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Transition Metals (TMs) are ubiquitous materials employed in a myriad of industrially and technologically relevant fields. These range from energy storage devices , through drug release nanotechnologies , and to heterogeneous catalysis , to name a few. The interaction of carbon monoxide (CO) with catalytic TM surfaces has been extensively studied in the past due to its importance to chemical industries . The CO properties paved the way to its use as a probe molecule to obtain atomistic information on the studied surfaces upon CO adsorption . Besides its use as a probe molecule in the field of Surface Science, it is also used a reactant, e.g., in the Fischer-Tropsch (FT) process, generating hydrocarbons from CO:H2 mixtures , a key ingredient for the carbon circular economy when CO is generated from previously captured and dissociated carbon dioxide (CO2). Aside, CO is a sought product, for instance, through the reverse water gas shift reaction, where CO2 can be revalued by reacting with H2 to yield CO and H2O (CO2 + H2 → CO + H2O, ΔH r o = 41 kJ•mol -1 ) , with the concomitant environmental implications in the fight against global warming and climate change. Apart from these, the CO molecule can be a key intermediate, e.g. as in the course of CO2 hydrogenation towards methanol fuel, again key in making carbon economy circular . Thus, the interaction of CO with TM-based catalysts has gained importance as a way, not only to gain atomistic insights of the latter using CO as a probe molecule, but also as a crucial species in diverse processes of industrial and environmental relevance.
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Thus, a systematic investigation of the CO interaction with TMs and its possible dissociation would not only allow the discovery of the key, acting descriptors unfolding the physicochemical properties of TM surfaces and set a predicting basis for complex systems, e.g. TM nanoparticles and bimetallic structures . It could also drive the description of single-atom alloys, which have become a hub of research in the recent years . Such an understanding could be gained by means of Surface Science techniques , yet experimental methods suffer from limitations and inaccuracies, e.g. having the need of using wellcharacterized single-crystal metal surfaces, a ultra-high vacuum chamber while controlling the dose of CO, and the unavoidable acquirement of mean, average information of all the molecules and active sites present on the sample. A suitable alternative to gain molecular and site-specific atomistic information is the use of accurate atomistic simulations. Within this Computational Surface Science field, Density Functional Theory (DFT) applied to surface slab models has excelled over other approaches, being an excellent compromise in between computational cost and accuracy.
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Herein we thoroughly investigate the CO molecule adsorption and breakage processes on TM surfaces to unfold the most prominent trends, driving forces, and chemical descriptors in a broad, general fashion. To this end, the CO adsorption is systematically studied by DFT means on all 3d, 4d, and 5d TMs displaying regular face-centred cubic (fcc), body-centred cubic (bcc), or hexagonal close-packed (hcp) crystallographic structures, accounting for 27 different TMs. The three lowest-index Miller surfaces from each TM are analyzed, accounting in all cases for the most stable regular surfaces , i.e. without featuring step edges. These are (001), (011), and (111) surfaces for both fcc and bcc TMs, and (0001), (101 ̅ 0), and (112 ̅ 0) surfaces for hcp TMs, see Fig. , making up 81 studied TM surfaces.
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The adsorption and dissociation of the CO molecule on the aforementioned 81 TM surfaces have been evaluated through periodic DFT calculations, as implemented in the Vienna Ab-Initio Simulation Package (VASP) code . Projector Augmented Wave (PAW) pseudopotentials have been used to describe core electrons density and its interaction with the valence electron density . For the DFT calculations, the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional was chosen , known to be among the most suited and accurate in the description of both bulk and surface TM properties . For the better description of the long-range, dispersive forces interactions, Grimme's D3 correction has been accounted in the calculations , previously proven to deliver results comparable to the more-grounded many-body dispersion .
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The TM surfaces were represented by six-layered supercell slab models, previously optimized so as to deliver slab-width converged results . During the DFT optimizations, the three bottommost layers were kept frozen to represent the materials bulk, while the topmost three layer were allowed to fully relax, along with the adsorbed CO molecule, or the adsorbed C or O adatom moieties, i.e. 3+3 approach. The slab models had a vacuum of 10 Å perpendicular to the modelled surface to prevent any spurious interactions between the periodically repeated layers. The supercells size was adjusted to maintain similar CO coverage between different surfaces. Thus, (3×3) supercells were used for fcc (111) surfaces, bcc (001) and (111) surfaces, and hcp (101 ̅ 0) surface, having nine atoms per layer, see Fig. .
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On the other hand, (2×2) supercells were employed for fcc (001) and (011) surfaces, bcc (011) surface, and hcp (0001) and (112 ̅ 0) surfaces, see Fig. , having eight atoms per layer. Thus, the resulting coverage of all the surfaces resulted in similar 1 /8 or 1 /9 of a monolayer (ML), depending on the number of metallic atoms forming each layer.
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The CO molecule was sampled and relaxed on each of the 81 TM surfaces, starting from a height of 2 Å for the CO atom closest to the TM surface, and with the CO molecule placed on highly symmetric positions, see Fig. and Figs. S1-S3 of Section S1 of the Supplementary Material (SM). This involved positions where the CO molecule laid perpendicular or parallel with respect to the surface plane. In the former, both orientations were examined, i.e., connected through C or O atoms. Upon relaxation, the strength of the adsorption was quantified through the adsorption energy, Eads, defined by the difference between the adsorbed system energy, EAS, and those of the adsorbate in vacuum, EA, and the clean surface, ES;
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In all the employed slabs, the reciprocal space was sampled using optimized Monkhorst-Pack k-point meshes of 3×3×1 dimensions. The geometric optimizations were carried out using a plane-wave basis set with a kinetic energy cutoff of 415 eV, enough to reach the chemical accuracy of ~0.04 eV as tested on adsorption energies, see below. The electron density optimization criterion was set to 10 -6 eV, while atomic relaxation stopped when consecutive geometries yielded differences in energy below 10 -5 eV. All calculations were considered closed shell, i.e. non-spin polarized, except for Co, Ni, and Fe magnetic surfaces . The placed CO molecule was optimized likewise isolated in the centre of a 10×10×10 Å 3 cubic unit cell and optimized at Γ-point. For evaluating the energy of isolated C and O atoms, the procedure was similar to the CO molecule but placed inside a 9×10×11 Å 3 broken-symmetry unit cells, so as to force and gain their correct orbital occupancies.
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Furthermore, the CO dissociation energy was estimated by co-adsorbing a C adatom with an O adatom in its proximity. To this end, we profited from previous research on the stability of C atoms on the TM surfaces . In addition, we explored the adsorption of O atoms likewise, sampling the same high symmetry sites as the perpendicular CO molecule, and using the O atom in vacuum as reference, modelled in the same box as the CO molecule, but spin-polarized to grant correct orbital occupancy, see Tables S1- of Section S2 of the SM. Different combinations of C and O adatoms were optimized. Likewise, the lowest energy structures were characterized through vibrational frequency analysis, and the energies corrected with ZPE. Thus, the CO dissociation energy change, ΔE, is calculated as the difference between the energy with both C and O atoms adsorbed, EC+O, with the energy of the CO molecule adsorbed, ECO, both their respective ZPE;
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Having characterized the initial and final states of the CO dissociation on the 81 TM surfaces, we extensively searched the CO dissociation reaction Transition States (TSs). To this end, the Improved Dimer (ID) and Climbing-Image Nudged Elastic Band (CI-NEB) methods were used. When necessary, i.e. when forces acting on the atoms in the TS were not sufficiently close to zero -implying that the found point is not a true stationary point of the potential energy surface-a Quasi-Newton optimization was carried out until forces were found to be below 0.03 eV•Å -1 . All the TSs were characterized as saddle points by vibrational frequency analysis, this is, with a single imaginary frequency.
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In this process, the CO σ-donates electron density to the TM surface, and the TM πbackdonates electron density to an antibonding orbital of the CO molecule, see Fig. . The electron density occupation of the CO antibonding orbital decreases its bond order, which is accompanied by a bond length elongation and a lower CO stretching vibrational frequency.
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Early TMs, with a high d-band centre, εd , are more prone to the σ-donation, and consequently, to the π-backdonation counterpart, making them better candidates for a strong CO adsorption compared to late TMs, which goes along with the calculated Eads shown in Tables S4-S6 of Section S3 of the SM.
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Aside, the strong adsorption and electron density donation/backdonation mechanism on early TMs is directly related to the coordination number of the CO molecule on the surface, as seen in the preferred sites, listed in Tables S4-S6 of Section S3 of the SM. Those TMs with a stronger interaction tend to have a more significant number of surface TM atoms participating in the molecular coordination. Still, the σ-donation, done through the CO C atom, plus the O electron density, featuring more coulombic/steric repulsion than the C one, leads to CO molecule not being perfectly planar, see Fig. , but with a minor tilt, in between 53º and 72º with respect the TM surface plane, see Tables a more elongated bond than perpendicular cases, with an R of 0.719, see Fig. .
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A similar situation is revealed on the CO stretching vibrational frequency reduction, a similar situation is revealed, see Fig. . Generally, ν decreases as the Eads decreases, from an initial value of 2131 cm -1 for CO in vacuum. Linear trends are found accounting for all values with an R of 0.855, but when decomposing by crystallographic structures, only bcc and hcp retain high R values of 0.816 and 0.870, while fcc cases have an R of 0.552. As before, the two trends are clearly distinguishable depending on whether CO is perpendicular or parallel to the surface. With an R of 0.765, the parallel adsorption mode decreases the CO stretching vibrational frequency in a much more accentuated way than the perpendicular mode does, with an R of 0.719, reinforcing the idea that the bonding mechanism and bonding structure play a major role than the crystallographic phase itself.
