Magnetic exchange and valence delocalization in a mixed valence [Fe2+Fe3+Te2]+ complex: insights from theory and interpretations of magnetic and spectroscopic data.

A mixed valence binuclear Fe2.5+-Fe2.5+ (Robin-Day Class III) transition metal complex, [Fe2.5+µTe2Fe2.5+]1-, composed of two FeN2Te2 pseudo-tetrahedral units with µ-bridging Te2- ligands was reported to exist in an unprecedented S = 3/2 ground state (Nature Chemistry, https://doi.org/10.1038/s41557-021-00853-5). For this and the homologous complexes containing Se2- and S2-, the Anderson-Hasegawa double exchange spin-Hamiltonian was broadly used to interpret the corresponding structural, spectroscopic and magnetic data. First principles multireference ab initio calculations are used here to simulate magnetic and spectroscopic EPR data; analysis of the results affords a rationale for the stabilization of the S = 3/2 ground state of the Fe2 pair. Complete Active Space Self-Consistent Field (CASSCF) calculations and dynamical correlation accounted for by means of N-Electron Valence Perturbation Theory to Second Order (NEVPT2) reproduce well the g-factors determined from simulations of X-band EPR spectra. A crucial technical tool to achieve these results is: (i) use of a localized orbital formulation of the many-particle problem at the scalar-relativistic CASSCF step; (ii) choice of state averaging over states of a given spin (at the CASCI/NEVPT2 step); and (iii) accounting for spin-orbit coupling within the non-relativistic Born-Oppenheimer (BO) many-particle basis using Quasi-Degenerate Perturbation Theory (QDPT). The inclusion of the S = 5/2 spin manifold reproduced the observed increase in the magnetic susceptibility (χT) in the high temperature range (T > 100 K), which is explained by thermal population of the S = 5/2 excited state at energy 160 cm-1 above the S = 3/2 ground state. Theoretical values of χT from experimentally reported data points in the temperature range from 3 to 30 K were further computed and analyzed using a model which takes spin-phonon coupling into account. The model considerations and the computational protocols of this study are generally applicable to any Class I/II mixed valence dimer. The work can potentially stimulate further experimental and theoretical work on bi- and oligonuclear transition metal complexes of importance to bioinorganic chemistry and life sciences.

Theoretical insights into the magnetostructural correlations in Mn3-based single-molecule magnets.

Density functional theory (DFT) and the valence bond configuration interaction (VBCI) model have been applied to the oximato-based Mn(III)(3)O single-molecule magnets (SMMs), allowing one to correlate the Mn(III)-Mn(III) exchange coupling energy (J) with the bridging geometry in terms of two structural angles: the Mn-O-N-Mn torsion angle (γ) and the Mn(3) out-of-plane shift of O (angle δθ). Using DFT, a two-dimensional (γ, δθ) energy surface of J is derived and shown to yield essentially good agreement with the reported J values deduced from magnetic susceptibility data on trigonal oximato-bridged Mn(3) SMMs. VBCI is used to understand and analyze the DFT results. It is shown that the exchange coupling in these systems is governed by a spin-polarization mechanism inducing a pronounced and dominating ferromagnetic exchange via the oximato bridge as opposed to kinetic exchange, which favors a weaker and antiferromagnetic exchange via the bridging oxide. In the light of these results, a discussion of the exchange coupling in the Mn(6) family of the SMM with a record demagnetization barrier is given.

Theoretical Studies on the Higher Oxidation States of Iron.

