Broken-symmetry Density Functional Theory Research Articles

S3 State Models of Nature's Water Oxidizing Complex: Analysis of Bonding and Magnetic Exchange Pathways, Assessment of Experimental Electron Paramagnetic Resonance Data, and Implications for the Water Oxidation Mechanism.

Broken symmetry density functional theory (BS-DFT) calculations on large models of Nature's water oxidizing complex (WOC) are used to investigate the electronic structure and associated magnetic interactions of this key intermediate state. The electronic origins of the ferromagnetic and antiferromagnetic couplings between neighboring Mn ions are investigated and illustrated by using corresponding orbital transformations. Protonation of the O4 and/or O6 atoms leads to large variation in the distribution of spin around the complex with associated changes in its magnetic resonance properties. Models for Sr2+ exchange and methanol addition indicate minor perturbations reflected in slightly altered spin projection coefficients for the Mn1 and Mn2 ions. These are shown to account for the observed changes observed experimentally via electron paramagnetic resonance methods and suggest a reinterpretation of the experimental findings. By comparison with experimental determinations, we show that the spin projections and resulting calculated 55Mn hyperfine couplings support the open cubane form of an oxo (O5)-hydroxo (O6) cluster in all cases with no need to invoke a closed cubane intermediate. The implications of these findings for the water oxidation mechanism are discussed.

X−[Pd(dmit)2]2 as a quasi-one-dimensional scalene Heisenberg model

From first principles, we calculate the Heisenberg interactions between neighboring dimers in several compounds within the Et$_{n}$Me$_{4-n}X$[Pd(dmit)$_2$]$_2$ (Et = ethyl, Me = methyl, dmit = 2-thioxo-1,3-dithiole-4,5-dithiolate) family using an atomistic approach; with broken-symmetry density functional theory. In all materials, we find a scalene triangular model where the strongest exchange coupling along one crystallographic axis is up to three times larger than the others and that frustration further enhances this quasi-one-dimensionality. We calculate the N\'eel ordering temperature via the chain random phase approximation (CRPA). We show that the difference in the frustrated interchain couplings is equivalent to a single bipartite interchain coupling, favoring long-range magnetic order. We find that the N\'eel ordering temperatures are in good agreement with the experimentally measured values for most compounds.

Evaluation of electron transport capability of armchair graphene nanoribbons (AGNRs) by calculating exchange interaction between terminally attached radicals

Electron tunneling efficiency of armchair graphene nanoribbons (AGNRs) with the different widths N (N = 5–14) was evaluated by calculating decay constant βJ of the exchange interaction J between terminal nitronyl nitroxides using broken-symmetry unrestricted density functional theory (UDFT) calculations. The open-shell character of the AGNR moiety originating from the “edge state” was effectively suppressed by the addition of peri-fused benzene ring. Thus calculated J values followed exponential decay against the molecular length, and the βJ values were much smaller for AGNRs with N = 3n − 1 than AGNRs with N = 3n or 3n + 1.

Mono- and tetranuclear Fe(II,III) complexes with primary 1,3-diaminopropane: Synthetic aspects, magnetic properties and thermal behavior

New iron carboxylate complexes with a aliphatic diamine, 1,3-diaminopropane (dap), were obtained under various synthesis conditions: in the air, [FeIII4O2(Piv)8(dap)2] (1, Piv is the pivalate anion), and in an inert atmosphere, [FeII(Piv)2(dap)2] (2). The structure of the compounds was determined by single crystal X-ray diffraction analysis. In mononuclear complex 2, the iron center coordinates two carboxylate ligands and two chelate dap. In the tetranuclear complex 1, the coordination environment of the metal ions is different, and only two ions coordinate the chelate dap. According to Mössbauer spectroscopy data, the Fe3+ ions in 1 and Fe2+ ion in 2 are in a high-spin state and in an octahedral environment of donor atoms. A DC magnetic susceptibility study and quantum-chemical analysis of intramolecular pathways using broken-symmetry density functional theory (DFT) showed that the magnetic exchange coupling between the Fe3+ ions of the central Fe2(μ-O)2 unit is weak (|J| ≤ 7 cm−1), while each of these ions is coupled by fairly strong antiferromagnetic exchange interactions with two other Fe3+ ions (J = −32.9/−43.2 cm−1). The thermal behavior of 1 and 2 was studied by simultaneous thermal analysis (STA).