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The orientation of the adsorbed CO molecule affects not only the stretching ν value but also its simulated IR intensity, which is directly proportional to the molecular dipole moment change perpendicular to the surface associated to the vibrational motion, known as surface dipole selection rule. This makes IR-visible perpendicular motions -or with a perpendicular component-while parallel cases get their dipole moment cancelled by a mirror counterdipole generated on the underlying TM surface electronic density. This is exemplified in Fig. for late, middle, and early TM surfaces with decreasing perpendicularity of the adsorbed CO molecule. The simulated IR can be found in Fig. of Section S5 of the SM.
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The presence of adsorbed CO still will depend on the working conditions of temperature, T, and pCO. Such are accounted in the thermodynamic phase diagrams, exemplified as well in Fig. for an early (Sc), middle (Fe), and late (Cu) TM, while similar behaviours can be found on the rest of simulated thermodynamic surface phase diagrams found in Fig. of Section S6 of the SM. In Fig. one observes that, in general terms, for a given TM, there is a difference of CO affinity for the different explored surfaces, but that the largest effect is found when going along the d series, revealing how thermodynamic phase diagrams reduce the adsorbing regions when going for TMs with more d electrons, up to cases, like in Cu, where surfaces can reach a CO-free at high temperatures even when having a standard pCO of 1 bar.
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However, the above discussed trends with respect the Eads are of properties of the adsorbed system. With the aim of unfolding the main descriptors involved in the interaction, this is, physicochemical properties of the pristine TM surfaces capable of predicting an adsorbate feature, an exploratory search including the d-band centre, εd, the width-corrected d-band centres, maximum Hillbert peaks of the density of states, surface energies, and workfunctions was carried out, all calculated using the same computational setup as the one here used . Their evaluation revealed that the d-band centre was the most suited choice, with an R of 0.908, see Fig. and Figures S6-S9 of Section S7 of the SM.
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Fig. shows the linear evolution of Eads as a function of εd, revealing that such a descriptor works rather well for close-packed crystallographic structures, this is, fcc and hcp, with R values of 0.916 and 0.952, respectively. However, the adequacy is lower for bcc TMs, with an R of 0.663. Clearly, crystal packing is a factor, but also the stacking, since the trends captured for fcc and hcp are different. The worse performance on bcc can be attributed to DFT lower accuracy on describing virtual orbitals or bands, whose weight is more important on early TMs εd estimates, exactly where bcc TMs are placed.
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The adsorptive landscape for isolated C atoms was explored in earlier works using the very same TM surface models and computational setup, with the caveat that were carried out neglecting long-range interactions . Thus, the most stable configurations were taken from literature and recalculated at PBE-D3 level, alongside the here calculated O adatom situations, see Tables only that in the C+O the C atom is located at the formed square. As found for C and O adatoms , and shown for CO adsorbate, the εd descriptor is the most suited as well for the C+O coadsorption, as seen in Fig. , where the similarity is evident, again best performing for fcc an hcp TM surfaces, with R values of 0.912 and 0.929, respectively, but with less accuracy for bcc TM surfaces, with an R of 0.758.
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The CO dissociation leads to C+O and the feasibility of the process is determined by their difference in energy, ΔE, listed in Tables Another way of analyzing the TM surface preferences towards CO dissociation is a parity plot of the energy barrier, Ea, against the CO desorption energy, seized here as minus the Eads. The question mark here would be whether it would be easier for an adsorbed CO molecule to desorb or dissociate into C+O. This competitive process is represented in Fig. and reveals that, on most fcc TM surfaces, CO would preferentially desorb, except for the Ni (001) surface. On the other hand, on most bcc surfaces, CO would be prompted to dissociate, except for Fe (011) and (111) surfaces. Some bcc TM surfaces, such as Nb and Mo (111), are in the equilibrium line where dissociation and desorption compete. Finally, as found in previous analyses, hcp TMs show scattered trends depending on whether it is an early, middle, or late TM. It is worth mentioning that Tc (112 ̅ 0) and Re (0001) surfaces, which would walk the parity line, where both CO desorption and dissociation are kinetically equally likely.
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Fig. qualitatively assess whether the reaction energy barrier, Ea, is also defined by εd, like the molecular and atomic Eads as found above. The plot shows how fcc has a different behaviour when compared to hcp and bcc, and the better linearity for close-packed crystallographic phases than for bcc TMs. Figs. 9, 11, and 12 illustrate that, in general, εd defines the reactants and products adsorption energies, and these, in turn, define the reaction energy difference, ΔE. The reaction energy also conditions the extent of the reaction energy barrier, Ea, aligned with the Brønsted-Evans-Polanyi (BEP) relationships .
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The BEP is indeed evaluated in Fig. . Notice that two limits define a Ea/ΔE region where a BEP is possible. One is a limit case for earliest TSs -located very close to the reactants energy level-where there is essentially no energy barrier, regardless the value ΔE has, i.e. Ea = 0 eV, and so, basically the linear equation of Ea = a•ΔE + b has a slope a of zero, and a b intercept of 0. On the other hand, latest TSs -located very close to the products energy level-are significant for endothermic situations, where the energy barrier is basically the difference in energy between reactants and products, i.e. Ea = ΔE, and so, basically, the linear equation of Ea = a•ΔE + b has a slope a of one, and a b intercept of 0.
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Notice how the gained BEP relation is good with a regression coefficient R of 0.899, even if mixing different surface terminations crystallographic structures, and reaction mechanisms, see Fig. , and as good as a descriptor as the εd, shown in Fig. , underscoring that εd is, perchance, a suited descriptor of the TMs surfaces chemical activity, and, in an indirect way, of the chemical reactivity, as ΔE does. Aside, the BEP slope of 0.667 is in between the limits of 0 and 1, implying that is not simply defined by ΔE, but also other TM surface factors play a role in the TS definition and the estimate of the Ea.
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Notice that in the above highlighted cases, except for Fe (001) surface, all are hcp (112 ̅ 0) surfaces. This underscores how the surface geometry seems to be crucial to promote the CO dissociation. The (112 ̅ 0) surfaces, compared to the (0001) and (101 ̅ 0) ones, have an atomic layout that permits a higher coordination towards the CO adsorbate, effectively fostering the interaction, thus, weakening the CO bond and allowing for a better dissociation.
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However, the hcp (112 ̅ 0) surfaces are the least stable ones according to their surface energies, which in turn explains in part their enhanced chemical activity . This surface has to be engineered in any Re, Os, Co, or Ru catalyst that such surface sites have to be engineered, e.g.
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Oxo-and hydroxo-bridged oligonuclear metal centers are structural motifs commonly encountered in inorganic and bioinorganic chemistry. In these magnetic complexes, unpaired electrons localised at transition metal centers can interact either through direct exchange, where the d orbitals of different metal sites overlap spatially, or through superexchange mechanisms (Figure ). These kinds of mechanism are indirect magnetic interactions mediated by doubly occupied ligand orbitals that bridge the metal centers, enabling spin alignment through virtual electron hopping. For example, a previous study on the [Mn(III) 2 (µ-O)(µ-OAc) 2 (Me 3 tacn) 2 ] 2+ complex identified three significant superexchange pathways: two symmetric π pathways involving orbitals perpendicular to the Mn 2 O 2 plane and a mixed in-plane σ/π pathway. In general, direct exchange is much more rare for oligonuclear metal complexes than superexchange. Taking together both mechanisms over all pairs of magnetic orbitals influences whether the spins on the transition metal centers align parallel, resulting in ferromagnetic coupling, or antiparallel, resulting in antiferromagnetic coupling. (a) 180 The sum of all two electron interactions in magnetically coupled systems is usually quantified with the phenomenological Heisenberg-Dirac-van Vleck-Hamiltonian (eq. 1). ĤHDvV = -2
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In this equation, Ŝi/j represents the total number of unpaired spins on both metal centers i and j, and J ij is the isotropic exchange coupling constant that quantifies the strength of the interaction. It is by definition positive for ferromagnetic and negative for antiferromagnetic interactions. Using localized magnetic orbitals, the overall J coupling can be decomposed into ferromagnetic (J F,ab ) and antiferromagnetic (J AF,ab ) contributions for each orbital pair (ab):
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Kahn and Briat developed a model based on the Heitler-London valence bond theory to relate the magnetic coupling to the exchange interaction term (K ab , ferromagnetic coupling), the overlap of magnetic orbitals (S ab ), and an effective one-electron operator (β = ⟨a| ĥ (1) |b⟩, antiferromagnetic coupling). J ab = 2K ab + 4βS ab (3) An alternative approach to decompose magnetic interactions was proposed by Hay, Thibeault, and Hoffmann who use symmetry-adapted magnetic orbitals (ϵ g/u ): 12
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Both Kahn and Briat's localized orbital approach and Hay, Thibeault, and Hoffmann's symmetry-adapted orbital method emphasize that ferromagnetic coupling depends on two-electron exchange integrals, while antiferromagnetic coupling involves both one-and twoelectron integrals. R. Hoffmann et al. noted in 1975 that for small structural changes or variations in the substituents, changes in the two-electron parts are negligible compared to changes in the orbital energies. This implies that small geometric adjustments can significantly alter the overlap of the magnetic orbital pairs and the squared orbital energy differences while leaving the exchange and Coulomb interactions relatively unaffected. Thus, the total magnetic coupling can be decomposed into ferromagnetic and antiferromagnetic components through a multicomponent fitting using equation 2. This decomposition procedure was first demonstrated by Ruiz and coworkers, who illustrate a linear dependence of the overall J coupling on the squared orbital energy differences of the σ orbitals in hydroxoand alkoxo-bridged copper dinuclear complexes using canonical orbitals from DFT. The overlap of magnetic orbitals S ab can be obtained via orbital transformations from broken-symmetry DFT (BS-DFT). However, since broken-symmetry solutions are not spin eigenstates, the resulting energy differences between high-spin and broken-symmetry determinants cannot be directly compared with experimental data. Instead, projection schemes, such as those proposed by Noodleman, Ruiz et al., and Yamaguchi, must be applied to extract meaningful J coupling constants. Among these, the Yamaguchi scheme is widely used due to its robustness in predicting magnetic coupling constants across a broad range of coupling strengths. While BS-DFT is useful for predicting the sign and magnitude of the magnetic coupling, it has major limitations in decomposing the individual ferromagnetic and antiferromagnetic contributions. First, magnetic orbitals, though derived from canonical orbitals, do not contain energy information since they are not optimized in a self-consistent field. Second, the total interaction is simplified to the sum of pairwise orbital interactions, (e.g., a pair of σ g,u -orbitals), neglecting dynamic charge polarization or spin polarization effects, which can significantly contribute to the overall coupling in systems with non-negligible hole-particle excitations.
