Performance of nonrelativistic and quasi-relativistic hybrid DFT for the prediction of electric and magnetic hyperfine parameters in 57Fe Mössbauer spectra

57Fe electric and magnetic hyperfine parameters were calculated for a series of 10 iron model complexes, covering a wide range of oxidation and spin states. Employing the B3LYP hybrid method, results from nonrelativistic density functional theory (DFT) and quasi-relativistic DFT within the zero-order regular approximation (ZORA) were compared. Electron densities at the iron nuclei were calculated and correlated with experimental isomer shifts. It was shown that the fit parameters do not depend on a specific training set of iron complexes and are, therefore, more universal than might be expected. The nonrelativistic and quasi-relativistic electron densities gave fit parameters of similar quality; the ZORA densities are only shifted by a factor of 1.32, upward in the direction of the four-component Dirac-Fock value. From a correlation of calculated electric field gradients and experimental quadrupole splittings, the value of the 57Fe nuclear quadrupole moment was redetermined to a value of 0.16 barn, in good agreement with other studies. The ZORA approach gave no additional improvement of the calculated quadrupole splittings in comparison to the nonrelativistic approach. The comparison of the calculated and measured 57Fe isotropic hyperfine coupling constants (hfcc's) revealed that both the ZORA approach and the inclusion of spin-orbit contributions lead to better agreement between theory and experiment in comparison to the nonrelativistic results. For all iron complexes with small spin-orbit contributions (high-spin ferric and ferryl systems), a distinct underestimation of the isotropic hfcc's was found. Scaling factors of 1.81 (nonrelativistic DFT) and 1.69 (ZORA) are suggested. The calculated 57Fe isotropic hfcc's of the remaining model systems (low-spin ferric and high-spin ferrous systems) contain 10-50% second-order contributions and were found to be in reasonable agreement with the experimental results. This is assumed to be the consequence of error cancellation because g-tensor calculations for these systems are of poor quality with the existing DFT approaches. Excellent agreement between theory and experiment was found for the 57Fe anisotropic hfcc's. Finally, all of the obtained fit parameters were used for an application study of the [Fe(H2O)6]3+ ion. The calculated spectroscopic data are in good agreement with the Mossbauer and electron paramagnetic resonance results discussed in detail in a forthcoming paper.     

Theoretical evidence for the singlet diradical character of square planar nickel complexes containing two o-semiquinonato type ligands

Density functional theory and complete active space self-consistent field computations are applied to elucidate the singlet diradical character of square planar, diamagnetic nickel complexes that contain two bidentate ligands derived from o-catecholates, o-phenylenediamines, o-benzodithiolates, o-aminophenolates, and o-aminothiophenolates. In the density functional framework, the singlet diradical character is discussed within the broken symmetry formalism. The singlet-triplet energy gaps, the energy gained from symmetry breaking, the spin distribution in the lowest triplet state, and the form of the magnetic orbitals are applied as indicators for the singlet diradical character. Moreover, a new index for the diradical character is proposed that is based on symmetry breaking. All symmetry breaking criteria show that the complexes obtained from o-catecholates and o-benzodithiolates have the largest and the smallest singlet diradical character, respectively. The singlet diradical character should be intermediate for the complexes derived from o-phenylenediamines, o-aminophenolates, and o-aminothiophenolates. The diradical character of all complexes suggests the presence of Ni(II) central atoms. This is also indicated by the d-populations computed by means of the natural population analysis.     

Tuning the electronic structure of octahedral iron complexes [FeL(X)] (L = 1-alkyl-4,7-bis(4-tert-butyl-2-mercaptobenzyl)-1,4,7-triazacyclononane,X = Cl,CH(3)O,CN, NO). The S = 1/2 <==>3/2 Spin equilibrium of [FeL(Pr)(NO)

