Organic Molecular Magnets

Abstract:
Organic diradical dications, due to reduced intermolecular interactions, exhibit a greater tendency to adopt high spin states in the solid phase compared to their neutral diradical counterparts. This characteristic makes them promising candidates for applications involving organic electronics. We present a theoretical study of a recently synthesized sulfur-based diradical dication, a unique system exhibiting a robust triplet ground state. Using a number of density functional theory (DFT)-based methods (e.g., standard broken-symmetry DFT, constrained DFT, spin-flip TDDFT) and wave function-based multireference CASSCF+NEVPT2 methods, we investigate its magnetic properties and explore the influence of chalcogen substitution on magnetic exchange coupling. An active space scanning method was adopted to overcome the difficulties in choosing the correct active space for multireference calculation. Our findings highlight the critical role of multireference methods in accurately capturing the magnetic behavior of highly π-conjugated systems. The study reveals a surprising variation in magnetic properties among sulfur, selenium, and tellurium-based diradical dications despite being elements of the same group. These results offer valuable insights into the design and tuning of magnetic properties in organic diradical dications.

Abstract:

The molecular properties of conjugated spacers, such as the π-conjugation, aromaticity, length of the couplers, etc., that couple two localized spin-centers influence the intramolecular magnetic exchange interactions (2J) mediated through them. In recent years, the development and synthesis of highly conjugated polyaromatic hydrocarbons (PAHs) in the context of graphene nano-ribbon carbonaceous materials, prompted us to investigate their role as magnetic couplers. Apart from the highly conjugated nature of various PAHs, the intriguing open-shell characteristic dominates the electronic structures and properties of the PAHs. The extent of the open-shell behaviors of the PAHs could be quantified with the radicaloid character (y) applying density functional theory (DFT) calculations. In this work, we observed a strong correlation between the radicaloid character of the spacer and the strength of the magnetic exchange interactions mediated through it. The larger the radicaloid character the stronger the magnetic exchange interactions within the fixed length of the couplers.

Abstract:
In the quest of obtaining organic molecular magnets based on stable diradicals, we have tuned the inherent zwitterionic ground state of tetraphenylhexaazaanthracene (TPHA), a molecule containing two Blatter's moieties, by adopting two different strategies. In the first strategy, we have increased the length of the coupler between the two radical moieties and observed a transition from the zwitterionic ground state to the diradicalized state. With a larger coupler, ferromagnetic interactions are realized based on density functional theory (DFT) and wave-function theory (WFT) based complete active space self-consistent field (CASSCF)-N-electron valence state perturbation theory (NEVPT2) methods. An analysis based on the extent of spin contamination, diradical character, CASSCF orbital occupation number, Head-Gordon's index, HOMO–LUMO and SOMOs energy gaps is demonstrated that marks the transition of the ground state in these systems. In another approach, we systematically explore the effect of push–pull substitution on the way to obtain molecules based on a TPHA skeleton with diradicaloid state and, in some cases, even a triplet ground state.

Abstract:
The electronic and magnetic properties of polyacenes become quite fascinating as the number of linearly conjugated benzene rings increases. Higher-order conjugated polyacenes develop radicaloid characters due to the transition of electronic structures from closed-shell to the open-shell system. Here we have investigated the role of such polyacenes as the magnetic coupler when placed between the two spin-sources based on nitroxy radicals. To do so, the magnetic exchange interactions (2J) are computed employing broken-symmetry (BS) approach within the density functional theory (DFT). In this approach, various genre of exchange- correlation (XC) functionals such as generalized gradient approximation (GGA), meta-GGA, hybrid functional, constrained spin density (i.e. CDFT) and on-site Coulomb correlation corrected GGA + U functionals are adopted. All DFT based calculations estimate an exponential increase in 2J values with the length of the couplers. This observation has been understood in terms of increase in number of near-degenerate or quasi-degenerate molecular orbitals (MOs), reduction of HOMO-LUMO energy gap and descend of low-lying excited states as the number of fused benzene rings are increased.

