Additive Decomposition of the Physical Components of the Magnetic Coupling from Broken Symmetry Density Functional Theory Calculations

What governs magnetic exchange couplings in radical-bridged dinuclear complexes?

Coupling transition metal or lanthanide ions through a radical bridging ligand is a promising route to increase performances in the area of single molecular magnets. A better understanding of the underlying physical mechanisms governing the magnetic exchange couplings is thus of valuable importance to design future compounds. Here, couplings in three series of metal-radical-metal compounds based on transition metal ions are investigated by means of the decomposition/recomposition methods. This work presents the generalisation and first application of the method to systems with an arbitrary number of magnetic centres featuring several unpaired electrons. Thanks to the decomposition into the three main contributions (direct exchange, kinetic exchange, and spin polarisation) as well as a description in terms of electron-electron interactions, we study the influence of the nature of the metal centre and the radical ligand on the couplings. We combine the energetic contributions extracted with orbital and charge population analysis to rationalise the results.

Natural orbitals and two-particle correlators as tools for the analysis of effective exchange couplings in solids

Using generalizations of spin-averaged natural orbitals and two-particle charge correlators for solids, we investigate the electronic structure of antiferromagnetic transition-metal oxides with a fully self-consistent, imaginary-time GW method. Our findings disagree with the Goodenough-Kanamori (GK) rules that are commonly used for the qualitative interpretation of such solids. First, we found a strong dependence of the natural orbital occupancies on momenta, contradicting GK assumptions. Second, along the momentum path, the character of natural orbitals changes. In particular, the contributions of oxygen 2s orbitals are important, which has not been considered in the GK rules. To analyze the influence of the electronic correlation on the values of effective exchange coupling constants, we use both natural orbitals and two-particle correlators and show that electronic screening modulates the degree of superexchange by stabilizing the charge-transfer contributions, which greatly affects these coupling constants. Finally, we give a set of predictions and recommendations regarding the use of density functional, Green's function, and wave-function methods for evaluating effective magnetic couplings in molecules and solids.

Revisiting magnetic exchange couplings in heterodinuclear complexes through the decomposition method in KS-DFT

Providing tools to understand the physical mechanisms governing magnetic properties in transition metal-based compounds is still of great interest. Here, the magnetic exchange coupling in a series of heterodinuclear complexes is investigated by means of the decomposition method. This work presents the first application of the decomposition method to systems where magnetic centres may bear more than one unpaired electron. By decomposing the coupling into three physical contributions (direct exchange, kinetic exchange, and spin polarisation), we provide numerical arguments to confirm or infirm the rationalisation allowed by the conceptual analysis of the magnetic d orbitals. We also take advantage of the recently proposed generalisation of the method [David et al., J. Chem. Theory Comput., 2023, 19, 157] to get more insights into the underlying mechanisms by disentangling the coupling between centres into its electron-electron interactions.

Satellite ligand effects on magnetic exchange in dimers. A structural, magnetic and theoretical investigation of Cu2L2X4 (L = methylisothiazolinone and X = Cl-, Br-)

Halide-bridged polymers have gained significant interest due to their diverse properties and potential applications. Stacked Cu₂L₂X₄ dimers, where L is an organic ligand and X can be Cl^- or Br^-, are of interest because a chloride analogue where L = 2-pyridone, had previously been reported to exhibit bulk ferromagnetism, which augured great potentiality for this class of compounds. The synthesis, structural characterization, magnetic susceptibility measurements, and computational studies of two isostructural CuClMI (MI = methylisothiazolinone) and CuBrMI polymers of Cu(II), along with a related CuClPYR (PYR = 2-pyridone) is reported. CuClMI and CuBrMI were found to exhibit AFM bulk properties, due to FM/AFM alternating chains along the halide-bridged polymer axis, while FM bulk properties were confirmed for CuClPYR exhibiting a FM spin ladder. In combination with a benzamide analogue, CuClBA, three O-donor amides, CuClMI, CuClBA and CuClPYR were analyzed and revealed that the kinetic exchange is affected by the identity, but more importantly, the orientation of the satellite ligands. The torsional angle of the ligand with the dimer plane is shown to significantly affect the magnetic exchange in the dimer, and between dimers, explaining the reported FM bulk properties of CuClPYR. This finding is exceedingly important, as it suggests that a spin device can be constructed to flip between singlet/triplet states by manipulating the orientation of the satellite/terminal ligand.

Understanding the Exchange Interaction between Paramagnetic Metal Ions and Radical Ligands: DFT and Ab Initio Study on Semiquinonato Cu(II) Complexes

The exchange coupling, represented by the J parameter, is of tremendous importance in understanding the reactivity and magnetic behavior of open-shell molecular systems. In the past, it was the subject of theoretical investigations, but these studies are mostly limited to the interaction between metallic centers. The exchange coupling between paramagnetic metal ions and radical ligands has hitherto received scant attention in theoretical studies, and thus the understanding of the factors governing this interaction is lacking. In this paper, we use DFT, CASSCF, CASSCF/NEVPT2, and DDCI3 methods to provide insight into exchange interaction in semiquinonato copper(II) complexes. Our primary objective is to identify structural features that affect this magnetic interaction. We demonstrate that the magnetic character of Cu(II)-semiquinone complexes are mainly determined by the relative position of the semiquinone ligand to the Cu(II) ion. The results can support the experimental interpretation of magnetic data for similar systems and can be used for the in-silico design of magnetic complexes with radical ligands.