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Both limitations can be tackled by using post-Hartree-Fock methods like complete active space self-consistent field (CASSCF), which furthermore provides access to the individual spin state energies. CASSCF captures the multiconfigurational character of the orbitals, with dynamical correlation effects introduced through perturbative theories like CASPT2 or NEVPT2. While the orbital energies remain unknown for the CASSCF wavefunction, Hartree-Fock orbital energies can be obtained. This implies that a multicomponent fitting procedure can evaluate the ferromagnetic and antiferromagnetic components of individual coupling paths. However, certain quantitative limitations will remain since correlation effects are included only indirectly in the underlying orbital basis.
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In this work, we apply the idea of decomposing ferromagnetic and pairwise antiferromagnetic contributions in a proof-of-concept study using CASSCF and NEVPT2 calculations for different active space sizes. We apply this approach to simplified dinuclear model systems with a single µ-oxo bridge that have varying numbers of coupling pathways: one σ path in
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2+ and one σ, two π and one δ path in [Fe 2 (µ-O)(NH 3 ) 10 ] 2+ . The usage of ammonia ligands to complete the coordination spheres is motivated by their simplicity, minimal steric hindrance and considers common structural motifs for the respective transition metals. As noted previously, this choice reduces potential biases toward specific geometries and electronic structures that might arise with bulkier or more complex ligands.
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The methodology used here to decompose ferromagnetic and antiferromagnetic contributions to the overall observed exchange coupling constant relies on the fundamental equations eq. 2 and eq. 3. We propose that for a qualitative picture of these contributions in realistic complexes beyond simplified models with two electrons in two orbitals, CASSCF/NEVPT2 calculations can be used. In principle, any active space size and composition can be chosen, as long as the magnetic orbitals and the orbitals contributing to the superexchange mechanism are included. Pairwise orbital energy differences are central to the fitting procedure.
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The small variations in orbital energies required for Hoffman's treatment are generated from scans of the bridging angle or dihedral angle with otherwise frozen geometries in 1 • / 5 • increments in comparison to the relaxed geometry. The resulting squared changes in orbital energy differences, together with the J-coupling constants derived from spin state energies, serve as input for the multiple linear regression analysis described by equation 4.
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This regression procedure provides two outputs: (i) the y-intercept, which corresponds to the total ferromagnetic coupling in the system and is identical to twice the sum of the classical Hartree-Fock (HF) exchange interactions of the magnetic orbital pairs; (ii) the slopes for each active orbital pair, which quantifies the antiferromagnetic contribution to the overall coupling and is inversely proportional to the difference of the inter-and intra-site Coulomb interaction of the respective orbital pair. Since the multicomponent fitting procedure uses linear regression, a single minimum is obtained. For [Fe 2 (µ-O)(NH 3 ) 10 ] 2+ , the system with the largest number of coupling paths in this study (four in total), a minimum of five data points is required in the scan to avoid underfitting. To ensure clear trends in the analysis, this study utilizes 11 data points for the M -O -M angle scans and 14 data points for the M -O -M -N dihedral scans.
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[Fe 2 (µ-O)(NH 3 ) 10 ] 2+ underwent optimization in a two-step procedure. Initially, unrestricted KS-DFT geometry optimizations were performed for the high-spin states, which involve ferromagnetic coupling between the two centers, and these were succeeded by BS-DFT optimizations. This approach guaranteed that subsequent unrelaxed angle scans started from local minima on the corresponding potential energy surfaces. All computations utilized the def2-TZVP basis set, and the construction of Coulomb integrals were sped up using the related def2/J auxiliary basis set. Grimme's D4 dispersion correction was incorporated to address long-range interactions between the metal-oxo bridge and the coordinating ammonia ligands. Geometry optimizations employed the defGrid3 integration grid, with both the SCF and optimization steps being subject to tight convergence criteria (VeryTightSCF, Very-TightOpt). To improve convergence stability, the SlowConv option was utilized throughout the SCF cycles.
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To correctly model electron correlation effects in BS-DFT, three hybrid functionals (TPSSh, 31 B3LYP, 32 and PBE0 33 ) were evaluated. These functionals have been shown to reliably predict the electronic structures of transition metal complexes. Although the geometries of the copper complex showed minimal sensitivity to the choice of functional, minor variations in the M -O -M angles were noted for the nickel and iron complexes. In the end, the PBE0-optimized geometries were chosen for unrelaxed angle scans, as they showed greater alignment with the anticipated Mulliken spin populations on the metal centers. Information on all geometries acquired using the different functionals are provided in the SI.
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To examine the decomposition of magnetic interactions via small geometric changes, the M -O -M angles were altered in 1 • increments within a ±5 • range around the BS-DFT minimum, while the M -O -M -N dihedrals were scanned in 5 • increments across a ±30 • range. At every scan point, single-point BS-DFT and CASSCF calculations were executed to determine the J coupling constants and characterize the magnetically active orbitals. For the BS-DFT calculations, the Yamaguchi, Ruiz et al., and Noodleman projection methods were applied to extract J coupling values.
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CASSCF calculations with follow-up NEVPT2 corrections were performed using the def2-TZVP basis set and def2/J auxiliary basis set, consistent with the BS-DFT geometry optimizations. The resolution of identity approximation was applied to accelerate the computation of Coulomb and exchange integrals (RIJK). Initially, minimal active spaces were utilized: (2,2) for the copper dimer, (4,4) for the nickel dimer, and (8,8) for the iron dimer.
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To assess the role of doubly occupied oxygen 2p orbitals in mediating the magnetic coupling via the superexchange mechanism, the active spaces were expanded to (8,5) for the copper complex, (10,7) for the nickel complex, and (14,11) for the iron complex. These enlarged active spaces were used to assess their influence on the ferromagnetic and antiferromagnetic contributions to the magnetic coupling, within both the CASSCF and the NEVPT2 frameworks.
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The structures of the dicopper, dinickel, and diiron complexes were designed to mirror typical coordination environments for each metal atom; see Figure for the BS-DFT-optimized geometries. Three ammonia molecules coordinate each Cu +II ion in the copper complex in a square planar structure, with a single µ-oxo group connecting the two metal centers. In contrast, the iron complex has two Fe +II ions each coordinated by five ammonia ligands, forming an octahedral geometry, whereas the nickel complex has two Ni +II ions arranged in a tetrahedral coordination environment.
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The angles of the bent M +II -O -M +II core are fairly similar: 127.0 • for copper, 139.4 • for nickel, and 142.5 • for iron, as illustrated in Figure . The mean Cu-O and Fe-O bond lengths are 1.86 Å each, whereas the Ni-O bond length is slightly shorter at 1.83 Å. The intermetallic distances are, in every instance, sufficiently large to render direct magnetic coupling paths negligible. The magnetic coupling is thus anticipated to be mediated primarily drals have a considerable impact on the total magnetic coupling strength in µ-oxo-bridged metal complexes because of the relative ligand sphere orientations. The twisting of these M -O -M -N dihedrals thus modifies the amount of antiferromagnetic coupling along the σ-pathway by changing the overlap of the magnetically active orbitals. Solomon's examination of dinuclear copper systems, for instance, revealed a dramatic transition from strong antiferromagnetic coupling (-321 cm -1 ) for collineary aligned magnetic orbitals, to strong ferromagnetic coupling (+325 cm -1 ) for almost orthogonal magnetic orbitals.
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Table summarizes our single-point BS-DFT calculations, which reveal that the copper complex exhibits a strong antiferromagnetic coupling, whereas the nickel complex shows a coupling strength that is about half that of the copper complex and the iron complex displays an even weaker antiferromagnetic coupling. Experimental data for comparable complexes also show this pattern of a weakening antiferromagnetic coupling strength, with experimental J values ranging from -322 to -536 cm -1 for copper, -39 to -98 cm -1 for nickel, and -16 to -34 cm -1 for iron. Notably, functionals with similar Hartree-Fock (HF) exchange contributions, such as PBE0 and TPSS0 (both with 25% HF exchange), yield comparable results. In contrast, TPSSh with less HF exchange enhances the antiferromagnetic interactions. This pattern is consistent with what Kahn and Briat's model (eq. 3) predicts, which indicates a relationship between the quantity of the HF exchange and the ferromagnetic part of the J coupling.