Density functional theory (DFT) and multiconfiguration self-consistent field (MCSCF) calculations on the oxo FeO(4)(2)(-) (Fe(VI)) and the hypothetical oxo FeO(4)(-) (Fe(VII)), and FeO(4) (Fe(VIII)) and peroxo FeO(2)(O-O)(z)() [z = -2 (Fe(IV)), z = -1 (Fe(V)), z = 0 (Fe(VI))], Fe(O-O)(2)(z)() [z = -2 (Fe(II)), z = -1 (Fe(III)), z = 0 (Fe(IV))], and FeO(O-O)(2)(z)() [z = -2 (Fe(IV)), z = -1 (Fe(V)), z = 0 (Fe(VI))] clusters are presented and discussed. The results show the potential of stabilizing Fe(VII) and Fe(VIII) in tetrahedral oxo coordination. On the basis of absolute electronegativities calculated using DFT, it is predicted that FeO(4) will be rather oxidizing, even stronger than Cl(2) and O(2). On the basis of a comparison between total bonding energies of M(1)M(2)Fe(VI)O(4) (M(1), M(2) = Li, K), MFe(VII)O(4) (M = Li, K), and Fe(VI)O(4) clusters, possible synthetic routes for electrochemical preparation of FeO(4)(-) and FeO(4) species are discussed.

Charge-Transfer Spectra and Bonding in Tetrahedral Mn(VI), Cr(V), and V(IV) and Mn(VII), Cr(VI), and V(V) Oxo Anions.

Density functional theory (DFT) calculations on the tetrahedral Mn(VI), Cr(V), and V(IV)(d(1)) oxo anions in their ground and lowest excited d-d and O --> M charge transfer (CT) states are reported and used to assign the electronic absorption spectra by reference to the spectra of the isoelectronic Mn(VII), Cr(VI), and V(V) (d(0)) and the Mn(V) and Cr(IV) (d(2)) anions. Calculated geometrical shifts along the totally symmetric metal-ligand vibration (alpha(1)) for electronic excitations are in agreement with data deduced from experimental vibronic fine structures, supporting the proposed assignments. Using a CT model including (as different from DFT) configuration interaction (CICT), it is shown that the CT excited states of MnO(4)(2)(-) at 17 000, 23 300, and 28 200 cm(-)(1) are due to d(2) (3)A(2)(2e(2)), (1)E(2e(2)), and (3)A(2)(2e(2)) final states combining with a single hole (L) on the ligand 1t(1) and 4t(2) orbitals, respectively. The higher 10Dq and smaller B values for the d(2)L(d(1)) states compared to those of the d(2) systems correlate with the shortening of the metal-ligand bond accompanying the removal of electrons from the antibonding d orbitals, leading to an increase in covalency and a change in the ordering of CT states for Cr(V) with (3)T(2)(2e(1)5t(2)(1))L (10Dq) at a higher energy than (1)E(2e(2))L (8B + 2C) as compared to Cr(IV) with nearly degenerate (3)T(2)(2e(1)5t(2)(1)) and (1)E(2e(2)) terms. This allows one to estimate the energy of the (3)A(2)(2e(2))L --> (1)E(2e(2))L transition from the CT (d(2)L) spectrum of Cr(V)(d(1)), which could not be observed for Cr(IV). From a comparison of calculated and experimental oscillator strengths and Huang-Rhys factors (S) for the lowest CT band in the V(V), Cr(VI), and Mn(VII) (d(0)) and the V(IV), Cr(V), and Mn(VI) (d(1)) oxo anions, it is shown that the increase in covalency from left to right in this series is accompanied by a reduction in band intensity and S for the progression in the alpha(1) vibration. An explanation of this result in terms of ionic contributions to the metal-ligand bond increasing from Mn(VI) to Cr(V) and V(IV) is proposed. Intensities of "d-d" transitions display the opposite trend; increasing covalency leads to stronger mixing between d --> d and CT excited states and thus an increase in intensity.

Ground states, excited states, and metal-ligand bonding in rare earth hexachloro complexes: a DFT-based ligand field study.