Bonding and Magnetic Exchange Pathways in Nature's Water-Oxidizing Complex.

The nature of the bonding and magnetic exchange pathways of the water-oxidizing complex of photosystem 2 is explored using broken symmetry density functional theory. The electronic structure and superexchange pathways are illustrated and analyzed using corresponding orbitals and intrinsic bond orbitals. These demonstrate a dominating influence on the bonding and magnetic interactions by both the geometrical structure of the Mn4CaO5 core complex and the ionic interactions of the oxo bridges with the neighboring Ca2+ ion. The demonstrated ionic nature of the Ca2+ bonds is proposed to contribute to the stabilization of the oxygen atoms participating in O-O bond formation.

New Syntheses, Analytic Spin Hamiltonians, Structural and Computational Characterization for a Series of Tri-, Hexa- and Hepta-Nuclear Copper (II) Complexes with Prototypic Patterns

We present a series of pyrazolato-bridged copper complexes with interesting structures that can be considered prototypic patterns for tri-, hexa- and hepta- nuclear systems. The trinuclear shows an almost regular triangle with a μ3-OH central group. The hexanuclear has identical monomer units, the Cu6 system forming a regular hexagon. The heptanuclear can be described as two trinuclear moieties sandwiching a central copper ion via carboxylate bridges. In the heptanuclear system, the pyrazolate bridges are consolidating the triangular faces, which are sketching an elongated trigonal antiprism. The magnetic properties of these systems, dominated by the strong antiferromagnetism along the pyrazolate bridges, were described transparently, outlining the energy levels formulas in terms of Heisenberg exchange parameters J, within the specific topologies. We succeeded in finding a simple Kambe-type resolution of the Heisenberg spin Hamiltonian for the rather complex case of the heptanuclear. In a similar manner, the weak intermolecular coupling of two trimer units (aside from the strong exchange inside triangles) was resolved by closed energy formulas. The hexanuclear can be legitimately proposed as a case of coordination-based aromaticity, since the phenomenology of the six-spins problem resembles the bonding in benzene. The Broken-Symmetry Density Functional Theory (BS-DFT) calculations are non-trivial results, being intrinsically difficult at high nuclearities.

Spin-projected QM/MM Free Energy Simulations for Oxidation Reaction of Guanine in B-DNA by Singlet Oxygen.

Guanine is the most susceptible base to oxidation damage induced by reactive oxygen species including singlet oxygen (1O2, 1Δg). We clarify whether the first step of guanine oxidation in B−DNA proceeds via either a zwitterionic or a diradical intermediate. The free energy profiles are calculated by means of a combined quantum mechanical and molecular mechanical (QM/MM) method coupled with the adaptive biasing force (ABF) method. To describe the open‐shell electronic structure of 1O2 correctly, the broken‐symmetry spin‐unrestricted density functional theory (BS−UDFT) with an approximate spin projection (AP) correction is applied to the QM region. We find that the effect of spin contamination on the activation and reaction free energies is up to ∼8 kcal mol−1, which is too large to be neglected. The QM(AP−ULC−BLYP)/MM‐based free energy calculations also reveal that the reaction proceeds through a diradical transition state, followed by a conversion to a zwitterionic intermediate. Our computed activation energy of 5.2 kcal mol−1 matches experimentally observed range (0∼6 kcal mol−1).