Abstract:
The recent accomplishments in obtaining strong ferromagnetic exchange interactions in organic diradicals have made the field quite fascinating and even more promising toward its technological applications. In this context, herein, we report a unique combination of remarkably strong ferromagnetic exchange interactions coupled with molecular rigidity, utilizing superstable Blatter’s radical as a spin source. The planar analogues of the parent Blatter’s radical obtained by annulation with a chalcogen coupled to nitronyl nitroxide (NN) are investigated using density functional theory along with the wave function-based multiconfigurational self-consistent field methods, for example, complete active space self-consistent field (CASSCF)–N-electron valence state perturbation theory (NEVPT2). The calculations reveal phenomenal modulation in exchange couplings upon annulation such that remarkably strong ferromagnetic interactions are realized especially for a certain class of the Blatter-NN diradicals. The modulation of spin–spin interactions is rationalized by variation in spin density distribution and molecular torsional angles. We demonstrate that annulation in OMMs opens an additional coupling pathway via auxiliary X-atom acting as the atomic relay center which strongly manipulates the magnitude of exchange couplings.

Abstract:
With ongoing efforts to synthesize super-stable Blatter’s diradicals having strong ferromagnetic exchange interactions, all the 10 possible isomers of di-Blatter diradical coupled through the fused benzene rings are investigated. A variety of electronic structure theory such as broken-symmetry methods in density functional theory (DFT), spin-constraint DFT (CDFT), and wave function-based multi-configurational methods, e.g., CASSCF/NEVPT2 are applied to compute the magnetic exchange interactions. Surprisingly, anti-ferromagnetic interactions are revealed for all the stable isomers of di-Blatter diradicals. Indeed, it is commensurate with the experimental observations for the only available synthesized isomer. However, the other nine isomeric diradicals in the series are yet to be synthesized. Despite a good match between theory and experiment, the anti-ferromagnetic exchange interactions could not be explained based on the spin alternation rule due to unique spin distributions in the triazinyl ring. Thus, we propose the zonal spin-alternation rule, which explains the observed ground spin-state for the conjugated di-Blatter diradicals quite accurately. Further, the fractional spin-moment localization on the N-atoms activates multiple exchange pathways and the dominating exchange interactions render anti-ferromagnetic interactions in the conjugated isomers. The study further reveals that, due to strong steric hindrance in certain coupled isomers, the exchange interaction switches from anti-ferromagnetic to weak ferromagnetic interactions with the cost of stabilization energy of the radicals. Thus, it questions the possibility of synthesizing ferromagnetic di-Blatter diradicals.

Abstract:
The stable organic diradicals that exhibit strong intramolecular ferromagnetic exchange interactions are suitable building blocks for organic magnetic materials (OMMs). Based on the ab initio calculations, here, we report the electronic and magnetic properties of 1,2,4-benzotriazinyl-based mono- and diradicals (known as Blatter’s radicals). The quantum mechanical calculations based on the density functional theory (DFT) reveal the merostability of the superstable Blatter’s radicals. The stability could further be enhanced by tuning the spin densities on the radical centers via the extended π-conjugation. The magnetic exchange interactions (2J) have been investigated for Blatter’s radical coupled to the nitronyl nitroxide radical (i.e., Bl-NN) as the prototypical system that has recently been synthesized by Rajca et al.. The broken-symmetry (BS) approach within the standard DFT and constraint spin-density DFT (CDFT) methods are applied to compute the exchange interactions, while for wave function-based multireference methods, the spin symmetry-adopted (e.g., CASSCF/NEVPT2) approach is applied. It is observed that the CBS-DFT provides much better 2J values as compared to the standard BS-DFT. The multireference calculations based on the minimal active space [i.e., CAS(2,2)] incorporating the delocalized magnetic orbitals provide quite reliable exchange interactions. After validating the applied computational methods, a number of ferromagnetically coupled hybrid diradicals are modeled by coupling Blatter’s monoradical with various known stable organic radicals. A few of them turned out to be quite promising candidates for the building block of OMMs.

Abstract:
Switching of the magnetic exchange coupling from ferro- to antiferromagnetic or vice versa in a single molecule is an appealing but rarely occurring phenomenon in molecular magnetism. Here, we report this for an unprecedented pure organic system, computationally designed by tailoring a conformationally restricted, known nitroxide-diradical (Rajca et al. J. Am. Chem. Soc.2007, 129, 10159). This ferro- to antiferromagnetic coupling switching of an “m-phenylene” based diradical is governed by a stereoelectronic effect and controlled by a redox-driven chemical reaction.