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The decomposition method for ferromagnetic and antiferromagnetic components is first tested on the copper complex. The minimal (2,2) space includes the two magnetically active orbitals forming a single σ-coupling pathway, which upon inclusion of the three oxygen 2p orbitals is expanded to an (8,5) active space, see Figure . A Löwdin orbital analysis of the canonical orbitals reveals that the pair of magnetically active orbitals consists predomi-nantly of singly occupied d z 2 orbitals (89-92%) localized at the two metal centers, with small contributions (2-4%) from p y and p z orbitals on the bridging oxygen, which are necessary to form the σ-superexchange pathway. These orbitals closely resemble those described by Hoffmann using the extended Hückel model, making them well-suited for the intended analysis. Further details of the Löwdin orbital analysis on all complexes can be found in the SI. The energy difference between the gerade and ungerade σ pair is approximately 7400 cm -1 , significantly smaller than the energy gap to the nearest p orbital, which is 32900 cm -1 . As a result, the primary configurations of the two spin states involve only doubly occupied oxygen 2p orbitals. Referring to Hoffmann et al., small geometric changes primarily affect the energy splitting of the σ-pair and consequently influence the J coupling, without significantly altering the exchange or Coulomb interactions. The impact of varying the Cu -O -Cu angle in small steps between 123 • and 131 • on the overall magnetic coupling, as determined by CASSCF, NEVPT2, and BS-DFT calculations, is illustrated in Figure .
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Both BS-DFT and CASSCF/NEVPT2 calculations show a nearly linear decrease in J In BS-DFT, the projection methods of Noodleman and Ruiz represent the extreme cases of weak and strong overlap between magnetic orbitals, respectively. Due to only small amounts of spin contamination encountered in all three model complexes, the denominator term found in Yamaguchi's formula approaches the term found in the weak coupling limit described by Noodleman, resulting in similar J coupling constants for both projection schemes.
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Expanding the active space and incorporating dynamic correlation effects in NEVPT2 enhances the electronic structure description by perturbatively accounting for excitations into higher-lying orbitals, such as the 4d double-shell orbitals. This adjustment brings J NEVPT2 closer to the J Yamaguchi values. Despite the differences between the CASSCF, NEVPT2, and ting procedure. It is expected that larger active spaces combined with NEVPT2 will account for missing dynamic correlation, aligning the results more closely. As highlighted in the fundamental review by Roald Hoffmann, the magnetic interaction in this system consists of one ferromagnetic and one antiferromagnetic component. By applying a linear regression analysis to the magnetic coupling using equation 4, the exchange interaction and the difference in intra-and inter-site Coulomb interactions between the gerade and ungerade σ orbitals can be extracted. These values can then be used to quantify the strength of the ferromagnetic and antiferromagnetic contributions along the σ-coupling pathway. The resulting variations in magnetic coupling as a function of the squared orbital energy difference (ε i -ε j ) 2 for all CASSCF and NEVPT2 scans are shown in Figure , which highlights clear linear correlation regimes across all four fits.
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The linear regressions found for the CASSCF and NEVPT2 calculations confirm the linear relationship between the squared orbital energy differences and the overall J coupling, validating the principle for extracting exchange and Coulomb interaction differences despite the observed deviations in the fit parameters. Notably, the slopes of the plots nearly double when dynamic correlation effects are incorporated: from -1.5 • 10 -6 cm in the CASSCF calculations to -3.6 • 10 -6 cm in the extended NEVPT2 calculations. Conversely, the yintercept shows an inverted trend, decreasing from +33.8 cm -1 in the minimal CASSCF model to +21.1 cm -1 in the extended NEVPT2 framework. This trends suggests that dynamic correlation effects significantly influence both the antiferromagnetic and ferromagnetic contributions. We attribute the observed deviation from linear behavior in the NEVPT2 calculations with an (8,5) active space to additional dynamic charge polarization introduced when the Cu-O-Cu angle is bent beyond its equilibrium geometry (vide infra).
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Focusing on the linear sections, the ferromagnetic and antiferromagnetic contributions in the σ g,u orbital pair are quantified. The extracted ferromagnetic components, see Table , fall within a relatively narrow range of +21 to +34 cm -1 across all scans, in line with expectations formulated by Hoffmann et al. (+1 to +50 cm -1 ). The antiferromagnetic coupling along the σ path increases substantially with the inclusion of perturbation theory, from values of -83 and -87 cm -1 for the small and large active space to -148 and -192 cm -1 , respectively. This further highlights the influence of dynamic charge polarization in the NEVPT2 calculations.
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This deviation can likely be attributed to higher 1p1h excitations, which include dynamic charge and spin polarization effects that are implicitly captured in the NEVPT2 calculations Table : Ferromagnetic and antiferromagnetic contributions (J AF,σ/F ) for the equilibrium geometry of the copper complex, calculated with the Cu -O -Cu angle scan approach using CASSCF and NEVPT2 calculations with (2,2) and (8,5) active spaces.
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involving oxygen 2p orbitals. It is important to note that these effects are not accounted for in the general equation of magnetic coupling (eq. 4). By examining the formulations for dynamic charge polarization (eq. 5) and spin polarization (eq. 6) proposed by Malrieu et al. over several studies, we can estimate the impact of these excitations on the observed J-coupling trends. 9,47,48
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Both types of 1h1p excitation contribute significantly to the J coupling only when the energy differences between the ligand orbitals and the magnetically active orbitals are sufficiently small. Important to note is that, these excitations influence the ferromagnetic and antiferromagnetic components differently: dynamic charge polarization increases the antiferromagnetic contribution by reducing the effective difference between inter-and intra-site Coulomb interactions; in contrast, spin polarization increases the number of accessible configurations with unpaired electrons, stabilizing the high-spin (and intermediate) states and thereby enhancing the ferromagnetic component. As a result, spin polarization shifts the linear trends in the squared orbital energy difference diagrams, while dynamic charge polarization dampens the linear progression.
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Compared to the copper complex, the nickel complex features an additional δ g,u magnetic orbital pair, while the iron complex contains additional δ g,u , π x/g,u , and π y/g,u magnetic orbital pairs, as illustrated in Figure . Löwdin analyses indicate that the magnetic orbitals in these complexes contain 93-98% metal d character, while the remaining 1-4% are primarily contributed by oxygen 2p orbitals and less than 3% stem from nitrogen 2p orbitals, see SI for details. This composition is sufficiently analogous to that of the σ g,u orbital pair in the copper complex, as well as to predictions from extended Hückel theory, to support the decomposition of the magnetic interactions. Numerous BS-DFT studies have indicated that the orbital overlaps for corresponding δ g,u orbital pairs in different bridged transition metal complexes contribute very little to the overall coupling, making them negligible. These findings are in good agreement with the energy differences seen for the canonical orbitals in our CASSCF calculations. The energy splitting of the σ g,u orbital pair is 10100 cm -1 in the nickel complex and 9650 cm -1 in the iron complex, both in the same order of magnitude as the splitting value found in the copper complex of 7400 cm -1 . In contrast, the energy splitting of the δ g,u orbitals is significantly smaller at 63 cm -1 in the nickel complex and 16 cm -1 in the iron complex. Since the squares of these energy splittings influence the respective antiferromagnetic J couplings, the σ coupling paths in the CASSCF calculations are up to 5-6 orders of magnitude stronger than the δ paths. In the iron complex, the π x/g,u and π y/g,u orbital pairs in the iron complex are split by 8000 cm -1 and 7800 cm -1 , respectively, which is similar to the energy splitting of the σ g,u orbitals across all complexes. Their contribution to the overall coupling path should therefore only be marginally smaller than the σ path in the same complex.
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The overall J couplings in the angle scan are distinctly smaller with the (4,4) and (10,7) active spaces using CASSCF and NEVPT2 than found for the BS-DFT calculations, see Figure . Interestingly, when compared to the copper results, all scan curves are noticeably flattened. Additional angle scans with increased scan ranges between 125 • and 180 • reveal no significant changes in the ∆J CAS/BS-DFT trends, see SI. This leads us to the conclusion that the observed variations in ∆J are not a result of a too small structural change, but rather are characteristic for the electronic structure of the nickel complex.
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Using these data in a multiple linear regression analysis, we extracted the total ferro- magnetic contribution as well as the antiferromagnetic σ and δ components. Similar to the copper complex, NEVPT2 data for angles greater than 141 • in the nickel complex deviated from the underlying fitting model and were thus excluded in the linear regression.
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As shown in Table , the general ferromagnetic and antiferromagnetic σ components are nearly identical in magnitude to those of the copper complex. The antiferromagnetic δ component in the nickel complex is, as expected from magnetic orbital overlap considerations, essentially negligible. Introducing additional dynamic correlation via NEVPT2 increases the ferromagnetic and antiferromagnetic coupling contributions in the nickel complex, whereas for the copper complex only the antiferromagnetic contributions increased. While the rise in the δ antiferromagnetic contribution can be explained by dynamic charge polarization similar to the explanation for the σ contributions, spin polarization plays a significant role for the Table : Ferromagnetic and antiferromagnetic contributions (J AF,σ,δ/F ) for the equilibrium geometry of the nickel complex in (4,4) and (10,7) CASSCF and NEVPT2 calculations with the Ni -O -Ni angle scan method.
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overall ferromagnetism in this system due to the presence of multiple unpaired electrons per metal center. We point out that the canonical orbital energies remain unchanged between the CASSCF and NEVPT2 calculations, indicating that the additional dynamic correlation is captured only in the overall J coupling and not reflected in the orbital energies. This introduces a source of error when performing scans using perturbation theory methods such as CASPT2 or NEVPT2, in addition to the unaccounted 1p1h effects. Nevertheless, qualitative trends for different coupling strengths along the σ and δ paths can be reliably extracted from both CASSCF and NEVPT2 calculations.