Influence of the Increasing Number of Organic Radicals on the Structural, Magnetic, and Electrochemical Properties of the Copper(II)–Dioxothiadiazole Family of Complexes

The preparation, structures, and electrochemical and magnetic properties supported by density functional theory (DFT) calculations of three new copper(II) compounds with [1,2,5]thiadiazolo[3,4-f][1,10]phenanthroline 1,1-dioxide (td) and its radical anion (td·–) are reported: {[CuIICl(td)](μ-Cl)2[CuIICl(td)]} (1), which incorporates only neutral td ligands; [CuIICl(td·–)(td)]·2MeCN (2), which comprises one neutral td and one radical td·–; and PPN[CuIICl(td·–)2]·2DMA (3), where CuII ions are coordinated by two radical anions td·– (DMA, dimethylacetamide; PPN+, the bis(triphenylphosphine)iminium cation). All three compounds show interesting paramagnetic behavior with low-temperature features indicating significant antiferromagnetic coupling. The magnetic properties of 1 are dominated by CuII···CuII interactions (JCuCu) mediated through the Cl– bridges, while the magnetic properties of 2 and 3 are governed mainly by the td·–···td·– (Jtdtd) and CuII–td·– (JCutd) exchange interactions. The structure of 2 features only two major magnetic coupling pathways enabling the fitting of experimental data with Jtdtd = −36.0(5) cm–1 and JCutd = −12.6(2) cm–1 only. Compound 3 exhibits a complex network of magnetic contacts. Attempt to approximate its magnetic behavior using only a local magnetic contacts model resulted in Jtdtd = −5.6(1) cm–1 and two JCutd constants, −12.4(2) and −22.6(4) cm–1. The experimental fitting is critically compared with the results of broken symmetry density functional theory (BS DFT) calculations for inter- and intramolecular contacts. More consistent results were obtained with the M06 functional as opposed to popular B3LYP, which encountered problems reproducing some of the experimental intermolecular exchange interactions. Electrochemical measurements of 2 and 3 in MeCN showed three reversible nearly overlapping redox peaks appearing in a narrow potential range of −600 to −100 mV vs Fc/Fc+. Small differences between the redox events suggest that such compounds may be good candidates for new switchable materials, where the electron transfer between the metal and the ligand center is triggered by temperature, pressure, or light (valence tautomerism).

Model Dimeric Manganese(IV) Complexes Featuring Terminal Tris-hydroxotetraazaadamantane and Various Bridging Ligands.

A series of model dinuclear manganese(IV) complexes of the general formula [(H3COH)(L')MnIV(μ-L)2MnIV(L')(HOCH3)] is presented. These compounds feature capping 4,6,10-trihydroxo-3,5,7-trimethyl-1,4,6,10-tetraazaadamantane ligands derived from a polydentate oxime compound (L'). The bridging ligands L include azide (1), methoxide (2), and oxalate (3) anions. The magnetic properties and high-field (HF) EPR spectra of 1-3 were studied in detail and revealed varying weak antiferromagnetic coupling and modest zero-field splitting (ZFS) of the local quartet spin sites. Our HF EPR studies provide insight into the dimer ZFS, including determination of the corresponding parameters by giant spin approach for methoxido-bridged complex 2. Furthermore, the physicochemical properties of 1-3 were studied using IR, UV-vis, and electrochemical (cyclic voltammetry) methods. Theoretical exchange coupling constants were obtained using broken-symmetry (BS) density functional theory (DFT). Computational estimates of the local quartet ground spins state ZFSs of 1-3 were obtained using coupled-perturbed (CP) DFT and complete active space self-consistent field (CASSCF) calculations with n-electron valence state perturbation theory (NEVPT2) corrections. We found that the CP DFT calculations which used the B3LYP functional and models derived experimental structures performed best in reproducing both the magnitude and the sign of the experimental D values. Moreover, our computational investigation of 1-3 suggests that we observe metals sites which have an increased +3 character and are supported by redox noninnocent 4,6,10-trihydroxo-3,5,7-trimethyl-1,4,6,10-tetraazaadamantane ligands. The latter conclusion is further corroborated by the observation that the free ligand can be readily oxidized to yield a NO-based radical.