Abstract:
The spin-polarized electronic structure of iron octaethylporphyrin (FeOEP) molecules adsorbed on a pristine and on a $c$($2\times 2$) oxygen-reconstructed Co(100) surface has been analyzed by means of spin-polarized photoemission spectroscopy (SPPES) and first-principles density functional theory with the on-site Coulomb repulsion $U$ term ($\mathrm{DFT}+U$) calculations with and without Van der Waals corrections. The aim is to examine the magnetic exchange mechanism between the FeOEP molecules and the Co(100) substrate in the presence or absence of the oxygen mediator. The results demonstrate that the magnetic coupling from the ferromagnetic substrate to the adsorbed FeOEP molecules is ferromagnetic, whereas, the coupling is antiferromagnetic for the FeOEP on the $c$($2\times 2$)O/Co(100) system. Spin-resolved partial densities of states extracted from ab initio $\mathrm{DFT}+U$ modeling are in fairly good comparison with the electronic spectral densities seen in angle-integrated SPPES energy dispersion curves for submonolayer coverages of FeOEP. Through combined analysis of these spectra and theoretical results, we determine that hybridization of 2$p$ orbitals of N and O with Co 3$d$ orbitals facilitates indirect magnetic exchange interactions between Fe and Co, whereas, a direct Fe-Co interaction involving the Fe $d_{z^2}$ orbital is also found for FeOEP on Co. It is observed through SPPES that the spin polarization of the photoemission-visible molecular overlayers decreases to zero as coverage is increased beyond the submonolayer regime, indicating that only interfacial magnetic coupling is at work. Microspot low-energy electron diffraction and low-energy electron microscopy were performed to characterize the physical order of the molecular coverage, revealing that FeOEP structural domains are orders of magnitude greater in size on $c$($2\times 2$)O/Co(100) than on clean Co(100), which coincides with reduced scattering from the disorder and sharper features seen in SPPES.

Abstract:

Abstract:
The role of noncovalent ion−π interactions in controlling the intramolecular magnetic exchange interaction in 1,3-phenylene-based bis(aminoxyl) diradical has been investigated computationally through deploying an external ion in the vicinity of the π-cloud of the phenylene coupler. Using spin-polarized hybrid density functional theory-based calculations, we observe that the anions drastically enhance the magnetic exchange interaction for distances below the equilibrium distance. The phenomenon could be understood by two simultaneously occurring effects, which influence the intramolecular magnetic exchange interaction. The first one is the enhancement of the paratropic current density on the aryl couplers due to a small amount of charge transfer. The other one is the attainment of magnetization density on the anionic species due to such charge transfer, favorably altering the magnetic exchange pathway. The achieved understanding provides prospects of a completely new strategy of enhancing the intramolecular ferromagnetic coupling through the assistance of external ionic species inserted in molecular crystals.

Abstract:
We apply the density functional theory + U (DFT+U) and unrestricted hybrid functional DFT-UB3LYP methods to study the electronic structure and magnetic properties of two prototypical iron porphines: iron(III) porphine chloride (FePCl) and difluoro iron(III−IV) porphine. Plain DFT within the generalized gradient approximation (GGA) implementation fails in describing the correct high-spin ground state of these porphine molecules, whereas DFT+U and UB3LYP provide an improved description. For a range of U values (4−8 eV), we compare the results of the DFT+U approach to those obtained previously with the hybrid functional (B3LYP) and with the CASPT2 approach. The DFT+U and UB3LYP methods successfully predict the molecular high spin (S = 5/2) ground state of FePCl, and also provide the nontrivial S = 3 high spin ground state for FePF₂. For the latter six-coordinated Fe porphine, our DFT+U calculations show that the S = 2, S = 5/2, and S = 3 states are energetically very close together (differences of 30 meV). Nonetheless, S = 3 is obtained as the ground state of the whole molecule, in accordance with the spin expected from the electron count. Our DFT+U calculations show furthermore that the Fe 3d occupancy is similar for FePF₂ and FePCl, i.e., DFT+U does not support Fe(IV) for FePF₂, but rather an Fe(III) porphyrin π-cation radical species, with an Fe high spin S_Fe = 5/2, and an additional S = 1/2 stemming from spin density distributed over the porphine ring. This observation is also supported by our UB3LYP calculations.

Abstract:
We have investigated the effect of nitroxide radical-water hydrogen bonding (NO(*)...H(2)O) on the intramolecular magnetic exchange interaction (J) for biologically relevant aminoxyl diradicals. We adopt a combination of broken-symmetry density functional theory and the quantum mechanics/molecular mechanics (QM/MM) approach. We find that the presence of hydrogen bonding reorients the radical spin density on -NO(*). This phenomenon reduces the effective distance between the two interacting localized spin centers that eventually increases the intramolecular magnetic exchange interaction. We have also investigated the functional variation of the magnetic exchange interaction, using various GGA (BLYP, PBE, HCTH407), meta-GGA (TPSS, VXSC), and hybrid (O3LYP, B3LYP, B3P86, B3PW91, and PBE0) functionals.