Two new pentadentate, pendent arm macrocyclic ligands of the type 1-alkyl-4,7-bis(4-tert-butyl-2-mercaptobenzyl)-1,4,7-triazacyclononane where alkyl represents an isopropyl, (L(Pr))(2-), or an ethyl group, (L(Et))(2-), have been synthesized. It is shown that they bind strongly to ferric ions generating six-coordinate species of the type [Fe(L(alk))X]. The ground state of these complexes is governed by the nature of the sixth ligand, X: [Fe(III)(L(Et))Cl] (2) possesses an S = 5/2 ground state as do [Fe(III)(L(Et))(OCH(3))] (3) and [Fe(III)(L(Pr))(OCH(3))] (4). In contrast, the cyano complexes [Fe(III)(L(Et))(CN)] (5) and [Fe(III)(L(Pr))(CN)] (6) are low spin ferric species (S = 1/2). The octahedral [FeNO](7) nitrosyl complex [Fe(L(Pr))(NO)] (7) displays spin equilibrium behavior S = 1/2<==>S = (3)/(2) in the solid state. Complexes [Zn(L(Pr))] (1), 4.CH(3)OH, 5.0.5toluene.CH(2)Cl(2), and 7.2.5CH(2)Cl(2) have been structurally characterized by low-temperature (100 K) X-ray crystallography. All iron complexes have been carefully studied by zero- and applied-field M?ssbauer spectroscopy. In addition, Sellmann's complexes [Fe(pyS(4))(NO)](0/1+) and [Fe(pyS(4))X] (X = PR(3), CO, SR(2)) have been studied by EPR and M?ssbauer spectroscopies and DFT calculations (pyS(4) = 2,6-bis(2-mercaptophenylthiomethyl)pyridine(2-)). It is concluded that the electronic structure of 7 with an S = 1/2 ground state is low spin ferrous (S(Fe) = 0) with a coordinated neutral NO radical (Fe(II)-NO) whereas the S = 3/2 state corresponds to a high spin ferric (S(Fe) = 5/2) antiferromagnetically coupled to an NO(-) anion (S = 1). The S = 1/2<==>S = 3/2 equilibrium is then that of valence tautomers rather than that of a simple high spin<==>low spin crossover.     

Molecular and electronic structure of four- and five-coordinate cobalt complexes containing two o-phenylenediamine- or two o-aminophenol-type ligands at various oxidation levels: an experimental, density functional, and correlated ab initio study

The bidentate ligands N-phenyl-o-phenylenediamine, H(2)((2)L(N)IP), or its analogue 2-(2-trifluoromethyl)anilino-4,6-di-tert-butylphenol, ((4)L(N)IP), react with [Co(II)(CH(3)CO(2))(2)]4H(2)O and triethylamine in acetonitrile in the presence of air yielding the square-planar, four-coordinate species [Co((2)L(N))(2)] (1) and [Co((4)L(O))(2)] (4) with an S=1/2 ground state. The corresponding nickel complexes [Ni((4)L(O))(2)] (8) and its cobaltocene reduced form [Co(III)(Cp)(2)][Ni((4)L(O))(2)] (9) have also been synthesized. The five-coordinate species [Co((2)L(N))(2)(tBu-py)] (2) (S=1/2) and its one-electron oxidized forms [Co((2)L(N))(2)(tBu-py)](O(2)CCH(3)) (2 a) or [Co((2)L(N))(2)I] (3) with diamagnetic ground states (S=0) have been prepared, as has the species [Co((4)L(O))(2)(CH(2)CN)] (7). The one-electron reduced form of 4, namely [Co(Cp)(2)][Co((4)L(O))(2)] (5) has been generated through the reduction of 4 with [Co(Cp)(2)]. Complexes 1, 2, 2 a, 3, 4, 5, 7, 8, and 9 have been characterized by X-ray crystallography (100 K). The ligands are non-innocent and may exist as catecholate-like dianions ((2)L(N)IP)(2-), ((4)L(N)IP)(2-) or pi-radical semiquinonate monoanions ((2)L(N)ISQ)(*) (-), ((4)L(N)ISQ)(*) (-) or as neutral benzoquinones ((2) L(N)IBQ)(0), ((4) L(N)IBQ)(0); the spectroscopic oxidation states of the central metal ions vary accordingly. Electronic absorption, magnetic circular dichroism, and EPR spectroscopy, as well as variable temperature magnetic susceptibility measurements have been used to experimentally determine the electronic structures of these complexes. Density functional theoretical (DFT) and correlated ab initio calculation have been performed on the neutral and monoanionic species [Co((1)L(N))(2)](0,-) in order to understand the structural and spectroscopic properties of complexes. It is shown that the corresponding nickel complexes 8 and 9 contain a low-spin nickel(II) ion regardless of the oxidation level of the ligand, whereas for the corresponding cobalt complexes the situation is more complicated. Spectroscopic oxidation states describing a d(6) (Co(III)) or d(7) (Co(II)) electron configuration cannot be unambiguously assigned.     