Molecular Identification of a High-Spin Deprotonated Intermediate during the S2 to S3 Transition of Nature's Water-Oxidizing Complex.

The identity of a key intermediate in the S2 to S3 transition of nature's water-oxidizing complex (WOC) in Photosystem 2 is presented. Broken-symmetry density functional theory (BS-DFT) calculations and Heisenberg-Dirac-van Vleck (HDvV) spin ladder calculations show that an S2 state open cubane model of the WOC containing a μ-hydroxo O4 changes from an S = 5/2 form to an S = 7/2, form upon deprotonation of W1. Combined with X-band electron paramagnetic resonance (EPR) spectral analysis, this indicates that the g = 4.1 EPR signal corresponds to an S = 5/2 form of the WOC with W1 present as a water ligand to Mn4, while the g = 4.8/4.9 form observed at high pH values corresponds to an S = 7/2 form, with W1 as a hydroxo ligand. The latter is also likely to represent the form needed to progress to S3 in the functioning enzyme.

A trinuclear nickel(II) cluster containing a ditopic redox active ligand: Structural and magnetic properties

The preparation of a trinuclear Ni2+ ionic complex containing the bridging ligand 2,6-bis-(8-quinolylamino)-4-(tert-butyl)phenol (H3LtBu) as a phenolate monoanion and perchlorate counteranions is described. The structure contains a rare nearly planar disc-like Ni3O3 core with large Ni-O-Ni angles, with each equivalent of the ligand bridging two Ni2+ ions binding facially to each ion. Variable temperature magnetic susceptibility data from 1 indicate moderate intramolecular antiferromagnetic interactions between the three S = 1 Ni2+ ions (JNi-Ni = −20.7 cm−1) and a diamagnetic (S = 0) ground state. Broken symmetry density functional theory calculations (DFT) at the UB3LYP/def2-TZVP level support the experimental results. The structure and properties of 1 stand in contrast to the other reported complex of H3LtBu, Cu4(LtBu)4, which features the ligand in an unusual dianion-aminyl radical oxidation state. Oxidation of 1 produced a black intractable material that could not be adequately characterized.

A Neutral Fe4tBuL4 All Ferric Grid Complex: Structural and Variable Temperature Magnetic Properties

A neutral all ferric [2×2] grid complex Fe4tBuL4 1 was synthesized and characterized in the solid‐state by X‐ray crystallography, variable temperature magnetic susceptibility and Mössbauer spectroscopy. The absence of any coordinate bond or other structural changes between 90(2) and 320(2) K indicated no changes to the electronic structure of 1 occurred in the solid‐state over this temperature range. Variable temperature magnetic susceptibility data were fitted to an isotropic spin Hamiltonian model and suggested weak antiferromagnetic exchange coupling between the high‐spin ferric ions (J = –16.1 cm‐1). Mössbauer spectroscopy parameters (δ = 0.416(9) mm s–1 & ΔEQ = 0.87(7) mm s‐1), powder EPR spectra, and broken symmetry density functional theory calculations supported the high‐spin ferric oxidation state assignment.

Probing the electronic structure of [Ru(L1)2]Z (z = 0, 1+ and 2+) (H2L1: a tridentate 2-aminophenol derivative) complexes in three ligand redox levels.