Abstract:
We predict the intramolecular magnetic exchange coupling constant (J) for eleven nitronyl nitroxide diradicals (NN) with different linear and angular polyacene couplers from broken-symmetry density functional treatment. For the linear acene couplers, J initially decreases with increase in the number of fused rings. But from anthracene coupler onward, the J value increases with the number of benzenoid rings due to an increasing diradical character of the coupler moiety. The J value for the diradical with a fused bent coupler is always found to be smaller than that for a diradical with a linear coupler of the same size. The nuclear independent chemical shift (NICS) is calculated, and it is observed that the average of the NICS values per benzenoid ring in the diradical is less than that in the normal polyacene molecule. An empirical formula for the magnetic exchange coupling constant of a NN diradical with an aromatic spacer is obtained by combining the Wiberg bond order (BO), the angle of twist (φ) of the monoradical (NN) plane from the plane of the coupler, and the NICS values. A comparison of the formula with the computed values reveals that, from tetracene onward, the diradical nature of the linear acene couplers becomes prominent thereby leading to an increase in the ferromagnetic coupling constant. Isotropic hyperfine coupling constants are calculated by using a polarized continuum model for the diradicals in different solvents and in vacuum.

Abstract:
We predict the photoswitching magnetic properties of four substituted dihydropyrenes from density functional broken-symmetry calculations. The magnetic exchange coupling constants differ up to 9.44 cm^-1. The intramolecular exchange interactions are ferromagnetic in nature. The calculated coupling constants are much larger than those reported earlier for photomagnetic organic molecules.

Abstract:
We have investigated the magnetic properties of four recently synthesized stable TMM-type nitroxide diradicals. Four new diradicals are proposed by tailoring one of the species in such a way that both conjugation and planarity increase. As a remarkable consequence, the intramolecular ferromagnetic exchange interaction was found to be quite high in the proposed radicals. The calculated coupling constants were in the range of +102 to +140 cm^-1. The MO and spin density analysis are provided to interpret the exchange interactions. We observed the existence of intramolecular π−π-interactions for the species 2. This slightly increased the J value by shortening the length of the spacer between the two spin sources.

Abstract:
A series of nitronyl nitroxide (NN) diradicals with linear conjugated couplers and another series with aromatic couplers have been investigated by the broken-symmetry (BS) DFT approach. The overlap integral between the magnetically active orbitals in the BS state has been explicitly computed and used for the evaluation of the magnetic exchange coupling constant (J). The calculated J values are in very good agreement with the observed values in the literature. The magnitude of J depends on the length of the coupler as well as the conformation of the radical units. The aromaticity of the spacer decreases the strength of the exchange coupling constant. The SOMO−SOMO energy splitting analysis, where SOMO stands for the singly occupied molecular orbital, and the calculation of electron paramagnetic resonance (EPR) parameters have also been carried out. The computed hyperfine coupling constants support the intramolecular magnetic interactions. The nature of magnetic exchange coupling constant can also be predicted from the shape of the SOMOs as well as the spin alternation rule in the unrestricted Hartree−Fock (UHF) treatment. It is found that π-conjugation along with the spin-polarization plays the major role in controlling the magnitude and sign of the coupling constant.