Coexistence of Two Different Distorted Octahedral [MnF6]3− Sites in K3[MnF6]: Manifestation in Spectroscopy and Magnetism

As a consequence of the static Jahn-Teller effect of the ⁵E ground state of Mn^III in cubic structures with octahedral parent geometries, their octahedral coordination spheres become distorted. In the case of six fluorido ligands, [MnF₆]³⁻ anions with two longer and four shorter Mn−F bonds making elongated octahedra are usually observed. Herein, we report the synthesis of the compound K₃[MnF₆] through a high-temperature approach and its crystallization by a high-pressure/high-temperature route. The main structural motifs are two quasi-isolated, octahedron-like [MnF₆]³⁻ anions of quite different nature compared to that met in ideal octahedral Mn^III Jahn-Teller systems. Owing to the internal electric field of C_i symmetry dominated by the next-neighbour K⁺ ions acting on the Mn^III sites, both sites, the pseudo-rhombic (site 1) and the pseudo-tetragonally elongated (site 2) [MnF₆]³⁻ anions are present in K₃[MnF₆]. The compound was characterized by single-crystal and powder X-ray diffraction, and magnetometry as well as by FTIR, Raman, and ligand field spectroscopy. A theoretical interpretation of the electronic structure and molecular geometry of the two Mn sites in the lattice is given by using a vibronic coupling model with parameters adjusted from multireference ab-initio cluster calculations.     

On the Reaction Mechanism of the Complete Intermolecular O2 Transfer between Mononuclear Nickel and Manganese Complexes with Macrocyclic Ligands

The recently described intermolecular O₂ transfer between the side‐on Ni‐O₂ complex [(12‐TMC)Ni‐O₂]⁺ and the manganese complex [(14‐TMC)Mn]²⁺, where 12‐TMC and 14‐TMC are 12‐ and 14‐membered macrocyclic ligands, 12‐TMC=1,4,7,10‐tetramethyl‐1,4,7,10‐tetraazacyclododecane and 14‐TMC=1,4,8,11‐tetramethyl‐1,4,8,11‐tetraazacyclotetradecane, is studied by means of DFT methods. B3LYP calculations including long‐range corrections and solvent effects are performed to elucidate the mechanism. The potential energy surfaces (PESs) compatible with different electronic states of the reactants have been analyzed. The calculations confirm a two‐step reaction, with a first rate‐determining bimolecular step and predict the exothermic character of the global process. The relative stability of the products and the reverse barrier are in line with the fact that no reverse reaction is experimentally observed. An intermediate with a μ‐η¹:η¹‐O₂ coordination and two transition states are identified on the triplet PES, slightly below the corresponding stationary points of the quintet PES, suggesting an intersystem crossing before the first transition state. The calculated activation parameters and the relative energies of the two transition sates and the products are in very good agreement with the experimental data. The calculations suggest that a superoxide anion is transferred during the reaction.     