Aerobic reaction between [RuII(DMSO)4Cl2], a redox-active 2-aminophenol-based ligand (H2L1: 2-[2-(benzylthio)phenylamino]-4,6-di-tert-butylphenol) and Et3N in MeOH under refluxing conditions afforded a purple complex [Ru(L1)2] (S = 0). Structural analysis reveals that the tridentate ligand coordinates in a mer conformation providing a distorted octahedral RuN2O2S2 coordination. Cyclic voltammetry on 1 in CH2Cl2 reveals the accessability of the monocation, dication and monoanion forms. Reddish purple monocation [Ru(L1)2](PF6)·CH2Cl2 ([1OX1](PF6)·CH2Cl2; S = 1/2) and green dication [Ru(L1)2](BF4)2·H2O ([1OX2](BF4)2·H2O; S = 0) have been isolated through the chemical oxidation of 1 in CH2Cl2 by [FeIII(η5-C5H5)2](PF6) and AgBF4, respectively. A structural analysis of the single crystals of the monocation and the dication with the compositions [1OX1](PF6)·CH2Cl2·H2O (2) and [1OX2](BF4)2·1.7H2O (3), respectively, has been done. Metrical (metal-ligand and ligand backbone) parameters, values of metrical oxidation states of coordinated ligands, 1H NMR spectra of 1 and [1OX2](BF4)2·H2O, EPR spectra of [1OX1](PF6)·CH2Cl2, X-ray photoelectron and UV-VIS-NIR spectra of 1-3, spin population analysis from broken-symmetry (BS) density functional theory (DFT) calculations and quasi-restricted orbital (QRO) analysis have allowed us to assign the electronic structure of the complexes. The complexes exhibit highly covalent metal-ligand interactions. The electronic states of 1, [1OX1]1+ and [1OX2]2+ are best described as [RuII{(LISQ)˙-}2] ↔ [RuIII{(LAP)2-}{(LISQ)˙-}] (S = 0), [RuIII{(LISQ)˙-}2]1+ (S = 1/2) and [RuII{(LIBQ)0}2]2+ ↔ [RuIII{(LISQ)˙-}{(LIBQ)0}]2+ (S = 0), respectively. Notably, all redox processes are ligand-centred. Absorption spectral properties have been rationalized based on time-dependent (TD)-DFT calculations. For 1, the appearance of an IVCT band at 1100 nm supports its Class II-III (borderline) ligand-based mixed-valence character.

Coordination bonding in dicopper and dichromium tetrakis(μ-acetato)-diaqua complexes: Nature, strength, length, and topology.

Geometry optimization, energetics, electronic structure, and topology of electron density of dicopper (I) and dichromium (II) tetrakis(μ-acetato)-diaqua complexes are studied focusing on the metal-metal interactions. The performance of broken symmetry (BS) single-determinant ab initio (Hartree-Fock, Møller-Plesset perturbation theory to the second and third orders, coupled clusters singles and doubles) and density functional theory (BLYP, B3LYP, B3LYP-D3, B2PLYP, MPW2PLYP) methods is compared to multideterminant ab initio (CASSCF, NEVPT2) methods as well as to the multipole model of charge density from a single-crystal X-ray diffraction experiment (Herich et al., Acta Cryst. 2018, B74, 681-692). In vacuo DFT geometry optimizations (improper axial water ligand orientation) are compared against the periodic ones. The singlet state is found to be energetically preferred. J coupling of (I) becomes underestimated for all ab initio methods used, when compared to experiment. It is concluded that the strength of the direct M─M interactions correlates closely with the J coupling magnitude at a given level of theory. The double potential well character of (II) and of the dehydrated form of (II) are considered with respect to the Cr─Cr distance. The physical effective bond order of the metal-metal interaction is small (below 0.1 e) in (I) and moderate (0.4 e) in (II). The CASSCF results overestimate the electron density of the metal-metal bond critical point by 20% and 50% in (I) and (II), respectively, when compared to the multipole model. © 2019 Wiley Periodicals, Inc.

Proton Isomers Rationalize the High- and Low-Spin Forms of the S2 State Intermediate in the Water-Oxidizing Reaction of PhotosystemII.