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Having demonstrated that angular scans and subsequent decoupling of the ferromagnetic and antiferromagnetic components are feasible for both the copper and nickel complexes, we now turn to the iron complex, which features the largest number of coupling paths in this study. While the overall pattern of the angle scans is similar to the copper and nickel complexes (see Figure , top), the larger number of magnetic coupling paths leads to a significant reduction in the overall J coupling variation across all scans. In the iron complex, the J coupling changes are ∆J CAS,Fe = 0.10 cm -1 and ∆J BS-DFT,Fe = 0.04 cm -1 , nearly vanishing within the numerical precision. This precludes a meaningful multiple linear regression approach since the small differences in the overall J coupling correspond to an equally small variation in orbital overlaps during the scan. Recently, Heyer and coworkers demonstrated that by rotating the ligand spheres in µ-oxo-bridged copper complexes relative to each other, it is possible to switch the J coupling from strongly antiferromagnetic for collinear magnetic orbitals to strongly ferromagnetic for nearly orthogonal magnetic orbitals. Following this approach, we performed an M -O -M -N dihedral scan in 5 • steps across a ±30 • range around the minimum at 31.0 • . This significantly increased the variation in the J coupling, reaching ∆J CAS,Fe = 1.01 cm -1 and ∆J BS-DFT,Fe = 1.43 cm -1 (see Figure , bottom), pushing the results beyond the numerical error range of both CASSCF and BS-DFT calculations.
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The reason for the magnitude differences of the J coupling variations in both scans is the higher deviation in the canonical orbital energies of the δ g,u orbital pairs throughout the dihedral scans compared to the σ g,u orbitals. Figure illustrates this distinctness in the nickel and iron complexes by depicting the energy trends of the σ g,u and δ g,u orbitals.
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While the σ g,u orbital energies remain parallel in both scanning approaches-resulting in negligible differences in the squared orbital energy changes-the behavior of the δ g,u orbital pairs diverges significantly. We emphasize that the energy difference of the δ g,u orbitals remains small and the orbital energy lines remain almost parallel in the angle scan. In the dihedral scan, a crossover point emerges close to the equilibrium geometry and the orbital pairs gradually diverge from there, reaching the scan extremes at about 2000 cm -1 for the nickel complex and 400 cm -1 for the iron complex.
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Within the orbital overlap model, a phase rotation of one δ g,u orbital during the dihedral scan is responsible for these sharp differences. The behavior of the corresponding δ g,u orbital pair differs significantly from that of the σ g,u orbitals, which only undergo slight changes in their overlap due to minor structural perturbations in the bent M -O -M bridges or the rotation of the ligand field at one metal center. Changing the M -O -M angle within the restricted range used here does not result in such a severe phase change in the δ g,u orbitals. Despite its smaller overlap by three orders of magnitude, rotating the ligand field at one center over a 60 • range during the dihedral scan induces a complete character inversion in the δ g,u orbitals, thus shifting the character of the δ g orbital from bonding to antibonding character and vice versa. Such a drastic phase change is not induced in these orbitals when the M -O -M angle is varied. A similar trend to the δ g,u orbital pairs is observed for the iron complex in the two π g,u orbital pairs, which remain largely unaffected by the choice of scanning approach. A more detailed analysis of the variations observed across all three coupling paths in the iron complex is shown in the SI.
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Comparing the extracted total ferromagnetic and individual antiferromagnetic contributions from the angle and dihedral scans, Table , allows us to better estimate the error range of the general decomposition approach, independent of uncertainties in the exact scanning range of both methods. Across all scanning methods, the ferromagnetic component derived from pure CASSCF calculations stays within a small range of +34 to +27 cm -1 for the copper complex and +37 to +13 cm -1 for the nickel complex. These values are consistent with the range of + (1 -50) cm -1 expected by Hoffmann et al. These findings reinforce our earlier Table : Ferromagnetic and antiferromagnetic contributions (J F/AF,σ,π,δ ) to the overall magnetic coupling constant for the equilibrium geometries of copper, nickel, and iron complexes, calculated using CASSCF and NEVPT2 methods with the M -O -M -N dihedral scan approach.
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conclusion that the ferromagnetic component of the couplings is nearly constant across the series of complexes examined here. Turning to the antiferromagnetic contributions for the copper and nickel complexes, the two scanning techniques show a similar behaviour: the absolute coupling strength of the σ contribution in the copper complex remains within a narrow range of -87 to -83 cm -1 , and a slightly wider window of -67 to -46 cm -1 in the nickel complex. The δ-coupling contribution remains 5-6 orders of magnitude smaller than the σ component.
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The received ferromagnetic contribution in the nickel complex varies significantly, with extreme values of +205 cm -1 for the minimal active space and +11 cm -1 for the extended active space in the dihedral scan. The variability is much smaller in the copper case. This implies that spin polarization necessitates excitations into much higher lying orbitals in the copper system than in the nickel complex. This effect thus appears negligible for a cop-per complex with only one magnetically active orbital pair, but not for cases with multiple active orbital pairs. Similarly, we find that the derived antiferromagnetic contributions for both complexes in the NEVPT2 calculations change significantly between the two scanning procedures (copper: -210 to -148 cm -1 , nickel: -262 to -102 cm -1 ). With values ranging from -86 • 10 -3 to -4 • 10 -3 cm -1 , the δ-path in the nickel complex exhibits a similar trend, though its overall contribution remains irrelevant. We attribute these significant differences again to the lack of dynamic charge polarisation in the underlying model.
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The main purpose of introducing the dihedral scan was to access the ferromagnetic and antiferromagnetic contributions in the iron complex. The ferromagnetic component in the iron complex is evaluated at +19 cm -1 for the minimal active space and +22 cm -1 for the increased active space using the CASSCF approach. This is, as expected, similar to the ferromagnetic coupling contribution of both other complexes. The antiferromagnetic σ path is found to contribute -(20( )) cm -1 with the minimal (increased) active space.
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The antiferromagnetic π contributions in the iron complex are about half as strong as the σ contributions, consistent with BS-DFT orbital overlap calculations. This confirms the expectation that the π x and π y paths are non-negligible. The antiferromagnetic coupling along the δ path remains five orders of magnitude weaker than the σ and π paths, as it was also found for the other examples. With the NEVPT2 approach, the variability of the coupling contributions using the two active space sizes is similar in magnitude as in the nickel complex. The deviations are most pronounced in the (14,11) NEVPT2 calculations for J AF,πy and J AF,δ in the iron complex.
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There are several contributing factors for the deviations between the CASSCF and NEVPT2 results in the dihedral scans. In the (14,11) NEVPT2 calculations for the iron complex, antiferromagnetic couplings are incorrectly fitted as well as ferromagnetic due to missing hole-particle excitations in the fitting equation. As discussed further above additional dynamic correlation effects also play a role. For future quantitative analyses of ferromagnetic and antiferromagnetic components, these missing factors must be considered. Moreover, in complexes with iron or manganese that have up to five unpaired electrons per magnetically active center, the ferromagnetic and antiferromagnetic contributions will become so small that the effect of the isotropic biquadratic term on the overall magnetic coupling should be included in a decomposition analysis of magnetic coupling paths.
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Building on the foundational equations by R. Hoffmann et al. and O. Kahn and B. Briat, we propose here an approach to decompose magnetic coupling in dinuclear complexes with multiple coupling paths into ferromagnetic and antiferromagnetic contributions. We use CASSCF and NEVPT2 calculations in conjunction with M -O -M angle and M -O -M -N dihedral scans, where the exchange integral and the difference between the intra-side and interside Coulomb interaction integrals stay effectively unchanged, so that the squared changes in orbital energy differences can be related with the magnitude of the overall magnetic coupling strength.
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Contrary to expectations, there was no maximum scan range beyond which the linear relationship between the J coupling constant and the squared orbital energy difference broke down. Rather, the fitting range was limited by either encountering irrelevant electronic structures, or by encountering regions in which 1h1p excitations became relevant that are not included in the model assumptions. The latter, in addition to further polarisation and dynamical correlation effects, also limited the use of NEVPT2 results that would normally be expected to be more robust and quantitatively meaningful. Future developments aiming to decompose the overall J coupling constant into ferromagnetic and antiferromagnetic contributions should therefore expand the fitting equation to incorporate these missing spin polarization and dynamic charge polarization effects.
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The method was developed with and applied to three model complexes, [Cu 2 (µ-O)(NH 3 ) 6 ] +2 , [Ni 2 (µ-O)(NH 3 ) 6 ] +2 and [Fe 2 (µ-O)(NH 3 ) 10 ] +2 , with increasing numbers and different types of exchange coupling paths. Importantly, different types of structural variation are needed to obtain meaningful variations in the overall J coupling constant: while a simple angular scan was sufficient for the copper and nickel cases, a scan of the M -O -M -N dihedral angle was needed for the iron example due to the limited response of the magnetic coupling towards a variation in the M -O -M angle. For future application studies, we recommend a minimal change of the J coupling constant of 1 cm -1 over the scan range. We find that the ferromagnetic components remain fairly consistent across these complexes within a range of 13 -32 cm -1 , matching the expectations of R. Hoffmann. The antiferromagnetic contribution of the σ path gradually weakens from copper to nickel to iron, and the π paths each contribute approximately half as much as the σ path to the overall coupling in the iron complexes. In all complexes, the δ paths are irrelevant for the overall coupling, as expected.
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Our method provides a first step towards quantifying the old adage 'ferromagnetic coupling is the absence of antiferromagnetic coupling' in real-life complexes. We envision that future application studies can focus on interpreting the influence of different active space choices, and evaluate chemical changes such as the nature of the bridge, the influence of ligands trans to the bridge, and even oxidation state changes if double exchange effects are appropriately accounted for in the fitting equations.
