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.

Exchange Coupling Interactions from the Density Matrix Renormalization Group and N-Electron Valence Perturbation Theory: Application to a Biomimetic Mixed-Valence Manganese Complex

The accurate description of magnetic level energetics in oligonuclear exchange-coupled transition-metal complexes remains a formidable challenge for quantum chemistry. The density matrix renormalization group (DMRG) brings such systems for the first time easily within reach of multireference wave function methods by enabling the use of unprecedentedly large active spaces. But does this guarantee systematic improvement in predictive ability and, if so, under which conditions? We identify operational parameters in the use of DMRG using as a test system an experimentally characterized mixed-valence bis-μ-oxo/μ-acetato Mn(III,IV) dimer, a model for the oxygen-evolving complex of photosystem II. A complete active space of all metal 3d and bridge 2p orbitals proved to be the smallest meaningful starting point; this is readily accessible with DMRG and greatly improves on the unrealistic metal-only configuration interaction or complete active space self-consistent field (CASSCF) values. Orbital optimization is critical for stabilizing the antiferromagnetic state, while a state-averaged approach over all spin states involved is required to avoid artificial deviations from isotropic behavior that are associated with state-specific calculations. Selective inclusion of localized orbital subspaces enables probing the relative contributions of different ligands and distinct superexchange pathways. Overall, however, full-valence DMRG-CASSCF calculations fall short of providing a quantitative description of the exchange coupling owing to insufficient recovery of dynamic correlation. Quantitatively accurate results can be achieved through a DMRG implementation of second order N-electron valence perturbation theory (NEVPT2) in conjunction with a full-valence metal and ligand active space. Perspectives for future applications of DMRG-CASSCF/NEVPT2 to exchange coupling in oligonuclear clusters are discussed.

On the magnetic and spectroscopic properties of high-valent Mn3CaO4 cubanes as structural units of natural and artificial water-oxidizing catalysts

The Mn(IV)3CaO4 cubane is a structural motif present in the oxygen-evolving complex (OEC) of photosystem II and in water-oxidizing Mn/Ca layered oxides. This work investigates the magnetic and spectroscopic properties of two recently synthesized complexes and a series of idealized models that incorporate this structural unit. Magnetic interactions, accessible spin states, and (55)Mn isotropic hyperfine couplings are computed with quantum chemical methods and form the basis for structure-property correlations. Additionally, the effects of oxo-bridge protonation and one-electron reduction are examined. The calculated properties are found to be in excellent agreement with available experimental data. It is established that all synthetic and model Mn(IV)3CaO4 cubane complexes have the same high-spin S = (9)/2 ground state. The magnetic coupling conditions under which different ground spin states can be accessed are determined. Substitution of Mn(IV) magnetic centers by diamagnetic ions [e.g., Ge(IV)] allows one to "switch off" specific spin sites in order to examine the magnetic orbitals along individual Mn-Mn exchange pathways, which confirms the predominance of ferromagnetic interactions within the cubane framework. The span of the Heisenberg spin ladder is found to correlate inversely with the number of protonated oxo bridges. Energetic comparisons for protonated models show that the tris-μ-oxo bridge connecting only Mn ions in the cubane has the lowest proton affinity and that the average relaxation energy per additional proton is on the order of 18 kcal·mol(-1), thus making access to ground states other than the high-spin S = (9)/2 state in these cubanes unlikely. The relevance of these cubanes for the OEC and synthetic oxides is discussed.

THEORETICAL STUDY ON METHANE HYDROXYLATION BY MIMIC METHANE MONOOXYGENASE WITH bis(μ-OXO)DIMANGANESE CORE

The reaction mechanism for methane hydroxylation catalyzed by mimic methane monooxygenase (MMO) with bis(μ-oxo)dimanganese core has been investigated on the septet and nonet potential energy surfaces by hybrid density functional method B3LYP. The key reactive compound Q of MMO was modeled by trans- (H2CNH)(COOH) Mn(μ-O)2(μ-HCOO)2Mn(H2CNH)(COOH) . The ground state of Q is located on the septet state, which has a diamond-core structure with two Mn(IV) atoms. It is shown that the reaction proceeds via a radical-rebound mechanism, in which the step of C–H cleavage is the rate-determining step both in the gas phase and solution. Furthermore, the reaction may proceed more easily as the polarity of solution is larger. On the other hand, the kinetic isotope effects (KIEs) for H atom abstraction from methane are taken into account on the basis of transition state theory with Wigner tunneling corrections. The mimic MMO with bis(μ-oxo)dimanganese core might be an effective mimic catalyst for methane hydroxylation.