A new paradigm for the high- and low-spin forms of the S2 state of nature's water-oxidizing complex in Photosystem II is found. Broken symmetry density functional theory calculations combined with Heisenberg-Dirac-van Vleck spin ladder calculations show that an open cubane form of the water-oxidizing complex changes from a low-spin, S = 1/2, to a high-spin, S = 5/2, form on protonation of the bridging O4 oxo. We show that such models are fully compatible with structural determinations of the S2 state by X-ray free-electron laser crystallography and extended X-ray absorption fine structure and provide a clear rationale for the effect of various treatments on the relative populations of each form observed experimentally in electron paramagnetic resonance studies.

Analysis of the Puzzling Exchange-Coupling Constants in a Series of Heterobimetallic Complexes.

The exchange-coupling constants (J) in a series of bimetallic complexes with an M2+(μ-OH)Fe3+ core (M = Mn, Fe, Ni, and Cu; series 1), which were reported in a recent study ( Sano et al. Inorg. Chem. 2017 , 56 , 14118 - 14128 ), have been analyzed with the help of density functional theory (DFT) calculations. The experimental J values of series 1 showed the remarkable property that they were virtually independent of metal M. This behavior contrasts with that observed for a related series of complexes with M2+Fe3+ cores reported by Chaudhuri and co-workers ( Biswas et al. Inorg. Chem. 2010 , 49 , 626 - 641 ) (series 2) in which J increases toward the upper end of the series. Broken symmetry DFT calculations for J, which yielded values in good agreement for the MnFe and NiFe complexes of series 1, gave for the CuFe complex a J value that was persistently much larger than that obtained from the experiment. Attempts to bridge the discrepancy by invoking various basis sets and corrections for hydrogen-bonding effects on J were not successful. The J values for series 1 were subsequently analyzed in the context of an exchange pathway model. From this analysis, it emerged that, in addition to the regular 2e-pathways, which contribute antiferromagnetic terms to J, there are also 3e-pathways that contribute ferromagnetic terms and have the propensity to keep J constant along series 1. It is shown that, while DFT evaluates the 2e-pathway terms reliably, this method seriously underestimates the 3e-pathway contributions, resulting in a too high J value for the CuFe complex of series 1. The pathway analysis of series 2 reveals that the 3e-pathway contributions to J are considerably smaller than those in series 1, resulting in J values that increase toward the upper end of the series, in accordance with the experiment.

NMR chemical shifts of urea loaded copper benzoate. A joint solid-state NMR and DFT study

We report solid-state 13C NMR spectra of urea-loaded copper benzoate, Cu2(C6H5CO2)4·2(urea), a simplified model for copper paddlewheel-based metal-organic frameworks (MOFs), along with first-principles density functional theory (DFT) computation of the paramagnetic NMR (pNMR) chemical shifts. Assuming a Boltzmann distribution between a diamagnetic open-shell singlet ground state (in a broken-symmetry Kohn-Sham DFT description) and an excited triplet state, the observed δ(13C) values are reproduced reasonably well at the PBE0-⅓/IGLO-II//PBE0-D3/AE1 level. Using the proposed assignments of the signals, the mean absolute deviation between computed and observed 13C chemical shifts is below 30 ppm over a range of more than 1100 ppm.

Theoretical Study on Reactions of Alkylperoxy Radicals.

