmentation-Based Method.

We extend the application of our multilayer molecules-in-molecules (MIM) fragmentation-based method to the study of open-shell systems, particularly organic radicals. A test set of organic mono-, di- and polyradicals with a wide range in size, containing up to 360 atoms, was investigated. Total energies computed with MIM using density functional theory (DFT) were compared with full, unfragmented energies to assess the performance of MIM and to develop a systematic protocol for the treatment of large radical systems. More specifically, a two-layer (MIM2) model with a fragmentation scheme along the backbone involving covalently bonded dimers, trimers, or tetramers was considered, with DFT at a smaller basis set serving as the low level of theory. The MIM method was evaluated on the high-spin state and several possible broken-symmetry (BS) states for di- and polyradicals. When relevant spin-spin interactions were considered, the errors in total energies were less than 1 kcal mol-1. In addition, the applicability of MIM2 was extended to predict the intersite magnetic exchange coupling constants (J), which were compared with reference values. Further, since the energy levels derived from Hamiltonian diagonalization are physically more meaningful, the calculated J values estimated from the BS-DFT methodology were used to obtain the lower spin state energies of the polyradicals. The difference in calculated total energies of the lower spin state between full and MIM2 lie within 1 kcal mol-1 in the majority of these cases. Our rigorous, quantum chemical study demonstrates that MIM can be successfully applied to the study of large organic radicals reliably and accurately within the framework of BS-DFT.