Validation of broken-symmetry density functional methods for the calculation of electron paramagnetic resonance parameters of dinuclear mixed-valence MnIVMnIII complexes

. The EPR parameters of a series of dinuclear manganese(III,IV) complexes with mono(μ-oxo), bis(μ-oxo), (μ-oxo)(μ-carboxylato), bis(μ-oxo)(μ-carboxylato), and (μ-oxo)bis(μ-carboxylato) bridges were studied by broken-symmetry density functional (DFT) methods. The influence of the exchange-correlation functional on the agreement with experiment has been evaluated systematically for g tensors; 55Mn, 14N, and 1H hyperfine coupling tensors; and Heisenberg exchange couplings. 14N and 1H hyperfine couplings, 55Mn hyperfine anisotropies, g tensors, and exchange couplings are well described by hybrid functionals with moderate exact-exchange admixtures such as B3LYP. The isotropic 55Mn hyperfine couplings require larger exact-exchange admixtures. However, the errors of the B3LYP calculations are systematic and may be corrected by a constant scaling factor, providing good predictive power for a wide range of EPR parameters with broken-symmetry DFT and standard functionals. The influence of terminal and bridging ligands on structure, spin-density distributions, and EPR parameters are evaluated systematically. Computed hyperfine and g tensors are not covariant to each other. This may have consequences for spectra simulations. The nature of the broken-symmetry state and the origin of its spin contamination were analyzed by an expansion into restricted determinants, based on paired orbitals.

Density Functional Study on Geometrical Features and Electronic Structures of Di-μ-oxo-Bridged [Mn2O2(H2O)8]q+ with Mn(II), Mn(III), and Mn(IV)

We report the geometrical features and electronic structures of di-mu-oxo-bridged Mn-Mn binuclear complexes with H2O ligands [Mn2O2(H2O)8]q+ in the iso- and mixed-valence oxidation states. All of the combinations among Mn(II), Mn(III), and Mn(IV) ions are considered the oxidation states of the Mn-Mn center, and the changes in molecular structure induced by the different electron configurations of Mn-based orbitals are investigated in relation to the oxygen-evolving complex (OEC) of photosystem II. The stable geometries of complexes are determined by using the hybrid-type density functional theory for both of the highest- and lowest-spin couplings between Mn sites, and the lowest-spin-coupled states are energetically more favorable than the highest-spin-coupled states except in the case of the complexes with the Mn(II) ion. The coordination positions of H2O ligands at the Mn(II) site tend to shift from the octahedral positions in contrast to those at the Mn(III) and Mn(IV) sites. The shape of the Mn2O2 core and the distances between the Mn ions and the H2O ligands vary depending on the electron occupations of the octahedral eg orbitals on the Mn site with an antibonding nature for the Mn-ligand interactions, indicating the trend as Mn(II)-O > Mn(III)-O and Mn(IV)-O, O-Mn(II)-O > O-Mn(III)-O > O-Mn(IV)-O among the iso-valence Mn2O2 cores, and O-Mn(lower)-O < O-Mn(higher)-O within the mixed-valence Mn2O2 core, and as Mn(II)-OH2 and Mn(III)-OH2 > Mn(IV)-OH2 for the axial H2O ligand. The optimized geometries of model complexes are compared with the X-ray structure of the OEC, and it is suggested that the cubane-like Mn cluster of the active site may not contain a Mn(II) ion. The effective exchange integrals are estimated by applying the approximate spin projection to clarify the magnetic coupling between Mn sites, and the superexchange pathways through the di-mu-oxo bridge are examined on the basis of the singly occupied magnetic orbitals derived from the singlet-coupled natural orbitals in the broken-symmetry state. The comparisons of the calculated results between [Mn2O2(H2O)8]q+ in this study and [Mn2O2(NH3)8]q+ reported by McGrady et al. suggest that the symmetric pathways are dominant to the exchange coupling constant, and the crossed pathway would be less important for the former than it would for the latter in the Mn(III)-Mn(III), Mn(IV)-Mn(IV), and Mn(III)-Mn(IV) oxidation states.