We carried out a theoretical study on geometries, relative energies of stationary points, and reaction rate constants for ethyl + O2, propyl + O2, and butyl + O2 reactions, which are important reactions in the low-temperature oxidation of corresponding alkanes. Geometries with CCSD(T)/aug-cc-pVTZ for the ethyl + O2 system are adopted as the benchmark to choose a proper exchange-correlation functional for geometry optimization. Our results show that B3LYP with 6-311+G(d,p) can provide reliable structures for this system, and structures of the other two systems are determined with this functional. The performances of the explicitly correlated CCSD(T)-F12a and the locally correlated DLPNO-CCSD(T) methods on barrier heights and reaction energies are evaluated by comparing their results with those of CCSD(T)/aug-cc-pVQZ for the ethyl + O2 system. Our results indicate that reliable energy differences for this system are achieved with CCSD(T)-F12a using the cc-pVDZ-F12 basis set, and this method is employed in calculating single-point energies for the other two systems. The single-reference equation-of-motion spin-flip coupled-cluster method is adopted to obtain the potential energy surface of the barrierless reaction C2H5· + O2 → CH3CH2OO·, and the results are compared with those using broken-symmetry density functional theory and the Morse potential. Differences between energies with these methods are <1.6 kcal/mol, but the difference in the rate constants could be sizable at temperatures <500 K, and rate constants obtained in this work are reliable only for temperatures >500 K. Pressure-dependent rate constants for these reactions are determined using the Rice-Ramsperger-Kassel-Marcus/Master equation method. The obtained reaction energies, barrier heights, and rate constants could be valuable for reactions between the large alkane radical and O2, which are important in the low-temperature combustion of fuels such as kerosene and gasoline.

Hubbard Trimer with Spin–Orbit Coupling: Hartree–Fock Solutions, (Non)Collinearity, and Anisotropic Spin Hamiltonian

We present unrestricted and generalized Hartree-Fock solutions (UHF and GHF, respectively) for the single-band Hubbard model of an equilateral triangle. Spin-orbit coupling (SOC) is treated self-consistently, and HF stability and properties of different spin structures are studied in detail. The GHF solution switches from noncollinear to collinear when crossing a high-symmetry point in parameter space (spanned by the amplitudes of spin-conserving and spin-dependent hopping, i.e., kinetic energy and SOC, respectively). The collinear GHF solution represents a simple example to disprove the notion that a collinear vector spin density in a Slater determinant necessarily entails a defined spin projection. Spin Hamiltonian parameters for the anisotropic interaction between three spin-1/2 centers are extracted from HF energies and subsequently compared to exact results from effective Hamiltonian theory. This provides an unambiguous benchmark for interpreting broken-symmetry mean-field solutions in terms of spin configurations and puts this semiclassical approach (frequently applied in broken-symmetry density functional theory) on a firmer basis.

Meeting the Challenge of Magnetic Coupling in a Triply-Bridged Chromium Dimer: Complementary Broken-Symmetry Density Functional Theory and Multireference Density Matrix Renormalization Group Perspectives.

Face-sharing octahedral dinuclear Cr(III) compounds with d3–d3 electronic configurations represent nontrivial examples of electronic complexity, posing particular challenges for theoretical and computational studies. A tris-hydroxy-bridged Cr(III)–Cr(III) system has proven to be a richly rewarding target for studies of magnetism and electron paramagnetic resonance spectroscopy. It was also reported to be a peculiarly difficult system to treat with density functional theory (DFT). In this work the magnetic coupling problem for this dimer is approached with broken-symmetry (BS)-DFT and multireference calculations that utilize the density matrix renormalization group (DMRG) to handle full-valence active spaces. BS-DFT is shown to recover the correct ordering and energy spacing of Heisenberg spin states if used in conjunction with appropriate spin projection procedures, albeit with pronounced functional sensitivity. The contrasting conclusions of previous studies are traced to incorrect inclusion of electronically excited configurations. Analysis of the direct and differential overlap of corresponding orbital pairs from the BS-DFT solution indicates that metal–metal through-space interaction is the dominant contributor to antiferromagnetic coupling. At the DFT level a procedure that utilizes pseudopotential substitution is demonstrated that allows evaluation of the direct exchange vs superexchange contributions. A complementary description is obtained with DMRG-SCF calculations that enable state-averaged CASSCF calculations with both metal and bridge orbitals in the active space. A localized orbital subspace analysis supports the DFT conclusions that in contrast to doubly bridged isoelectronic analogues, antiferromagnetic coupling in the chromium dimer arises primarily from direct metal–metal interaction but is significantly enhanced by ligand-mediated superexchange.