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The massive industrial use of aluminum, the most abundant metal in the Earth's crust, has implied its introduction into the biosphere, contrary to previous natural conditions in which complex geochemical cycles prevented its solubilization. Consequently, humans are nowadays highly exposed to this metal, a fact linked to various diseases, starting from early evidence of dialysis encephalopathy or osteodystrophy in patients with renal failure under dialysis treatment to more recent evidence linking aluminum to several neurodegenerative disorders. However, the molecular bases for these toxic effects are still not well understood, partially due to the inherent difficulties of interpreting experimental data. In this sense, theoretical calculations have become fundamental to get insight into the bioinorganic chemistry of aluminum and its potentially harmful effects. The pro-oxidant ability of aluminum is one of its most known toxic effects, a factor frequently underestimated due to its nonredox nature. That is, the oxidation state +3 of aluminum in a biological system is maintained unaltered in different biochemical environments, as demonstrated recently. However, this does not imply that aluminum can not alter important redox cycles in vitro and in vivo. The early hypothesis of the possibility of forming an aluminum-superoxide complex, which would augment the lifetime of this radical species, has been proven computationally. The thermodynamic stabilization of a metalsuperoxide complex is not by itself explanatory of the mechanism behind the pro-oxidant ability of aluminum. However, Fukuzumi et al. have reported a linear relationship between the strength of a metal-superoxide interaction and its oxidant activity of a metal. Despite these circumstantial pieces of evidence that point to aluminum as a promoter of oxidative stress, the topic is still highly controversial due to the lack of direct measures of the effect of aluminum in the redox potentials of radical species.
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They investigated the promotion of the radical scav-enging reaction of hydroquinone derivatives (Me n QH 2 , n=0-4) by aluminum ion, using 2,2-diphenyl-1-picrylhydrazyl (DPPH•) as a model for a peroxyl radical. The authors were able to determine the reduction/oxidation potentials of DPPH•/Me n QH 2 in the absence and presence of aluminum, concluding unequivocally that Al(III) enhances the electronaccepting ability of DPPH• and consequently accelerates the DPPH• scavenging reaction by hydroquinones. This supported previous studies where it was established that radical scavenging reactions can be affected by redox inactive metals, e.g., Mg(II), Al(III) and Sc(III). In the present work, we give computational support to this study, determining how the presence of aluminum can alter the oxidation/reduction potential of these species. To achieve our goal, we investigated the different coordination modes that aluminum can form with DPPH• and QH 2 mimicking the experimental conditions and assuming an outer-sphere mechanism, as done in the reference experimental study. Our results show a good agreement with experiments, and they allow us to identify the key species involved in promoting the redox reaction by aluminum. This gives valuable insights into the properties of aluminum that favor the electron transfer from hydroquinones to the 2,2-diphenyl-1-picrylhydrazyl radical, allowing us to identify unambiguously aluminum as a potential factor that alters the redox potentials of these species. Thus, our results provide a solid ground to identify Al 3+ as a possible toxic factor in biological media by affecting the thermodynamics of essential redox reactions, despite the non-redox nature of this metal.
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(PCM) approach (hereinafter referred to as L1 level of theory). The characterization of optimized structures (at 298.15K and 1atm.) confirmed all minima have no imaginary frequencies Electronic and solvation energies were further refined by single-point calculations at the M06-2X/6-311++G(3df,2p)/PCM(ethanol) level of theory (hereinafter referred to as L2 level of theory). Final free energies reported in this study also take into account the free energy change associated with moving from a standard-state gas phase of 1 atm of pressure to gas-phase state with specific concentrations (∆G •/ * ). Then, the total Gibbs energy (G) is given by:
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| 3 |
The concentrations used to estimate ∆G •/ * are in agreement with the experimental conditions described in ref. 20 in order the results to be comparable. Thereby, the following gasphase concentrations were used: 5.54 M for water, 15.36 M for ethanol, 2.4x10 -3 M for QH 2 and its derivatives, 2x10 -3 M for DPPH• and its derivatives, 0.2 M for Al 3+ and its derivatives, and different proton concentrations according to the pH in each situation. Limiting reagent's concentration is the one that defines the concentration of any formed intermediate specie. See Supporting Information (SI) for further details.
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were ∆G is the free energy change associated with the reduction process at the specific conditions studied, n is the number of electrons involved in the redox reaction, F is the Faraday constant, and E • SCE is the absolute reduction potential of the reference calomel electrode, which has a value of +4.521eV. See SI for further details.
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The one-electron redox potentials of QH 2 , Me 4 QH 2 , and DPPH• (Figure ) with and without the presence of the Al 3+ ion in solution were studied computationally and compared with the experimental redox potentials presented in ref. 20 in order to validate the level of theory and results. Experimental values are summarized in Table . Considering the contrary relation between redox potentials and free energies ( E=-∆G/nF ), experimental results exhibit that the oneelectron donating ability of hydroquinones decreases with the presence of Al 3+ , while the electron-accepting ability of DPPH• increases. However, the reduction of DPPH• is more promoted rather than the oxidation of hydroquinones impeded, and as a consequence, the global redox DPPH• radical scavenging reaction of hydroquinones in the hydroalcoholic medium evolves from non-spontaneous (E reac < 0) to spontaneous (E reac > 0) by the presence of Al . Both electron transfer (ET) and PCET oxidation and reduction processes were analyzed. For hydroquinones (i.e. QH 2 and Me 4 QH 2 ), the computed oxidation potentials of PCET reactions are clearly the ones that agree with experimental values (reactions b and f). E ox (reac. b) highly matches with the experimental value and E ox (reac. f) differs 0.17 eV from the experiment, which lies in the accepted error range. Overall, this allow us to establish that the oneelectron oxidation processes measured for hydroquinones are PCET. In contrast, the assignation is unclear for DPPH• because both ET and PCET computed reduction potentials have values close to the experiment, differing up to 0.09 eV.
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Finally, we can analyze the effect of methylation in hydroxyquinones. Methyl groups are inductive electron-donating groups, and therefore, methylation enriches the electron density of hydroquinones making the system more nu-cleophilic and stabilizing the oxidized forms. As a result of the stabilization, oxidation and deprotonation reactions are less endergonic and their respective oxidation potentials less negative. This tendency, which clearly comes out in experimental data, is also qualitatively picked up in our calculations. Methylated hydroquinone exhibits shifts in the oxidation potentials with respect to the non-methylated case of +0.29 eV and +0.04 eV for the ET and PCET processes, respectively. These shifts are comparable with the experimental one of +0.20 eV.
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When Al 3+ is present in solution, different coordination complexes with solvent molecules and the redox species (i.e. DPPH• and QH 2 ) can be formed. Apart from the formation of organometallic complexes with a positive trivalent charge, aluminum, as a strong Lewis acid, can reduce the pKa of the coordinated ligands, and prompt their deprotonation and the formation of coordination complexes of lower charge.
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The good description of the relative stabilities of the Al 3+ complexes included in Table is not straightforward, as it has been already reported for aqueous media and [Al(H 2 O) 6 ] 3+ species. The inclusion of explicit solvent molecules describing up to the second solvation sphere of the complex was revealed necessary to properly describe Al 3+ -water interactions. Specifically, the explicit description of hydrogen-bond nets that solvent molecules and ligands form in aque- ous or hydroalcoholic media seems necessary to successfully determine the corresponding pKa values of these Al 3+ complexes and to properly estimate their relative energies between protonated and deprotonated forms. However, for practical reasons, we have not considered additional explicit solvation spheres here and the solvent is just described using the PCM approach. Then, redox potentials of hydroquinones and DPPH• Al 3+ complexes that lie within a ∆G confidence interval of 10 kcal/mol are analyzed.
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Oxidation reactions that exhibit potential energy values consistent with experimental results are Q2, Q7, and Q9. Each reaction evolves from a different thermodynamic species; i.e., i) [Al(EtOH) 6 ] 3+ + QH 2 , ii) [Al(EtOH) 5 (EtO -)] 2+ + QH 2 , and iii) [Al(EtOH) 5 (QH -)] 2+ , respectively. Oxidation reactions with higher negative oxidation potentials than Q2, Q7, and Q9 reactions entail more endergonic processes than these where unstable species are formed and, consequently, they can be automatically discarded as possible hydroquinone's oxidation reactions in solution with the presence of Al 3+ . Q4 and Q10 reactions deserve further comments because entail exergonic and spontaneous processes that should be preferred over endergonic ones. However, further remarks can be made taking into account the experimental conditions.
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Considering the acidic experimental conditions (pH=1.5), a further justification of the most likely hydroquinone's oxidation process in the presence of Al 3+ can be done. Despite in Q10 we have considered reagent [Al(EtOH) 5 (QH -)] 2+ , it can not be formed directly by [Al(EtOH) 6 ] 3+ + QH -because at pH=1.5 deprotonated hydroquinones are not present in solution. Instead, it may come from the deprotonation of other Al 3+ complex such as [Al(EtOH) 5 (QH 2 )] 3+ through a multistep process as it is shown in Figure ). [Al(EtOH) 5 (QH 2 )] 3+ is a high energy complex (∆G of 11.8 kcal/mol, reported in Table ), which acts as an intermediate preventing the formation of [Al(EtOH) 5 (QH -)] 2+ and precluding reactions Q8, Q9, and Q10 to be feasible oxidation processes. A similar situation may happen for Q4. Q4 reaction entails two unfavourable processes together (ethanol deprotonation and hydroquinone PCET), which involves that the formation of an endergonic intermediate is highly likely (like the ones of Q3 or Q1) through a multi-step reaction mechanism (see Figure ). The high energy necessary to form these intermediates prevents the formation of [Al(EtOH) 4 (EtO -)(QH•)] 2+ through them.