Consistent Evaluation of Magnetic Exchange Couplings in Multicenter Compounds in KS-DFT: The Recomposition Method

The use of broken-symmetry calculations in Kohn-Sham density functional theory has offered an affordable route to study magnetic exchange couplings in transition-metal-based compounds. However, computing this property in compounds exhibiting several couplings is still challenging and especially due to the difficulties to overcome the well-known problem of spin contamination. Here, we present a new and general method to compute magnetic exchange couplings in systems featuring several spin sites. To provide a consistent spin decontamination of J values, our strategy exploits the decomposition method of the magnetic exchange coupling proposed by Coulaud et al. and generalizes our previous work on diradical compounds where the overall magnetic exchange coupling is defined as the sum of its three main and properly extracted physical contributions (direct exchange, kinetic exchange, and spin polarization). In this aim, the generalized extraction of all contributions is presented to systems with multiple spin sites bearing one unpaired electron. This is done by proposing a new paradigm to treat the kinetic exchange contribution, which proceeds through monorelaxations of the magnetic orbitals. This method, so-called the recomposition method, is applied to a compound featuring three Cu(II) ions with a linear arrangement and to a recently synthesized complex containing a Cu₄O₄ cubane unit presenting an unusual magnetic behavior.

Antiferromagnetic Coupling Supported by Metallophilic Interactions: Theoretical View

The antiferromagnetic coupling supported by metallophilic interactions has been studied in the framework of the broken symmetry approach (BS) and multiconfigurational calculations (CASSCF). A series of heterobimetallic complexes of the form [PtCo(X)₄(Y)]₂ (X = tba thiobenzoate, SAc thioacetate, and Y = H₂O, NO₂py, py), previously reported, have been used as model systems. Magnetic coupling constants were found in good agreement with the experimental reports, and it could be concluded that axial ligands with a pure σ-donor character have a marked effect on the J value strengthening the antiferromagnetic coupling, as shown for [PtCo(SAc)₄(H₂O)]₂ and [PtNi(SAc)₄(H₂O)]₂. The latter complex, included for comparative purposes, also made it possible to evidence that the interaction between magnetic orbitals and low-level excitation in the Pt···Pt region is also relevant favoring the stronger antiferromagnetic coupling found in this case. A careful analysis of the energetic components involved in Pt···Pt interaction suggests that the stabilization arises from a combination of favorable orbital contributions, which allows a weak covalent Pt···Pt σ(dz²...dz²) bond. Theoretical tools evidence that the weak σ-bond found between monomeric units is responsible for a spin polarization mechanism resulting in the observed antiferromagnetic interaction. Multiconfigurational calculations finally allowed us to establish that the spin polarization mechanism involves not only the d_z² orbitals in the M-Pt···Pt-M bond direction but also the empty 6p_z orbitals of Pt atoms. The inclusion of these orbitals favors a correlation-induced delocalization of magnetic orbitals and therefore a better balance among direct and kinetic exchange. The results shown in this work are relevant in the molecular design of systems supported by metallophilic interactions not only between platinum atoms but also could be extended to other cases with similar interactions.

Energy decomposition analysis based on broken symmetry unrestricted density functional theory

In this paper, the generalized Kohn-Sham energy decomposition analysis (GKS-EDA) scheme is extended to molecular interactions in open shell singlet states, which is a challenge for many popular EDA methods due to the multireference character. Based on broken symmetry (BS) unrestricted density functional theory with a spin projection approximation, the extension scheme, named GKS-EDA(BS) in this paper, divides the total interaction energy into electrostatic, exchange-repulsion, polarization, correlation, and dispersion terms. Test examples include the pancake bond in the phenalenyl dimer, the ligand interactions in the Fe(ii)-porphyrin complexes, and the radical interactions in dehydrogenated guanine-cytosine base pairs and show that GKS-EDA(BS) is a practical EDA tool for open shell singlet systems.

Assessing the Calculation of Exchange Coupling Constants and Spin Crossover Gaps Using the Approximate Projection Model To Improve Density Functional Calculations

This work evaluates the quality of exchange coupling constant and spin crossover gap calculations using density functional theory corrected by the approximate projection model. Results show that improvements using the approximate projection model range from modest to significant. This study demonstrates that, at least for the class of systems examined here, spin projection generally improves the quality of density functional theory calculations of J-coupling constants and spin crossover gaps. Furthermore, it is shown that spin projection can be important for both geometry optimization and energy evaluations. The approximate projection model provides an affordable and practical approach for effectively correcting spin-contamination errors in such calculations.

Dependence of magnetic coupling on ligands at the axial positions of NiII in phenoxido bridged dimers: experimental observations and DFT studies

Experimental and theoretical results reveal that the magnetic coupling in diphenoxido bridged dinuclear Ni^II compounds is strongly dependent on the axially coordinated non-bridging ligands.

Spin decontamination of broken-symmetry density functional theory calculations: deeper insight and new formulations

This work proposes rigorous and physically based spin decontamination factors for broken-symmetry treatments of diradicals.