Metal (4f)-ligand (Cl 3p) bonding in LnCl(6)(3-) (Ln = Ce to Yb) complexes has been studied on the basis of 4f-->4f and Cl,3p-->4f charge-transfer spectra and on the analysis of these spectra within the valence bond configuration interaction model to show that mixing of Cl 3p into the Ln 4f ligand field orbitals does not exceed 1%. Contrary to this, Kohn-Sham formalism of density functional theory using currently available approximations to the exchange-correlation functional tends to strongly overestimate 4f-3p covalency, yielding, for YbCl(6)(3-), a much larger mixing of Cl 3p-->4f charge transfer into the f(13) ionic ground-state wave function. Thus, ligand field density functional theory, which was recently developed and applied with success to complexes of 3d metals in our group, yields anomalously large ligand field splittings for Ln, the discrepancy with experiment increasing from left to the right of the Ln 4f series. It is shown that eliminating artificial ligand-to-metal charge transfer in Kohn-Sham calculations by a procedure described in this work leads to energies of 4f-4f transitions in good agreement with experiment. We recall an earlier concept of Ballhausen and Dahl which describes ligand field in terms of a pseudopotential and give a thorough analysis of the contributions to the ligand field from electrostatics (crystal field) and exchange (Pauli) repulsion. The close relation of the present results with those obtained using the first-principles based and electron density dependent effective embedding potential is pointed out along with implications for applications to other systems.

DFT-based pseudo-Jahn-Teller coupling studies on the steric and energetic lone pair effect of four- and five-coordinate halide molecules and complexes with central ions from the fifth, sixth, and seventh main groups.

The energetical and stereochemical effect of the s(2) lone pair in the title molecules and complexes is investigated using a pseudo-Jahn-Teller coupling model with parameters adjusted to energies and wave functions from DFT calculations. Vibronic coupling parameters were calculated and compared with those of the coordination number (CN) 3. Inspecting the correlation between the chemical hardness and the vibronic coupling energy (hardness rule), it is found that the tendency to distort decreases with increasing CN. While all considered molecules AX(3) (A(III) = P to Bi; X(-) = F to I) undergo lone pair deformations (D(3h)---> C(3v)), only part of the AX(4)(-) and BX(4) species (B(IV) = S to Po) do so (T(d)---> C(2v)-and even less the ones with CN = 5 (D(3h)---> C(2v) (congruent with C(4v)), AX(5)(2-), BX(5)(-), and CF(5) (C(V); Cl to I). The distorted polyhedra of minimum energy possess usually the butterfly C(2v) shape (CN = 4, tau(2)(zeta) displacement path) and a C(2v) = C(4v)geometry (CN = 5, epsilon' (epsilon) distortion path). A further symmetry lowering to C(s) occurs, if the central ion becomes too small with respect to the ligands (ionic size influence, PCl(Br)(4)(-), PCl(5)(2-)), with the tendency to reduce the CN toward 3 + 1 and 4 + 1, respectively. For CN = 4 the various stationary points of, for example, compressed and elongated C(3v), C(4v), etc. in the multidimensional ground-state potential surface have been characterized. Though of higher energy than the absolute C(2v) minimum, they are shown to govern the dynamics and reactivity of the CN = 4 species to a large extent. To simulate the chemical environment (positively charged counterions, polar solvents), the DFT calculations were performed using the polarizable continuum model COSMO (conductor-like screening model). Though the electronic energy gain upon distortion is not significantly affected by the solvent, the total stabilization energy is distinctly enhanced, frequently leading to lone pair deformations of otherwise electronically stable species. All results obtained by the combined vibronic/DFT approach are well in accord with available experimental data.

New synthetic and structural aspects in the chemistry of alkylaluminum fluorides. The mutual influence of hard and soft ligands and the hybridization as rigorous structural criterion.

A general synthetic strategy starting from metal alkyls is reported based on the hydrogen difluoride anion as a suitable reagent for obtaining organometallic fluorides. The newly prepared compounds are [Me(4)N][(i-Bu)(2)AlF(2)] (1), [Ph(4)P][(i-Bu)(2)AlF(2)] (2), and [Ph(4)P][AlF(4)] (3), containing the tetrahedral anions [(i-Bu)(2)AlF(2)](-) and [AlF(4)](-). The actual structures are prototypes that allowed a comparison of inorganic and organometallic fluorides in the frame of the hard and soft acid and base principle, by means of ab initio calculations. A new theoretical model is designed to put in equation form the qualitative statements of the Bent rule. The model allows the rationalization of the tendencies of bond angle variation in [R(2)MX(2)] systems containing a main group metal (M), in terms of hybridization of the central atom and the reciprocal influence of hard and soft ligands.