Abstract:
The magnetic properties of the monoradicals 2-(4-phenyl acetylene)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidozolyl-oxyl (1) and 2-(4-phenyl acetylene)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazole-1-oxyl-3-oxide (2) and the diradicals 2,2‘-(1,2-ethynediyldi-4,1-phenylene)bis[4,4,5,5-tetramethyl-4,5-dihydro-1H-imidozolyl-oxyl] (3), 2,2‘-(1,2-ethynediyldi-4,1 3,1-phenylene)bis[4,4,5,5-tetramethyl-4,5-dihydro-1H-imidozolyl-oxyl] (4), and 2,2‘-(1,2-ethynediyldi-4,1 3,1-phenylene)bis[4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazole-1-oxyl-3-oxide] (5) are investigated by ab initio quantum chemical methods. The rule of spin alternation in the unrestricted Hartree−Fock (UHF) method clearly shows that the radical sites are antiferromagnetically coupled in 3 and ferromagnetically coupled in 4 and 5, which is consistent with a previous experiment. The molecular geometries are optimized at Hartree−Fock levels. This is followed by single-point calculations using the density functional (UB3LYP) treatment and the multiconfigurational complete active space self-consistent field (CASSCF) methodology. Magnetic exchange coupling constants are determined from the broken-symmetry approach. The calculated J values, −3.60 cm^-1 for 3, 0.16 cm^-1 for 4, and 0.67 cm^-1 for 5, are in excellent agreement with the observed values. Because of the very large size of the diradicals 3−5, the CASSCF (10,10) calculations cannot yield realistic J values. Nevertheless, the CASSCF calculations support the antiferromagnetic nature of the magnetic coupling in 3 and the ferromagnetic nature of the coupling in 4 and 5. The existence of an intramolecular magnetic coupling in 3−5 is also confirmed through computations of the isotropic hyperfine coupling constants for monoradicals 1 and 2 as well as diradicals 3−5.

Abstract:
We show that an ethylenic coupler provides a very strong intramolecular magnetic interaction. A recently synthesized nitronyl nitroxide derivative, D-NIT2, is investigated by ab initio quantum chemical methods. The broken symmetry approach yields a coupling constant −541 K that is in good agreement with the observed value in solid state.

Abstract:
The ground-state spins of seven diradicals belonging to the fused ring system have been investigated by ab initio restricted and unrestricted formalisms. The systems under study are (1) 4-oxy-2-naphthalenyl methyl, (2) 1,8-naphthalenediylbis(methyl), (3) 8-imino-1-naphthalenyl methyl, (4) 1,8- naphthalenediylbis(amidogen), (5) 8-methyl-1-naphthyl carbene, (6) 8-methyl-1-naphthalenyl imidogen, and (7) 8-methyl-1-naphthyl diazomethane. Out of the seven molecules, only 1 was theoretically investigated earlier. To our knowledge, for 2−7, this work represents the first ab initio investigation. A variety of basis sets have been employed in these calculations. For each spin state, the molecular geometry has been fully optimized at the unrestricted Hartree−Fock (UHF) level using the STO-3G, 4-31G, 6-311G(d), and 6-311G(d,p) basis sets. The UHF optimized geometries have been used for Møller−Plesset (MP) and coupled cluster (CC) calculations as well as the density functional (UB3LYP) treatment. Results in the unrestricted formalism have been given only at UHF and UB3LYP levels for the 6-311G(d) basis. The UHF calculations yield an unrealistically large singlet−triplet (S−T) splitting. Splittings calculated with different bases disagree seriously. The S−T gap is smaller in the split-valence bases. The basis set truncation error can be considerably overcome by calculations involving electron correlation. For these diradicals, any meaningful result would require larger bases with polarization functions. Apart form this difficulty, the optimized geometry turned out to be highly spin-contaminated. The spin-contamination can be significantly reduced by the density functional UB3LYP treatment. Nevertheless, for most of the diradicals, the UB3LYP method did not yield a systematic trend. To avoid spin contamination completely, we have repeated computations in the restricted (open-shell) Hartree−Fock framework. Geometry optimizations were carried out using STO-3G, 6-311G(d), and 6-311G(d,p) bases at the R(O)HF level and 6-311G(d,p) basis at the R(O)B3LYP level for each spin state. The R(O)B3LYP/6-311G(d,p) optimized geometry yields the best total energy for each spin state and hence the most reliable S−T energy difference. Molecules 1−6 are found as ground-state triplets. The calculated results are in agreement with the available experimental findings. Molecules 3 and 7 have widely different geometries in the singlet and triplet states. The calculations using 6-311G(d) and 6-311G(d,p) basis sets show that in molecule 3 the substituents of naphthalene are −NH₂ and −CH in singlet but −NH and −CH₂ in triplet. The two optimized geometries are tautomeric forms. Molecule 7 is expected to be either a ground-state triplet with a very little S−T gap or a ground-state singlet. This prediction is borne out by the computed results. The R(O)B3LYP/6-311G(d,p) calculation yields a S−T splitting of −21.9 kcal mol^-1. The singlet state becomes stabilized by forming an additional condensed ring. The UHF spin density plots obtained from the 4-31G optimized geometries manifest the phenomenon of spin alternation in the ground state.