Decay of Iron(V) Nitride Complexes By a NN Bond‐Coupling Reaction in Solution: A Combined Spectroscopic and Theoretical Analysis

Cryogenically trapped Fe^V nitride complexes with cyclam‐based ligands were found to decay by bimolecular reactions, forming exclusively Fe^II compounds. Characterization of educts and products by Mössbauer spectroscopy, mass spectrometry, and spectroscopy‐oriented DFT calculations showed that the reaction mechanism is reductive nitride coupling and release of dinitrogen (2 Fe^V?N→Fe^II‐N?N‐Fe^II→2 Fe^II+N₂). The reaction pathways, representing an “inverse” of the Haber–Bosch reaction, were computationally explored in detail, also to judge the feasibility of yielding catalytically competent Fe^V(N). Implications for the photolytic cleavage of Fe^III azides used to generate high‐valent Fe nitrides are discussed.     

Binding free energies in the SAMPL5 octa-acid host–guest challenge calculated with DFT-D3 and CCSD(T)

We have tried to calculate the free energy for the binding of six small ligands to two variants of the octa-acid deep cavitand host in the SAMPL5 blind challenge. We employed structures minimised with dispersion-corrected density-functional theory with small basis sets and energies were calculated using large basis sets. Solvation energies were calculated with continuum methods and thermostatistical corrections were obtained from frequencies calculated at the HF-3c level. Care was taken to minimise the effects of the flexibility of the host by keeping the complexes as symmetric and similar as possible. In some calculations, the large net charge of the host was reduced by removing the propionate and benzoate groups. In addition, the effect of a restricted molecular dynamics sampling of structures was tested. Finally, we tried to improve the energies by using the DLPNO–CCSD(T) approach. Unfortunately, results of quite poor quality were obtained, with no correlation to the experimental data, systematically too positive affinities (by ~50 kJ/mol) and a mean absolute error (after removal of the systematic error) of 11–16 kJ/mol. DLPNO–CCSD(T) did not improve the results, so the accuracy is not limited by the energy function. Instead, four likely sources of errors were identified: first, the minimised structures were often incorrect, owing to the omission of explicit solvent. They could be partly improved by performing the minimisations in a continuum solvent with four water molecules around the charged groups of the ligands. Second, some ligands could bind in several different conformations, requiring sampling of reasonable structures. Third, there is an indication the continuum-solvation model has problems to accurately describe the binding of both the negatively and positively charged guest molecules. Fourth, different methods to calculate the thermostatistical corrections gave results that differed by up to 30 kJ/mol and there is an indication that HF-3c overestimates the entropy term. In conclusion, it is a challenge to calculate binding affinities for this octa-acid system with quantum–mechanical methods.     

Metal oxidation states in biological water splitting

A central question in biological water splitting concerns the oxidation states of the manganese ions that comprise the oxygen-evolving complex of photosystem II. Understanding the nature and order of oxidation events that occur during the catalytic cycle of five S_i states (i = 0–4) is of fundamental importance both for the natural system and for artificial water oxidation catalysts. Despite the widespread adoption of the so-called “high-valent scheme”—where, for example, the Mn oxidation states in the S₂ state are assigned as III, IV, IV, IV—the competing “low-valent scheme” that differs by a total of two metal unpaired electrons (i.e. III, III, III, IV in the S₂ state) is favored by several recent studies for the biological catalyst. The question of the correct oxidation state assignment is addressed here by a detailed computational comparison of the two schemes using a common structural platform and theoretical approach. Models based on crystallographic constraints were constructed for all conceivable oxidation state assignments in the four (semi)stable S states of the oxygen evolving complex, sampling various protonation levels and patterns to ensure comprehensive coverage. The models are evaluated with respect to their geometric, energetic, electronic, and spectroscopic properties against available experimental EXAFS, XFEL-XRD, EPR, ENDOR and Mn K pre-edge XANES data. New 2.5 K ⁵⁵Mn ENDOR data of the S₂ state are also reported. Our results conclusively show that the entire S state phenomenology can only be accommodated within the high-valent scheme by adopting a single motif and protonation pattern that progresses smoothly from S₀ (III, III, III, IV) to S₃ (IV, IV, IV, IV), satisfying all experimental constraints and reproducing all observables. By contrast, it was impossible to construct a consistent cycle based on the low-valent scheme for all S states. Instead, the low-valent models developed here may provide new insight into the over-reduced S states and the states involved in the assembly of the catalytically active water oxidizing cluster.