The Binding Properties of Terminal and Bridging Fluoride and of Aqua Ligands – a Semiempirical Vibronic Coupling and DFT Study of Mixed-Ligand Manganese(III) Complexes

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 5 E ground state of MnIII 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 MnIII Jahn-Teller systems. Owing to the internal electric field of Ci symmetry dominated by the next-neighbour K+ ions acting on the MnIII 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.

Terminal and bridging fluorine ligands in TiF4 as studied by 19F NMR in solids

To examine bonding nature of fluorine ligands in a metal coordinated system, ¹⁹F high-resolution solid-state NMR has been applied to TiF₄, which bears both bridging and terminal fluorines. Observed 12 isotropic signals are assigned to 12 crystallographically different fluorines (6 terminal and 6 bridging fluorines) in TiF₄ by referring to the calculated isotropic shifts using density functional theory (DFT). The isotropic chemical shift (δ_iso) for terminal F (F_T) appears at high frequency (420-480 ppm from δ(CCl₃F) = 0 ppm) with large shielding anisotropy Δσ ∼ 850 ppm. Whereas the δ_iso and Δσ values for bridging F (F_B) are moderate; δ_iso ∼ 0-25 ppm and Δσ ∼ 250 ppm. The origin of the observed high-frequency shift for F_T is ascribed to the second-order paramagnetic shift with increased covalency, shorter Ti-F bonds, and smaller energy difference between the occupied and vacant orbitals. Examination of the orientation of the shielding tensor relative to the molecular structure shows that the most deshielded component of the shielding tensor is oriented along the Ti-F bond. The characteristic orientation is consistent with a Ti-F σ bond formed by d_YZ of Ti and p_z of F. Further, we show that the selectively observed spinning sideband patterns and the theoretical patterns with the calculated Δσ and η (shielding asymmetry) values are not consistent with each other for F_B, indicating deficiency of the present DFT calculation in evaluating Δσ.

Development and applications of the LFDFT: the non-empirical account of ligand field and the simulation of the f-d transitions by density functional theory

Ligand field density functional theory (LFDFT) is a methodology consisting of non-standard handling of DFT calculations and post-computation analysis, emulating the ligand field parameters in a non-empirical way. Recently, the procedure was extended for two-open-shell systems, with relevance for inter-shell transitions in lanthanides, of utmost importance in understanding the optical and magnetic properties of rare-earth materials. Here, we expand the model to the calculation of intensities of f → d transitions, enabling the simulation of spectral profiles. We focus on Eu(2+)-based systems: this lanthanide ion undergoes many dipole-allowed transitions from the initial 4f(7)((8)S7/2) state to the final 4f(6)5d(1) ones, considering the free ion and doped materials. The relativistic calculations showed a good agreement with experimental data for a gaseous Eu(2+) ion, producing reliable Slater-Condon and spin-orbit coupling parameters. The Eu(2+) ion-doped fluorite-type lattices, CaF2:Eu(2+) and SrCl2:Eu(2+), in sites with octahedral symmetry, are studied in detail. The related Slater-Condon and spin-orbit coupling parameters from the doped materials are compared to those for the free ion, revealing small changes for the 4f shell side and relatively important shifts for those associated with the 5d shell. The ligand field scheme, in Wybourne parameterization, shows a good agreement with the phenomenological interpretation of the experiment. The non-empirical computed parameters are used to calculate the energy and intensity of the 4f(7)-4f(6)5d(1) transitions, rendering a realistic convoluted spectrum.

DFT-Based Studies on the Jahn−Teller Effect in 3d Hexacyanometalates with Orbitally Degenerate Ground States

The topology of the ground-state potential energy surface of M(CN)(6) with orbitally degenerate (2)T(2g) (M = Ti(III) (t(2g)(1)), Fe(III) and Mn(II) (both low-spin t(2g)(5))) and (3)T(1g) ground states (M = V(III) (t(2g)(2)), Mn(III) and Cr(II) (both low-spin t(2g)(4))) has been studied with linear and quadratic Jahn-Teller coupling models in the five-dimensional space of the epsilon(g) and tau(2g) octahedral vibrations (Tg[symbol: see text](epsilon(g)+tau(2g)) Jahn-Teller coupling problem (T(g) = (2)T(2g), (3)T(1g))). A procedure is proposed to give access to all vibronic coupling parameters from geometry optimization with density functional theory (DFT) and the energies of a restricted number of Slater determinants, derived from electron replacements within the t(2g)(1,5) or t(2g)(2,4) ground-state electronic configurations. The results show that coupling to the tau(2g) bending mode is dominant and leads to a stabilization of D(3d) structures (absolute minima on the ground-state potential energy surface) for all complexes considered, except for [Ti(CN)(6)](3-), where the minimum is of D(4h) symmetry. The Jahn-Teller stabilization energies for the D3d minima are found to increase in the order of increasing CN-M pi back-donation (Ti(III) < V(III) < Mn(III) < Fe(III) < Mn(II) < Cr(II)). With the angular overlap model and bonding parameters derived from angular distortions, which correspond to the stable D(3d) minima, the effect of configuration interaction and spin-orbit coupling on the ground-state potential energy surface is explored. This approach is used to correlate Jahn-Teller distortion parameters with structures from X-ray diffraction data. Jahn-Teller coupling to trigonal modes is also used to reinterpret the anisotropy of magnetic susceptibilities and g tensors of [Fe(CN)(6)](3-), and the (3)T(1g) ground-state splitting of [Mn(CN)(6)](3-), deduced from near-IR spectra. The implications of the pseudo Jahn-Teller coupling due to t(2g)-e(g) orbital mixing via the trigonal modes (tau(2g)) and the effect of the dynamic Jahn-Teller coupling on the magnetic susceptibilities and g tensors of [Fe(CN)(6)](3-) are also addressed.