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| 11 |
In summary, our computational study reveals that reactions Q2 and Q7 describe the most likely hydroquinone's oxidation reactions for the given experimental conditions in solution and with the presence of Al 3+ . They differ -0.07 and -0.01 eV with the experimental reference, respectively, and, energetically, both results are equiprobable. However, given the acidic experimental conditions (pH=1.5), [Al(EtOH) 6 ] 3+ is a more likely populated species than [Al(EtOH) 5 EtO -] 2+ , and therefore, Q2 should be considered the preferred oxidation process. Both reactions entail a PCET process; which it is the same oxidation process than the one observed without the presence of Al 3+ ions in solution (b in Table ). If we compare oxidation potentials reported in Table with E ox (b) of Table , the oxidation potential shift due to the presence of aluminum (∆E ∅→Al ox ) can be studied. We can observe that when Al 3+ is present, more negative results are obtained. This trend is also observed experimentally (Table ) and our results replicate it quantitatively. Then, we can conclude that QH 2 oxidation reactions are more endergonic and unfavored when Al 3+ ion is present in solution. The reason for this increase in endergonicity is a balance between the promotion of proton release and the disfavor of electron lose in the presence of aluminum. Thus, on one hand, aluminum has a tendency to favor deprotonation of the ligands that are attached to it, so that it can interact with a negatively charged species, however for the same reason, it tends to disfavor the lose of negative charge of the ligands, since this implies a decrease of the electrostatic interaction between the ligand and aluminun. In PCET processes, where both reactions coexist, the lose of an electron has a higher energetic cost than the lose of a proton in these aluminum complexes, and the overall effect is a more negative oxidation potential in the presence of aluminum. Notice for example that in the case of Q4 where one electron is released but two protons are unbound instead Assuming that the oxidation process will evolve following the same trend as for QH 2 , only the key oxidation reactions determined before (i.e., Q2, Q7, and Q9) have been studied here. However, as discussed before, the existence of the reagent [Al(EtOH) 5 (Me 4 QH -)] 2+ of reaction MeQ9 is less likely than the existence of the other Al 3+ reagents involved in MeQ2 and MeQ7 reactions. The [Al(EtOH) 5 (Me 4 QH -)] 2+ reagent complex of MeQ9 is more unstable (∆G of 10.8 kcal/mol) than the equivalent nonmethylated form [Al(EtOH) 5 (QH -)] 2+ (∆G of 8.7 kcal/mol) compared with the most stable form at pH=1.5, [Al(EtOH) 6 ] 3+ , (Table ). Moreover, it can neither be formed directly by [Al(EtOH) 6 ] 3+ + Me 4 QH -because the deprotonated form of Me 4 QH 2 is not present in solutions at pH=1.5 as its pKa value is > 11. Overall, we consider that MeQ2 and MeQ7 are the oxidation reactions of Me 4 QH 2 that better represent experimental results. Then, as for the QH 2 case, the most likely oxidation reactions of Me 4 QH 2 comparing to the experimental oxidation potential are dehydrogenation reactions (PCET reactions) that also imply the coordi-nation of Me 4 QH 2 with the Al 3+ complex.
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618b984bda1506e90d9ce178
| 12 |
Calculated oxidation potentials of Me 4 QH 2 in the presence of Al 3+ differ between 0.11-0.18 eV from the experimental E ox of -0.28 eV. The deviation from the experimental value is moderate but acceptable. However, we would like to remember that calculated oxidation potentials of Me 4 QH 2 without considering Al 3+ presence already exhibited a moderate deviation from the experimental value. In fact, regarding the shift of the oxidation potentials when aluminum is considered (∆E ∅→Al ox ) or upon methylation ∆E M et ox , the agreement with experimental figures is very reasonable. In this sense, our calculations replicate the experimental trend that Al 3+ disfavors Me 4 QH 2 oxidation (i.e., negative (∆E ∅→Al ox ) , and that methylation favors oxidation (positive values of ∆E M et ox ).
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618b984bda1506e90d9ce178
| 13 |
Takin into account precedent experimental studies, the one-electron reduction potential of DPPH• in the presence of Al 3+ has been studied here considering a solution with a pH value of 5.5. As it happened for hydroquinones, the presence of Al 3+ reduces the original pH of the solution without Al 3+ (for the DPPH• case the reduction goes from 7.5 to 5.5 pH units). Globally, the pH of the DPPH• solution with the presence of Al 3+ is more basic than the pH of equivalent hydroquinone solutions and it has an -0.28 -0.09 0.27 effect in the relative stability of the Al 3+ complexes that may be formed. As it can be observed in Table , when the solution becomes more basic, an extra stabilization of less charged complexes is achieved. We This could be expected from the chelation of alcohol ligands to aluminum, which causes important shifts in their pKa values. Table 6 reports all the one-electron reduction potentials analyzed for DPPH• considering Al 3+ present in solution. In all Al 3+ -complexes where DPPH• is coordinated to Al 3+ , the coordination is done through an orto nitro group of the picryl substituent of DPPH•, kO, (Figure ) because this coordination mode is always more stable than the diazane coordination, kN (see Table ).
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618b984bda1506e90d9ce178
| 14 |
One-electron reduction potentials reported in Table includes several redox reactions of DPPH• that present higher positive E red values than D12. Despite their E red values imply these reactions are more exergonic and thermodynamically favoured than the ones previously proposed, they were unfea-Table : One-electron reduction potentials, in eV, of DPPH• in the presence of Al 3+ complexes at pH=5.5, and relative reduction potential with respect to the values in the absence of aluminum. In the case of D1, D2, D5a, D5b, D8 and D10 the reactions are classified as electron transfer process and therefore, a value of 0.27 eV have been considered as the theoretical reference of the reduction potential without aluminum. In the case of D3, D4, D6, D7 and D9, since the reactions are of proton-coupled electron-transfer type, we consider +0.32 eV as the reference in absence of aluminum.
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618b984bda1506e90d9ce178
| 15 |
All the potential reactions D5a, D5b, and D7 evolve from a divalent Al 3+ -complex to a monovalent one. The significance of the charge reduction is clearly demonstrated if we compare D6 and D7 reduction rections. Both reactions imply the reduction of DPPH• with its further protonation and coordination to Al 3+ . While in reaction D7 the protonation takes place at the expense of the deprotonation of an ethanol ligand already coordinated to Al 3+ (Figure ), reducing the final charge of the Al 3+ -complex to +1, in reaction D6 the DPPH• protonation is assisted by an extra proton of the media that makes the final charge of the Al 3+ -complex to be +2. This small difference between the two reactions completely changes their thermochemistry, evolving from a spontaneous reaction (D7) with a E red that perfectly matches with experimental data to a non-spontaneous reaction (D6) with a E red that is absolutely in disagreement with experimental results. The difference between reactions D5a and D5b lies on the relative coordination of DPPH -and the deprotonated ethanol group (in cis for the D5a reaction and in trans for D5b) (see Figure ) while they describe the same chemical reaction. Specifically, the reduction reaction that presents a E red with the highest agreement with the experimental value is D7. This reaction accounts for the reduction of DPPH• coupled to its coordination to Al 3+ and an intramolecular protonation assisted by an ethanol ligand. Once again, as we saw for hydroquinones and for the redox reactions without the presence of Al 3+ , the global redox process is better de- ), we can see that the presence of aluminum increases the E red values (∆E ∅→Al red ), leading to a more exergonic process and stabilizing the reduced DPPH-H species.
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618b984bda1506e90d9ce178
| 16 |
It is clear from the data of Table that aluminum acts as a promoter of this scavenging reaction, passing from an endergonic process in the absence of aluminum (+0.16/+0.08 eV for exp/theo values) to an exergonic spontaneous reaction when aluminum is present,-0.15/-0.05 eV. The methylation of hydroquinones also promotes the scavenging reaction. We observe synergy between methylation and the presence of aluminum, obtaining the highest exergonicity with a value of -0.42/-0.28 eV for the reaction with methylated hydroquinone in the presence of aluminum. In summary, aluminum, albeit a non-redox metal, can enhance the electron transfer process, and it does so by strongly stabilizing the reduced form of DPPH•.
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618b984bda1506e90d9ce178
| 17 |
Our theoretical results allow us to get insight into the origins of this stabilization. On the one hand, there is an electrostatic stabilization of the highly charged Al 3+ of the increase of negative charge of the reduced DPPH -species. On the other hand, a proton transfer from one of the ethanols bound to aluminum further stabilizes the formal DPPH -, forming a DPPH-H species. This internal proton transfer increases the local negative charge around the aluminum atom in the first coordination shell, because the unprotonated ethanol is directly bound to the metal in contrast to the diazine nitrogen. In addition, this proton transfer stabilizes the excess of negative charge at the diazine nitrogen upon electron transfer. Together, all these effects make the aluminum promotion of the DPPH•'s reduction higher than the decrease of electron donor ability of hydroquinones. Therefore, the net result is a promotion of the overall redox reaction. Thus, the present work demonstrates how a strong Lewis acid such as aluminum can alter the thermodynamics of a paradigmatic test-case redox reaction. This finding has high relevance in a biological context since one would expect that the presence of aluminum has consequences for the proper and necessary balance of free radicals in a biological medium.
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618b984bda1506e90d9ce178
| 18 |
Free radicals are species that have an independent existence, for however brief a period, and contain at least one unpaired electron. The production of free radicals is inherent to normal cell behavior. Many redox processes produce and consume them. Superoxide (O •- 2 ) is the most typical oxygen-containing species enclosing a free radical. It is formed as a side product of the energy production process in the mitochondrion. O •- 2 , peroxides and hydroxyl radicals (OH • ) are included under the general heading of reactive oxygen species (ROS). The unbalance of free radicals leads to the so-called oxidative stress, and it is at the origin of multiple diseases like cancer, diabetes, Alzheimer's, or Parkinson's diseases. The human brain is a highly aerobic organ with high oxygen consumption, with a high energy requirement of neurons driven by mitochondrial oxidative phosphorylation. Part of this oxygen is converted into ROS, which in a healthy individual are effectively detoxified by several antioxidants, like enzymes (glutathione peroxidase and catalase for hydrogen peroxide, 51 and superoxide dismutase for superoxide ) or low molecular mass antioxidants. These antioxidants can perform a radical-scavenging process with ROS, receiving/donating an electron from/to a radical, forming stable byproducts. For instance, in lipid peroxidation within the mitochondrial membranes, the reduced form of the coenzyme Q 10 (ubiquinol, UQH 2 ) acts as the main chain-breaking antioxidant that decreases the damage of this process. The active center of the Q 10 antioxidant is formed precisely by hydroquinone (QH 2 ).
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618b984bda1506e90d9ce178
| 19 |
However, ROS increases markedly uncontrolled in an aged brain or under different circumstances due to mitochondrial dysfunction. In this context, the presence and accumulation of exometals can induce or enhance oxidative stress in the cell. The co-localization of aluminum and neurofibrillary tangles in familial Alzheimer's disease and aluminum and iron in nuclei of nerve cells in the brains of patients with Alzheimer's disease have been recently unambiguously established. The presence of aluminum, in addition to the wellknown implication of oxidative stress in neurodegeneration, suggests that this metal can promote oxidative damage to DNA or inhibit the repair of oxidatively damaged DNA. In previous work, we demonstrated how aluminum could thermodynamically stabilize a superoxide anion, promoting Fenton reaction and the generation of radical species. In the present work, we underline the effect aluminum could have in promoting a radical scavenging reaction. Both phenomena are of different nature, in that in the former, there is a promotion of oxidative activity, whereas, in the latter, there is a protective effect. However, both cases have in common the ability of aluminum to alter the thermodynamics of key redox processes in biological systems. Indeed, long-term exposure to AlCl 3 even at a low dose promotes oxidative stress, although high aluminum concentrations tend to decrease oxidative stress in zebrafish. In any case, aluminum is affecting the concentration of radical species. This behavior is due to the physicochemical properties of Al +3 , a strong Lewis acid with a substantial stabilization ability of negatively charged ions. This property allows aluminum to alter the thermodynamics of biological essential redox processes in different and subtle ways.
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618b984bda1506e90d9ce178
| 20 |
We have presented an accurate theoretical evaluation of reduction/oxidation potentials in the presence/absence of aluminum for a test case redox reaction between DPPH • and hydroquinone. The relevant species' reduction and oxidation potentials have been previously determined experimentally in the absence and presence of aluminum, allowing comparison between experimental and theoretical data provided in this work. To the best of our knowledge, this is the first time that such a comparison has been made in the context of aluminum biochemistry. The results given here support the experimental predictions that aluminum alters the thermodynamics of the scavenging reaction, being able to shift the process from an endergonic situation to a spontaneous exergonic one.
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618b984bda1506e90d9ce178
| 21 |
At the origin of this effect, there is the ability of Al +3 to stabilize the reduced form of DPPH • , not only by stabilizing the negatively charged DPPH -but also by promoting proton transfer from the first shell ethanol molecules to the nitrogen of diazine. This proton transfer is favor-able due to the significant lowering of the pKa of ligands bound to aluminum. All these properties stem from the fact that aluminum is a very strong Lewis acid, which can differentially stabilize charged species formed in redox reactions without the need to receive/release electrons directly.
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618b984bda1506e90d9ce178
| 22 |
Consequently, we can conclude that the presence of aluminum in biological media can not be considered an inert factor since it can affect the thermodynamic equilibrium of processes in which the production/scavenging of radicals takes part. The alteration of the proper balance of radicals in biological media due to the presence of aluminum could be behind some of the most important toxic effects of aluminum in biological media, as early hypothesized in the literature but often underestimated due to the non-redox nature of this exogenous metal, and the long-held prejudice to consider aluminum as an intrinsically inert agent in biological medium.
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6466d172a32ceeff2ddee872
| 0 |
Structural knowledge of the active pharmaceutical ingredient (API) solid form is extremely important in drug development. Conventional API solid forms include polymorphs of the pure drug molecule, its salts, solvates/hydrates and co-crystals between the drug molecule and other pharmaceutically accepted co-formers. Due to differences in lattice interactions, the solid forms adopted by an API can exhibit large differences in their stability, solubility and dissolution properties, and ultimately, the overall bioavailability of the API. Therefore, the physicochemical properties of solid formulated drugs can be tailored by specific solid form selection and identifying and characterising the available solid forms of an API is critical for selecting, or even engineering, the optimal solid form. Preparing and characterising a large proportion of the available solid forms of an API can be a challenging process that often requires a sound screening strategy with intelligent and high-throughput experimentation .
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6466d172a32ceeff2ddee872
| 1 |
Single-crystal X-ray crystallography (SCXRD) provides detailed structural information from the solid state. Although the vast majority of small molecule crystal structures are determined by SCXRD, the technique is limited by crystal size and quality requirements, and as a result, SCXRD is unfeasible for phase analysis. Instead, powder X-ray diffraction (PXRD) is commonly used during various stages of solid form screening to identify and characterise new forms. However, peak overlapping resulting from the three-dimensional diffraction data being compressed into one dimension can limit phase identification, especially when the sample contains phases with similar unit cell parameters, large unit cell parameters or low symmetry space groups . Additionally, minor phases present in very low amounts may not be detected.
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6466d172a32ceeff2ddee872
| 2 |
3D electron diffraction (3D ED), also known as MicroED, is a crystallographic technique capable of structure determination from micrometre-sized crystals and has been used to determine a number of small molecule crystal structures . Two studies from 2018 highlighted the potential of 3D ED (also known as MicroED) as a phase analysis tool for the pharmaceutical industry by rapid structure determination and solving numerous small molecule structures from an artificial heterogeneous mixture . When collecting 3D ED data, single crystals can be selected from multiphasic mixtures, allowing the crystal structures of individual phases to be determined. Since structure determination can be achieved from just one crystal, phases in nanomolar amounts can also be detected and characterised. Yet, most 3D ED data collection is performed manually and is a time-consuming process. Generally, only a few datasets (10 to 20) are collected over a half-day session, even though there are usually thousands of crystals on the grid, meaning typical sample sizes are inadequate in describing the bulk material for phase analysis and minor phases may go undetected.
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6466d172a32ceeff2ddee872
| 3 |
Several automated 3D ED data collection procedures have been developed to reduce the operating time of the user and increase throughput . Serial electron diffraction (SerialED), involving the acquisition of a single frame from each crystal, has been developed with crystal mapping in low-mag imaging and scanning transmission electron microscopy (STEM) modes. Although these methods lower dose accumulation, increase resolution and are fully automated, identifying phases from multiphasic systems with similar unit cell parameters from single frames can be challenging. Building on SerialED, serial rotation electron diffraction (SerialRED) has been developed as a fully automated technique for three-dimensional data collection and applied for the phase identification of multiphasic zeolite and metal-organic framework mixtures . Recently, by automatically and rapidly examining hundreds of crystals, SerialRED enables high-throughput phase analysis and allows the exploration of complex synthesis systems . However, the rotation ranges of each dataset are often low in the current implementation due to the alignment of the goniometer and relative high electron dose rate used in the current SerialRED implementation . This can lead to reduced accuracy in unit cell parameters, which can hinder phase identification from multiphasic systems with similar unit cells. In addition, structure determination of any new phases often requires merging datasets collected on multiple crystals, limiting the method's sensitivity to detect and characterise minor phases.
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6466d172a32ceeff2ddee872
| 4 |
Rapid and accurate phase analysis of pharmaceuticals is of great importance. In order to apply SerialRED to more beam-sensitive pharmaceuticals crystals, cryo-EM and low dose 3D ED data collection protocol, similar to those used for study protein crystals by MicroED were applied. Furthermore, we combined the widely available commercial software EPU-D (Thermo Fisher Scientific) for batch data collection with the program edtools for semi-automated data processing and clustering . When collecting data in batch mode, crystal locations are manually selected and added to a list. Tilt-series are then automatically collected from all positions on the list with a constant rotation range. The mechanical eucentric height near each pre-defined crystal position was automatically aligned before 3D ED data collection, to improve overall tilt range. Using this method, hundreds of datasets with large rotation ranges, typically greater than 80 degrees, can be collected and processed in only a few days. Furthermore, the accumulated electron dose of each dataset was less than 1 e -/Å 2 (~3.8 MGy).
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6466d172a32ceeff2ddee872
| 5 |
Here, we demonstrate the application of the high-throughput method in the phase analysis of a polycrystalline product resulting from the melt crystallisation of a griseofulvin (GSF) and polyethylene (PEG) mixture. GSF is an orally-administered antifungal drug and has five polymorphic forms (Table ) . Since the drug is poorly water-soluble, GSF has been formulated as an inclusion complex (IC) with PEG (GSF-PEG IC) to improve the dissolution behaviour . During previous studies on the melt crystallisation of GSF from dispersions with PEG , we discovered a spherulite nucleating at 80 °C in 90% GSF-10% PEG 1000. The spherulite had a unique melting behaviour (transforming completely to GSF Form V once heated above 120 °C) and showed a small shift in the Raman spectrum at 1660 cm -1 (Figures and). These properties indicated the discovery of a new crystal form.
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6466d172a32ceeff2ddee872
| 6 |
The new crystal form was however not stable. By PXRD data collected over 10 days, we found that a series of phase transformation events had occurred. The final phase-stable spherulite is a mixture of the new GSF crystal form and a few other GSF polymorphs, as some peaks in the PXRD pattern (at 10, 15 and 23 2θ, in particular) related strongly to peaks of GSF Form I (Figure and). To gain a more accurate understanding of the phases present in the GSF/PEG melt crystallisation product, we applied the high-throughput 3D ED method.
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